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CHARACTERIZATION OF LATTICE IMPERFECTIONS IN NANOCRYSTALLINE
MATERIALS BY POSITRON ANNIHILATION, X-RAY DIFFRACTION AND OTHER METHODS
DISSERTATION SUBMITTED TO THE UNIVERSITY OF BURDWAN IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF DOCTOR OF PHILOSOPHY IN SCIENCE (PHYSICS)
ABHIJIT BANERJEE
MATERIAL SCIENCE LABORATORY DEPARTMENT OF PHYSICS
THE UNIVERSITY OF BURDWAN BURDWAN-713104
WEST BENGAL INDIA
2012
Dedicated to my parents
Late Mahadeb Banerjee
and
Basanti Banerjee
Prof. S. K. Pradhan, Ph.D. Department of Physics, Ex-Visiting Prof., University of Trento, Italy Ex-Visiting Prof., Central Michigan University, USA. Programme Coordinator, Centre of Advanced Study
THE UNIVERSITY OF BURDWAN GOLAPBAG, BURDWAN : 713 104
WEST BENGAL INDIA
Phone: (0342) 2657800 (O) (0342) 2657282 (R) Mobile: 09800162193 Fax : +91 342 2657800 e-mail: skp_bu@yahoo.com
Date:
Certificate from the Supervisor
This is to certify that the research works incorporated in the dissertation entitled “Characterization of lattice imperfections in nanocrystalline materials by positron
annihilation, x- ray diffraction and other methods”, have been carried out at The
University of Burdwan, Burdwan by Abhijit Banerjee, M.Sc. under my supervision.
Mr. Banerjee has followed the rules and regulations as laid down by University of
Burdwan for the fulfillment of requirements for the degree of Doctor of Philosophy in
Science. As far as I know, any other worker anywhere has not published the results
included in the dissertation.
(Prof. Swapan Kumar Pradhan)
i
The dissertation reports the results of preparation and microstructure
characterization of some nanocrystalline materials of potential industrial applications
are prepared by (i) mechanical alloying the metal oxide ingredients in a high-energy
planetary ball mill and by (ii) chemical route (co-precipitation technique). The
microstructure characterization of the prepared materials has been investigated using
Positron annihilation lifetime (PAL), Positron annihilation spectroscopy (PAS)
experiments, X-ray powder diffraction data employing the Rietveld’s method of
structure/microstructure refinement and in some cases by Mössbauer spectroscopy,
high-resolution transmission electron microscopy (HRTEM), UV-Vis spectrometer.
The thesis is divided into two parts. Part I consists of three chapters and
provides a general idea about different types of lattice imperfections, microstructure
characterization of nanocrystalline materials with a brief review of earlier works,
theoretical background and present considerations of microstructure analysis and
experimental details of material preparation and characterization.
Part II consists of six chapters and is concerned with the experimental results of
the microstructure characterization of nanocrystalline materials prepared by different
preparation routes and phase stability study of the prepared nanomaterials at elevated
temperatures. For microstructure characterization by X-ray powder diffraction,
basically the Rietveld powder structure refinement method has been employed. From
X-ray line profile analysis, the lattice strain has been estimated which is considerably
high for all ball-milled samples. By the analysis of the PAL spectrum we have noticed
the nature of vacancy-type defects, vacancy clusters, and microvoids in different
kinds of nanomaterial. The other positron annihilation spectroscopy (PAS) technique,
Doppler broadening of the positron annihilation radiation line-shape measurement
have been used to study the momentum distribution of electron in a material.
Mössbauer spectra of all ball-milled Fe2O3 samples consist of a doublet which is
attributed to the superparamagnetic behaviour of ferromagnetic fine particles and a
broad sextet which is presumably due to high internal strain. The decrease in
hyperfine field, broadening of lines and asymmetry of line shape implies a broad
particle size distribution in the ball-milled sample. From the figures of high-resolution
transmission electron microscopes (HRTEM) we have measured the particle sizes of
Preface
PREFACE
ii
the unmilled and milled samples milled for different hours. Employing the UV-Vis
absorption spectroscopic method the changes in the band gap for direct transitions for
all the samples (milled and unmilled Fe2O3) have been measured.
Most of the experimental investigations have been carried out at the Materials
Science Laboratory of the Department of Physics of the University of Burdwan,
Burdwan under the supervision of Dr. S.K. Pradhan, Professor, Department of
Physics, University of Burdwan, Golapbag, Burdwan 713104, W. Bengal, India ;
Variable Energy Cyclotron Center, Department of Atomic Energy, 1/AF Bidhan
Nagar, Calcutta 700064, India; Department of Physics, University of Calcutta, 92
Acharya Prafulla Chandra Road, Kolkata 700 009, India; UGC-DAE Consortium for
Scientific Research , Kolkata 700 098, India.
Almost all the experimental results have already been published in the form of
research papers in different journals of international repute.
iii
ACKNOWLEDGEMENT
I would like to take this opportunity of expressing my word of thanks to Prof. S. K.
Pradhan, Department of Physics, The University of Burdwan for suggesting the
problem and for his continued interest with constant encouragement and guidance
during the progress of the investigation. Dr. Dirtha Sanyal, SOF, VECC, Salt Lake,
Kolkata and Dr. Mahua Chakroborty, Department of Physics, The University of
Calcutta are greatly acknowledged for their continuous help to complete the research
work. I would also thankful to Dr. Dipankar Das, Scientist, UGC-DAE Consortium
for Scientific Research, Kolkata; Dr. Udayan De, Scientist, VECC, Salt Lake,
Kolkata; Mr. Anindya Sarkar, Asst. Professor of Bangobasi College, Kolkata and Dr.
Hema Dutta, Asst. Professor of Vivakananda College, Burdwan. The cooperation of
colleagues of the Dept. of Physics of Burdwan University, Soumitra Patra, Amrita
Sen, Sumanta Sain, Anshuman Nandy, Sushovan Lala, Ujjwal Kumar Bhaskar are
also greatly acknowledged. I also thankful to the Secretary and Head Master and
colleagues of the Hatni P.C. Vidyamandir, Hatni, Hooghly. I also put my best regards
to Late Prof. Dilip Banerjee, Department of Physics, The University of Calcutta and
my parents for their constant mental support to complete the research work
successfully. Finally, I convey my great thanks to the authorities of the University of
Burdwan, Variable Energy of Cyclotron Center, Kolkata; The University of Calcutta;
UGC-DAE Consortium for Scientific Research, Kolkata; for providing the necessary
laboratory facilities for pursuing experimental research work.
Finally, I would like to thanks my family and my friends for their unceasing
inspiration, which helps me to carry on my research work and to make it successful.
Date: Dept. of Physics,
The University of Burdwan,
Golapbag, Burdwan-713104,
West Bengal, India. (ABHIJIT BANERJEE)
iv
Contents
PART: I Introductory remarks, Theoretical considerations and
Experimental considerations Page no.
CHAPTER-1: Introductory remarks 1-52 1.1 Introduction 2 1.2 Defect in crystals 3 1.2.1 Point defects 3 1.2.2 Line defects 4 1.2.2 (a) Edge dislocations 5 1.2.2 (b) Screw dislocation 5 1.2.3 Planar defects 6 1.2.3 (a) stacking faults 6 1.2.3 (b) Grain boundaries 7 1.2.4 Bulk defects 7 1.3 Types of imperfections 8 1.4 Background of X-ray crystallography 8 1.5 Imperfection of crystal investigated by X- ray, Positron annihilation and other methods: Direct and Indirect observations
9
1.6 A review on the microstructure characterization by X- ray powder diffraction 14 1.6.1 Past works on microstructural characterization using integral breadth, variance, Warren-Averbach method
15
1.6.2 Microstructural characterization using the Rietveld method 15 1.6.3 Recent works on microstructural characterization using modified Warren-
Averbach method 23
1.7 Review on Positron annihilation studies for lattice imperfection measurement 26 1.8 Review on research work done using Mössbauer spectroscopy 36 1.9 The aim and objectives of the present work 40 1.10 References 41 CHAPTER-2: Theoretical considerations 53-80 2.1 Introduction 54 2.2 X-ray line profile analysis: Theoretical considerations 54 2.3 Integral Breadth method 55 2.4 Different methods of X-ray diffraction pattern analysis 56 Limitations of different methods 2.4.1 Fourier method
57
2.4.2 Warren-Averbach method 57 2.4.3 Whole Powder Pattern Decomposition (WPPD) method 57 2.5 The Rietveld method 58 2.6 MAUD: a user friendly computer software based on Java for Materials Analysis
Using Diffraction 62
2.7 Positron annihilation technique 64 2.7.1 Positron Annihilation Spectroscopy (PAS) 64
v
2.7.1(a) Positron annihilation lifetime (PAL) measurement 66 2.7.1(b) Coincidence Doppler Broadened Positron Annihilation Radiation Line shape (CDBPARL) measurement
68
2.8 The Mössbauer effect 70 2.8.1 Fundamentals of Mössbauer Spectroscopy 73 2.8.1(a) Isomer Shift 74 2.8.1(b) Quadrupole Splitting 75 2.8.1(c) Magnetic Splitting (Hyperfine Interaction) 76 2.9 References 77 CHAPTER-3: Experimental considerations 81-109 3.1 Introduction 82 3.2 Different fabrication techniques of nano materials 82 3.2.1 Sol-gel method 82 3.2.1.1 Advantages of Sol-gel Technique: Sol-gel process 84 3.2.2 Ball- milling process 84 3.3 Potential of mechanical alloying 85 3.3.1 High energy ball-milling 85 3.3.2 The planetary ball-mill (P5) 86 3.3.3 Mechanism of a planetary ball mill 86 3.3.4 The merits and demerits of planetary ball-mill 87 3.3.5 The mechanochemical transformation during milling 88 3.3.6 Use of ball milling for synthesis of nanocrystalline materials 88 3.4 Preparation of powder specimens for X-ray powder diffractometry 89 3.4.1 Choice of radiation 89 3.4.2 Choice of instrumental standard 89 3.4.3 Recording of X-ray powder diffraction data 89 3.5 Transmission electron microscope (TEM) used for microstructure study 90 3.6 The outline of positron annihilation experiment 91 3.6.1 The Positron Source 93 3.6.2 The positron source preparation for positron annihilation experiments 94 3.6.3 Implantation profile 94 3.7 Positron Annihilation Lifetime (PAL) Measurement 95 3.7.1 The positron annihilation lifetime (PAL) spectrometer 95 3.7.2 Positron Annihilation Lifetime Data Analysis 97 3.7.2 (a) Mathematical analysis of the positron annihilation lifetime data 97 3.7.2 (b) Positron annihilation lifetime data analysis 98 3.8 Doppler Broadening of the Electron Positron Annihilation Radiation Measurement 98 3.8.1 Coincidence Doppler broadening of the electron positron annihilationradiation measurement
99
3.8.2 The coincidence Doppler broadening of the electron positron annihilation radiation (CDBEPAR) spectrometer
100
3.8.3 The Doppler broadening data analysis 101
3.8.3 (a) Line shape analysis 101
3.8.3 (b) Ratio-curve analysis 102 3.9 A outline of Mössbauer spectroscopy experiment 102 3.9.1 The Mössbauer Spectroscopy 102 3.9.2 Radiation Sources 105
vi
3.9.3 The Absorber 105 3.9.4 Detection and Recording Systems 105 3.9.5 Experimental set up of Mössbauer spectroscopy 106 3.10 References 107
PART: II
Experimental investigations on some nanomaterials
CHAPTER-4 Nanophase iron oxides by ball-mill grinding and their Mössbauer characterization
110-119
4.1 Introduction 111 4.2 Experimental details 111 4.3 Method of X-ray line profile analysis 112 4.4 Results and discussion 112 4.5 Conclusions 118 4.6 References 118 CHAPTER-5 Annealing effect on nano-ZnO powder studied from positron lifetime and optical absorption spectroscopy
120-133
5.1 Introduction 121 5.2 Experiment and data analysis 122 5.3 Results and discussion 123 5.4 Conclusions 130 5.5 References 131 CHAPTER-6 Particle size dependence of optical and defect parameters in mechanically milled Fe2O3
134-147
6.1 Introduction 135 6.2 Experimental outline 136 6.3 Results and discussion 138 6.4 Conclusions 146 6.5 References 146 CHAPTER-7 Microstructure, Mössbauer and Optical Characterizations of Nanocrystalline α-Fe2O3 Synthesized by Chemical Route
148-163
7.1 Introduction 149 7.2 Experimental outline 150 7.3 Method of microstructure analysis by Rietveld refinement 151 7.4 Results and Discussion 153
7.4.1 Microstructure Characterization Using XRD and HRTEM 153 7.4.2 Magnetic Characterization Using Mössbauer Spectroscopy 156 7.4.3 Optical Characterization Using UV-Vis Spectroscopy 159 7.5 Conclusions 161 7.6 References 161
vii
CHAPTER-8 Microstructural changes and effect of variation of lattice strain on positron annihilation lifetime parameters of zinc ferrite nanocomposites prepared by high enegy ball-milling
164-178
8.1 Introduction 165 8.2 Experimental method 166 8.3 Method of analysis 167 8.4 Results and discussion 167 8.4.1 X-ray diffraction analysis 167 8.4.2 Positron Annihilation Spectroscopy 172 8.5 Conclusions 177 8.6 References 177 CHAPTER-9 Microstructure and positron annihilation studies of mechanosysthesized CdFe2O4
179-192
9.1 Introduction 180 9.2 Experimental 181 9.3 Method of analysis 181 9.4 Results and Discussion 182 9.4.1 X-ray diffraction analysis 182 9.4.2 Positron Annihilation Spectroscopy 186 9.5 Conclusions 190 9.6 References 191 General conclusions 193 Future plan of research work 195 List of Publications 196
PART: I
Introductory remarks, Theoretical considerations and Experimental considerations
CHAPTER-1
Introductory remarks
INTRODUCTORY REMARKS CHAPTER-1
~ 2 ~
1.1 Introduction
Materials in nanocrystalline form are now being prepared widely because of
their wide range of applications in different fields. Structural imperfections in such
nanomaterials contribute a massive change in different properties of these materials.
Material characterizations in terms of detailed study of lattice imperfections in
particular, are essential for the systematic development of such nanomaterials as well
as for qualification of materials for design and fabrication. Today, there are several
techniques for material characterization. They often depend on how a given sample
responds to a probe. The probe may be electrons, positrons, neutrons, ions,
electromagnetic radiation (x-ray, gamma rays etc), ultra sound etc. In this dissertation,
positron annihilation lifetime (PAL) spectroscopy, X-ray powder diffraction (XRD)
and few other methods of microstructure characterization would be discussed which
are usually used for characterization of nanomaterials.
Positron annihilation lifetime (PAL) spectroscopy deals with the measurement
of the lifetime of positrons (~100-400 ps) in a solid. Positrons injected from a
radioactive source (like 22Na) get thermalized within 1-10 ps inside a solid and
annihilate with an electron of that material. It is well known that positrons
preferentially populate (and annihilate) in the regions where electron density,
compared to the bulk of the material is lower (e.g., vacancy-type defects, vacancy
clusters, and microvoids). The lifetime of positrons trapped in defects is
comparatively longer with respect to those that annihilate at defect free regions. An
analysis of the PAL spectrum thus throws light on the nature and abundance of
defects in the material. The other positron annihilation spectroscopy (PAS)
technique, Doppler broadening of the positron annihilation radiation line-shape
measurement is useful to study the momentum distribution of electron in a material.
Depending on the electron momentum, the 511-keV γ rays are Doppler shifted along
the direction of measurement. The wing region of the 511-keV spectra carries the
information about the annihilation of positrons with the core electrons. The momenta
of the core electrons are element specific and hence the atoms surrounding a defect
can be probed by proper analysis of the measured spectra.
The objects of the dissertation are to (i) synthesis of some nanocrystalline
materials by physical and chemical methods (ii) characterization of the
nanocrystalline materials in terms of lattice imperfections of different kinds primarily
INTRODUCTORY REMARKS CHAPTER-1
~ 3 ~
employing X-ray powder diffraction method of line profile analysis and in some cases
by PAL, PAS, HRTEM and Mössbauer spectroscopy.
1.2 Defects in crystals Atoms may be arranged in many ways – tetragonal fashion or hexagonal
close-packed fashion or face centered cubic fashion or others. The reason that atoms
have a regular or homogeneous way to stack themselves is because such arrangement
results in a stable or low energy configuration. The homogeneously arranged portion
of atoms is called a phase.
It has been found that certain deviations of the crystals from their perfect
regularity i.e. the existence of certain imperfections, are required for accounting the
properties such as colour of crystals, plasticity, increased conductivity of pure
semiconductors, strength of crystals, melting and growth of crystals, luminescence,
diffusion of atoms through solids, etc. Thus, the concept that the atoms in the solids
are not arranged strictly in a perfect regular manner is also equally important. This
means that the actual crystals must behave as if containing essentially certain defects.
The real crystals are always imperfect in one respect or the other. The nature of
imperfections is better understood for some solids than for others. There are
essentially three kinds of imperfections that can occur in crystals: point defects, line
defects, and plane defects.
1.2.1 Point defects A point defect is very localized interruption in the regularity of the lattice. It
produces strain in the small volume of the crystal surrounding the defect, but does not
affects the perfection of more distant parts of the crystal. These defects may be in the
form of either impurities, or vacancies i.e. the unoccupied lattice sites, or vacancies
with the bound electrons/holes which are usually called as the colour centres
(Fig 1.1).
INTRODUCTORY REMARKS CHAPTER-1
~ 4 ~
Fig.1.1 Different kinds of point defects.
1.2.2 Line defects The line defects are those which extend along some direction in an imperfect
crystal. One such defect can be considered as the boundary between two regions of a
surface which are perfect themselves but out of register with each other. In case of
crystals it arises, for example, when one part of the crystal shifts or slips relative to
the rest of the crystal such that the atomic displacement terminates within the crystal.
If the displacement dose not terminate within the crystal, but continues throughout the
crystal instead, it may not introduce any defect in the crystal. This emphasizes that it
is only the termination of the displacement which introduces the defect. This defect is
centered along a line which is also the boundary between the slipped and unslipped
regions of the crystal. This defect is commonly called a dislocation and the boundary
as the dislocation line (Fig.1.2).
Fig.1.2 The dislocation line
INTRODUCTORY REMARKS CHAPTER-1
~ 5 ~
There are two basic types of dislocations: (a) Edge dislocation and (b) Screw
dislocation.
1.2.2 (a) Edge dislocations Edge dislocations are caused by the termination of a plane of atoms in the
middle of a crystal. In such a case, the adjacent planes are not straight, but instead
bend around the edge of the terminating plane so that the crystal structure is perfectly
ordered on either side. The analogy with a stack of paper may be noticed: if a half a
piece of paper is inserted in a stack of paper, the defect in the stack is only noticeable
at the edge of the half sheet [Fig. 1.3].
Fig. 1.3 Edge dislocation
1.2.2 (b) Screw dislocation The screw dislocation is more difficult to visualise, but basically comprises a
structure in which a helical path is traced around the linear defect (dislocation line) by
the atomic planes of atoms in the crystal lattice [Fig. 1.4].
Fig. 1.4 Screw dislocation
INTRODUCTORY REMARKS CHAPTER-1
~ 6 ~
1.2.3 Planar defects These defects are those which have an areal extent. Planar defects are the most
serious defects. The stacking faults and grain boundaries are the most common
defects in the various types of planar defects.
1.2.3 (a) Stacking faults The stacking faults are usually produced during the grain growth of the
crystals. When close-packed layers grow one over the other to form a close- packed
crystal, it is possible for a layer to start stack incorrectly. A stacking fault results when
in the regular stacking sequence of a crystal one plane is out of sequence, while the
lattice on the either side of the fault is perfect. A crystal having this defect is usually
said to be twinned and the common plane is a twin plane.
Stacking faults occur in a number of crystal structures, but the common
example is in close-packed structures. Face-centered cubic (fcc) structures differ from
hexagonal close packed (hcp) structures only in stacking order. Both structures have
close packed
Fig. 1.5 Close packing of equal spheres
atomic planes with sixfold symmetry. The atoms form equilateral triangles. When
stacking one of these layers on top of another, the atoms are not directly on top of one
another [Fig. 1.5].The first two layers are identical for hcp and fcc, and labeled AB. If
the third layer is placed so that its atoms are directly above those of the first layer, the
stacking will be ABA. This is the hcp structure, and it continues ABABABAB.
INTRODUCTORY REMARKS CHAPTER-1
~ 7 ~
However, there is another location for the third layer, such that its atoms are not
above the first layer. Instead, the fourth layer is placed so that its atoms are directly
above the first layer. This produces the stacking ABCABCABC, and is actually a
cubic arrangement of the atoms. A stacking fault is a one or two layer interruption in
the stacking sequence, for example, if the sequence ABCABABCAB were found in
an fcc structure.
1.2.3 (b) Grain boundaries Most of the material of practical importance consists of many small
interlocking crystallites or grains having random orientations. The boundary between
the two adjacent grains is called the grain boundary. It is a type of defect between the
two grains. Suppose the two grains, which can grow in size, are separated by a fairy
thick non-crystalline layer. Now as the grains grow, they force the atoms at their
surfaces to assume positions (consistent with their respective grains) in the region
between them. This process continues until two grains are separated by only few
atom-distance. At this distance, as the inter- grain forces come into play, each
competing grain pulls on the boundary layer atoms with comparable forces, and the
atoms thus assume positions that conform some kind of a compromise between the
requirements of the structure of either grain. Impurities such as foreign atoms,
interstitials, etc., which might be expelled by the grains during their growth are also
collected at the boundaries.
1.2.4 Bulk defects Voids are small regions where there are no atoms, and can be thought of as
clusters of vacancies. Impurities can cluster together to form small regions of a
different phase. These are often called precipitates.
INTRODUCTORY REMARKS CHAPTER-1
~ 8 ~
1.3 Types of imperfections Point defects: Interstitial Extra atom in an interstitial site.
Schottky defect Atoms missing from correct sites.
Frankel defect Atom displaced to interstitial site creating
nearby vacancy.
Line defects: Edge dislocation Rows of atoms making edge of a
crystallographic plane extending only
part way in crystal. Burger vector is
normal to the line of dislocation.
Screw dislocation Rows of atoms about which a normal
crystallographic plane appears to spiral.
Burger vector is parallel to the line of
dislocation.
Planar defects: Lineage boundary Boundary between two adjacent perfect
regions in the same crystal that are
slightly tilted with respect to each other.
Grain boundary Boundary between two crystallites in a
polycrystalline solid.
Stacking fault Boundary between two parts of a closest
packing having alternate stacking
sequence.
Volume
imperfections
Transients:
Voids and precipitates Generate from cluster of vacancies,
interstitials and solute/ impurity atoms.
Generated and annihilated in a crystal
due to phonon-phonon, phonon-atom and
phonon-electron interactions.
1.4 Background of X- ray crystallography In the year 1912 Max Von Laue published his discovery that X- rays could be
diffracted by crystal [1]. In the next year, W. Lawrence Bragg [2] extended Laue’s
INTRODUCTORY REMARKS CHAPTER-1
~ 9 ~
idea by showing that each diffracted beam can be considered as ‘reflection’ by an
array of parallel lattice planes with interplanar spacing dhkl, where hkl are miller
indices of the possible crystal face parallel to the array, provided that the beam of
wavelength λ is incident at a particular glancing angle θhkl to be ‘reflected’, naturally,
at the same angle and successfully interpreted the diffraction patterns of ZnS. This
idea of Laue brought a momentous change in the concept of crystalline solid. In 1914
W.H.Bragg and W.L.Bragg using orientation dependence of X-ray diffraction from a
single crystal solved the structure of NaCl, diamond, copper etc. as reported by
Mosley [3].
In the year 1916, Debye and Scherrer in Germany and in the year 1917 Hall in
the United States discovered independently ‘the powder method of X-ray’. In those
days powder diffraction patterns were recorded photographically and the primary
objective was to determine the atomic arrangement in metals and their alloys. As the
time passed by, the field of X-ray diffraction extends far beyond the early goal.
Sophisticated diffractometers were devised to produce diffractograms indicating the
locations of diffraction peaks as well as intensity of reflections very accurately in a
short time. Gradually, scientists are engaged their attention to the problems associated
with the behavior of metals under conditions of stress and strain, the influence of
alloying additions, the behavior of alloys at high temperatures, the anisotropy
produced by cold working, the production of intermetallic compounds with
semiconducting and thermoelectric properties etc. Recently, X-ray diffraction
methods are being used to study the microstructure in the grain size range of 10-4 to
10-8 cm and for identification of various phases present in the sample.
1.5 Imperfection of crystal investigated by X-ray, Positron Annihilation and other methods: Direct and Indirect observations J.G. Byrne [4] have been reviewed the different types of lattice imperfections
by the different types of methods. These methods can be categorized into two groups:
(1) Direct observations, (2) Indirect observations.
(1) Direct observations
(a) Etching and decoration technique
(b) Field ion microscopy (FIM)
(c) X- ray fluorescence (XRF)
(d) X- ray and synchrotron X- ray topography (XRT and SXRT)
INTRODUCTORY REMARKS CHAPTER-1
~ 10 ~
(e) Secondary ion mass spectroscopy (SIMS)
(f) Auger and photoelectron spectroscopy (AES, XPS)
(g) High and low- energy electron diffraction (HEED, LEED)
(h) Transmission, scanning, scanning transmission and high resolution electron
microscopy (TEM, SEM, STEM, HREM)
(2) Indirect observations
(a) Mechanical properties studies
(b) Electrical resistivity
(c) Ultrasonic method
(d) Mössbauer spectroscopy
(e) Solid diffusion
(f) Quenching and annealing phenomena
(g) X-ray diffraction and small angle X- ray scattering
(h) Neutron irradiation
(i) Replica- electron microscopy
(j) Channeling studies
(k) Rutherford back scattering
(l) Positron annihilation techniques.
Detailed discussions of all these methods are beyond the scope of the thesis
and only a few ones are discussed below in brief:
X- ray diffraction topography [5,6] is an important and elegant tool to observe
directly lattice imperfections in as- grown single crystal. ‘Lang’ transmission
topography has been found to be a very powerful non-destructive method to
characterize crystal microstructure involving dislocations, stacking faults, precipitates,
grain boundaries etc. Topography with the use of synchrotron radiation in recent years
has become a powerful and challenging method.
Auger and photo-electron spectroscopy (AES, XPS) techniques are used to
identify the presence of physical and chemical imperfections (interstitials, precipitates
etc.) in the surrounding matrix elements.
The scanning electron microscopy (SEM) provides a direct means of
examining surface topography of a sample at high magnification with high resolution.
INTRODUCTORY REMARKS CHAPTER-1
~ 11 ~
The transmission electron microscopy (TEM) is the most advanced and
probably the most versatile technique for direct observations of high density of lattice
imperfections amongst the listed direct methods. The electron source used in TEM
has a wavelength around hundredth of a nanometer, which means it has the power
hundred times better than the X-ray. We can determine the shape of the defect
structures and what kind of displacements has occurred to the atomic arrangements at
the defects. The energy of electron source in conventional TEMs is usually below 120
KeV.TEM was mainly developed at the Cavandish Laboratory in Cambridge by
Hirsch, Whelan and Howie [7] and by Ballman [8] in order to look at the dislocations
in a more direct confirmatory manner. In TEM an electron beam is accelerated to 100
to 2000 KV. This accelerated beam impinges on the thin sample placed in ultra high
vacuum chamber and gets diffracted. From the sample two beams emerge, one direct
and other diffracted beam. Out of these two, the undesired beam is suppressed, while
allowing the other beam to form an image on the photographic plate. Due to
displacement of atoms from their ideal position phase contrast is present in Bragg
diffraction, which helps to locate defects in crystal. In TEM dislocations appear as
dark lines and stacking faults give rise to interference fringes. It is also possible to
image other type of crystallographic defects, if the Burger vectors of dislocations and
displacement vectors of stacking faults are known. A good electron micrographs
originating from diffraction contrast, reveals the position of dislocation, stationary or
moving extended nodes and even separation of partials resulting in weak beam
technique to estimate stacking fault energy [9,10]. In recent years, million- volt
electron microscopes have come into existence so that a thicker specimen,
representative of bulk, may be used.
The energy of electron source of high resolution transmission electron
microscopy (HRTEM) is at least 200 KeV or even 1 MeV. The most important
difference between TEM and HRTEM is that TEMs cannot resolve atomic images,
but HRTEMs can and thus helps in studying the atomic and defect structures in the
vicinity of interfaces.
The measurements of broadening, shift and asymmetry of X- ray diffraction
line profile from polycrystalline specimens were developed by Warren school [11,12]
and have been extensively applied in the past decades [13] to elucidate qualitatively
as well as quantitatively the microstructure of the materials ( deformed, vapor-grown
INTRODUCTORY REMARKS CHAPTER-1
~ 12 ~
etc.) characterized by various types of imperfections, namely, intrinsic, extrinsic, twin
or growth faults, coherently diffracting domain, residual stress, dislocation density
and stacking fault energy etc. In this method, analysis is done with individual
diffraction lines and hence this method fails to characterize the materials having low
symmetry where diffraction lines are found to be seriously overlapping. In 1966 H.
M. Rietveld suggested a method, known as Rietveld method, in which total X- ray
powder diffraction pattern is simulated and fitted with a suitable profile fitting
function and then structural refinement is carried out until the best fit is obtained
between the entire observed pattern and the entire calculated pattern [14]. In 1981,
Powley suggested whole-powder-pattern-decomposition method for refining unit-cell
parameters without reference to structural model. These methods have turned out to
be extremely elegant and powerful for studying the microstructures of various
materials [15].
Amongst the above-listed indirect methods Positron annihilation technique is
one of the most important methods to determine the different types of defects in the
materials. By this method we can easily detect the point defects, voids, cluster, micro-
voids which are not observed from X- ray diffraction pattern. To understand the
electron density distribution and electron momentum distribution in a defect-free
regions we can use an analysis of the PAL (positron annihilation lifetime) spectrum.
Positron annihilation spectroscopy (PAS) is well known non-destructive nuclear
technique. After entering a material positrons are trapped in the defect sites (lower
electron density region) in material such as dislocations, monovacancies, vacancy
clusters, micro voids, small and large angle grain boundaries etc. There is an another
technique to study the electron momentum distribution in the material is Doppler
broadening of the positron annihilation γ-ray radiation line shape (DBPARL) analysis.
In the DBPARL techniques positron from the radioactive 22Na source has been
thermalized inside the studied material and annihilate with an electron of the studied
material emitting two oppositely directed 511 KeV γ-rays. Depending upon the
momentum of the electron (p) these 511keV γ-rays are to be Doppler shifted by an
amount ±∆E (∆E=pLc/2) in the laboratory frame, where pL is the component of the
electron momentum, p, along the detector direction. Using high-resolution high-purity
germanium (HPGe) detectors one can measure the spectrum of Doppler-shift 511KeV
γ-rays. The wing region of the 511KeV spectra (higher value of pL) carries the
INTRODUCTORY REMARKS CHAPTER-1
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information about the annihilation of positrons with the core electrons. The momenta
of the core electrons are element specific and hence the atoms surrounding a defect
can be probed by proper analysis of the measured spectra.
Positron annihilation lifetime (PAL) spectroscopy deals with the measurement
of the lifetime of positrons (~100-400ps) in a solid. Positrons injected from a radio-
active source (here 22Na) get thermalized within 1-10ps inside a solid and annihilate
with an electron of that material. It is well known that positrons preferentially
populate (and annihilate) in the regions where electron density, compared to the bulk
of the material, is lower (e.g., vacancy-type defects, vacancy clusters, and
microvoids). The lifetime of positrons trapped in defects is comparatively longer with
respect to those that annihilate and abundance of defects in the material.
In the indirect methods, Mössbauer technique is a very useful to determined
the superparamagnetic state and also ferromagnetic state by seeing the two- finger and
six- finger pattern of Mössbauer spectrum respectively. It is noted that the nature of
the Mössbauer spectrum depends on the relation between the time of measurement
and that of the magnetization vector relaxation. If the time of observation is much less
than the relaxation time, the particles exhibit ferromagnetism, while in the opposite
case one observes superparamagnetism. This Mössbauer spectroscopic [16,17,18,19]
technique is only one technique to detect the different phases/ states of magnetic
materials.
In 1958, R.L. Mössbauer in Germany, made a very important discovery in the
field of gamma-ray physics, which won him the Nobel prize in Physics in 1961.Under
certain circumstances, Mössbauer observed that gamma-rays could be emitted from
nuclei without any loss of energy due to the recoil of the emitting nucleus. As such
these gamma-rays have the same energy as the transition energy between the two
states. This type of transition is known as the recoilless transition and the effect is
known as Mössbauer effect. Mössbauer’s discovery has been used to test Albert
Einstein’s theory of general Relativity.
From Mössbauer effect we get some definitions which are given below:
(a) Hyperfine splitting of the nuclear energy levels:
Hyperfine splitting of the atomic energy levels arises from the magnetic
interactions of the nuclear magnetic moment with the magnetic field due to the orbital
electrons at the nucleus.
INTRODUCTORY REMARKS CHAPTER-1
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(b) Isomeric or chemical shift:
Mössbauer effect considered so far refers to identical atoms in the emitting
and absorbing systems, i.e., the atoms at the lattice sites have identical chemical
compositions. Hence whatever effects the electronic environment may have on the
nuclear levels are the same in both the emitting and absorbing atoms. If however, the
atoms in the two have different chemical compositions, then the nuclear levels will be
influenced by different amounts in the emitting and absorbing atoms.
Chemical shifts are usually very small (∆E/E ~ 10-12) and can be determined
by Mössbauer method by moving the source at velocities ~ 0.1mm/s relative to the
absorber. It has been found that Rex (nuclear radii in excited states) may be greater or
less than Rg (nuclear radii in ground states). For 57Fe, Rex < Rg by 0-1% while for 119Sn, Rex > Rg by 0.01%.
(c) Gravitational red shift:
R. V. Pound and G.A. Rebka (Jr.) carried out an experiment based on
Mössbauer method to measure the effect in the earth’s gravitational field (1960) on
the frequency of light. According to the General Theory of Relativity, a photon of
energy Eγ = (h/2π)ω behaves like a particle of mass m = Eγ / c2 in a gravitational field.
Hence in rising through a height l in the gravitational field of the earth, its potential
energy will increase by an amount ∆Egr = mgl = (Eγ/c2) gl , where g is the
acceleration due to gravity. Thus the energy of the photon will decrease by the same
amount. So the frequency of the light will decrease by ∆Vgr = ∆Egr /h = Eγ gl / c2 h ,
This decrease causes the light of shorter wavelength to shift towards longer
wavelength, an effect known as the gravitational red shift. In the reverse case, if light
moves downwards against the force of gravity, it will suffer a blue shift.
It may be mentioned that Mössbauer method has been used by Hay, Schiffer,
Cranshaw and Egelstaff (1960) to provide experimental verification of time-dilatation,
predicted by the Special Theory of Relativity.
1.6 A review on the microstructure characterization by X-ray powder diffraction
A large number of crystallographers had been studied on the nature of
imperfections introduced into crystalline materials as a result of growth and plastic
deformation processes for the past decades. As a complementary to electron
microscopy which is very useful for studying materials with little stacking fault, X-
INTRODUCTORY REMARKS CHAPTER-1
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ray diffraction methods are mainly of value in the investigation of high density of
stacking fault in heavily deformed materials. Experimental work in this field of study
has been adequately mentioned in the text of Wilson [20], Barrett and Massalski [21],
Warren [12], and Klug and Alexander [22]. Here we are discussing a short review on
the significant experimental and theoretical works that have been made in the recent
past on microstructure characterization of materials.
1.6.1 Past works on microstructural characterization using integral breadth, variance, Warren-Averbach method There are a large number of publications (theoretical as well as experimental)
between 1950-1970 embarking on comprehensive X-ray studies of crystallite size,
microstrain, stacking faults energies and dislocation densities in various metals, alloys
and compounds have been made adopting integral breadth, variance and Fourier
methods. Only the few significant references are mentioned here. These include:
Bertaut [23], Barrett [24], Warren and Averbach [25,26], Warren and Warekois [27],
Williamson and Smallman [28], Wagner [29,30], Michell and Hiag [31], Smallman
and Westmacott [32], Christian and Spreadborough [33], Cahn and Davies [34],
Vassamillet[35], Davies and cahn [36], Klein et al. [37], Welch and Otte [38], Alder
and Wagner [39], Foley, Cahn and Raynor [40], Vassamillet and Massalski [41],
Howie and Swann [42], Sundahl and Sivertsen [43], Koda et al.[44], Vassamillet and
Massalski [45], Nakajima and Numakura [46], Wagner and Helion [47], Lele et
al.[48,49], Otte [50], Sengupta and Quader [51], Goswami, Sengupta and Quader
[52], De and Sengupta [53], Rao and Rao [54], Delehouzee and Deruyttere [55],
Ahlers and Vassamillet [56].
1.6.2 Microstructural characterization using the Rietveld method
The Rietveld method was first reported at the seventh Congress of the IUCr in
Moscow by H.M. Rietveld in 1966 [57,58]. In 1974, the Rietveld refinement using
time-of-flight neutron powder diffraction data was performed for the first time to
analyze the monoclinic phase of KCN by Decker et al. [59]. In 1975, Carpenter et al.
attempted to apply Rietveld method to spallation pulsed neutron source data and
proposed a suitable peak shape function based on a convolution of separate rising and
falling exponential for representing the time dependence of the initial neutron pulse
[60]. In 1976, Windsor and Sinclair obtained a good fit for nickel data from a pulsed
INTRODUCTORY REMARKS CHAPTER-1
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neutron source at Harwell Linac [61] using Rietveld refinement. In 1977, Mueller et
al. used a tabulated numerical peak shape function to fit data for Th4D15 from the
ZING-P pulsed neutron source at Argonne and got satisfactory result. Till 1977 the
method was mainly used to refine structures from data obtained by fixed wavelength
neutron diffraction and a total of 172 structures were refined in this way before 1977
[62].
The application of the Rietveld method to X-ray patterns slowly developed,
primarily because of the asymmetric and non-Gaussian nature and multiple spectral
components in most X-ray diffraction profiles. In the mid-1970’s application of
Rietveld method was extended to X-ray data obtained with a diffractometer. Mackie
and Young [63], Malmros and Thomas [64], Young et al. [65], and Khattak and Cox
[66] gave the first application of Rietveld method to X-ray data. The work of Wiles
and Young in 1981 [67] marked the beginning of the much wider development of this
method.
The popularity of the Rietveld method led to the development of many
sophisticated computer programs, usually based on Rietveld’s original work [68].
Among these most widely used are:
(i) The DBWS program written by Wiles, Sakthivel and Young for main
frame computers and later adapted for PC use [69]. It operates with X-ray and neutron
diffraction data in angle-dispersive mode. The other version of this program are
LHPM [70], ALFRIET1 [71] to refine only f (x) by deconvoluting a split Pearson VII-
modeled g(x) from the observed data, ALFRIET2 [72] to refine structure with
incommensurate modulations and FULLPROF [73]. The latter version has been
written in to cover a variety of situations.
(ii) In 1987, Larson and Von Dreele [74] developed GSAS, which offers a
high flexibility and runs on a VAX-VMS machine and was recently adopted for PC
use. It works with angle dispersive and energy dispersive (time-of-flight) data. X-ray
and neutron diffraction data can be used simultaneously or independently in a
structure refinement. The program includes provisions for applying constrains on
bond lengths and angles.
(iii) XRS-82, The X-ray Rietveld System [75] is based on a collection of
crystallographic programs for the refinement of structures from single crystal data.
INTRODUCTORY REMARKS CHAPTER-1
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(iv) In 1992 Lutterrotti et al. developed a program, LS1 for simultaneous
refinement of structural and microstructural parameters [76] using psuedo-Voigt
function. Izumi (1995) developed another program, called RIETAN for joint
refinement with X-ray and neutron data under non-linear constraints [77-78].
Lutterotti et al. (1994) developed a user-friendly software, the MAUD, based on Java
platform, for material analyzing using diffraction pattern. It can perform simultaneous
crystal structure refinement, measurement of line-broadening, texture and quantitative
phase abundances of a mixed phase material [79-84].
Databases play a useful role in the course of structure determination for
detecting isostructural chemically related compounds. Among useful databases there
are:
-PDF-2 maintained, updated and marketed by the International Centre for
Diffraction Data (ICDD, http://www.icdd.com). The PDF contains experimental data
for over 87,500 substances and more than 49,000 patterns calculated from the ICSD
database. It is consulted after collecting the powder data.
-NIST Crystal Data File (CDF) is a compilation of crystallographic and
chemical data on more than 200,000 entries and is marketed by ICDD. This is a useful
database as soon as the unit cell is known from pattern indexing.
-Inorganic Crystal Structure Database (ICSD) contains a complete
crystallographic information over 50,000 inorganic structures (http://barns.ill.fr
/dif/icsd/).
-SDPD database contains references over 500 crystal structure determined ab
initio from powder diffraction data (http://sdpd.univ-lemans.fr/iniref.html).
Most programs used for the Rietveld method incorporate as iterative procedure
for pattern matching [85] by fitting a calculated pattern to the observed data without
the use of a structure model, but using constraints on the positions of reflections
allowed by the space group conditions. The accuracy of results obtained as the output
of refinement in the programs available for Rietveld analysis depends on the judicious
choice of the profile function. One can use a single function or convolution of two or
more functions for approximating the observed diffraction profiles. Pearson VII [86],
Split Pearson VII [87], and psuedo-Voigt [88] functions have been demonstrated to
give the best fit to the observed X-ray profile fitting [89-90] in structural and
microstructural analysis using Rietveld method. Dollase (1986) showed performance
of March function in Rietveld refinement [91] for preferred orientation measurement.
INTRODUCTORY REMARKS CHAPTER-1
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Many authors then incorporated March-Dollase function in Rietveld refinement codes
and confirmed Dollases’s evaluation. Another interesting and apparently very
powerful preferred orientation function was given by Ahtee et al. (1989) in which the
preferred orientation effect was modeled by expanding the orientation distribution in
spherical harmonies [92]. Wenk et al. introduced WIMV method for texture analysis
and got tremendous success [93].
The microstructural study by Rietveld method is now become very popular
among powder diffractionists. In 1988, Langford for the first time determined
crystallite size and microstrain using Rietveld method [94]. In 1993, Delhez et al.
developed a theory for the crystallite-microstrain separation [95] and reported that as
long as microstructure effects are isotropic, they can be accounted for easily in
Rietveld refinements. Bokhimi et al. [96] and Sanchez et al. [97] characterized the
particle size of magnesium and titanium oxides prepared by the sol-gel technique, by
using DBDW and WYRIET. Xiao et al. reported that the Rietveld refinement of
nanostructured hollandite powders do not converged well, due to anistropic effects
associated with a fiber axis in the b direction and fitted the powder pattern realized
with a highly packed sample taking into account the preferred orientation correction
and reducing the contribution of the narrowest reflections and reported a mean
crystallite size of 108 A0 with zero microstrain [98].
The Rietveld method can determine the degree of crystallinity in
semicrystalline materials. Riello et al. modeling the crystalline peak profiles by
psuedo-Voigt for a sample of polyethylene terephtalate and simultaneously
optimizing the background contributions estimated quantitatively the volume fraction
of silicate glass in ceramic by RIETQUAN [99].
Ungar et al. (1999) applied the dislocation based model of strain anisotropy in
the Fourier formalism of profile fitting and fitted the powder pattern of Li-Mn
(spinel), refining the parameters, namely the average dislocation density, the average
coherent domain size, the dislocation arrangement parameter and the dislocation
contrast factor[100]. In 1998, Popa developed a method especially for anisotropic
crystallite shape including the harmonic expansion [101] for better fitting of X-ray
profiles. In 1999, Scardi and Leoni reported that anisotropic line broadening of X-ray
diffraction profiles due to line and plane lattice defects can be Fourier modeled and a
detailed information on the defect structure (dislocation density and cut-off radius,
stacking and twin fault probabilities were refined together with the structural
INTRODUCTORY REMARKS CHAPTER-1
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parameters) can be obtained when applied to face-centered cubic structure materials
[102]. Ungar et al. established a simple preocedure for the experimental determination
of the average contrast factor of dislocations [103], in terms of a simple parameter q
which can be used in Rietveld structure refinement.
Studies on Rietveld refinement reveal that only size-effect is much easier to
handle than both size and microstrain. Being confirmed from the transmission
electron micrograph of the powder that only size effect is present, the size distribution
of single crystal nano particles can be estimated by two approaches. One approach
consists in Monte Carlo fitting of wide-angle X-ray scattering peak shape [104].
Another method applies maximum entropy for determining the column-length
distributions from size-broadened diffraction removing instrument broadening [105].
Line profile analysis is incorporated in Rietveld method for refinement of
crystallite size, microstrain, lattice distortion due to dislocations (edge/screw); planar
defects (twin and deformation faults) [106-107]. Lutterotti et al. analyzed the material
composed of silicate glass in ceramic matrix by the Rietveld method and determined
the content of amorphous phase in ceramic materials [108] and characterized its
defect structure.
Bokhimi et al. [109] prepared samples in the MgO-TiO2 system via the sol-gel
technique. Samples were characterized with X-ray powder diffraction and to quantify
the concentration and the crystallography of the phases in the samples, their
crystalline structures were refined using the Rietveld method.
Blouin et al. [110] followed the kinetics of formation and structural evolution of
nanocrystalline phases by mechanochemical reaction between Ti and RuO2 by
performing a Rietveld refinement analysis of X-ray diffraction profile.
Rixecker et al. [111] identified ternary phases with the cubic structure in both
the Fe-Nb-Si and Fe-Ta-Si systems formed during the crystallization of mechanically
alloyed amorphous materials during heat treatments. The X-ray powder diffraction
data were evaluated both by local line fit and by Rietveld analysis.
Wang et al. [112] prepared iron-doped titania photocatalysts with different
iron contents by using a sol-gel method in acidic media. The crystalline structures of
the various phases calcined at different temperatures were studied by using the
Rietveld technique in combination with XRD experiments.
Bose et al. [113] prepared five compositions of Cd-Ag alloy in different
phases and phase boundary regions have been prepared and analyzed both in the
INTRODUCTORY REMARKS CHAPTER-1
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annealed and cold-worked states employing Rietveld’s powder structure refinement
method and Warren-Averbach’s method of X-ray line profile analysis.
In 2002 Bose et al. synthesized nanocrystalline Ni3Fe in sol-gel method [114]
and made X-ray microstructure characterization of the same material employing
Rietveld’s powder structure refinement method, the Warren-Averrbach’s method and
the modified Williamson-Hall method.
Pratapa et al. [115] made a comparative study of single-line and Rietveld
strain-size evaluation procedures using MgO ceramics. Strain-size evaluations from
diffraction line broadening for MgO ceramic materials have been compared using
single-line integral-breadth and Rietveld procedures with the Voigt function.
Bid et al. [116] reported formation of fully stabilized c-ZrO2 phase from m-
ZrO2 phase in ball milling process without using any additive. Microstructural
parameters of ball milled ZrO2 milled at four different BPMR (ball to powder mass
ratio) and different milling hrs were obtained by Rietveld powder structure refinement
analysis.
Dutta et al. [117] prepared nanocrystalline V2O5 by high energy ball milling
and studied the anisotropic nature of particle size and strain through Rietveld’s
analysis.
Manik et al. [118] prepared for the first time of nanocrystalline orthorhombic
polymorphs of CaTiO3 by high energy ball milling method and studied the
microstructural parameters of the phases during its evolution and at different post-
annealing temperature.
The same author prepared Nanocrystalline powders of CaCu3Ti4O12 (CCTO)
by high-energy ball milling the powder mixture of CaO, CuO, TiO2 and studied
structural and microstructural changes in terms of lattice imperfections from the
analysis of X-ray powder diffraction data by Rietveld's powder structure refinement
method [119].
Sarkar et al. [120] made an application of Stephens’s phenomenological model
for anisotropic line broadening of ZrSiO4 sample and the Rietveld’s refinement with
and without the model showed that the model improved the quality of fit.
A large number of successful refinements by Rietveld method has been
reported; reviews have been given by Taylor (1985), Hewat (1986), Cheetham and
Wilkinson (1992), Young (1993), Harris and Tremayne (1996), Masciocchi & Sironi
(1997), Harris et al (2001) and Devid et al (2002). It was mentioned in a review report
INTRODUCTORY REMARKS CHAPTER-1
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by H.M. Rietveld himself that a total of 172 structures were refined before 1977. In
the period January 1987 to May 1989 a total of 341 papers were published with
reference to or using the Rietveld method, of which nearly half using neutron
diffraction. In the year 1991, the number of papers published with reference to the
Rietveld method is 257. In the year 1994 the number rises to 350. In a lecture in
XVIIIth IUCR conference at Glasgow, Scotland, H.M. Rietveld himself told that
now-a-days Rietveld method is used in more than 500 publications per year [121].
Recently Rietveld method is used in over 2000 publication per year.
Z. K. Heiba et al. [122] studied the mixed oxides Zn1-xMgxO (ZMO) prepared
as nano-polycrystalline powders and thin films by a simple sol–gel process and dip
coating method. Structural and microstructural analysises were carried out applying x-
ray diffraction (XRD) and Rietveld method. Analysis showed that for x < 0.25, Mg
replaces Zn substitutionally yielding ZMO single phase, while for x ≥ 0.25 two phases
are identified ZMO and MgO. Replacing Zn2+ by Mg2+ distorts the cation tetrahedrons
and decreases the lattice constants ratio c/a of the wurtzite ZMO which deviate the
lattice gradually from the hexagonal structure as Mg+2 increases. These distortions are
attributed to the difference in electronic configuration of the two cations which
suppress the paraelectric-ferroelectric phase transition in the ZMO wurtzite.
Lemine et al. [123] studied the effects of milling times on the mechanically
milled ZnO powder. The milled powders are analysed by X-ray diffraction (XRD)
and scanning electron microscope (SEM). In order to quantify these effects, analysis
by the Rietveld method is carried out. It is shown that the application of mechanical
milling is a simple technique to produce nanocrystalline powder. A clear reduction of
grain size with an increase of microstrain and lattice parameters is observed with
increasing milling time.
Sivestrini et al. [124] studied the synthesis, morphology and luminescence
properties of europium (III)-doped zirconium carbonates prepared as bulk materials
and as silicasupported nanoparticles with differing calcinations treatments are
reported. Transmission electron microscopy and X-ray diffraction analyses have,
respectively, been used to study the morphology and to quantify the atomic amount of
europium present in the optically active phases of the variously prepared
nanomaterials. Rietveld analysis was used to quantify the constituting phases and to
determinate the europium content. Silica particles with an approximate size of 30 nm
INTRODUCTORY REMARKS CHAPTER-1
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were coated with 2 nm carbonate nanoparticles, prepared in situ on the surface of the
silica core.
Tebib et al. [125] studied that the Elemental Fe and red phosphorus powders
with a composition close to FexP (x = 10, 15 and 20 wt. %) were mechanically alloyed
in a planetary ball mill under an argon atmosphere. Structural changes were studied
by X-ray diffraction. The complete dissolution of the elemental powders is achieved
within 3 h of milling. Detailed analysis of the X-ray diffraction patterns reveal the
formation of a Fe(P) solid solution with two structures (α-Fe1 and α-Fe2) having
different lattice parameters, crystallite size and microstrains.
Albores et al. [126] studied the ZnO nanorods synthesized by induced seeds
by chemical bath deposition using hexamethylenetetramine (HMT) as a precipitant
agent and zinc nitrate (ZN) as Zn2+ source at 90°C. The influence of reactants ratio
was studied from 2 to 0.25 ZN/HMT molar. Microstructural information was obtained
by Rietveld refinement of grazing incidence X-ray diffraction data. These results
evidence low-textured materials with oriented volumes less than 18% coming from
(101) planes in Bragg condition.
Vagadia et al. [127] carried out a comparative study of structural,
microstructural and magnetic properties of the two sets of Co-doped ZnO samples
synthesized by solid state reaction and sol-gel method. Rietveld refinement of the X-
ray diffraction data reveals single phase hexagonal wurtzite structure for all the
samples, while the tunnelling electron microscopy measurements show the presence
of nano-phase in the sol-gel grown Co-doped ZnO samples.
Abbas et al. [128] studied the nanocrystalline cobalt ferrite synthesized using
two different methods: ceramic and co-precipitation techniques. The nanocrystalline
ferrite phase was formed after 3h of sintering at 1000°C. The structural and
microstructural evolutions of the nanophase were studied using X-ray powder
diffraction and the Rietveld method. The refinement result showed that the type of the
cationic distribution over the tetrahedral and octahedral sites in the nanocrystalline
lattice was partially an inverse spinel. The transmission electronic microscope
analysis confirmed the X-ray results.
Cherian et al. [129] studied that the sol–gel auto-combustion method adopted
to prepare solid solutions of nano-crystalline spinel oxides, (Ni1−xZnx) Fe2O4
(0≤x≤1).The phases are characterized by X-ray diffraction (XRD), high-resolution
INTRODUCTORY REMARKS CHAPTER-1
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transmission electron microscopy, selected area electron diffraction, and Brunauer–
Emmett–Teller surface area. The cubic lattice parameters, calculated by Rietveld
refinement of XRD data by taking into account the cationic distribution and affinity of
Zn ions to tetrahedral sites, show almost Vegard’s law behavior.
1.6.3 Recent works on microstructural characterization using modified Warren- Averbach method
Leine et al. in 1980 investigated the microstructure of the spalat-cooled
Aluminium rich alloys using modified Warren-Averbach method [130]. Tonejc and
Aluminium in 1980 determined crystallite size, microstrain and stacking fault
probabilities for splat-quenched Ag- (6,8.2,11) at. % Sn alloys and compared the
results with cold-worked filings and bulk compressed alloys [131]. Delhez et al. in
1980 and 1982 modified the classical theory of Warren (1969) for single line analysis
and discussed about the errors involved in the analysis from theoretical aspects
[132,133]. Ghosh, De and Sengupta characterized the microstructures if Cu-Ge and
Ag-Al alloys in deformed state [134-136]. Ekstrom and Chafield using X-ray line
profile broadening analysis studied the milling behavior of commercial alumina
(Al2O3) powders [137]. Reddy and Suryanarayana reported that the microstrain is the
major source of line broadening in Ag-Cd-In and Ag-Cd-Zn alloys [138].
Bhikshamaiah and Suryanarayana determined the stacking fault energy in Ni and
dilute Ni-Fe alloys as a function of temperature [139]. Delhez et al. in 1986 and
Langford et al. in 1988 made a detailed discussion about systematic errors developed
due to truncation of experimental line profiles at a finite range [140,133]. Pradhan et
al. studied the microstructure of binary Cu-Al, Cu-Si and ternary Cu-Mn-Si and Cu-
Ge-Si alloys in the deformed state [141-144]. David and Bonnet observed stacking-
fault pyramid in the phase Ni73..5Al9 Ti 14Cr3.5, when deformed at 7400C [145]. Yang
and Wan studied the influence of Al on the stacking fault energy in Fe-Al-Mn-C
alloys [146]. Balzer et al. analyzed the line-broadening effects in superconductors and
reported that stacking fault energy increases with increasing Tc [147]. Vermeulen et
al. suggested a method for correcting errors arising due to truncation of line profiles
[148,149]. Rosengard and Skriver made a comparative study of intrinsic, extrinsic and
twin fault probabilities found in 3d, 4d and 5d transitional metals [150]. Pal et al.
studied the microstructure of (Ag, Cu)-Zn and Cu-Ni-Sn alloys [151,152]. Drits et al.
studied thickness distribution and microstrain for illite and illite-smectite crystallites
INTRODUCTORY REMARKS CHAPTER-1
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[153]. Chatterjee et al. studied microstructure of Pb(1-x)Snx alloys using the above
method [154] and Mukherjee et al. studied lattice imperfections in deformed
Zirconium-base alloys[155].
Jayan et al. [156] studied the Coarsening of nano-sized M23C6 carbide
precipitate in 2.25Cr–1Mo steel. Carbide specimens were prepared by electrochemical
extraction of boiler tube specimens subjected to extend ageing in a thermal power
plant. The crystallite size was computed by Warren-Averbach and integral breadth
methods from X-ray diffraction line profiles. It is found that coarsening of nano sized
M23C6 particles reflected in diffraction pattern as increased crystallite size with
ageing.
Ortiza et al. [157] studied the crystallite size, lattice microstrain, lattice
parameter, and formation of solid solutions of a nanocrystalline Al93Fe3Cr2Ti2 alloy
prepared via mechanical alloying (MA) starting from elemental powders have been
investigated using the Rietveld method of X-ray diffraction (XRD) in conjunction
with line-broadening analyses through the variance, Warren–Averbach, and Stokes
and Wilson methods. Detailed analyses using transmission electron microscopy
(TEM), scanning electron microscopy (SEM), and inductively coupled plasma-optical
emission spectroscopy (ICP) have also been conducted in order to corroborate the
formation of solid solutions and the grain size measurement determined from the
XRD analyses.
Haluska et al. [158] studied the nanostructural features of the gas-phase
displacement reaction 2Mg (g) +SiO2 -2MgO(s) + Si, where SiO2 is in the form of
diatom shells were studied via X-ray diffraction and Fourier methods. Diatomaceous
powder heated to 700 C in a sealed graphite cell in the presence of Mg vapor formed
MgO via a displacement reaction. Warren-Averbach analysis performed on samples
reacted for different times showed an initial sharp MgO grain size distribution which
broadened with time.
Uvarov et al. [159] determined the crystallite size by X-ray diffraction
methods for 210 TiO2 (anatase) nanocrystalline powders with crystallite size from 3
nm to 35 nm. Each X-ray diffraction pattern was processed using different free and
commercial software. The crystallite size calculations were performed using Scherrer
equation and Warren–Averbach method. Statistical treatment and comparative
assessment of the obtained results were performed for the purpose of an ascertainment
of statistical significance of the obtained differences.
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Biju et al. [160] studied that the lattice strain contribution to the X-ray
diffraction line broadening in nanocrystalline silver samples with an average
crystallite size of about 50 nm using Williamson-Hall analysis assuming uniform
deformation, uniform deformation stress and uniform deformation energy density
models. The lattice strain in nanocrystalline silver seems to have contributions from
dislocations over and above the contribution from excess volume of grain boundaries
associated with vacancies.
Oba et al. [161] studied the origin of the ferromagnetism that appears in the
core region of Pd nanoparticles. In order to consider the contribution of crystal
structure to the appearance of ferromagnetism in the Pd nanoparticles, they performed
x-ray diffraction experiments and Warren-Averbach analysis. The results revealed
that the standard deviation of strain ∆ε showed a positive correlation with the
saturation magnetization, with the ferromagnetism appearing when ∆ε became larger
than about 0.5%. This suggests that the strains induce internal ferromagnetism in the
Pd nanoparticle.
Ebnalwaled et al. [162] studied the nanocrystalline Al-Mg-Mn synthesized by
ball milling technique. Microstructure of these alloys has been studied from X-ray
line broadening. The crystallite size of nanocrystalline Al-Mg-Mn system decreases
by increasing the Mg content, while the micro-strain, median diameter, increases by
increasing the Mg content.
Ganjkhanlou et al. [163] studied that Y2O3:Eu nanopowder was prepared by
urea solution combustion method. The samples were then characterized by X-ray
diffraction (XRD) and high resolution transmission electron microscopy (HRTEM).
The XRD patterns of samples were investigated by Warren-Averbach method in order
to determine crystallite size and strain distribution. An innovative method was
developed for prediction of dopant ion distribution in host lattice using Warren-
Averbach method and micro-strain distribution. Analyzing of Y2O3:Eu nanopowder
by this method revealed that the Eu ions preferentially accumulated in near the grain
boundaries more than the inner parts of crystallites.
Rivnay et al. [164] studied the crystallite size and cumulative lattice disorder
of three prototypical, high-performing organic semiconducting materials investigated
using a Fourier-transform peak shape analysis routine based on the method of Warren
and Averbach (WA). A simple analysis based on trends of peak widths and
INTRODUCTORY REMARKS CHAPTER-1
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Lorentzian components of pseudo-Voigt line shapes as a function of diffraction order
is also discussed as an approach to more easily and qualitatively assess the amount
and type of disorder present in a sample.
Wardecki et al. [165] studied that the microstructure of electrodeposited
nanocrystalline chromium (n-Cr) was studied by using synchrotron radiation (SR)
diffraction, SEM, TEM, and EDX techniques. The presence of the Cr oxide phases
was studied by performing X-ray diffraction studies at room temperature with a
laboratory X-ray diffractometer Seifert ID-3003 (Mo Ka radiation) operating at 40 kV
and 30 mA (University of Warsaw). The average column length and the microstrain
fluctuation were calculated from SR diffraction data by using the Warren-Averbach
method.
Back et al. [166] observed an optical study of Tb3+-doped Y2O3 nanocrystals
synthesized by Pechini-type sol–gel method. The particles are investigated in terms of
size and morphology by means of X-ray diffraction and transmission electron
microscopy analysis. The reflection broadening in the XRD patterns is attributed
mainly to three kinds of contributions: crystallite size, microstrain, and the instrument
itself. The Warren–Averbach method was used for the line profile analysis of
reflections to separate the effect of crystallite size and microstrain on reflection
broadening. The software based on Warren–Averbach Fourier transfer method was
used to calculate the distribution of crystallite size and microstrain of the samples
1.7 Review on positron annihilation studies for lattice imperfection
measurement The temperature dependence of positron annihilation in aluminum has been
investigated by Fluss et al. [167] over the range 20-435°C by simultaneous
measurements of positron lifetime and Doppler broadening of the annihilation
spectrum.
Krishnan et al. [168] studied that the preferential sensitivity of positrons
towards micro-defect domains which are not assessable by other techniques makes it
an attractive tool for many materials science problems. The study is intended as a
brief introduction on the principle of measurements and its potential is exemplified
with the help of results on some metallic and ceramic systems.
INTRODUCTORY REMARKS CHAPTER-1
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Chidambaram et al. [169] studied a positron annihilation study of the
icosahedral Al-Cu-Fe alloy system which has been carried out using both Doppler
broadening and lifetime measurement techniques.
Yongming et al. [170] have calculated the one- and two-dimensional angular
correlation distribution of electron-positron annihilation (ACAR) as well as the
electron momentum distribution (EMD) for graphite.
Hübner et al. [171] calculate the fraction of positrons reaching particle surface
(FPS). The presence of defects in the particles can drastically reduce FPS depending
on the defect concentration and capture rate. They demonstrate that for small-grained
materials the grain surface can influence the lifetime signal significantly.
Sandreczki et al. [172] studied that the positron annihilation lifetime
spectroscopy is used to monitor the sub-glass-transition-temperature (Tg) annealing of
a polycarbonate sample. The intensity of ortho-positronium annihilation decreases as
a stretched-exponential function of annealing time at Tg − 121 K.
Haung et al. [173] performed two-dimensional angular correlation of electron-
positron annihilation radiation (2D-ACAR) measurements on a series of porous
silicon with photoluminescence (PL) peak energy in the range from 1.6 to 2.0 eV. The
electron-positron momentum spectra of porous silicons can be well resolved into two
peaks with different line width. The result shows two distinct momentum spectra for
the studied samples.
Shantarovich et al. [174] studied that the positron annihilation lifetime (PAL)
spectroscopy was applied to measure free-volume size distribution in polymer
samples with unusually long lifetimes: in dense films of poly (trimethylsilylpropyne)
(PTMSP) and in porous membranes prepared from poly (phenylene oxide) (PPO).
PAL data were treated by finite-term lifetime analysis (PATFIT program) and
continuous lifetime analysis (CONTIN program).
Wurschum et al. [175] studied that the atomic free volumes and vacancies in
the ultrafine grained alloys Pd84Zr16, Cu 0.1 wt % ZrO2, and Fe91Zr9 were studied by
means of positron lifetime.
Staab et al. [176] investigate the changes in the microstructure on a nano-scale
(nano-structure) in technically used AlCuMg 2024 alloys. How the annihilation
parameters, i.e. the positron lifetimes and corresponding intensities, are changing
during natural and artificial aging is observing here. It turns out that positron
annihilation spectroscopy is very sensitive to changes occurring in the nano-structure
INTRODUCTORY REMARKS CHAPTER-1
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but which are not always reflected or measurable in the materials properties such as
hardness.
Dull et al. [177] studied an existing model that relates the annihilation lifetime
of positronium trapped in subnanometer pores to the average size of the pores is
extended to account for positronium in any size pore and at any temperature. This
extension enables the use of positronium annihilation lifetime spectroscopy in
characterizing nanoporous and mesoporous materials, in particular thin insulating
films where the introduction of porosity is crucial to achieving a low dielectric
constant, K.
Lizama et al. [178] studied that a series of thermoplastic/elastomer composite
particles has been prepared by two step emulsion polymerization techniques. The
morphology of the obtained composite particles as a function of the system
composition has been studied by transmission electron microscopy. Afterwards, a
correlation between the structural behavior of the composites and the ortho-
positronium lifetime and formation probability was also established. This correlation
can be explained in terms of free volume changes associated to phase transitions in
the particles.
Grafutin [179] studied that the measurements of positron lifetimes, the
determination of positron 3γ- and 2γ-annihilation probabilities, and an investigation of
the effects of different external factors on the fundamental characteristics of
annihilation constitute the basis for this promising method.
Zheng et al. [180] studied that the synthesis of nanoparticles SiO2 that have
enabled the processing of exciting new nanoparticle/epoxy composites. Ultrasonic and
mechanical methods were used to disperse the nanoparticles in epoxy resin. The
nanocomposites were characterized by tensile and impact testing as well as TEM
studies. Additionally, the effects of nanometer-sized SiO2 particles on free volume of
nanocomposites were studied using positron annihilation lifetime spectroscopy.
Mokrushin et al. [181] studied the measurements of the angular correlation of
annihilation radiation and infrared absorption spectra conducted with porous silicon
samples, containing capillary macropores with a diameter of about 1 m. The set of
data shows that a high proportion of Si-O bonds contribute to positron annihilation
and IR absorption for porous silicon. Annihilation parameters and estimated values of
the specific surface area point to the availability of a nanoporous system in the
INTRODUCTORY REMARKS CHAPTER-1
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macroporous silicon. Most likely the macropore surface is covered by the nanoporous
material to a thickness of 100-200 nm.
Nagai et al. [182] studied the irradiation-induced vacancy-type defects in Fe-
based dilute binary alloys ~Fe-C, Fe-Si, Fe-P, Fe-Mn, Fe-Ni, and Fe-Cu!, model
alloys of nuclear reactor pressure vessel steels by positron annihilation methods,
positron lifetime, and Coincidence Doppler Broadening (CDB) of positron
annihilation radiation. The vacancy-type defects were induced by 3 MeV electron
irradiation at room temperature. The defect concentrations are much higher than that
in pure Fe irradiated in the same condition, indicating strong interactions between the
vacancies and the solute atoms and the formation of vacancy-solute complexes.
Chen et al. [183] studied the defects in hydrothermal grown ZnO single
crystals studied as a function of annealing temperature using positron annihilation, x-
ray diffraction, Rutherford backscattering, Hall, and cathodoluminescence
measurements. Positron lifetime measurements reveal the existence of Zn vacancy
related defects in the as-grown state. The positron lifetime decreases upon annealing
above 600°C, which implies the disappearance of Zn vacancy related defects, and
then remains constant up to 900°C.
Galindo et al. [184] studied the colloidal silica particles introduced in methyl
silicate (SiO1.5CH3) coating (obtained from methyltrimethoxysilane as a precursor) to
increase the hardness, the elastic modulus and the fracture toughness. In order to
obtain a more detailed structural analysis Positron Beam Analysis (PBA) using the
Doppler Broadening (DB) and the 2D-Angular Correlation of Annihilation Radiation
(2D-ACAR) techniques was performed.
Chakrabarti et al. [185] studied the particle size of the ball-milled Bi2O3
powder has been determined by the x-ray powder diffraction method and transmission
electron microscopy. The absorption spectra, in the spectral range 300–1300 nm,
indicate an increase of the optical bandgap for both the direct and indirect transitions
due to the reduction of grain size. The defects introduced in Bi2O3 during grinding
have been investigated by the positron annihilation technique. Positron annihilation
results indicate an increase of defects due to ball milling.
Cassidy et al. [186] studied the high-density gas of interacting positronium
(Ps) atoms by irradiating a thin film of nanoporous silica with intense positron bursts
and measured the Ps lifetime using a new single-shot technique. When the positrons
INTRODUCTORY REMARKS CHAPTER-1
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were compressed to 3.3×1010 cm-2, the apparent intensity of the ortho-positronium
lifetime component was found to decrease by 33%.
Kuriplach studied [187] the nanoparticles embedded in a matrix can trap
positrons under certain conditions. In such cases nanoparticles can be effectively
studied by means of positron annihilation because positron annihilation characteristics
contain information related to nanoparticles' electronic and atomic structure.
Zheng et al. [188] studied that the effects of SiO2 nanoparticles on the
properties of glass-fiber composites show that the SiO2 nanoparticles can generally
promote their properties especially the bend strength that ends up with 69.4%
enhancement. This is attributed to the promoted bonding forces between glass fibers
and matrices owing to the presence of nanoparticles. The size and concentration of
free volume were tested by positron annihilation spectroscopy.
Kar et al. [189] studied that the quantum confinement effects in
nanocrystalline CdS studied using positrons as spectroscopic probes to explore the
defect characteristics. The lifetime of positrons annihilating at the vacancy clusters on
nanocrystalline grain surfaces increased remarkably consequent to the onset of such
finite-size effects. The Doppler broadened line shape was also found to reflect rather
sensitively such distinct changes in the electron momentum redistribution scanned by
the positrons, owing to the widening of the band gap.
Kar et al. [190] studied the Positron lifetimes measured in different
nanosystems of FeS2—granular samples, ribbons, oxidized ribbons, rods, and a
mixture of wires and tubes. To identify the positron trapping sites, the 511–511 keV
gamma rays coincidence-gated Doppler-broadened spectra were recorded and it
appeared that the trapping of positrons took place mainly in the vacancies created by
the absence of Fe2+ ions. The positron lifetimes in the nanogranular sample were
conspicuously larger compared to those in the coarse-grained bulk due to trapping and
annihilation at the grain surfaces.
Thosar et al. [191] studied the measurements of the value 2 and the intensity
I2 of the long component in the life-time spectra of positrons annihilating in some
simple unassociated, polar, and associated organic liquids are reported as a function of
temperature. A semi-empirical free volume model for the formation and quenching of
ortho-positronium atoms is developed for simple molecular materials to explain the
correlation between viscosity η, density ρ, and 2 observed in unassociated and polar
INTRODUCTORY REMARKS CHAPTER-1
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liquids. Such a correlation is not observed for associated liquids in which the presence
of hydrogen bonds between molecules apparently influences the annihilation process.
Roy et al. [192] studied the nanosize zinc ferrite samples with an average
particle size of 6–65 nm prepared by a new chemical reaction involving nitrates of Zn
and Fe and investigated for magnetic behaviour and defect structure. The sample with
an average particle size of 6 nm has considerable inversion in cation distribution as
shown by its hysteresis loop and increased magnetization.
Chakrabarti et al. [193] studied that Polyacrylonitrile (PAN)-based carbon
fibers, embedded with multi-wall carbon nanotubes (MWCNT) in different
concentrations, have been prepared by an electrospinning technique and investigated
using scanning electron microscopy, Raman, and positron annihilation spectroscopy.
An analysis of the positron lifetime and Doppler broadened spectral line shape has
been made. Positron lifetime spectra for all the samples give best fit for three distinct
lifetime components.
Biswas et al. [194] studied nanostructures of ZnS, both particles and rods,
synthesized through solvothermal processes and characterized by x-ray diffraction
and high resolution transmission electron microscopy. Positron lifetime and Doppler
broadening measurements were made to study the features related to the defect
nanostructures present in the samples. The nanocrystalline grain surfaces and
interfaces, which trapped significant fractions of positrons, gradually disappeared
during grain growth, as indicated by the decreasing fraction of ortho-positronium
atoms. The crystal vacancies present within the grains also trapped positrons. These
vacancies further agglomerated into clusters during the thermal treatment given to
effect grain growth.
Acosta et al. [195] studied the one of the basic mechanisms of radiation
embrittlement of steels is due to matrix damage. Embrittlement results in a raise in the
ductile-to-brittle transition temperature, which is used as indicator of the degradation
status of the material. The positron annihilation spectroscopy in lifetime set-up is used
for study the microstructural changes of matrix due to embrittlement.
Mishra et al. [196] studied the defects present in ZnO nanocrystals prepared
by a wet chemical method have been characterized by photoluminescence (PL) and
positron annihilation spectroscopy (PAS) techniques. The as-prepared sample was
heat treated at different temperatures to obtain nanocrystals in the size range of 19–39
nm. Positron annihilation spectroscopy has been employed to understand the
INTRODUCTORY REMARKS CHAPTER-1
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dynamics of the vacancy-type defects and their annealing behavior. The observed
variation of the defect related lifetime components with heat-treatment temperature
has been successfully explained by using a three-state trapping model. The results of
PL and PAS studies in the present case are found to be complementary to each other.
Nghiep et al. [197] studied the positron annihilation rate measurement in
Polyethylene Terephthalate (PET) films. The correlation between annihilation rates
and the PET film thickness was established.
Lichard et al. [198] studied the excitation curve of e+e- annihilation into four
charged pions in the ρ (770) region calculated using three existing models with ρ
mesons and pions in intermediate states supplemented by Feynman diagrams with the
a1(1260) π intermediate states.
Chaplygin et al. [199] shows that an effective method to define the size of
nano-objects (vacancies, vacancy, clusters, free pore volumes, cavities, and holes),
and their concentration and chemical composition, is positron annihilation
spectroscopy (PAS). A review of the state of the art of the application of the PAS
technique to probe nanostructures in porous silicon, silicon and single crystal quartz
samples is presented.
Ridder et al. [200] studied the production rates for two, three, four, and five
jets in electron-positron annihilation at the third order in the QCD coupling constant.
At this order, three-jet production is described to next-to-next-to-leading order in
perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-
leading order.
Itoh et al. [201] studied the three main classes of materials, metals,
semiconductors and polymers, studied by using the Positron annihilation lifetime
spectroscopy (PALS) technique which is a powerful tool for the investigation of
microstructure.
Sanyal et al. [202] studied the coincidence Doppler broadening of the positron
annihilation technique employed to identify the defects in thermally annealed 'as-
received' ZnO and thermally annealed ball-milled nanocrystalline ZnO. Results
indicate that a significant amount of oxygen vacancy has been created in ZnO due to
annealing at about 500 °C and above.
Cheng-Xiao et al. [203] studied the influence of dopants in ZnO films on
defects is investigated by slow positron annihilation technique. The dopant
concentration could determine the position of Fermi level in materials, while defect
INTRODUCTORY REMARKS CHAPTER-1
~ 33 ~
formation energy of zinc vacancy strongly depends on the position of Fermi level, so
its concentration varies with dopant element and dopant concentration.
Ghoshal [204] studied the ZnO samples in the form of hexagonal-based
bipyramids and particles of nanometer dimensions synthesized through solvothermal
route and characterized by x-ray diffraction and transmission electron microscopy.
Positron annihilation experiments were performed to study the structural defects such
as vacancies and surfaces in these nanosystems. From coincidence Doppler
broadening measurements, the positron trapping sites were identified as Zn vacancies
or Zn–O–Zn trivacancy clusters. The positron lifetimes, their relative intensities, and
the Doppler broadened lineshape parameter S all showed characteristic changes across
the nano bipyramid size corresponding to the thermal diffusion length of positrons.
Tang et al.[205] studied the momentum density distributions determined by
the analysis of positron annihilation radiation in embedded nano Cu clusters in iron
were studied by using a first-principles method. A momentum smearing effect
originated from the positron localization in the embedded clusters is observed. The
smearing effect is found to scale linearly with the cube root of the cluster's volume,
indicating that the momentum density techniques of positron annihilation can be
employed to explore the atomic-scaled microscopic structures of a variety of impurity
aggregations in materials.
Heng et al. [206] investigated the nature of violet-blue emission from (Ge, Er)
co-doped Si oxides (Ge+Er+SiO2) using photoluminescence (PL) and positron
annihilation spectroscopy (PAS) measurements. The PL spectra and PAS analysis for
a control Ge-doped SiO2 (Ge+SiO2) indicate that Ge-associated neutral oxygen
vacancies (Ge-NOV) are likely responsible for the major emission in the violet-blue
band.
Das et al. [207] studied that the nanocrystalline samples of nickel oxide
synthesized through solvothermal and sol-gel routes, and the grain sizes determined
through x-ray diffraction and transmission electron microscopy. Fourier transform
infrared, optical absorption and positron annihilation spectroscopy studies were done
to characterize them further and study the defects at nanoscale. The onset of quantum
confinement effects is indicated by characteristic blue-shift in optical absorption
spectra and widening of the band gap. Positron annihilation parameters changed as a
result and the causes are discussed.
INTRODUCTORY REMARKS CHAPTER-1
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Mangalam et al. [208] studied the room temperature ferromagnetism in
nanoparticles of otherwise nonmagnetic materials attributed to point defects at the
surface of the nanoparticles. They have employed positron annihilation spectroscopy
to identify the nature of defects in multiferroic BaTiO3 nanocrystalline materials with
varying average particle sizes. Ratio curve analysis of the Doppler broadening profile
to a reference profile suggests that the defect is an oxygen vacancy. The decrease of
intensity of the intermediate lifetime component with increasing particle size indicates
a decrease of surface defect concentration. The large defect concentration in
nanocrystalline BaTiO3 can explain the observed room temperature ferromagnetism.
Oberdorfer et al. [209] studied the exact solution of a diffusion-reaction model
for the trapping and annihilation of positrons in grain boundaries of polycrystalline
materials with competitive trapping at intragranular point defects is presented.
Closed-form expressions are obtained for the mean positron lifetime and for the
intensities of the positron lifetime components associated with trapping at grain
boundaries and at intragranular point defects.
Hain et al. [210] investigated a friction stir welded (FSW) Al alloy sample by
Doppler broadening spectroscopy (DBS) of the positron annihilation line. The
spatially resolved defect distribution showed that the material in the joint zone
becomes completely annealed during the welding process at the shoulder of the FSW
tool, whereas at the tip, annealing is prevailed by the deterioration of the material due
to the tool movement.
R. Burcl et al. [211] studied the chemical composition of the material at the
annihilation sites (silicon atoms of the pore “wall”), the size of nanodefects, and their
concentration in porous silicon and single-crystal silicon wafers irradiated by protons
determined using the angular distribution of annihilation photons.
Wang et al. [212] studied the high purity ZnO nanopowders pressed into
pellets and annealed in air between 100o and 1200°C. The crystal quality and grain
size of the ZnO nanocrystals were investigated by x-ray diffraction. Positron
annihilation measurements reveal vacancy defects including Zn vacancies, vacancy
clusters, and voids in the grain boundary region. The voids show an easy recovery
after annealing at 100–700°C. However, Zn vacancies and vacancy clusters observed
by positrons remain unchanged after annealing at temperatures below 500°C and
begin to recover at higher temperatures. After annealing at temperatures higher than
1000°C, no positron trapping by the interfacial defects can be observed.
INTRODUCTORY REMARKS CHAPTER-1
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Acharya et al. [213] studied the Diffusion Trapping Model used to obtain the
positron annihilation Doppler broadening lineshape parameter in ZnO and O+, B+, N+,
Al+ implanted ZnO films. The concentration of vacancy clusters is found to be related
to the atomic number and the fluence of the implanted ion. The S-parameter is found
to be largest in the case of implantation of Al+ ions and is minimum for the
implantation of B+ ions. Thus, the vacancy clusters are found to be largest in the case
of Al+ implantation. The calculated results have been compared with the experimental
value.
Nambissan [214] reported that positron annihilation spectroscopy (PAS) is a
very useful tool to study the defect properties of nanoscale materials. The ability of
thermalized positrons to diffuse over to the surfaces of nanocrystallites prior to
annihilation helps to explore the disordered atomic arrangement over there and is very
useful in understanding the structure and properties of nanomaterials.
Pati et al. [215] studied the nanocomposites of Fe–NiO synthesized by the
mechanical milling technique. The phase purity of the sample was checked by X-ray
diffraction (XRD), which shows only lines of α-Fe and NiO. Presence of defects in
Fe–NiO nanocomposites ball-milled for prolonged durations is confirmed by positron
annihilation lifetime spectroscopy (PALS) measurements.
Simpson et al. [216] studied the silicon nanoclusters/nanocrystals (Si-nc) in
SiO2 matrix exhibit strong visible luminescence, and so are of interest in the pursuit of
a silicon-based light emitter for optoelectronics. They have investigated the formation
of Si-nc by implanting excess Si at 90 keV into SiO2 films and then annealing to form
nanoclusters by precipitation and ripening. Positron annihilation provides information
on vacancy-type defects produced during implantation. They suggest that defects may
play a key role in Si-nc formation.
Sarkar et al. [217] measured the room temperature positron annihilation
lifetime for single crystalline ZnO as 164 ± 1 ps. The single component lifetime value
is very close to but higher than the theoretically predicted value of ~154 ps.
Photoluminescence study (at 10 K) indicates the presence of hydrogen and other
defects, mainly acceptor related, in the crystal. The bulk positron lifetime in ZnO is
expected to be a little less than 164 ps.
Haynes et al. [218] studied the Fermi surface of the ferromagnetic shape-
memory alloy Ni2MnGa experimentally with two-dimensional angular correlation of
electron–positron annihilation radiation.
INTRODUCTORY REMARKS CHAPTER-1
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Maki et al. [219] studied the positron lifetime results under high-power steady-
state and transient optical excitation. The temperature dependences of transient and
steady-state measurements are studied, suggesting the possibility of analyzing the
positron trapping to extended defects and vacancy clusters in semiconductors.
1.8 Review on research work done using Mössbauer spectroscopy
Yuanzheng et al. [220] studied the nano-crystalline elemental iron powder
successfully formed by high-energy ball grinding. The x-ray diffraction, transmission
electron microscopy and Mössbauer spectroscopy were employed to follow the
structure changes in the process of mechanical grinding with milling time. The
broadening of Mössbauer spectrum is attributed to the large fraction of iron atoms
existing at the interfaces for the powder milled.
Ma et al. [221] studied the nickel ferrite ultrafine powders with different grain
sizes (8, 12, 20, 40 and 80 nm) synthesized chemically. Mössbauer spectra of 57Fe
nucleus in the samples composed of the nickel ferrite ultrafine powder before and
after the high pressure treatments have been measured. The superparamagnetic
relaxation is markedly suppressed by high pressure. The intensity of the sextets in
Mössbauer spectra increases with increasing the grain size or pressure.
Vijaya Kumar et al. [222] studied the magnetite nanorods prepared by the
sonication of aqueous iron (II) acetate in the presence of β-cyclodextrin. The
properties of the magnetite nanorods were characterized by x-ray diffraction,
Mössbauer spectroscopy, transmission electron microscopy, thermogravimetric
analysis, and magnetization measurements. The as-prepared magnetite nanorods are
ferromagnetic and their magnetization at room temperature is ~78emu/g.
Grave et al. [223] studied the various aspects, revealed by Mössbauer
spectroscopy, of structural and magnetic properties of Al-substituted small-particle
soil-related oxides. The ferrimagnetic-like behaviour reflected in the external-field
Mössbauer spectra (4.2 K, 60 kOe) of certain Al goethites is presented.
Predoi et al. [224] studied the two systems of nanoparticles with different
surface states have been prepared by sol-gel methods and analysed by X-ray
diffractometry, transmission electron microscopy, thermal analysis and temperature
dependent Mossbauer spectroscopy.
INTRODUCTORY REMARKS CHAPTER-1
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Malini et al. [225] studied the nanocomposites with magnetic components
possessing nanometric dimensions, lying in the range 1–10 nm, are found to be
exhibiting superior physical properties with respect to their coarser sized counterparts.
Magnetic nanocomposites based on gamma iron oxide embedded in a polymer matrix
have been prepared and characterized. The behaviour of these samples at low
temperatures have been studied using Mössbauer spectroscopy. Mössbauer studies
indicate that the composites consist of very fine particles of γ-Fe2O3 of which some
amount exists in the superparamagnetic phase. The cycling of the preparative
conditions were found to increase the amount of γ -Fe2O3 in the matrix.
Liu et al. [226] studied the Fe2O3–Al2O3 nano-composites synthesized by sol–
gel means. The properties of samples sintered at various thermal treatment
temperatures were investigated by X-ray diffraction (XRD) and Mössbauer
spectroscopy (MS). The experimental results show that the γ- to α-Al2O3
transformation occurs at lower temperature after iron oxide doping.
Chakraverty et al. [227] studied the theory of relaxation of single domain
magnetic nanoparticles, appropriate for analyzing measurements of Mössbauer
spectra, magnetization response, and hysteretic coercivity. With a special focus of
attention in the theoretical formulation is the presence of dipolar interaction between
the magnetic particles.
Sharma et al. [228] studied the nano particles of chromium substituted cobalt
zinc ferrite synthesized by a chemical co-precipitation method. X-ray diffraction
studies of the nano particles of CrxCo0.5−xZn0.5Fe2O4 (x = 0.1 to 0.5) heat-treated at
300 °C show that the particle sizes are in the range of 2 to 7 nm. Room temperature
Fe-57 Mössbauer spectra of all the samples show only two doublets, confirming the
presence of superparamagnetic relaxation in the nano particles. An exponential
decrease in the superparamagnetic blocking temperature, with increasing chromium
concentration, is observed for these samples.
Bahl et al. [229] demonstrate the exchange interactions between
antiferromagnetic nanoparticles of 57Fe-doped NiO varied by simple macroscopic
treatments. Mössbauer spectroscopy studies of the superparamagnetic relaxation
behaviour show that grinding or suspension in water of nanoparticles of NiO can
significantly reduce interparticle interactions.
Bandyopadhyay [230] write a comprehensive review on the recent
contributions of Mössbauer spectroscopy in materials science and engineering. After a
INTRODUCTORY REMARKS CHAPTER-1
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brief introduction to the basic methodology, examples of the application of 57Fe and 119Sn Mössbauer spectroscopy in both transmission and back-scattering mode are
presented and discussed.
Delcroix et al. [231] showed the Mössbauer spectra reflect the strong
sensitivity of the distribution of hyperfine magnetic field distributions (HMFDs) of
near equiatomic Fe–Cr alloys to the method of preparation of samples. Whatever the
way a bcc Fe0.51Cr0.49 alloy is prepared, powders produced from it by ball milling or
by filing exhibit a unique HMFD at room temperature.
Mukherjee et al. [232] studied the Fe–MgO nanocomposites synthesized by
the mechanical high-energy transfer technique characterized by x-ray diffraction
(XRD), transmission electron microscopy, Mössbauer spectroscopy and dc
magnetization studies. By varying the duration of milling, powder with different grain
sizes in the range 17–40 nm was produced. XRD and Mössbauer measurements could
not detect the presence of any form of iron oxide in the nanocomposites. Transmission
electron micrographs showed a shape transformation from spherical to acicular-like
geometry in the samples ball milled for more than 36 h.
Felner et al. [233] studied the 57Fe (1%) doped SrCoO3 obtained by high-
pressure method, investigated by magnetization and Mössbauer spectroscopy studies
(MS) in the temperature range 4.2 K to 300 K. The ferromagnetic ordering
temperature TC obtained is 272(2) K. Isothermal magnetization curves have been
measured at various temperatures, from which the saturation moments (M sat) have
been deduced.
Kiseleva et al. [234] used the Mossbauer spectroscopy and X-ray diffraction
for structural study of nanopowders resulting from a 60% Fe + 40% Al mixture after
mechanical activation, as well as their nanocomposite derivatives arising in the
process of self-propagating high-temperature synthesis. The different nature of the
iron-aluminum interaction in these nanotechnological processes is demonstrated.
Filoti et al. [235] showed that the laser pyrolysis became a useful tool,
providing various ways, in production of nano materials. The iron Mössbauer
spectroscopy is one very accurate method in evidencing the physical properties and
related processes in the nano scale compounds. The effect of pressure, laser spot area
and induced combustion, of gas mixture and laser power on the phase composition
and inside particle distribution, grain size as well as the related phenomena were
investigated by temperature dependent Mössbauer spectroscopy.
INTRODUCTORY REMARKS CHAPTER-1
~ 39 ~
Thakur et al. [236] studied the nano-nickel-zinc-indium ferrite (NZIFO)
(Ni0.58Zn0.42InxFe2−xO4) with varied quantities of indium (x = 0,0.1,0.2) synthesized
via reverse micelle technique. The addition of indium in nickel-zinc ferrite (NZFO)
has been shown to play a crucial role in enhancing the magnetic properties. Room
temperature Mössbauer spectra revealed that the nano-NZFO ferrite exhibit collective
magnetic excitations, while indium doped NZFO samples have the ferromagnetic
phase. The dependence of Mössbauer parameters, viz. isomer shift, quadrupole
splitting, linewidth, and hyperfine magnetic field, on In3+ concentration has been
studied.
Lyubutin et al. [237] used a thermal reduction method developed to prepare
magnetite/hematite nanocomposites and pure magnetite nanoparticles targeted for
specific applications. The relative content of hematite α-Fe2O3 and magnetite Fe3O4
nanoparticles in the product was ensured by maintaining proper conditions in the
thermal reduction of α-Fe2O3 powder in the presence of a high boiling point solvent.
The structural, electronic, and magnetic properties of the nanocomposites were
investigated by 57Fe-Mössbauer spectroscopy, x-ray diffraction, and magnetic
measurements.
Andrade et al. [238] studied the nano-sized materials often present chemical,
electronic, magnetic, and mechanical properties that are potentially interesting for
many technological applications comparatively to their corresponding bulk properties.
This paper describes the main differences in magnetic properties among
nanomagnetite powders prepared by three methods: (I) reduction-precipitation of
ferric chloride by reaction with Na2SO3; (II) reduction of hematite with coal, and (III)
reduction of hematite with hydrogen gas. XRD and Mössbauer spectroscopy results at
298 K showed the clear effect of the preparation routes on the crystallographic
structure and crystallite size of the magnetic species.
Mishra et al. [239] studied the behavior of strain, magnetization, and
resistivity of a nanoporous Au0.55Fe0.45 alloy studied in situ during electrochemically
induced charge variations on the surface of the alloy. In situ Mössbauer spectra
recorded during charging and decharging showed a systematic variation in quadrupole
splitting.
Babilas [240] studied on Fe72B20Si4Nb4 metallic glass in form of ribbons. The
amorphous structure of tested samples was examined by XRD and TEM. Mössbauer
spectroscopy method was applied to comparison of structure in studied amorphous
INTRODUCTORY REMARKS CHAPTER-1
~ 40 ~
samples with different thickness (cooling rates).The paper presents a structure
characterization of selected Fe-based metallic glass in as-cast state.
Chakrabarti et al. [241] reported that the Mössbauer Spectroscopic technique
is an important nuclear solid technique which has been used to probe the local
magnetic properties of a solid. They have reported Mössbauer spectroscopic studies
on different ferrites.
Antic et al.[242] studied that the structural and magnetic properties of
(Mn,Fe)3-δO4 nanoparticles synthesized by soft mechanochemistry using Mn(OH)2× 2
H2O and Fe(OH)3 powders as starting compounds. The Combined results of XRPD,
Mössbauer spectroscopy, and EDX analysis suggest that there is a deviation from
stoichiometry in the nanoparticle core compared to the shell, accompanied by creation
of cation polyvalence and vacancies. The value of saturation magnetization, MS, of
73.5 emu/g at room temperature, is among the highest reported so far among
nanocrystalline ferrite systems of similar composition.
Zakharova et al. [243] studied that the Mössbauer spectroscopy has been used
to study maghemite (γ-Fe2O3) particles with average dimensions on the microscopic
(~1 μm, “bulk” state) and nanoscopic (15 and 20 nm) levels. Data provided by this
method on the thickness of a surface region of magnetic nanoparticles and features of
their magnetic state have been analyzed.
1.9 The aim and objectives of the present work
Materials in nanocrystalline form are now being prepared widely because of
their wide range of applications in different fields. Structural imperfections in such
nanomaterials contribute a massive change in different properties of these materials.
Material characterizations in terms of detailed study of lattice imperfections in
particular, are essential for the systematic development of such nanomaterials as well
as for qualification of materials for design and fabrication. Today, there are several
techniques for material characterization. They often depend on how a given sample
responds to a probe. The probe may be electrons, positrons, neutrons, ions,
electromagnetic radiation (x-ray, gamma rays etc), ultra sound etc. In this research
work, Positron Annihilation Lifetime (PAL) spectroscopy, X-ray powder diffraction
(XRD) and few other methods of microstructure characterization would be discussed
which are usually used for characterization of nanomaterials.
INTRODUCTORY REMARKS CHAPTER-1
~ 41 ~
Presently, oxides in its nanocrystalline phase become very important due to
their wide applications. The large surface to-volume ratio of these nanomaterials
makes them different from the bulk of the material. Among them, magnetic
nanomaterials have received special attention as they can be used in different fields
like magnetic resonance imaging, drug delivery agents, etc. Among different
magnetic nanoparticles, α-Fe2O3 has large applications in chemical industry. It can be
used as catalyst, gas sensing material to detect combustible gases like CH4 and C3H8
etc. Further, an unusual characteristic like superparamagnetism in nanocrystalline
state of these materials makes them object of great interest for fundamental studies.
Among different iron oxides, α-Fe2O3 is the most stable polymorph in nature under
ambient condition and can be easily found as mineral hematite. Again nanocrystalline
materials, semiconductors in particular (ZnO), are being widely investigated at
present because of their interesting electronic and optical properties which may find
applications in devices such as solar cells, light emitting diodes, ultraviolet (UV)
lasers, fluorescent displays, etc. Ferrites are a group of technologically important
materials used in magnetic, electronic and microwave fields. Magnetic
nanocrystalline materials hold great promise for atomic engineering of materials with
functional magnetic properties. Magnetic nanocrystals have been extensively applied
in magnetic recording medium, information storage, bio-processing and magneto-
optical devices. Usually, magnetic nanocrystals show superparamagnetic behaviour
below a certain critical size.
The objects of the dissertation are to (i) preparation of nanocrystalline oxide
materials of different kinds by mechanical alloying and chemical route, (ii) analyze
the structure and microstructure of the nanocrystalline materials by X-ray line profile
analysis employing the Rietveld structure and microstructure refinement and HRTEM
(iii) characterize the defect state of nanocrystalline materials in terms of lattice
imperfections employing Positron Annihilation Lifetime Spectroscopy, (iv) Magnetic
characterization of some magnetic nanoparticles using Mossbauer Spectroscopy (v)
measurement of optical band gap in some cases using UV-Vis absorption
spectrometer.
1.10 References [1] M. Laue, W. Friedrich and P. Knipping, Ann, Phys. Lpz., 41 (1912) 199.
[2] W.L. Bragg, Proc. Camb. Phil. Soc., 17 (1913) 43.
INTRODUCTORY REMARKS CHAPTER-1
~ 42 ~
[3] H.G.J. Moseley, Phil. Mag. (1913) 1024.
[4] J.G. Byrne,’Recovery, Crystallization and Grain Growth’, McMillan Co., N.
Y. (1965).
[5] J.B. Newkirk, J. Appl. Phys., 29 (1958) 995.
[6] J.B. Newkirk, Trans. AIME., 215 (1959) 483.
[7] P.B. Hirsch, A. Howie and M.J. Whelan, Phil. Trans. Roy. Soc., A252 (1960)
499.
[8] W. Bollmann, Phys. Rev., 103 (1956) 1588.
[9] W.M. Stobbs and C.H. Sworn, Phil. Mag., 24 (1971) 1365.
[10] D.H.J. Cockayne, M.L. Jenkins and I.L. Ray, Phil. Mag., 24 (1971) 1383.
[11] B.E. Warren, Prog. Met. Phys., 8 (1959) 147.
[12] B.E. Warren, ‘X-ray diffraction’, Addision-Wesley, Reading, Mass, (1969).
[13] C.N.J. Wagner, Local Atomic Arrangement Studied by X-ray Diffraction’, ed.
J. B. Cohen and J.E. Hilliard, N.Y., Gordon Breach, (1966).
[14] H.M. Rietveld, Acta Crystallogr., A228 (1966) 21.
[15] G.S. Pawley, J. Appl. Cryst., 14 (1981) 357.
[16] E. Jartych, J.K. Zurawicz, D. Oleszak, M. Pekala, J. Mag. Matter, 208(2000)
221.
[17] S. Kumar, K. Roy, K. Maity, T.P. Sinha, D. Banerjee, K.C. Das, R.
Bhattacharya, Phys. Stat Sol. (a), 167 (1998) 12.
[18] S. Kumar, K. Roy, K. Maity, T.P. Sinha, D. Banerjee, K.C. Das, R.
Bhattacharya, Phys., Stat Sol. (a) 175 (1999) 927.
[19] E. Jartych, J.K. Zurawicz, D. Oleszak, M. Pekala, J. Magn. Magn. Mater. 208
221 (2000).
[20] A.J.C. Wilson, ‘Mathematical Theory of X-ray Powder Diffractometry’
Centrex Publishing Co., Eindhoven, (1963) 66.
[21] C.S. Barrett and T.B. Massalski, ‘Structure of Metals’, McGraw-Hill, Inc., N.
Y. (1966).
[22] H.P. Klug and L.F. Alexander, ‘X-ray diffraction Procedures’, John-Wiley and
Sons., N. Y. (1974).
[23] E.F. Bertaut, C.R. Acad. Sci., Paris, 228 (1949) 492.
[24] C.S. Barrett, Trans. AIME, 188 (1950) 123.
[25] B.E. Warren and B.L. Averbach, J. Appl. Phys., 21 (1950) 595.
[26] B. E. Warren and B.L. Averbach, J. Appl. Phys., 23 (1952) 497.
INTRODUCTORY REMARKS CHAPTER-1
~ 43 ~
[27] B.E. Warren and E.P. Warekois, Acta. Met., 3 (1955) 473.
[28] G.K. Williamson and R.E. Smallman, Phil. Mag., 1 (1956) 34.
[29] C.N.J. Wagner, Acta. Met., 5 (1957) 427.
[30] C.N.J. Wagner, Acta. Met., 5 (1957) 477.
[31] D. Michell and F.D. Hiag, Phil. Mag., 2 (1957) 15.
[32] R.E. Smallman and K.H. Westmacott, Phil. Mag., 2 (1957) 669.
[33] J.W. Christian and Spreadborough, Proc. Phys. Soc. (London), B70 (1957)
1151.
[34] R.W. Chan and R.G. Davies, Phil. Mag., 5 (1960) 1119.
[35] L.F. Vassamillet, J. Appl. Phys., 32 (1961) 778.
[36] R.G. Davies and R.W. Cahn, Acta. Met., 10 (1962) 621.
[37] M.J. Klein, J.L. Brimhall and R.A. Huggins, Acta. Met., 10 (1962) 13.
[38] D.O. Welch and H.M. Otte, Adv. X-ray Anal., 6 (1962) 96.
[39] R.P. I. Alder and C.N.J. Wagner, J. Appl. Phys., 33 (1962) 3451.
[40] J.H. Foley, R.W. Cahn and G.V. Raynor, Acta Met., 11 (1963) 355.
[41] L.F. Vassamillet and T.B. Massalski, J. Appl. Phys., 34 (1963) 3398.
[42] A. Howie and P.R. Swann, Phil. Mag., 6 (1961) 1215.
[43] R.C. Sundahl and J.M. Sivertsen, J. Appl. Phys., 34 (1963) 994.
[44] S. Koda, K. Nomaki and M. Nemoto, J. Phys. Soc. (Japan), 18 (1963) 118.
[45] L.F. Vassamillet and T.B. Massalski, J. Appl. Phys., 35 (1963) 2629.
[46] K. Nakajima and K. Numakura, Phil. Mag., 12 (1965) 361.
[47] C.N.J. Wagner and J.C. Helion, J. Appl. Phys., 36 (1965) 2830.
[48] S. Lele and T.R. Anatharamam, Z. Metallkunde, 58 (1967) 11.
[49] S. Lele and T.R. Anatharamam, Phil Mag., 58 (1967) 37.
[50] H.M. Otte, J. Appl. Phys., 38 (1967) 217.
[51] S.P. Sengupta and M.A. Quader, Acta. Cryst., 20 (1966) 798.
[52] K.N. Goswami, S.P. Sengupta and M.A. Quader, Acta. Cryst., 21 (1966) 243.
[53] M. De and S.P. Sengupta, Acta. Cryst., 24 (1968) 269.
[54] P.R. Rao and K.K. Rao, J Appl. Phys., 39 (1968) 4563.
[55] L. Delehouzee and A. Deruyttere Acta. Met., 15 (1967) 729.
[56] M. Ahlers and L.F. Vassamillet, ‘Adv. X-ray Analysis’, 10 (1967) 265.
[57] H.M. Rietveld, Acta Crystallogr., A228 (1966) 21.
[58] H.M. Rietveld Acta Cryst., 20 (1966) 508.
INTRODUCTORY REMARKS CHAPTER-1
~ 44 ~
[59] D.L. Decker, R.A. Beyerlein, G. Roult and T.G. Worlton, Phys. Rev B., 10
(1974) 3584.
[60] J.M. Carpenter, M.H. Mueller, R.A. Beyerlein, T.G. Worlton, J.D. Jorgensen,
T.O. Burn et al., Proc. Neutron Diffraction Conf., Petten, The Netherlands, 5-6
Aug., (1975) 192.
[61] C.G. Windsor and R.N. Sinclair, Acta Cryst., A32 (1976) 395.
[62] A.K. Cheetham and J.C. Taylor, J. Solid State Chem., 21 (1977) 253.
[63] P.E. Mackie and R.A. Young, Acta. Cryst., A31 (1975) 198.
[64] G. Malmros, and J.O. Thomas, J. Appl. Cryst., 10 (1977) 7.
[65] R.A. Young, P.E. Mackie and R.B. Von Dreele, J. Appl. Cryst., 10 (1977)
262.
[66] C.P. Khattak and D.E. Cox, J. Appl. Cryst., 10 (1977) 405.
[67] D.B. Wiles and R.A. Young, J. Appl. Cryst., 14 (1981) 149.
[68] H.M. Rietveld, Acta Cryst., 29 (1969) 65.
[69] R.A. Young, A. Sakthivel, T.S. Moss and C.O. Paiva-Santos, J. Appl. Cryst.,
28 (1995) 366.
[70] S.A. Howard, ‘Advances in Material Characterization II’ ed R.L. Synder, R.A.
Condrate and P.F. Johnson (New York: Plenum) (1985) 43.
[71] R.J. Hill and C.J. Howard, Austral. Atomic Energy Comm Rep. No. M112,
(1986).
[72] D.P. Matheis and R. L. Synder, Powder Diffrac., 9 (1994) 28.
[73] J. Rodriguez-Carvajal, ‘Collected Abstract of Powder Diffraction Meeting’,ed.
J. Galy Toulouse, France, (1990) 127.
[74] A.C. Larson and R.B. Von Dreele, Los Alamos Nat. Lab. Report No.
LA_UR86-748 (1987).
[75] C. Baerlocher, XRS-82, The X-ray Rietveld system, Inst. fur Krist., ETH,
Zurich, (1982).
[76] L. Lutterotti, P. Scardi and P. Maistrelli, J. Appl. Cryst., 25 (1992) 459.
[77] F. Izumi, Nippon Kessho Gakkai Shi (J. Cryst. Soc. Jpn.), 27 (1985) 23.
[78] F. Izumi, Rigaku. J., 6 (1989) 10.
[79] M. Ferrari and L. Lutterotti, J. Appl. Phys., 76 (1994) 7246.
[80] Werner,P.E,Mater Sci.Forum.,79-82 (1991) 197-206.
[81] M. Ferrai, L. Lutterotti, S. Mathies, P. Polonioli, H.R. Wenk, Mater. Sci.
Forum., 228-231 (1996) 83.
INTRODUCTORY REMARKS CHAPTER-1
~ 45 ~
[82] L. Lutterotti, S. Mathies, H.R. Wenk, A.J. Schultz, J. Richardson, J. Appl.
Phys., 81 (1997) 594.
[83] S. Mathies, L. Lutterotti, H.R. Wenk, J. Appl. Cryst., 30 (1997) 31.
[84] L. Lutterotti, S. Gialanella, Acta Materialia, 46 (1998) 101.
[85] A Le Bail, H. Duroy, J.L. Fourquet, Mater. Res. Bull., 23 (1988) 447.
[86] M.M. Hall Jnr., V.G. Veeraraghavan, H.Rubin, P.G. Winchell, J. Appl. Cryst.,
10 (1977) 66.
[87] J.I. Langford, J. Appl. Cryst. 11 (1978) 10.
[88] G.K. Wertheim, M.A. Butler, K.W. West, D.N.E. Buchanan, Rev. Sci.
Instrum., 11 (1974) 1369.
[89] R.A. Young, D.B. Wiles, J. Appl. Cryst., 15 (1982) 430.
[90] J.I. Langford, Prog. Cryst. Growth and Charact., 14 (1987) 185.
[91] W.A. Dollase, J. Appl. Cryst., 19 (1986) 267.
[92] M. Ahtee, M. Nurmela, P. Suortti, M. Jarvinen, J. Appl. Cryst., 22 (1989) 261.
[93] H.R. Wenk, S. Mathies, L. Lutterotti, Mater. Sci. Forum. 157-162 (1994) 473.
[94] J.I. Langford, R. Delhez, T.H. de Keijser, E.J. Mittemeijer, Austral. J. Phys.,
41 (1988) 173.
[95] R. Delhez, T.H. de Keijser, J.I. Langford, D. Louer, E.J. Mittemeijer, E.J.
Sonneveld, ‘The Rietveld Method’ ed by R. A. Young, Oxford University
Press, (1993) 132.
[96] X. Bokhimi, A. Morales, O. Novaro, T. Lόpez, E. Sánchez, R. Gόmez, J.
Mater. Research, 10 (1995) 2788.
[97] E. Sánchez, T. Lόpez, R. Gόmez, Bokhimi, A. Morales, O. Novaro, J. Solid
State Chem., 122 (1996) 309.
[98] Xiao, Bokhimi, Beniassa, Perez, Strutt, Yacaman, Acta Mater., 45 (1997)
1685.
[99] P. Riello, G. Fagherazzi, P. Canton, D. Clemente, M. Signoretto, J. Appl.
Cryst., 28 (1995) 121.
[100] T. Ungár, M. Leoni, P. Scardi, J. Appl. Cryst., 32 (1999) 290.
[101] N.C. Popa, J. Appl. Cryst., 31 (1998) 176.
[102] P. Scardi, M. Leoni, J. Appl. Cryst., 32 (1999) 671.
[103] T. Ungár, I. Dragomir, Á. Révész, A. Borbély, J. Appl. Cryst., 32 (1999) 992.
[104] P.E. Di Nunzio, S. Martelli, J. Appl. Cryst., 32 (1999) 546.
[105] N. Armstrong, W. Kalceff, J. Appl. Cryst., 32 (1999) 600.
INTRODUCTORY REMARKS CHAPTER-1
~ 46 ~
[106] P. Scardi, M. Leoni, Y.H. Dong, Eur. Phys. Journal B, 18 (2000) 23.
[107] P. Scardi, Y.H. Dong, M. Leoni, Proceeding of EPDIC-7 Barcelona, (2000)
20.
[108] L. Lutterotti, R. Ceccato, R. Dal Maschio, E. Pagani, Mater. Sci. Forum, 278-
281 (1998) 87.
[109] X. Bokhimi, J.L Boldu, E. Munoz, O. Novaro, T. López, J. Hernandez, R.
Gómez and A. Garcia-Ruiz, Chem. Mat., 11 (1999) 2716.
[110] M. Blouin, D. Guay, R. Schulz, J. Mater. Sci., 34 (1999) 5581.
[111] G. Rixecker, R. Haberkorn, J. Alloy. Compd., 316 (2001) 203.
[112] J.A. Wang, R. Limas-Ballesteros, T. López, A. Moreno, R. Gómez, O.
Novaro, X. Bokhimi, J. Phys. Chem. B ,105 (2001) 9692.
[113] P. Bose, S.K. Shee, S.K. Pradhan, M. De, Mater. Engg., 12 (2001) 353.
[114] P. Bose, S. Bid, S.K. Pradhan, M. Pal, D. Chakravorty, J. Alloy. Compd., 343
(2002) 192.
[115] S. Pratapa, B. O'Connor, B. Hunter, J. Appl. Crystallogr., 35 (2002) 155.
[116] S. Bid, S.K. Pradhan, J. Appl. Cryst., 35 (2002) 517.
[117] H. Dutta, S.K. Pradhan, Mater. Chem. Phys., 77 (2003) 868.
[118] S.K. Manik, S.K. Pradhan, Mater. Chem. Phys., 86 (2004) 284.
[119] S.K. Manik, S.K. Pradhan, Physica E, 33 (2006) 160.
[120] A. Sarkar, P. Mukherjee, P. Barat, Z. Kristallogr. Suppl., 26 (2007) 543.
[121] H.M. Rietveld, proceedings of XVIIth IUCR conf. Scottland, (1999) 14.
[122] Z.K. Heiba, L. Arda, Crystal Research and Technology, 44 (2009) 845.
[123] O.M. Lemine, A. Alyamani, M. Bououdina, International Journal of
Nanoparticles, 2 (1-6) (2009) 238.
[124] S. Sivestrini, P. Riello, I. Freris, D. Cristofori, F. Enrichi, A. Benedetti, J
Nanopart Res., 12 (2010) 993.
[125] Tebib, Wassila; Alleg, Safia; Bensalem, Rachid; Greneche, Jean-Marc,
International Journal of Nanoparticles, 3 (3) (2010) 237.
[126] F. Pola-Albores, F. Paraguay-Delgado, W. Antúnez-Flores, P. Amézaga-
Madrid, E. Ríos-Valdovinos, M. Miki-Yoshida, Journal of Nanomaterials,
2011 (2011), Article ID 643126, 11 pages doi:10.1155/2011/643126.
[127] M. Vagadia, A. Ravalia, U. Khachar, P.S. Solanki, R.R. Doshi, S. Rayaprol,
D.G. Kuberkar, Materials Research Bulletin, 46 Issue 11 (2011) 1933.
INTRODUCTORY REMARKS CHAPTER-1
~ 47 ~
[128] Y.M. Abbas, S.A. Mansour, M.H.Ibrahim, S.E. Ali, Journal of Magnetism and
Magnetic Materials, 323 Issue 22 (2011) 2748.
[129] C.T. Cherian, M.V. Reddy, G.V.S. Rao, C.H. Sow, B.V.R. Chowdari, J Solid
State Electrochem, 16 (2012) 1823.
[130] E.S.U. Laine, E.J. Hiltunen, M.H. Heinonen, Acta. Met., 28 (1990) 1565.
[131] A.M. Tonejc and A. Bonefacic, J. Mater. Sci., 15 (1970) 1561.
[132] R. Delhez, T.H. de Keijser, E.J. Mittemeijer, Acuuracy in Powder
Diffraction,’ ed S. Block, C.R. Hubbard, NBS spec. 567 (1980) 213.
[133] R. Delhez, Th. De Keijser, E.J. Mittemeijer, J.I. Langford, J. Appl. Cryst., 19
(1986) 459.
[134] S.K. Ghosh, M. De, S. P. Sengupta, J. Appl. phys., 54 (1983) 2073.
[135] S.K. Ghosh, M. De, S. P. Sengupta, J. Appl. phys., 56 (1984) 1213.
[136] S.K. Ghose, S. P. Sengupta, Metall. Trans. A, 16A (1985) 1427.
[137] T. Ekstrom, C. Chatfield, J. Mater. Sci., 20 (1985) 1266.
[138] S.V. Reddy, S.V. Suryanarayana, Bull. Mater. Sci., 8 (1986) 61.
[139] G. Bhikshamaiah, S.V. Suryanarayana, J. Less-Common Mat., 120 (1986)
189.
[140] R. Delhez, T.H. de Keijser, J.I. Langford, D. Louer, E.J. Mittemeijer, E.J.
Sonneveld, ‘The Rietveld Method’ ed by R. A. Young, Oxford University
Press, (1993) 132.
[141] S.K. Pradhan, A.K. Maity, M. De, S.P. Sengupta, J. Appl. Phys., 62 (1987)
1521.
[142] S.K. Pradhan, M. De, J. Appl. Phys., 64 (1988) 2324.
[143] S.K. Pradhan, M. De, Metall. Trans. A, 20(1989)1883.
[144] S.K. Shee, S.K. Pradhan, M. De, J. Alloys and Comps., 265 (1998) 249.
[145] D. David, R. Bonnet, Phil. Mag. Letts., 62 (1990) 89.
[146] W.S. Yang, C. N. Wan, J. Mater. Sci.,25 (1990) 1821.
[147] D. Balzer, H. Ledbetter, A. Rashko, Physica C, 185-189 (1991) 871.
[148] A.C. Vermeulen, R. Delhez, T.H. de Keijser, E.J. Mittemeijer, J. Mater. Sci.
Forum, 79-82 (1991) 119.
[149] A.C. Vermeulen, R. Delhez, T.H. de Keijser, E.J. Mittemeijer, J. Appl. Phys.,
71 (1992) 5303.
[150] M.N. Rosengard, H.L. Skriver, Phys. Rev. B., 47 (1993) 12865.
[151] H. Pal, S.K. Pradhan, M. De, Jpn. J. Appl. Phys., 32 (1993) 1164.
INTRODUCTORY REMARKS CHAPTER-1
~ 48 ~
[152] H. Pal, S.K. Pradhan, M. De, Mater. Trans. JIM., 36 (1995) 490.
[153] V.A. Drits, D.D. Eberl, J. Srodon, Clays and Clay Minerals., 46 (1998) 38.
[154] P. Chatterjee, S.P. Sengupta, J. Appl. Cryst., 32 (2000) 1060.
[155] P. Mukherjee, S.K. Chattopadhyay, S.K. Chatterjee, A.K. Meikap, P. Barat,
S.K. Bandyopadhyay, P. Sen, M.K. Mitra, Metall.and Mater.Trans.A, 31
(2000) 2405.
[156] V. Jayan, M.Y. Khan, M. Husain, Science Direct, 58 (2004) 2569.
[157] A.L. Ortiz, L. Shaw, Acta Materialia, 52 (2004) 2185.
[158] M.S. Haluska, I. C. Dragomir, K.H. Sandhage, R.L. Snyder, Powder Diffr., 20
(2005) 306.
[159] V. Uvarovand, I. Popov, ScienceDirect, 58 (2007) 883.
[160] V. Biju, N. Sugathan, V. Vrinda, S.L. Salini, Journal of Materials Science, 43
(2008) 1175.
[161] Y. Oba, T. Sato, T. Shinohara, Phys. Rev. B, 78 (2008) 224417.
[162] A.A. Ebnalwaled, M. Abou Zied, Journal of Nano Research, 9 (2010) 61.
[163] Y. Ganjkhanlou, F.A. Hessari, M. Kazemzad, G. Darbandi, physica status
solidi (c), 7 (2010) 2667.
[164] J. Rivnay, R. Noriega, R.J. Kline, A. Salleo, M.F. Toney, Physical Review B-
Condensed Matter and Materials Physics, 84 Issue 4 (2011) Article no.
045203.
[165] D. Wardecki, R. Przeniosło, A.N. Fitch, M. Bukowski, R. Hempelmann, J
Nanopart Res.,13 (2011) 1151.
[166] M. Back, A. Massari, M. Boffelli, F. Gonella, P. Riello, D. Cristofori, R.
Ricco, F. Enrichi, J Nanopart Res.,14 (2012) 792.
[167] M.J. Fluss, L.C. Smedskjaer, M.K. Chason, D.G. Legnini, R.W. Siegel, Phys.
Rev. B, 17 (1978) 3444.
[168] R. Krishnan, D.D. Upadhyaya, Pramana, 24 (1985) 351.
[169] R. Chidambaram, M.K. Sanyal, P.M.G. Nambissan, P. Sen , J. Phys.:
Condens. Matter 2, (1990) 9941.
[170] L. Yongming, B. Johansson, R.M. Nieminen, J. Phys.: Condens. Matter, 3
(1991) 2057.
[171] C. Hübner, T. Staab, R. Krause-Rehberg, Applied Physics A: Materials
Science & Processing, 61 (2) (1995) 203.
[172] T.C. Sandreczki, X.Hong, Y.C. Jean, Macromolecules, 29 (11) (1996) 4015.
INTRODUCTORY REMARKS CHAPTER-1
~ 49 ~
[173] C.C. Haung, I.M. Chang, Y.F. Chen, P.K. Tseng, Physica. B, Condensed
matter, 245 (1998) 9.
[174] V.P. Shantarovich, Z.K. Azamatova, Yu.A. Novikov, Yu.P. Yampolskii,
Macromolecules, 31 (12) (1998) 3963.
[175] R. Würschum, E. Shapiro, R. Dittmar, H. E. Schaefer, Phys. Rev. B, 62 (2000)
12021.
[176] T.E.M. Staab, E. Zschech, R. Krause-Rehberg, Journal of Materials Science,
35(18) (2000) 4667.
[177] T.L. Dull, W.E. Frieze, D.W. Gidley, J. Phys. Chem. B, 105 (20) 2001 4657.
[178] B. Lizama, R. López-Castañares, V. Vilchis, F. Vázquez and V. Castaño,
Materials Research Innovations, 5 (2) (2001) 63.
[179] V.I. Grafutin, E.P. Prokop'ev, (2002) Phys.-Usp. 45 59.
[180] Y. Zheng, Y. Zheng, R. Ninga, Materials Letters., 57 (2003) 2940.
[181] A. Mokrushin, I. Bardyshev, N. Serebryakova, V. Starkov, Physica Status
Solidi (a), 197 (2003) 212.
[182] Y. Nagai, K. Takadate, Z. Tang, H. Ohkubo, H. Sunaga, H. Takizawa, M.
Hasegawa, Physical Review B, 67 (2003) 224202.
[183] Z.Q.Chen, S.Yamamoto, M. Maekawa, A. Kawasuso, X.L. Yuan, T,
Sekiguchi, Journal of Applied Physics, 94 (2003) 4807.
[184] R.E. Galindoa, A.V. Veena, H. Schuta, C.V. Faluba, A.R. Balkenendeb, G.de
Withc, J.Th.M. De Hosson, Composites Science and Technology 63 (2003)
1133.
[185] M. Chakrabarti, S. Dutta, S. Chattapadhyay, A. Sarkar, D. Sanyal and A.
Chakrabarti, Nanotechnology, 15 (2004) 1792.
[186] D.B. Cassidy, S.H.M. Deng, R.G. Greaves, T. Maruo, N. Nishiyama, J.B.
Snyder, H.K.M. Tanaka, A.P. Mills, Jr. Phys. Rev. Lett., 95(2005) 195006.
[187] J. Kuriplach, Acta Physica Polonica A, 107 (5) (2005) 784.
[188] Y. Zheng, R. Ning, Y. Zheng, Journal of Reinforced Plastics and Composites,
24 (3) (2005) 223.
[189] S. Kar, S. Biswas, S. Chaudhuri, P.M.G. Nambissan, Phys. Rev. B, 72 (2005)
075338.
[190] S. Kar, S. Chaudhuri, P.M.G. Nambissan, Journal of Applied Physics, 97
(2005) 014301.
INTRODUCTORY REMARKS CHAPTER-1
~ 50 ~
[191] B.V. Thosar, R.G. Laciu, V.G. Kulkarni, G. Chandra, physica status solidi (b),
55 (2006) 415.
[192] M.K. Roy, B. Haldar, H.C. Verma, Nanotechnology, 17 (2006) 232.
[193] K. Chakrabarti, P.M.G. Nambissan, C.D. Mukherjee, K.K. Bardhan, C. Kim,
K.S. Yang, Carbon, 44 (2006) 948.
[194] S. Biswas, S. Kar, S. Chaudhuri, P.M.G. Nambissan, J. Chem. Phys., 125
(2006) 164719.
[195] B. Acosta, A. Zeman, L. Debarberis, International Journal of Microstructure
and Materials Properties, 1 (3-4) (2006) 310.
[196] A.K. Mishra, S.K. Chaudhuri, S. Mukherjee, A. Priyam, A. Saha, D. Das, J.
Appl. Phys., 102 (2007) 103514.
[197] T.D. Nghiep, K.T. Tuan, N.D. Du, International Journal of Nuclear Energy
Science and Technology, 3 (4) (2007) 422.
[198] P. Lichard, J. Juran, Phys. Rev. D, 76 (2007) 094030.
[199] Y.A. Chaplygin, S.A. Gavrilov, V.I. Grafutin, E. Svetlov-Prokopiev, S.P.
Timoshenkov, Proceedings of the Institution of Mechanical Engineers, Part N:
Journal of Nanoengineering and Nanosystems, 221 (4) (2007) 125.
[200] A. Gehrmann-De Ridder, T. Gehrmann, E.W. Glover, G Heinrich, Phys Rev
Lett., 100 (17) (2008) 172001.
[201] Y. Itoh , A Shimazu , Y Sadzuka , T Sonobe , S Itai , Int J Pharm., 358(1-2)
(2008) 91.
[202] D. Sanyal, T.K. Roy, M. Chakrabarti, S. Dechoudhury, D. Bhowmick , A.
Chakrabarti, Journal of Physics: Condensed Matter, 20 (2008) 045217.
[203] P. Cheng-Xiao, W. Hui-Min, Z. Yang, M. Xing-Ping, Y. Bang-Jiao, Chin.
Phys. Lett, 25(12) (2008) 4442.
[204] T. Ghoshal, S. Biswas, S. Kar, S. Chaudhuri, P.M.G. Nambissan, J. Chem.
Phys., 128 (2008) 074702.
[205] Z. Tang, T. Toyama, Y. Nagai, K. Inoue, Z.Q. Zhu , M. Hasegawa, Journal of
Physics: Condensed Matter, 20 (2008) 445203.
[206] C.L. Heng, E. Chelomentsev, Z.L. Peng, P. Mascher, P.J. Simpson, , Journal
of Applied Physics, 105 (2009) 014312.
[207] S. Das, T. Ghoshal, P.M.G. Nambissan, Physica Status Solidi (C), 6(2009)
2569.
INTRODUCTORY REMARKS CHAPTER-1
~ 51 ~
[208] R.V.K Mangalam, M. Chakrabrati, D Sanyal, A Chakrabati and A Sundaresan,
Journal of Physics: Condensed Matter, 21(2009) 445902.
[209] B. Oberdorfer , R. Würschum, Phys. Rev. B, 79 (2009) 184103.
[210] K. Hain, C. Hugenschmidt, P. Pikart, P. Böni, Sci. Technol. Adv. Mater., 11
(2010) 025001.
[211] R. Burcl, V.I. Grafutin, O.V. Ilyukhina, G.G. Myasishcheva, E.P. Prokop’ev,
S.P. Timoshenkov, Yu.V. Funtikov, Fizika Tverdogo Tela, 52 (4) (2010) 651.
[212] Wang, D. Chen, Z.Q. Wang, D.D. Qi, N. Gong, J. Cao, C.Y. Tang, Z., Journal
of Applied Physics, 107 (2010) 023524.
[213] A.D. Acharya, G. Singh, S.B. Shrivastava, Defect and Diffusion Forum,
Defects and Diffusion in Ceramics XI, 295-296 (2010) 1.
[214] P.M.G. Nambissan, J. Phys. Conf. Ser., 265 (2011) 012019.
[215] S.P. Pati, B. Bhushan, A. Basumallick, S. Kumar, D. Das, Materials Science
and Engineering B, 176, Issue 13, (2011) 1015.
[216] P.J Simpson, C.R Mokry, A.P Knights, J. Phys. Conf. Ser., 265 (2011)
012022.
[217] A. Sarkar, M. Chakrabarti, S.K Ray, D Bhowmick, D Sanyal, J. Phys.
Condens. Matter, 23 (2011) 155801.
[218] T.D. Haynes, R. J. Watts, J. Laverock, Zs Major, M.A. Alam, J. W. Taylor, J.
A. Duffy, S.B. Dugdale, New Journal of Physics, 14 (2012) 035020.
[219] J.M. Maki, T. Kuittinen, E. Korhonen, F. Tuomisto, New Journal of Physics,
14 (2012) 035023.
[220] Y. Yuanzheng, M. Xueming, D. Yuanda, H. Yizhen, W. Gengmiao, Chinese
Physics Letters, 9 (1992) 266.
[221] Y.G. Ma, M.Z. Jin, M.L. Liu, G. Chen, Y. Sui, Y. Tian, G.J. Zhang, Dr. Y.Q.
Jia, Materials Chemistry and Physics, 65 (2000) 79.
[222] R.V. Kumar, Y. Koltypin, X.N. Xu, Y. Yeshurun, A. Gedanken, I. Felner, J.
Appl. Phys., 89 (2001) 6324.
[223] E.D. Grave, C.A. Barrero, G.M.D. Costa, R.E. Vandenberghe, E.V. San, Clay
Minerals, 37 (4) (2002) 591.
[224] D. Predoi, V. Kuncser, G. Filoti, Romanian Reports in Physics, 56(3) (2004)
373.
[225] K.A. Malini, M.R. Anantharaman, A. Gupta, Bull. Mater., Sci., 27 (4) (2004)
361.
INTRODUCTORY REMARKS CHAPTER-1
~ 52 ~
[226] M. Liu, H. Li, L. Xiao, W. Yu, Y. Lu, Z. Zhao, Journal of Magnetism and
Magnetic Materials, 294 (2005) 294.
[227] S. Chakraverty, M. Bandyopadhyay, S. Chatterjee, S. Dattagupta, A. Frydman,
S. Sengupta, P.A. Sreeram, Phys. Rev. B, 71 (2005) 054401.
[228] R.K. Sharma, O.Suwalka, N. Lakshmi, K. Venugopalan, A. Banerjee, P.A.
Joy, Materials Letters, 59 (2005) 3402.
[229] C.R.H. Bahl, S. Mørup, Nanotechnology, 17 (2006) 2835.
[230] D. Bandyopadhyay, International Materials Reviews, 51 (3) (2006) 171.
[231] P. Delcroix, G.Le. Caër, B.F.O. Costa, Journal of Alloys and Compounds,
434-435 (2007) 584.
[232] S. Mukherjee, S. Kumar, D. Das, Journal of Physics D: Applied Physics, 40
(2007) 4425.
[233] I. Felner, I. Nowik, S. Balamurugan, E. Takayama-Muromachi, Hyperfine
Interactions, 184 (1-3) (2008) 111.
[234] T.Y. Kiseleva, T.F. Grigor’eva, D.V. Gostev, V.B. Potapkin, A.N. Falkova,
A.A. Novakova, Moscow University Physics Bulletin, 63 (1) (2008) 55.
[235] G. Filoti, V. Kuncser, G. Schinteie, P. Palade, I. Morjan, R. Alexandrescu, D.
Bica, L. Vekas, Hyperfine Interactions, 191 (1-3) (2009) 55.
[236] S. Thakur, S.C. Katyal, A. Gupta, V.R. Reddy, M. Singh, J. Appl. Phys., 105
(2009) 07A521.
[237] Lyubutin, I.S. Lin, C.R. Korzhetskiy, Y.V. Dmitrieva, T.V. Chiang, Journal of
Applied Physics, 106 (2009) 034311.
[238] A.L Andrade, D.M Souza, M.C Pereira, J.D Fabris, R.Z Domingues, Journal
of Nanoscience and Nanotechnology, 9(3) (2009) 2081.
[239] A.K. Mishra, C. Bansal, M. Ghafari, R. Kruk, H. Hahn ,Phys. Rev. B, 81
(2010) 155452.
[240] R. Babilas, M. Kądziołka-Gaweł, R. Nowosielski, Journal of Achievements in
Materials and Manufacturing Engineering, 45 (2011) 7.
[241] M. Chakrabarti, S. Chattopadhyay, D. Sanyal, A. Sarkar, D. Jana, Materials
Science Forum, 699 (2012) 1.
[242] B. Antic, A. Kremenovic, N. Jovic, M.B. Pavlovic, C. Jovalekic, A.S. Nikolic,
G.F. Goya, C. Weidenthaler, J. Appl. Phys., 111 (2012) 074309.
[243] I.N. Zakharova, M.A. Shipilin, V.P. Alekseev, A.M. Shipilin, Technical
Physics Letters, 38 (2012) 55.
CHAPTER-2
Theoretical considerations
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 54 ~
2.1 Introduction The X-rays powder diffraction technique is being used for many decades and
is still continuing due to its application in diffraction line profile analysis to study the
nature of crystal imperfections introduced during growth and plastic deformation of a
material. The earlier X-ray diffraction studies on cold- worked materials depict that
plastic deformation induces broadening of the X-rays diffraction profiles and such
peak broadening increases continuously with increase in degree of deformed. With the
use of modern techniques [1] like focussing curved crystal monochromator, counter or
solid state detector it is possible to locate and measure the shape of the X-ray
diffraction profiles with considerable accuracy. In the past decades extensive
theoretical and experimental studies have been made in this direction by Wilson [2],
Greenwough [1] and Warren [3]. A further development in this field was made by
Wagner [4], Warren [5] and Klug and Alexander [6], Enzo et al. [7], Langford et al.
[8], Mittemeijer et al. [9], Balzar et al. [10] and others. This chapter basically deals
with the various theoretical considerations in the X-rays diffraction line profile
analysis for microstructure characterization of polycrystalline and nanocrystalline
materials in terms of various lattice imperfections.
2.2 X-ray line profile analysis: Theoretical considerations When X-rays interact with the atoms, it gives rise to scattering in all
directions; in some of these directions the scattered beams will be completely in phase
and so reinforce each other to form diffracted beams following Bragg's law,
nλ sin θ2d = (2.1)
where λ is the wavelength of X-rays directed towards the set of parallel planes in a
crystal at an angle θ and n is the order of reflection, θ is called Bragg angle where
the maximum intensity occurs. At other angles there are little or no diffracted
intensities because of the destructive interference.
Each crystallographic phase in an ideal crystal has a characteristic set of d
spacings, which yields a discrete lines in the X-ray diffraction pattern at respective
Bragg anglesθ . But in the experiments with real crystals these discrete lines are
appear as peaks considerable amount of peak broadening. This is due to the facts that
it is hardly possible to have an incident beam composed of perfectly parallel and
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 55 ~
monochromatic radiation and a real crystal always has some departures from an ideal
structure due to the presence of crystal imperfections.
Small crystallite size, microstrain inside the crystallites and stacking faults are
mainly responsible for broadening of line profiles. Some instrumental parameters like
slit widths, sample size, penetration in the sample, imperfect focussing, unresolved
1α and 2α peaks etc. also give some extraneous broadening to the line profile. All
these extraneous sources of broadening are grouped together under the name
"instrumental broadening".
The first step towards the determination of crystallite size from X-ray line
profile analysis was made by Scherrer in 1918 [11]. He reported that the line breadth
varies inversely with the size of the crystallites according to the equation,
cos θ )iβsam(βKλD
−= (2.2)
known as Scherrer formula, where λ is the wavelength, samβ and iβ are the measure
of line breadth of sample and instrumental ‘standard’ respectively, θ is the Bragg
angle, K is Scherrer constant ( )89.0K0.1 >> and D is an apparent crystallite size.
The Scherrer formula actually gives the length of the crystal in the direction of the
diffraction planes and it is evident from equation (2.2) that size broadening is
independent of the order of reflection. It is important to note that lattice strain effect,
which also contributes to the broadening is not considered in the Scherrer formula.
This formula is also unsuitable for the study of crystals where the strain broadening is
present. This limitation hinder the use of Scherrer formula in many sophisticated
problems, but it is still being used in some simple cases where the size of crystals is
fairly less than hundred angstroms and the line broadening is primarily due to small
crystallite size.
2.3 Integral Breadth method This is the oldest method of line profile analysis for determining crystallite
size and microstrain simulteneously. Scherrer [11] defined the breadth of a diffraction
line as its angular width in radians at a point where the intensity has fallen to half of
its maximum value. In 1926, Laue gave another definition of the breadth of a
diffraction line as the integrated intensity of a line profile above background divided
by peak height.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 56 ~
∫= )()( θθβ 2d2II1
p
(2.3)
Hall in 1949, assuming that peak-bordening due to small crystalline size and
lattice strain can be described by Cauchy functions, suggested that the total
broadening is given by
SD βββ += (2.4) where βD is the line breadth measured by Scherrer (eqn 2.2) and βS is the broadening
arising from microstrain which can be expressed as
θεβ tan4=S (2.5)
So, eqn (2.4) can be written in the form
θεθλβββ tan4cos +=+= DKSD (2.6)
or, λθελθβ sincos 4D1 += (2.7)
Thus from the corrected integral breadth β of the X-ray line profiles, a plot of
λθβ cos against λθsin should be a straight line and the intercept on the
λθβ cos axis will give D1 , the reciprocal of the crystallite size, while the slope
will give ε , the average microstrain.
2.4 Different methods of X-ray diffraction pattern analysis For a polycrystalline specimen consisting of sufficiently large (~10-4 cm) and
strain free crystallites, diffraction theory predicts that the lines of the powder pattern
will be exceedingly sharp. However, for a real crystal, peaks are broadened due to
size and lattice strain. Hence an analysis of breadths of strain and/or size broadened
diffraction lines will give quantitative information about the crystallite size and strain
of the deformed crystallites.
The crystallite size and microstrain can be determined from the X-ray
diffraction pattern with the help of the following methods:
(1) Integral Breadth Method ( William- Hall plot)
(2) Warren-Averbach method of line profile analysis
(3) Whole powder pattern fitting method
(4) Rietveld method
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 57 ~
Limitations of different methods 2.4.1 Fourier method The principal sources of error in the Fourier (Warren-Averbach) analysis are:
(a) counting statistics;
(b) standard used to obtain g (instrumental) profiles;
(c) background determination;
(d) truncation of profiles at finite range;
(e) sampling interval (step length);
(f) choice of origin;
(g) limitations of approximation used in analysis.
These affect the analysis in different ways and by different amounts. Young et
al. [12] simulated the effect of (c), (d) and (e) and many other authors have since
discussed the treatment of errors in the Fourier method. Delhez et al. [13-14] have
given corrections for (a), (b) and (f). Procedures for improving the reliability of the
line profile analysis by the Fourier method have been represented by Zorn [15] and
Delhez et al.[16].
2.4.2 Warren-Averbach method The main drawbacks of Warren-Averbach method is the appearance of the
"hook effect". Two experimental errors giving rise to "hook" effect have been pointed
out are: (i) truncation of line profile and (ii) estimation of high background.
Crystallographers from all over the world tried their best to correct the "hook" effect,
but not a single established and valid procedure is found till date for the correction of
the "hook" effect.
Another drawback is that the method fails if the peaks are seriously
overlapping. Many materials having interesting technological applications display
diffraction patterns with overlapping peaks. Warren-Averbach method of line profile
analysis fails to characterize the microstructure of such materials.
2.4.3 Whole Powder Pattern Decomposition (WPPD) method Overlapping reflections at the same Bragg angle (intrinsic overlapping) can
not be perfectly decomposed by the WPPD methods. Thus the industrially important
materials, which usually exhibit severely overlapping lines are difficult to characterize
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 58 ~
using this method. It has been found that the effective separation limit in pattern
decomposition (measured as the shortest 2θ distance between the two adjacent peaks)
ranges from 0.1 to 0.5 times the FWHM (generally~0.25) and it is influenced by
several factors, namely, counting statistics, the 2θ-range of data included in the
analysis, and the resolution of the data.
The above mentioned disadvantages have been overcome in the Rietveld
method. So, this is the best method of line profile analysis.
2.5 The Rietveld method The Rietveld method introduced by H. M. Rietveld [17] is a total pattern
fitting method in which all observable Bragg reflections are assigned with the
simulation of a proper diffraction pattern and subsequently a refinement is carried out
until the best fit is obtained between the observed and simulated pattern. To simulate
the diffraction pattern this method needs two models: a structural model based on the
approximate atomic positions of the materials and a non-structural model, which takes
care of the instrumental features and specimen features such as aberrations due to
absorption, specimen displacement, crystallite size and microstrain effects etc. The
quality of fit in the subsequent refinement depends on the choice of these starting
models and in order to get best fit a reasonably good starting model which is close to
the correct one is required. The structural model helps to determine the total intensity
of Bragg reflection along with their positions and the non structural model gives a
description of individual profile in terms of an analytical of other differentiable
functions ( pseudo-Voigt function, Pearson VII function and Gaussian, Lorentzian and
modified Lorentzian functions are widely used).
In all cases, the ‘best-fit’ sought is the best least-squares fit to all of the
thousands of intensities Io’s simultaneously. In order to improve fitting the model
parameters namely, atomic positions, thermal and site occupancy parameters,
parameters for background, lattice parameters, parameters representing instrumental
geometrical-optical features and specimen aberration (e.g. specimen displacement and
transparency), parameter for amorphous component, specimen reflection profile
broadening parameters (crystallite size and microstrain) and often parameter for
extinction effect are refined in steps with the calculation of residual at every steps.
The quantity minimized in the least-squares refinement is the residual Sy
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 59 ~
( )∑ −=i
cioiiy IIWS 2 , (2.8)
where oii IW 1= , Ioi =observed (gross) intensity at the ith step, Ici =calculated
intensity at the ith step.
The best fit is said to obtain when yS reduces to minimum.
Many Bragg reflections contribute to the intensity yi , observed at any
arbitrarily chosen point, i, in the pattern. The calculated intensities, yci are determined
from the square of the absolute value of the structure factor, 2KF values calculated
from the structural model by summing of the calculated contributions from
neighbouring Bragg reflections plus the background:
( )∑ +−Φ=K
biKKiKKci IAPFLsI θθ 222 (2.9)
where S is the scale factor, K represents Miller indices, hkl for a Bragg
reflection, KL contains Lorentz polarization and multiplicative factor, Φ is a
reflection profile function which approximates the effect of both instrumental
features and specimen features such as aberration due to absorption, specimen
displacement, crystallite size and microstrain effects etc., KP is the preferred
orientation function, A is an absorption factor, KF is the structure factor for thK
Bragg reflection, biI is the background intensity at the thi step.
In the original Rietveld program, for angle dispersive data, the dependence of
the breadth H of the reflection profiles (measured as full-width-at-half-maximum,
FWHM ) was modelled as [18]
[ ] 212 WVUH ++= θθ tantan (2.10)
where U, V, and W are the refinable parameters.
This formula (termed as Caglioti formula) initially developed for the
‘medium’ (or less) resolution powder diffractometers and worked satisfactorily for
them, as did simple Gaussian reflection profile functions. Even though the
instrumental diffraction profiles of the typical X-ray powder diffractometers
operating on sealed-off X-ray tube or rotating anode sources are generally neither
Gaussian nor symmetric. The Caglioti relation was widely used for modeling the
instrumental broadening due to lack of anything better and simplified method. With
the reflection profiles from X-ray diffractometers and other comparatively high
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 60 ~
resolution instruments, such as Guinier cameras and high-resolution neutron powder
diffractometers, another complication arises. Their instrumental profiles are
sufficiently narrow so that broadening of the intrinsic diffraction profile from
specimen defects such as microstrain and small crystallite size is a significant part of
the total broadening and in these cases instrumental broadening may not be modeled
by Caglioti relation.
An essential step in Rietveld method applying on data from modern X-ray
diffractometers is to examine the variation of FWHM (or integral breadth) with θ2
or ∗d and to compare this with the resolution curve of the instrument used. If the two
curves are identical, indicating that sample effects are negligible, then Caglioti
formula can be used to model breadth variation. If the curves differ, but the scattering
for the sample curve is not greater than that would be expected from counting
statistics or there is no marked 'anisotropy', on the average, then also one can model
the breadth of the profile with Caglioti formula, but this time U , V and W should be
treated as refinable parameters. But if the sample curve exhibits a scattering which is
θ2 or ∗d dependent, then the nature of 'anisotropic' breadth variation must be
ascertained and the dependence of breadth on hkl has to be modelled with special
care.
The quality of fitting is judged through the calculation of weighted residual
error, WR ,
( )21
22
⎥⎥⎦
⎤
⎢⎢⎣
⎡−= ∑∑
ioii
icioiiw IwIIwR (2.11)
which is then minimized through a Marquardt least-squares program[19]. The
e.s.d. is calculated following the method proposed by Scott [20] and finally, the
goodness of fit (GoF ) is established by comparing WR with the expected error, expR :
expRRGoF w= (2.12)
where, ( )21
2exp
⎥⎥⎦
⎤
⎢⎢⎣
⎡−= ∑
ioii IwPNR
oiI and ciI are the experimental and calculated intensities, respectively, iw ( oiI1= ) and N are the weight and number of experimental observations respectively and P is the number of fitting parameters.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 61 ~
Refinement continues till convergence is reached with the value of the quality
factor, GOF approaching 1, which confirms the goodness of refinement.
In general, sample induced line broadening includes contributions which are
independent of θ2 or ∗d , known as 'size effect' and which depends on θ2 or ∗d ,
known as 'strain effect'. There have been various attempts to make allowance for
smoothly varying (isotropic) microstructural effects in Rietveld programs. David and
Matthemam [21] modelled experimental line profile by means of a Voigt function
and assigned the 'Lorentzian' and 'Gaussian' components to the 'size' effects and the
instrumental broadening respectively. A different approach was adopted by Howard
and Snyder in the program SHADOW [22] who convoluted a Lorentzian simple line
profiles, assumed to be due to 'crystallite size' and/or 'microstrains', with
experimentally determined instrumental profiles, to match the observed data. The
simultaneous presence of isotropic 'size' and 'strain' effects was considered by
Thompson et al.[23]. They used a pseudo-Voigt function to model the overall line
broadening and assigned the Lorentzian components of the pseudo-Voigt functions to
'size' effects and Gaussian components to the combined 'strain' and instrumental
contributions.
An early attempt to model anisotropic line broadening in the Rietveld method
was made by Greaves [24] who assumed that the crystallites had the form of platelets
with thickness H and infinitely large lateral dimensions. In this case the contribution
to the integral breadth of reflection from plates parallel to the surface, in the
reciprocal unit, is simply H1 . In order to allow for the direction dependence of
microstrain, some assumptions are made regarding the stress distribution. If
microstrain is assumed to be statistically isotropic, then the anisotropy of the elastic
constants leads to a hkl dependence of strain. Thompson et al. [25] expressed
microstrain as a function of hkl and refined appropriate strain parameters based on
elastic compliances. Simultaneous anisotropic ‘size’ and ‘strain’ broadening was
incorporated in the Rietveld method by Le Bail [26] and Lartigue et al. [27]. The hkl
dependent nature of these quantities was modeled by means of ellipsoids and Fourier
series were employed to represent the line profiles. The number of microstructural
parameters to be refined was restricted by adopting Lorentzian function for ‘size’
contributions and an intermediate Lorentz-Gauss function for ‘strain broadening. In a
similar approach Lutterotti and Scardi [28] included crystallite size and microstrain as
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 62 ~
refinable parameters, in the place of usual angular variation line-profile width.
Microstructural analysis based on approximate single line Fourier method was
introduced by Nandi et al. [29]. A program LS1 based on this approach was
developed by Lutterotti et al. [30]. In the field of materials analysis, there is a
constant demand for sophisticated tools, which can process enormous number of data
in a short time, deal with cases showing sample-induced anisotropy and extract more
information about the samples. In 1999, Lutteroti et al. developed a program, MAUD,
which is easy to use, can be applied to wide variety of materials and helps the user in
obtaining more information from data collected by traditional and new diffraction
instrument [31]. The outline and main features of MAUD are given here.
2.6 MAUD: a user friendly computer software based on Java for Materials Analysis Using Diffraction This program is written in Java, and run virtually in any computer
environment supporting the Java Virtual Machine with installers available for the
Macintosh and Windows platform.
The principal features of MAUD are:
(i) Simultaneous crystal structure refinement, line-broadening, texture (stress
under implementation) and quantitative phase analyses can be performed.
(ii) Multiple samples from different instruments can be analyzed at one time.
(iii) The diffraction patterns of a sample from different instruments, e.g. X-ray
tube, synchrotron, neutron constant wavelength and time of flight can be
analyzed simultaneously.
(iv) There is option for wizard or manual mode of refinement; the wizard mode
allows the user to select what kind of analysis the user needs to perform in
quantitative phase analysis, crystal structure analysis or texture analysis.
(v) There is option for adding different methodologies to the program by the
user without the need to recompile it or to know the internal structure of the
program. The plug-in-structure are included in instrument geometries and
correction/calibrations, data formats, line-broadening methods, texture
algorithms, peak intensity extraction, etc.
(vi) CIF (Crystal Information File) user friendly program is included. The
program uses, imports and supports CIF formats.
THEORETICAL CONSIDERATIONS CHAPTER-2
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(vii) Various data format, Philips, Rigaku, Siemens, GSAS, D1B etc. can be used
for input files (only ASCII).
(viii) Unlimited number of data files can be analyzed at a time. Till now some
analyses have been done loading simultaneously more than 1000 datafiles
(from the SKAT diffractometer at Dubna).
(ix) Space group and symmetries relationships computed using SgInfo [32]
linked as a native library to the package for ease of analysis.
(x) Popa model has been included to analyze the cases having anisotropic
crystallite size and microstrain [33].
(xi) In order to give better accuracy in the results, the square-root of actual
intensity is plotted against θ2 in the fitted pattern, which gives magnified
image of the weaker peaks.
This program is an upgraded version of LS1 and the underlying theory is
almost same as that of LS1, except some modifications are made in crystallite size-
microstrain separation, texture analysis and defect parameters study. The basic
methodology for the crystallite size-microstrain separation are performed using the
theory developed by Delhez et al. [34] and the calculation of crystallite size and
microstrain is performed using the recently published method of Popa [33].
To analyze the texture of multiphase samples, in addition to the classical
March-Dollase formula, harmonic texture [35] and the WIMV method [36] are
included in order to obtain the entire orientation distribution function, provided a
sufficient number of spectra at different tilting angles are available for the refinement.
Thus it can be concluded that MAUD is an elegant method for material
characterization. The program has been successfully applied by Lutterotti to analyze
the Y2O3 CPD Round Robin sample, to analyze the texture of various multiphase
samples, to refine spectra with anisotropic peak broadening, quantitative analysis of
polymers and samples containing silica glass etc. [31].
In the present study, MAUD software has been extensively used to analyze
the microstructure of various industrially important multiphase ferrite materials. The
detailed results of each analysis will be described in the respective chapter of the
present dissertation.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 64 ~
2.7 Positron annihilation technique
Positron annihilation technique is a nuclear solid state technique to study the
electron number density, characterization of defects and the electron momentum
distributions in a material.
Depending upon different electron density sites in a material positron
annihilation lifetime states are different. The annihilation lifetimes of positrons with
free electrons in a material varies in the range ~ 100 - 150 ps. The electron density
distributions in defect sites are less from those of a perfect lattice and hence the
annihilation lifetimes are more. Thus, by measuring the positron annihilation lifetimes
in a material one can also obtain the information about the nature and the size of these
defect sites (Table 1).
Table 1: Possible defects and their sizes with the positron annihilation lifetime values.
2.7.1 Positron Annihilation Spectroscopy (PAS)
Positron annihilation spectroscopy (PAS) is a non-destructive nuclear solid
state technique [37,38] (shown in Fig.2.1), employing which one can study the
electronic structure, defect properties, electron density distribution (EDD) and
electron momentum distribution (EMD) in a material, e.g., metals, alloys, ceramic,
oxides, polymers, superconductors, magnetic materials, semiconductors,
nanocrystalline materials etc.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 65 ~
Energetic positrons injected from a radioactive source (e.g.,22Na, 64Cu, 58Co
etc.) get thermalized within 1-10 ps inside a solid and annihilate with an electron of
that material. It is well known that positrons preferentially populate (and annihilate) in
the regions where electron density, compared to the bulk of the material, is lower (e.g.
vacancy type defects, vacancy clusters, micro-voids). The lifetime of positrons
trapped in defects is comparatively longer with respect to those annihilate at defect
free regions. Analysis of PAL spectrum, thus, throws light on the nature and
abundance of defects in the material. The other PAS technique, Doppler broadening
of the positron annihilation radiation lineshape measurement is useful to study the
momentum distribution of electrons in a material [39,40]. Depending on the electron
momentum (p), the 511 keV γ-rays (electron-positron annihilated) are Doppler shifted
by an amount ± ∆E = pL c/2 in the laboratory frame where pL is the component of the
electron momentum (p) along the direction of measurement. Using high-resolution
high purity germanium (HPGe) detectors, one can measure the spectrum of Doppler
shift 511 keV γ-rays.
The wing region of the 511 keV spectra (higher value of pL) carries the
information about the annihilation of positrons with the core electrons. The momenta
of the core electrons are element specific [41] and hence, the atoms surrounding a
defect can be probed by proper analysis of the measured spectra.
Mainly it has three principal categories:
(a) Positron annihilation lifetime (PAL) spectroscopy to measure the electron
density distribution (EDD) inside the sample,
Fig.2.1 Schematic diagram of defect characterization by Positron Annihilation Spectroscopy (PAS).
THEORETICAL CONSIDERATIONS CHAPTER-2
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(b) Coincidence Doppler broadening of positron annihilation radiation line
shape (CDBPARL) spectroscopy to probe the electron momentum
distribution (EMD) inside the material under investigation,
(c) Angular correlation of annihilation radiation spectroscopy for better
understanding the electron momentum distribution in a material.
2.7.1 (a) Positron annihilation lifetime (PAL) measurement
The positron annihilation lifetime, τ, (which is the reciprocal of the positron
annihilation rate,
λ =1/τ = πro2c ∫ |Ψ+(r)|2n-(r)dr (2.13)
where n-(r) is the electron density at the annihilation site and the positron density
n+(r) = |Ψ+(r)|2, ro is the classical electron radius, c is the speed of light and r the
position
Fig.2.2. Experimental setup of PAL measurement for studying electron density distribution in a solid
vector is inversely proportional to the electron number density [42]. Therefore by
measuring the positron annihilation lifetime (~ 100-400 ps) in a solid one can obtain
directly the information about the electron density at the site of positron annihilation
[43]. Positron-electron annihilated gamma rays bear information regarding the nature,
concentration and the environments of the related defect species [44]. This is
understood by analyzing the PAL spectrum by different computer programs [45].
Therefore, the analysis of PAL spectrum, thus, throws light on the nature and
abundance of defects in the material. For positron annihilation studies, a 10 µCi 22Na
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 67 ~
positron source (enclosed in thin mylar foils) has been sandwiched between two
identical plane faced pellets. The PAL spectrum, N(t) vs. t, has been measured with a
fast-slow coincidence assembly (shown in Fig.2.2.) with XP2020Q PMT coupled with
conical BaF2 crystals [46]. Here, N(t) is the number of coincidence events and t is the
time in ps. This spectrometer has the time resolution (TR) of 182±1 ps for the prompt 60Co γ-rays at the positron experimental window settings with the upper 60 % of the
Compton continuum of 1.276 MeV and 0.511 MeV γ- rays [47]. The measured
spectra have been analyzed by computer program PATFIT-88 [48] with necessary
source corrections to evaluate the possible lifetime components τi, and their
corresponding intensities Ii. All the lifetime spectra are found to be best fitted with
three lifetime components (variance of fit is less than one per channel), yielding a
very long (> 1.1 ns) positron lifetime component (τ3) with intensity 3-4%. A simple
but most convenient two-state trapping model [44, 42] assumes two processes:
(i) positron annihilation from Bloch state (in the bulk, non-defective lattice)
(ii) the same from a trapped state (in a defect).
According to its name, the model predicts a two-component fit of the PAL
spectrum. However, for the present samples, that makes the fitting parameters as well
as the significance of the fitting itself unreasonably poor. So, separate physical
process is necessary to analyze the spectrum data with another fitting parameter τ3.
The origin of τ3 is generally attributed to the formation of ortho-positronium and its
subsequent decay to para-positronium by pick-off annihilation [43]. In polycrystalline
samples, there always exist micro voids where positronium formation is favorable
[43,45]. Positronium formation, although more likely in voids, is not directly related
to defect trapping of positrons. Hence, it will not be discussed later on. Using the
above two-state trapping model, one can construct
the bulk lifetime, τB = (I1+I2)/(I1/τ1+I2/τ2)), (2.14)
and the average positron lifetime, τav = (τ1I1+τ2I2)/(I1+I2)) (2.15)
where τ1, τ2, I1 and I2 are the measured lifetime parameters. The shortest lifetime
component (τ1 ~ 145 ps) is generally attributed to free annihilation of positrons
[43,45,47]. However, in disordered systems, smaller vacancies [45,49] (like
monovacancies etc.) or shallow positron traps (like oxygen vacancies [50,51] in ZnO)
may be related with τ1. So, τ1 is indeed a weighted average of free and trapped
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 68 ~
positrons, hence, it is sometimes called reduced bulk lifetime [44]. But the correlation
of τ1 with the material properties is not yet conclusive. So, this issue has not been
discussed much in this thesis. Finally, the most important lifetime component is the
intermediate one, τ2, which arises from the annihilation of positrons at defect sites
[44,42,43]. However, τ2 contains some error due to least-square fitting procedure of
the spectrum with finite statistics. In particular, when several types of defects may
exist in the system, it is better to choose statistically more accurate parameter, τav,
without assuming any model. Depending on the nature of defects and other defect
specific physical parameters, τ2 or τav gets the importance, as will be discussed later
on. Generally, the increase of τav reflects the overall enhancement of defects and τav >
τB indicates the presence of defect in the system.
2.7.1 (b) Coincidence Doppler Broadened Positron Annihilation Radiation Line shape (CDBPARL) measurement
The other PAS technique, Doppler broadening of the positron annihilation
radiation line shape measurement is useful to study the momentum distribution of
electrons in a material [44]. Depending
on the electron momentum (p), the 511
keV γ−rays (electron-positron
annihilated) are Doppler shifted by an
amount ± ∆E = pLc/2 in the laboratory
frame where pL is the component of the
electron momentum (p) along the
direction of measurement. Using high-
resolution high purity germanium
(HPGe) detectors, one can measure the
spectrum of Doppler shift 511 keV γ-rays
spectrum [52]. So, by analyzing the
CDBEPAR spectrum, identification of
atoms surrounding a defect can be done.
But, due to large background in the spectrum, the analysis becomes cumbersome and
becomes unambiguous. Use of the two detectors in coincidence [53,54] help to
Fig.2.3. Experimental setup of CDBPARL measurement for studying electron momentum distribution in a solid
THEORETICAL CONSIDERATIONS CHAPTER-2
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suppress the background in measured Doppler broadened spectrum and hence, the
contributions of higher momentum electrons (core electrons) can be estimated
[55,56]. In the experiment, the two
detector coincidence Doppler broadened
electron-positron annihilation γ-radiation
(CDBEPAR) spectrum has been
measured by a HPGe detector (efficiency
13%, energy resolution of 1.3 keV for the
514 keV line of 85Sr) and a 3// × 3// NaI
(Tl) crystal coupled to a RCA 8850
photomultiplier tube placed at an angle of
180o [54] (shown in Fig.2.3). The peak to
background (607-615 keV) ratio is
14000:1 which allows successful analysis
of the wing region [47,57-60]. The
energy per channel of the multichannel
analyzer has been set to 22 eV. The peak
to background (607-615 keV) ratio has
been further enhanced to 105:1 by using another setup (at VECC, Kolkata) with two
identical HPGe detectors (Efficiency: 12
%; Type: PGC 1216sp of DSG,
Germany) having energy resolution of
1.1 keV at 514 keV of 85Sr and proper
∆E–E selection [61]. The energy per
channel in this set-up is 150 eV. The
CDBEPAR spectra have been recorded in
a dual ADC based - multiparameter data
acquisition system (MPA-3 of FAST
ComTec., Germany). The CDBEPAR
spectra for each sample have been
analyzed by evaluating the so-called
shape parameter (S-parameter) and wing
parameter (W-parameter) [44,42,54]. The S-parameter, calculated as the ratio of
Fig.2.4. Schematic representation of S-parameter
Fig.2.5 Schematic representation of W-parameter
THEORETICAL CONSIDERATIONS CHAPTER-2
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counts in the central area of the 511 keV photo peak (|511 keV − Eγ | ≤ 0.86 keV) and
the total area of the photo peak (|511 keV − Eγ | ≤ 4.25 keV), represents the fraction of
positrons annihilating with the lower momentum electrons (Fig.2.4.). The W-
parameter, calculated as the ratio of counts in the wing region of the 511 keV photo
peak (1.6 keV ≤ | Eγ − 511 keV | ≤ 4 keV) and the total area of the photo peak,
represents the fraction of positrons annihilating with the higher momentum electrons
(Fig.2.5.). Ratio curve [55,58,62] from each CDBEPAR spectra of ZnO samples has
been constructed by dividing the counts at the same energy with that of a standard
CDBEPAR spectrum (spectrum of a 99.9999 % purity Al single crystal in the same
set up). However, a new type of ratio curve has been constructed with respect the un-
annealed as standard, which becomes more informative [47].
2.8 The Mössbauer effect In a resonance absorption experiment, the energy of incident radiation should
match exactly the energy separation between the two levels of the absorption system.
For example, radiation of a Na atom matches exactly the excitation energy of the
other Na atom and is, therefore, effectively absorbed by it. Applying the same logic to
irradiation and absorption of gamma-rays, the same electromagnetic radiation as in
the case of Na atoms only of higher energy being emitted by atomic nuclei, one would
come to the same resonant condition which requires that the energy separation
between the two levels in the source nucleus and those in the absorber nucleus should
be exactly equal. Therefore, both the source and the absorber nuclei must necessarily
be identical. Provided this, one would expect effective absorption and reemission of
gamma rays by identical nuclei, but this is not enough for observation of nuclear
resonant fluorescence. During the process of emission of a gamma ray by a nucleus, a
certain amount of excitation energy (the recoil energy – ER) is given to the nucleus to
conserve momentum. That is why the energy of the emitted gamma quantum Eg is
reduced by the same amount.
ER=p2/2M=Eg2/2Mc2, Eg=Eo-ER (2.16)
p being the momentum given to the nucleus, equivalent to momentum of the gamma
photon, and M the mass of the emitting nucleus. Similarly, whenever a gamma
quantum is absorbed, the energy transferred to the nuclear excitation is reduced by ER
due to the recoil energy imparted to the absorbing nucleus. For optical transitions the
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 71 ~
energy loss to recoil is much smaller than the width of the absorption line, making
optical resonance fluorescence easily possible. But in the case of high energy nuclear
radiation, recoil energy is much larger than the line width which impedes nuclear
resonant fluorescence.
Nuclei in atoms undergo a variety of energy level transitions, often associated
with the emission or absorption of a gamma ray. These energy levels are influenced
by their surrounding environment, both electronic and magnetic, which can change or
split these energy levels. These changes in the energy levels can provide information
about the atom's local environment within a system and ought to be observed using
resonance-fluorescence. There are, however, two major obstacles in obtaining this
information:
(i) the 'hyperfine' interactions between the nucleus and its environment are
extremely small,
(ii) the recoil of the nucleus as the gamma-ray is emitted or absorbed
prevents resonance.
In a free nucleus during emission or absorption of a gamma ray it recoils due
to conservation of momentum, just like a gun recoils when firing a bullet, with a
recoil energy ER. This recoil is shown in Fig.2.6. The emitted gamma ray has ER less
energy than the nuclear transition but to be resonantly absorbed it must be ER greater
than the transition energy due to the recoil of the absorbing nucleus. To achieve
resonance the loss of the recoil energy must be overcome in some way.
Fig.2.6 Recoil of free nuclei during emission or absorption of gamma ray.
As the atoms will be moving due to random thermal motion the gamma-ray
energy has a spread of values ED caused by the Doppler effect. This produces a
gamma-ray energy profile as shown in Fig.2.7. To produce a resonant signal the two
energies need to overlap and this is shown in the red-shaded area. This area is shown
exaggerated as in reality it is extremely small, a millionth or less of the gamma-rays
are in this region, and impractical as a technique.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 72 ~
Fig.2.7 Emission and absorption profile of recoiled gamma rays.
What Mössbauer discovered is that when the atoms are within a solid matrix
the effective mass of the nucleus is very much greater. The recoiling mass is now
effectively the mass of the whole system, making ER and ED very small. If the
gamma-ray energy is small enough the recoil of the nucleus is too low to be
transmitted as a phonon (vibration in the crystal lattice) and so the whole system
recoils, making the recoil energy practically zero: a recoil-free event. In this situation,
as shown in Fig.2.8, if the emitting and absorbing nuclei are in a solid matrix the
emitted and absorbed gamma-ray is the same energy: resonance.
Fig.2.8 Recoilless emission and absorption of gamma rays by the source and the
absorber both embedded in respective lattice sites.
If emitting and absorbing nuclei are in identical, cubic environments then the
transition energies are identical and this produces a spectrum as shown in Fig.2.9 a
single absorption line.
Fig.2.9 Simple Mössbauer spectrum from identical source and absorber.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 73 ~
We can achieve resonant emission and absorption and use it to probe the tiny
hyperfine interactions between an atom's nucleus and its environment. The limiting
resolution now that recoil and doppler broadening have been eliminated is the natural
linewidth of the excited nuclear state. This is related to the average lifetime of the
excited state before it decays by emitting the gamma-ray. For the most common
Mössbauer isotope, 57Fe, this linewidth is 5x10-9ev. Compared to the Mössbauer
gamma-ray energy of 14.4keV this gives a resolution of 1 in 1012, or one sheet of
paper in the distance between the Sun and the Earth. This exceptional resolution is of
the order necessary to detect the hyperfine interactions in the nucleus.
As resonance only occurs when the transition energy of the emitting and
absorbing nucleus match exactly and the effect is isotope specific. The relative
number of recoil-free events (and hence the strength of the signal) is strongly
dependent upon the gamma-ray energy and so the Mössbauer effect is only detected
in isotopes with very low lying excited states. Similarly, the resolution is dependent
upon the lifetime of the excited state. These two factors limit the number of isotopes
that can be used successfully for Mössbauer spectroscopy. The most used is 57Fe,
which has both a very low energy gamma-ray and long-lived excited state, matching
both requirements well.
2.8.1 Fundamentals of Mössbauer Spectroscopy As shown previously the energy changes caused by the hyperfine interactions
we want to look at are very small, of the order of billionths of an electron volt. Such
miniscale variations of the original gamma-ray are quite easy to achieve by the use of
the doppler effect, i.e. the gamma-ray source moves towards and away from the
absorber. This is most often achieved by oscillating a radioactive source with a
velocity of a few mm/s and recording the spectrum in discrete velocity steps.
Fractions of mm/s compared to the speed of light (3x1011mm/s) gives the minute
energy shifts necessary to observe the hyperfine interactions. For convenience the
energy scale of a Mössbauer spectrum is thus quoted in terms of the source velocity,
as shown in Fig.2.10.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 74 ~
Fig.2.10 A typical Mössbauer spectrum showing the velocity scale and motion of
source relative to the absorber.
With an oscillating source we can now modulate the energy of the gamma-ray
in very small increments. Where the modulated gamma-ray energy matches precisely
the energy of a nuclear transition in the absorber the gamma-rays are resonantly
absorbed and we see a peak. As we're seeing this in the transmitted gamma-rays the
sample must be sufficiently thin to allow the gamma-rays to pass through, other wise
the relatively low energy gamma-rays are easily attenuated.
In Fig.2.10 the absorption peak occurs at 0mm/s, where source and absorber
are identical. The energy levels in the absorbing nuclei can be modified by their
environment in three main ways: by the Isomer Shift, Quadrupole Splitting and
Magnetic Splitting.
2.8.1 (a) Isomer Shift The isomer shift originates from the non-zero volume of the nucleus and the
electron charge density due to s-electrons within it. This leads to a monopole
(Coulomb) interaction, modifying the nuclear energy levels. The difference in the s-
electron environment between the source and absorber thus results in a shift in the
resonance energy of the transition. This leads to an overall shift of the whole spectrum
in the positive or negative direction depending upon the s-electron density, and
determines the position of the centroid of the spectrum.
As the shift cannot be measured directly it is referred relative to a known
absorber, viz. 57Fe Mössbauer spectra is often referred relative to alpha-iron at room
temperature. The isomer shift is very useful parameter for determining valency states,
ligand bonding states etc. for the samples under study.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 75 ~
The isomer shift is useful for determining valency states, ligand bonding
states, electron shielding and the electron-drawing power of electronegative groups.
For example, the electron configurations for Fe2+ and Fe3+ are (3d)6 and (3d)5
respectively. The ferrous ions have less s-electrons at the nucleus due to the greater
screening of the d-electrons. Thus ferrous ions have larger positive isomer shifts than
ferric ions.
2.8.1 (b) Quadrupole Splitting Nuclei in states with an angular momentum quantum number I > 1/2 have a
non-spherical charge distribution. This produces a nuclear quadrupole moment. In the
presence of an asymmetrical electric field (produced by an asymmetric electronic
charge distribution or ligand arrangement) this splits the nuclear energy levels. The
charge distribution is characterised by a single quantity called the Electric Field
Gradient (EFG).
In the case of an isotope with I = 3/2 excited state, such as 57Fe or 119Sn, the
excited state is split into two substates mI = ±1/2 and mI = ±3/2. This is shown in
Fig.2.11, giving a two line spectrum or 'doublet'.
Fig.2.11 Quadrupole splitting for a 3/2 to 1/2 transition. The magnitude of quadrupole
splitting, ∆, is also shown.
The magnitude of splitting, ∆ is related to the nuclear quadrupole moment, Q,
and the principle component of the Electric Field Gradient (EFG), Vzz, by the relation
(2.17)
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 76 ~
2.8.1(c) Magnetic Splitting (Hyperfine Interaction) In the presence of a magnetic field the nuclear spin moment experiences a
dipolar interaction with the magnetic field i.e, Zeeman splitting. There are many
sources of magnetic fields that can be experienced by the nucleus. The total effective
magnetic field at the nucleus, Beff is given by:
Beff = (Bcontact + Borbital + Bdipolar) + Bapplied (2.18)
the first three terms being due to the atom's own partially filled electron shells. Bcontact
is due to the spin on those electrons polarising the spin density at the nucleus, Borbital is
due to the orbital moment on those electrons, and Bdipolar is the dipolar field due to the
spin of those electrons.
This magnetic field splits nuclear levels with a spin of I into (2I + 1) substates.
This is shown in Fig.2.12 for 57Fe. Transitions between the excited state and ground
state can only occur where mI changes by 0 or 1. This gives six possible transitions
for a 3/2 to 1/2 transition, giving a sextet as illustrated in Fig.2.12, with the line
spacing being proportional to Beff.
Fig.2.12 Magnetic splitting of the nuclear energy levels.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 77 ~
The line positions are related to the splitting of the energy levels, but the
line intensities are related to the angle between the Mössbauer gamma-ray and the
nuclear spin moment. The outer, middle and inner line intensities are related by:
3 : (4sin2θ)/(1+cos2θ) : 1 (2.19)
meaning the outer and inner lines are always in the same proportion but the middle
lines can vary in relative intensity between 0 and 4 depending upon the angle the
nuclear spin moments make to the gamma-ray. In polycrystalline samples with no
applied field this value averages to 2 (as in Fig.2.12) but in single crystals or under
applied fields the relative line intensities can give information about moment
orientation and magnetic ordering.
These interactions, Isomer Shift, Quadrupole Splitting and Magnetic Splitting,
alone or in combination are the primary characteristics of many Mössbauer spectra
[63-71].
2.9 References [1] G.B. Greenough, Progr. Metal. Phys., 3 (1952) 176.
[2] A.J.C. Wilson, Proc. Roy. Soc., London, A180 (1942) 277.
[3] B.E. Warren, Prog. Met. Phys., 8 (1959) 147.
[4] C.N.J. Wagner, 'Local Atomic Arrangements Studied by X-ray Diffraction',
ed. J.B. Cohen and J.E. Hilliard, N.Y., Gordon Breach (1966).
[5] B.E. Warren, 'X-Ray diffraction', Addison-Wesley, (1969).
[6] H.P. Klug, L.F. Alexander, 'X-Ray diffraction Procedures', John-Wiley and
Sons., N.Y. (1974).
[7] S. Enzo, G. Fagherazzi, A. Benedetti, S. Polizzi, J. Appl. Cryst., 21 (1988)
536.
[8] J.I. Langford, A.J.C. Wilson, Proc. Symp. On Crystallography and Crystal
Fection, ed. G.N. Ramashandran, N.Y. Academic press, (1963) 207.
[9] E.J. Mittemeijer and R. Delhez, J. Appl. Phys., 49 (1978) 3875.
[10] D. Balzar, J. Res. Natl. Inst. Stand. Tech., 98 (1993) 321.
[11] P. Scherrer, Gittinger Nachrichten., 2 (1918) 98.
[12] R.A. Young, R.J. Gerdes and A.J.C. Wilson, Acta Cryst., 22 (1967) 155.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 78 ~
[13] R. Delhez, Th.H. de. Keijser and M.J. Mittemeijer, 'Accuracy in Powder
Diffraction', NBS special publication No.567 ed. S. Block and C. R. Hubbard,
NBS: Washington, DC 213 (1980) 213.
[14] R. Delhez, Th.H. de. Keijser, M.J. Mittemeijer and Fresenius, Z. Anal. Chem.,
312 (1982) 1.
[15] G. Zorn, Aust. J. Phys., 41 (1988) 237.
[16] R. Delhez, Th.H.de. Keiser, M.J. Mittemeijer and J.I. Langford, Aust. J. Phys.,
41 (1988) 213.
[17] H.M. Rietveld, J. Appl. Cryst., 2 (1969) 65.
[18] G. Caglioti, A. Paoletti and F.P. Ricci, Nucl. Instrum., 3 (1958) 223.
[19] W.N. Schreiner and R. Jenkins, X-Ray Spectrom., 8 (1983) 33.
[20] H.G. Scott, J. Appl. Cryst., 16 (1983) 156.
[21] W.I.F. David and J.C. Matthewman, J. Appl. Cryst., 18 (1985) 461.
[22] S.A. Howard and R.L. Snyder, Mat. Sci. Res. Symp. on Advances in Mat.
Res., 19 (1985) 57.
[23] P. Thompson, D.E. Cox and J.B. Hastings, J. Appl. Cryst., 20 (1987) 79.
[24] C. Greaves, J. Appl. Cryst., 18 (1985) 48.
[25] P. Thompson, J.J. Reilly and J.M. Hastings, J. Less. Com. Met., 129 (1987)
105.
[26] A. Le Bail, Proc.10th Colloque Rayons X, Siemens, Grenoble, (1985) 45.
[27] C. Lartigue, A. Le Bail and A. Percheron-Guégan, J. Less. Com. Met., 129
(1987) 65.
[28] L. Lutterotti and P. Scardi, J. Appl. Cryst., 23 (1990) 246.
[29] R.K. Nandi, H.K. Kuo, W. Schlosberg, G. Wissler, J.B. Cohen, B. Crist Jnr, J.
Appl. Cryst., 17 (1984) 22.
[30] L. Lutterotti, P. Scardi and P. Maistrelli, J. Appl. Cryst., 25 (1992) 459.
[31] http://www.iucr.org/iucr-top/comm/cpd/Newsletters/no21may1999/art17/art17.htmm
[32] R.W. Grosse-Kunstleve, Acta Cryst., A55 (1999) 383.
[33] N.C. Popa, J. Appl. Cryst. 31 (1998) 176.
[34] R. Delhez, Th.H. de. Keiser, J.I. Langford, D. Louër, M.J. Mittemeijer and E.
J. Sonneveld, 'The Rietveld method', ed. R.A. Young (Oxford:IUCR/OUP)
(1995) 132.
[35] L. Lutterotti, P. Polonioli, P.G. Orsini and M. Ferrari, Materials and Design
Technology ASME, PD-Vol. 62 (1994).
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 79 ~
[36] H.R. Wenk, S. Matthies and L. Lutterotti, Mater. Sci. Forum, 157-162 (1994)
473.
[37] R. Krause-Rehberg, HS. Leipner, Positron Annihilation in Semiconductors.
Heidelberg: Springer; 1999.
[38] P. Hautojarvi, C. Corbel, Positron Spectroscopy in Solids, edited A.
Dupasquier, A.P. Millis Jr. (IOS Press, Ohmsha, Amsterdam, 1995), 491.
[39] U. De, D. Sanyal, S. Chaudhuri, P.M.G. Nambissan, Wolf Th, Wühl H. Phys
Rev B, 62 (2000) 14519.
[40] M .Chakrabarti, A. Sarkar, S. Chattapadhayay, D. Sanyal, A.K Pradhan, R.
Bhattacharya, D. Banerjee, Solid State Commun., 128 (2003) 321.
[41] U. Myler, P.J. Simpson, Phys. Rev. B, 56 (1997) 14303.
[42] P, Hautojärvi, C. Corbel, Positron Spectroscopy of Solids. In: Dupasquier A,
Mills AP Jr, editors. IOS Press: Amsterdam; (1995) 491.
[43] D. Sanyal, D. Banerjee, U. De, Phys Rev B, 58 (1998) 15226.
[44] R. Krause-Rehberg, and H.S. Leipner, Positron Annihilation in
Semiconductors (Springer, Berlin, 1999), Chap. 3, 61.
[45] Z.Q. Chen, M. Maekawa, S. Yamamoto, A. Kawasuso, X.L. Yuan, T.
Sekiguchi, R. Suzuki, T. Ohdaira, Phys Rev B, 69 (2004) 035210.
[46] A. Banerjee, B.K. Chaudhuri, A. Sarkar, D. Sanyal, D. Banerjee, Physica B,
299 (2001) 130.
[47] S. Dutta, M. Chakrabarti, S. Chattopadhyay, D. Jana, D. Sanyal, A. Sarkar, J
Appl Phys., 98 (2005) 053513.
[48] P. Kirkegaard, N.J. Pedersen, M. Eldrup, Report of Riso National Lab (Riso-
M-2740), 1989.
[49] P.M.G. Nambissan, C. Upadhyay, H.C. Verma, J Appl Phys., 93 (2003) 6320.
[50] F. Tuomisto, V. Ranki, K. Saarinen, D.C. Look. Phys Rev Lett., 91 (2003)
205502.
[51] F. Tuomisto, K. Saarinen, D.C. Look, G.C. Farlow, Phys Rev B, 72 (2005)
085206.
[52] M. Chakrabarti, S. Dutta, S. Chattopadhayay, A. Sarkar, D. Sanyal, A.
Chakraborti, Nanotechnology, 15 (2004) 1792.
[53] K.G. Lynn, A.N. Goland, Solid State Commun., 18 (1976) 1549.
[54] M. Chakrabarti, A. Sarkar, S. Chattapadhayay, D. Sanyal, A.K. Pradhan, R.
Bhattacharya, D. Banerjee, Solid State Commun., 128 (2003) 321.
THEORETICAL CONSIDERATIONS CHAPTER-2
~ 80 ~
[55] R.S. Brusa, W. Deng, G.P. Karwasz, A. Zecca, Nucl Instr and Meth B, 194
(2002) 519.
[56] V.J. Ghosh, M. Alatalo, P. Asoka-Kumar, B. Nielsen, K.G. Lynn, A.C.
Kruseman, P.E.Mijnarends, Phys Rev B, 61 (2000) 10092.
[57] F. Tuomisto, A. Mycielski, K. Grasza, Superlatt and Microstr, 42 (2007) 21.
[58] M. Chakrabarti, A. Sarkar, D. Sanyal, G.P. Karwasz, A. Zecca, Phys Lett A,
321 (2004) 376.
[59] M. Chakrabarti, S. Chattopadhyay, A. Sarkar, D. Sanyal, A. Chakrabarti,
Physica C, 416 (2004) 25.
[60] M. Chakrabarti, D. Bhowmick, A. Sarkar, S. Chattopadhyay, S. Dechoudhury,
D. Sanyal, A. Chakrabarti, J Mater Sci, 40 (2005) 5265.
[61] D. Sanyal, T.K. Roy, M. Chakrabarti, S. Dechoudhury, D. Bhowmick, A.
Chakrabarti, J Phys Condens Matter, 20 (2008) 045217.
[62] P. Asoka-Kumar, M. Alatalo, V.J. Ghosh, A.C. Kruseman, B. Nielsen, K.G.
Lynn, Phys Rev Lett., 77 (1996) 2097.
[63] Mössbauer Spectroscopy and its Applications, T.E. Cranshaw, B.W. Dale,
G.O. Longworth and C.E. Johnson, (Cambridge Univ. Press: Cambridge)
1985.
[64] Mössbauer Spectroscopy, D.P.E Dickson and F.J. Berry, (Cambridge Univ.
Press: Cambridge) 1986.
[65] The Mössbauer Effect, H Frauenfelder, (Benjamin: New York) 1962.
[66] Principles of Mössbauer Spectroscopy, T.C. Gibb, (Chapman and Hall:
London) 1977.
[67] Mössbauer Spectroscopy, N.N Greenwood and T.C Gibb, (Chapman and Hall:
London) 1971.
[68] Chemical Applications of Mössbauer Spectroscopy, V.I Goldanskii and R.H
Herber ed., (Academic Press Inc: London) 1968.
[69] Mössbauer Spectroscopy Applied to Inorganic Chemistry Vols. 1-3, G J Long,
ed., (Plenum: New York) 1984-1989.
[70] Mössbauer Spectroscopy Applied to Magnetism and Materials Science Vol. 1,
G J Long and F Grandjean, eds., (Plenum: New York) 1993.
[71] M. Chakrabarti, S. Chattopadhyay, D. Sanyal, A. Sarkar, D. Jana, Material
Science Forum, 699 (2012) 1.
CHAPTER-3
Experimental considerations
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 82 ~
3.1 Introduction
Nanocrystalline oxides can be prepared by different methods, e.g., sol–gel,
hydrothermal, chemical vapor phase deposition, calcinations of hydroxides, radio
frequency sputtering, gas condensation technique, high-energy ball-milling process,
etc. Among these the high-energy ball-milling process has many potential advantages.
The main advantage is large quantities of samples can be produced in a very short
time, and the process is relatively simple and inexpensive without any effect of
chemical contamination.
3.2 Different fabrication techniques of nano materials Nanomaterial fabrication techniques are two types: (a) Chemical methods
(Bottom-up approach) (b) Physical methods (Top-down approach).
(a) Chemical methods (Bottom-up approach): It has five different types:
(i) Sol gel
(ii) Chemical vapor deposition beam epitaxy
(iii) Co-precipitation
(iv) Dip-coating
(v) Spin-coating
(b) Physical methods (Top-down approach): There are three different types such as:
(i) Physical vapor deposition,
(ii) Ball-milling, and
(iii) Molecular Beam Epitaxy (MBE)
Again the Physical vapor deposition technique has three different parts which are
(i) Sputtering
(ii) Pulsed laser deposition
(iii) Ion plating.
Here we have used two techniques for sample preparation; one from chemical
methods and another from physical methods which are discuss below in brief:
3.2.1 Sol-gel method This is a bottom-up approach, where materials and devices are built from
molecular atoms which assemble themselves chemically by principles of molecular
recognition i.e. this approach starts with atoms and molecules and create larger
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
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nanostructures. The sol-gel process is a wet-chemical technique (chemical solution
deposition) widely used recently in the fields of materials science and ceramic
engineering. Such methods are used primarily for the fabrication of materials
(typically a metal oxide) starting from a chemical solution (sol, short for solution)
which acts as the precursor for an integrated network (or gel) of either discrete
particles or network polymers. Typical precursors are metal alkoxides and metal
chlorides, which undergo hydrolysis and polycondensation reactions to form either a
network “elastic solid” or a colloidal suspension (or dispersion) – a system composed
of discrete (often amorphous) sub-micrometre particles dispersed to various degrees
in a host fluid. Formation of a metal oxide involves connecting the metal centers with
oxo (M-O-M) or hydroxo (M-OH-M) bridges, therefore generating metal-oxo or
metal-hydroxo polymers in solution. Thus, the sol evolves towards the formation of a
gel-like diphasic system containing both a liquid phase and solid phase whose
morphologies range from discrete particles to continuous polymer networks.
A sol is a dispersion of the solid particles (~0.1-1 mm) in a liquid where only
the Brownian motions suspend the particles. A gel is a state where both liquid and
solid are dispersed in each other, which presents a solid network containing liquid
components.
The precursor sol can be either deposited on a substrate to form a film (e.g. by
dip-coating or spin-coating), cast into a suitable container with the desired shape (e.g.
to obtain monolithic ceramics, glasses, fibers, membranes, aerogels), or used to
synthesize powders (e.g. microspheres, nanospheres). [Fig.3.1]
Fig.3.1 Sol-Gel process
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 84 ~
The reagent grade Fe(NO3)3.9H2O has been used as precursor for the
preparation of nanocrystalline α-Fe2O3 powder by chemical route. Initially, a solution
of Fe(NO3)3.9H2O is made with distilled water. A few drops of concentrated nitric
acid have been added to keep the pH level of the solution in acidic range. This
solution is then stirred for 1 h and then poured into a plastic flat-bottomed container
and left for three days in ambient atmosphere for gelation. The gel is then evaporated
to obtain “as-prepared” sample in powder form.
3.2.1.1 Advantages of Sol-gel Technique: Sol-gel process- (a) Can produce thin bond-coating to provide excellent adhesion between the
metallic substrate and the top coat.
(b) Can produce thick coating to provide corrosion protection performance.
(c) Can easily shape material into complex geometries in a gel state.
(d) Can produce high purity products because the organo-metallic precursor of the
desired ceramic oxides can be mixed, dissolved in a specified solvent and
hydrolyzed into a sol, and subsequently a gel, the composition can be highly
controllable.
(e) Can have low temperature sintering capability, usually 200-600 0 C.
(f) Can provide a sample, economic and effective method to produce high quality
coatings.
3.2.2 Ball- milling process A ball-mill is a type of grinder used to grind materials into fine powder for use
in paints, pyrotechnics and ceramics. Ball mills rotate around an axis, partially filled
with the material to be ground plus the grinding medium. An internal cascading effect
reduces the material to a fine powder. There are different types of ball milling
machine viz.
• Tumbler mill:- Energy depends on diameter and speed of drum. Primarily
used for large-scale industrial applications.
• Attrition mill:- High energy, small-industry scale (<100 kg).
• SPEX mill:- High energy, research-scale.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 85 ~
• Planetary mill (Pulverisette 5):- Medium-high energy research miller (<250
g). This can be used universally for high speed grinding of solid or liquid
inorganic samples for synthesis, analysis, quality control or material testing. It
is also used to mix and homogenize dry samples, emulsions or pastes.
3.3 Potential of mechanical alloying
Mechanical alloying (MA) is normally a dry, high energy ball milling
technique that has been employed in the production of a variety of commercially
useful and scientifically interesting materials. The formation of an amorphous phase
by mechanical grinding of a Y-Co intermetallic compound in 1981 [1] and in the Ni-
Nb system by ball milling of blended elemental powder mixtures in 1983 [2] brought
about the recognition of MA as a potential non equilibrium processing technique.
Beginning from the mid 1980s, several investigations have been carried out to
synthesize a variety of stable and metastable phases, including supersaturated solid
solutions, crystalline and quasi-crystalline intermediate phases and amorphous alloys
[3-7]. In addition it has been recognized that powder mixtures can be mechanically
activated to induce chemical reactions, i.e, mechanochemical reactions at room
temperature or at least at much lower temperatures than normally required to produce
pure metals, nanocomposites and a variety of commercially useful materials [8,9].
Efforts have also been under way since the early 1990s to understand the process
fundamentals of MA through modeling studies [10]. Because of all these special
attributes, this simple but effective processing technique has been applied to metals,
ceramics, polymers and composite materials.
3.3.1 High energy ball-milling High-energy milling usually refers to a dry milling process where fracture and
cold welding are the dominant processes. This technique was first introduced for
Oxide Dispersion strengthened (ODS) alloys in the late 1960s and has since been
extensively explored for many metallic, ceramics, metallic-ceramic systems [11],
ceramic-ceramic systems.
Different types of ball mills, such as attrition mills, vibratory ball mills, and
planetary ball mills, are used for different purposes. The milling balls and bowls are
generally made of same material depending upon mechanical performance, and
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 86 ~
contamination considerations. A few of the common materials are crome-steel,
zirconia, alumina, agate and tungsten carbide.
3.3.2 The planetary ball-mill (P5)
The laboratory planetary mill “pulverisette 5” (Fig.3.1) has been used for mechanical
alloying. It can be used for high speed grinding of solid or liquid inorganic and
organic samples for synthesis of nanocrystalline materials of different kind. It is also
used to mix and homogenise dry samples, emulsions or pastes.
Fig.3.1 Planetary Mill (pulverisette 5)
3.3.3 Mechanism of a planetary ball mill
The material to be ground is crushed and torn apart by grinding balls in 2 or 4
grinding bowls. The centrifugal forces created by the rotation of the grinding bowls
around their own axis and the rotating
supporting disc are applied to the grinding bowl
charge of material and grinding balls.
Since the directions of rotation of
grinding bowls and supporting disc are opposite
(Fig.3.2), the centrifugal forces are alternately
synchronised and opposite. Thus friction results
from the grinding balls and the material being Fig.3.2 Grinding mechanism of Planetary mill.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 87 ~
ground alternately rolling on the inner wall of the bowl, and impact results when they
are lifted and thrown across the bowl to strike the opposite wall. The impact is
intensified by the grinding balls striking one another. The impact energy of the
grinding balls in the normal direction attains values up to 40 times higher than
gravitational acceleration. Loss-free comminution is guaranteed by a hermetic seal
between grinding bowls and lid-even if suspensions are being ground.
The mechanics of this mill are characterized by the rotation speed of the disk,
Ω, that of the container relative to the disk, ω, the mass, m, size, and number of balls,
the radius of the disk, R, and the radius of the container, r. Gaffet [12] has shown that
depending on the relative values of ω/Ω and r/R, two extreme regimes may be
achieved: 1) the ball rolls on the inner surfaces of the container or 2) it escapes and
impacts an opposite portion of the surface. For both cases the energy transferred per
unit area scales with mΩ2 and the frequency of the occurrence of the impacts scales
with ω. The power induced to the powder sample therefore scales as P ∝ ml2Ω2ω
where l2 is a characteristic area of the order R2 or rR for the rolling or impact regime
respectively.
3.3.4 The merits and demerits of planetary ball-mill Merits 1. This method has the advantage of a top-down method for obtaining nano or
amorphous materials.
2. Room temperature synthesis of the material is possible.
3. Alloying and complete solid solubility of materials can be done.
4. Solid state amorphization of materials can be achieved.
5. The nanosized particles can be achieved in a short duration of time.
6. Energy of the milling media can be controlled by a large number of parameters,
such as, BPMR, rpm, duration of milling, size of balls/bowls etc.
Demerits 1. Possibility of contamination from milling media.
2. Stickiness of material during dry milling.
3. Excessive heating of material during milling.
4. Combustible liquids with boiling point <1200C can not be used.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 88 ~
5. Difficult to measure the transient temperature of the material surfaces during
milling.
6. Agglomeration of nanoparticles.
3.3.5 The mechanochemical transformation during milling Powder transformation during milling
is driven by the collisions between balls or
between balls and the vial. A number of
processes work simultaneously on the sample
but their relative importance differs during the
course of a milling experiment. In the
beginning, mixing of the constituent powders
dominates, after sometime fragmentation and
coalescence, and finally amorph-ization or
phase transformation. The Fig.3.3 illustrates
the milling action on powder trapped between colliding surfaces of two balls. The
pressure on these particles is very high and while some of them are fragmented others
are joined together by cold welding or localized melting. Plastic deformation and
joining of particles stacked on top of each other lead to a layered structure which is
continuously refined by further fracture and joining. Milling is usually considered
complete when these layers can no longer be observed. The final result can be an
amorphous mixture, a solid solution of one phase in the other, or a new phase formed
during milling depending on the thermodynamics of the system and the milling
parameters. Compounds normally developed only at elevated temperature or under
high pressure are often formed during high-energy milling.
3.3.6 Use of ball milling for synthesis of nanocrystalline materials Nanocrystalline α-Fe2O3 powders at different milling time are prepared by ball
milling the analytical grade α-Fe2O3 powder in open air at room temperature. A
number of nanocrystalline ferrites have been prepared and studied for this dissertation
by mechanical alloying the stoichiometric mixture of metal oxides in a high energy
planetary ball mill. All the starting materials are of analytical grade (purity >99%).
The methods of preparation of different polycrystalline ferrites are described in detail
F ig . 3 .3 B al l-pow d er col li si on o f pow d er m ix ture dur ing m ec ha ni ca l a llo yin g.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 89 ~
in the following sections. Nanosized ZnO powder is prepared by ball milling the
analytical grade ZnO powder for 3 hours. However, detailed preparation techniques
are described in respective sections.
3.4 Preparation of powder specimens for X-ray powder diffractometry The experimental powder samples were placed inside a rectangular slot (2cm.
X 1.5cm.) of the standard aluminium sample holder (M/S Philips). The sample was
pressed by a small aluminium hammer for better packing of the powder grains and the
upper surface of the sample facing the X-rays was made perfectly flat and smooth to
avoid error due to sample displacement.
3.4.1 Choice of radiation The proper choice of radiation depends on the nature of the sample under
experiment and the purpose for which the diffraction pattern is to be used. In this
study, CuKα radiation (λ=1.54184 A0) was used for recording of the diffraction
patterns of all the samples.
3.4.2 Choice of instrumental standard For instrumental broadening correction a specially processed Si standard (Van
Berkum, 1994) was used. The resolving of (111) reflection of Si at even ~28.40 2θ
into Kα1 and Kα2 components indicates that the instrumental broadening is very small.
The U, V, W coefficients of Caglioti formula (FWHM varies non-linearly with
increasing scattering angle) asymmetry and Gaussian content (vary linearly with
increasing scattering angle) were estimated and incorporated in the Rietveld software
as instrumental broadening.
3.4.3 Recording of X-ray powder diffraction data To carry out the Rietveld powder structure refinement of multiphase system,
the XRD pattern should be extremely accurate and clear. In order to obtain such high
quality line profile of XRD data, digitized step-scan data from a diffractometer of
high resolving power should be used and the X-ray generator must be highly
stabilized. The data fluctuation due to statistical errors can be minimized to a
considerable extent by recording large number counts.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 90 ~
In the present study, the X-ray powder diffraction step scan data were
recorded at room temperature and stored in a PC coupled with the diffractometer
using Ni-filtered CuKα radiation from a highly stabilized and automated Philips X-ray
generator (PW 1830) operated at 35kV and 25 mA. The generator is coupled with a
Philips X-ray powder diffractometer consisting of a PW 3710 mpd controller, PW
1050/37 goniometer, and a proportional counter. The step scan data of the
experimental samples was recorded for the entire angular range 15-900 2θ in step size
0.020 2θ and for 10sec counting time per each step. For experiment, 10 divergence slit,
0.2 mm receiving slit, 10 scatter slit were used.
3.5 Transmission electron microscope (TEM) used for microstructure study
Transmission electron microscopy
(TEM) (fig.3.4) is a microscopy technique
whereby a beam of electrons is transmitted
through an ultra thin specimen, interacting
with the specimen as it passes through. An
image is formed from the interaction of the
electrons transmitted through the
specimen; the image is magnified and
focused onto an imaging device, such as a
fluorescent screen, on a layer of
photographic film, or to be detected by a
sensor such as a CCD camera.
Fig3.4 Model HR-TEM 2100F, JEOL
TEMs are capable of imaging at a significantly higher resolution than light
microscopes, owing to the small de Broglie wavelength of electrons. This enables
the instrument's user to examine fine detail even as small as a single column of atoms,
which is tens of thousands times smaller than the smallest resolvable object in a light
microscope. TEM forms a major analysis method in a range of scientific fields, in
both physical and biological sciences. TEM investigations for this dissertation were
made utilizing a JEOL high resolution transmission electron microscope (Model HR-
TEM 2100F) operated at 200kV.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 91 ~
Transmission electron microscopy (TEM) specimens were prepared from ball
milled powders dispersed in doubly distilled acetone and mixed well under ultrasonic
vibrator to avoid agglomeration of the fine particles. A drop of this finely dispersed
colloidal solution was placed on the 3mm disc and the disc kept overnight under
vacuum to get completely dry and well distributed fine particles over the entire area of
the carbon coated grid. After drying, the grid was mounted in the sample holder of the
microscope for observation.
Transmission electron microscopy (TEM) with TECNAIS-TWIN (FEI
Company) electron microscope operating at 200 kV has been used to estimate the
average particle size of the different hour ball-milled Fe2O3 samples. Powder
ultrasonically dispersed in alcohol was put on a standard microscope grid for the TEM
work.
3.6 The outline of positron annihilation experiment In this experiment the positron annihilation lifetime can be measured with a
slow-fast coincidence assembly. In such a set-up there are two detectors, each
consisting of a BaF2 scintillator (25 mm in diameter and 25 mm long) coupled to
Philips XP2020Q photomultiplier tube. For each temperature, a total of ~ 106
coincidence counts, in form of N(t) vs. t data, is typically recorded with 8000:1 or so
peak to background ratio. For positron annihilation experiments, 22Na-source is the
most suitable and hence most widely used. It emits one 1.27 MeV γ-ray almost
simultaneously with the positron so that the former is considered as the birth signal of
the positron. The eventual “death” or annihilation of this positron with an electron of
the sample can be recorded by detecting one of the two 511 keV annihilation γ-rays.
Coincidence electronics measures the time gap between the detections of the birth and
death signals of the positron. The resolving time, FWHM of the lifetime spectrometer,
is measured with a 60Co. The recorded N(t) vs. t data is analyzed after necessary
source correction by a suitable computer programme e.g., POSITRONFIT, PATFIT-
88. From a measured positron annihilation lifetime spectrum, N(t) vs. t, one can
calculate the possible positron lifetime components, حi , and their intensities, Ii. These
lifetime components will correspond to individual characteristic lifetime of the
components, if the sample is a mixture of non-interacting components. However, if
the sample is single component substance, element or compound, with a characteristic
Bloch lifetime, detection of two or more lifetime components indicate the presence of
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 92 ~
one or more trapping site (s) or other physical processes like positronium formation.
The lifetime for annihilation from the positron-trap turns out to be longer of the two
lifetime components and denoted by 2ح. Here lifetime for annihilation from the Bloch
state, called حB and supposed to probe the intrinsic properties of the material, can be
easily shown to be given by the equation no. (2.14) in chapter-2.
So, in a trapping model, حB and 2ح are the physically significant quantities,
with 2ح resulting from annihilation in regions of lower electron density. Without
assuming any model, a mean positron lifetime which is shown in equation no. (2.15)
in chapter-2.
From a multichannel analyzer we get the Doppler broadened spectrum of N
(E) vs. E, the central portion of the spectrum corresponds to annihilation with very
low momentum electrons, e.g., the valence electrons. The annihilation of positrons
with higher momentum electrons, e.g., the core electrons are distributed over the
wings of this spectrum because they are more strongly Doppler shifted.
For the CDBEPAR (coincidence Doppler broadening of the electron positron
annihilation γ- radiation) measurement, two identical HPGe detectors (Efficiency:
12%; Type: PGC 1216sp of DSG, Germany) having energy resolution of 1.1 keV at
514 keV of 85Sr have been used as two 511 keV γ-ray detectors, while the CDBEPAR
spectra have been recorded in a dual ADC-based multiparameter data acquisition
system (MPA-3 of FAST ComTec., Germany). A 10µCi 22Na positron source
(enclosed in between thin Mylar foils) has been sandwiched between two identical
and plane faced pellets [13]. The peak-to-background ratio of this CDBEPAR
measurement system, with ± ∆E selection, is ~105:1 [14,15]. The CDBEPAR
spectrum has been analyzed by evaluating the so-called lineshape parameters [14,16]
(S parameter). The S parameter is calculated as the ratio of the counts in the central
area of the 511 keV photo peak (|511 keV- Eγ| ≤ 0.85 keV) and the total area of the
photo peak (|511 keV- Eγ| ≤ 4.25 keV). The S parameter represents the fraction of
positron annihilating with the lower momentum electrons with respect to the total
electrons annihilated. The statistical error is ~ 0.2% on the measured lineshape
parameters. The CDBEPAR spectra for the unmilled and the milled samples have
been also analyzed by constructing the ‘‘ratio-curves’’ [14,15,17] with respect to
defects-free 99.9999% pure Al single crystal (reference sample).
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
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3.6.1 The Positron Source Several nuclei emit positrons but there are only a few which are suitable for
the positron annihilation experiments. For positron annihilation experiments the
source should be such that there is continuous and steady flow of positrons from the
source. This source may be either the positron beam or a natural β+ emitting
radioactive source. In the experiments we use β+ emitting natural radioactive source.
The nuclei which are suitable for the positron annihilation experiments should have
the following characteristic properties:
• The source must emit a distinct γ ray after the emission of the positron from
the source. This prompt γ ray can be treated as the birth signal of the positron.
• The source must have a long half life so that the user can perform a series of
measurements with the same source.
• The source must emit positrons with sufficiently high end point energy so that
they can penetrate well inside the material under study.
• The source must have high positron yield.
• The source must be easily producible.
Considering the above all properties, 22Na source is the most suitable positron
(β+) source for the positron annihilation experiments. The decay scheme of this 22Na
is shown in Fig.3.5.
Fig.3.5 The decay scheme of 22Na.
The half-life of 22Na is ~ 2.6 years with 90.4 % of the decay via emission of
β+ particle. The end-point energy of the β+ particle feeding the 2+ state in 22Ne is
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 94 ~
545.4 keV. The 2+ excited state in 22Ne deexcites to the ground state (0+) by emitting
a γ-ray of energy 1.274 MeV. The half-life of the excited (2+) state is 3.7 ps, which is
much smaller than the positron lifetime in matter. Thus, the 1.274 MeV γ-ray is
considered as the birth signal of the β+ particle as the emission of β+ particle from the
nucleus 22Na and the emission of 1.274 MeV γ-ray from the nucleus of 22Ne is almost
simultaneous.
3.6.2 The positron source preparation for positron annihilation experiments About 10 µCi 22Na enclosed between two thin (2 µm) nickel foils has been
used as the positron source for the positron annihilation experiments. Carrier free,
high specific activity (~ 1.1 mCi per ml) 22NaCl dissolved in dilute HCl procured
from E.I. DuPont de Nemours & Co., Inc., (France) has been used for the preparation
of the positron source. In case of nickel covered 22Na β+ source a fraction of positrons
may be annihilating within the source cover (nickel foil). These annihilations
contribute additional lifetime components in the lifetime spectrum. In order to
eliminate this contribution, source correction is necessary. For this purpose, positron
annihilation lifetime spectrum has been recorded with a defects free 99.9999 % pure
Al single crystal. In pure Al, positron has only one lifetime component of value 166 ±
1 ps. Thus the remaining lifetime component (if any) is due to source itself. In the
present experiments, with Ni covered 22Na β+ source, in addition to 166 ±1 ps (98 %)
a second lifetime component of 743 ± 10 ps with 2 % intensity has been observed.
The lifetime component of 743 ± 10 ps with 2 % intensity is due to the annihilation of
positrons inside the source and Ni foil and has been considered as the source
component. This component is found to be temperature independent, and hence used
in the temperature dependent positron annihilation measurements.
3.6.3 Implantation profile From a radioactive source, positrons enter into the material and penetrate up to
a certain depth inside the material. The positron implantation profile [18] for this case
is
I (x) = I (0) e-αx (3.1)
where I(0) is the initial positron density, I(x) is the positron density at a distance x and
α is the absorption coefficient of the material for positrons. The value of α can be
obtained from the following equation
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 95 ~
α = (16 ± 1) ρ(Emax)-1.43 cm-1 (3.2)
where ρ is the density of the material under study in gm cm-3 and Emax is the end
point energy of the positron on MeV. For 22Na source, the value of Emax is 0.545
MeV. From this value of Emax, the relation between penetration depth and the
absorption coefficient is
1 / α = 0.026 / ρ cm (3.3)
3.7 Positron Annihilation Lifetime (PAL) Measurement On entering inside a material positrons from a radioactive source (here 22Na
source), gets thermalized and annihilates with an electron by emitting two oppositely
directed 511 keV γ- rays. One of these two 511 keV γ-rays is a signature of the
annihilation of the positron with an electron and hence considered as the death signal
of the positron. After 3.7 ps of the emission of β+ from 22Na source, the daughter
nucleus, 22Ne, de-excites to the ground state by emitting a γ-ray of energy 1.274 MeV,
which is considered as the birth signal of the positron. The timing interval between
the birth signal (1.274 MeV γ-ray) and the death signal (511 keV γ-ray) is considered
as the lifetime of the positron inside the material.
3.7.1 The positron annihilation lifetime (PAL) spectrometer The lifetime of the positron annihilation inside a material can vary from 100
ps to several nanoseconds. These sub-nanosecond lifetimes have been measured by a
standard nuclear technique, gamma-gamma coincidence technique. As the positron
annihilation lifetime values are very small (~ 100 ps) the detection of the γ-rays
should be very fast. The positron annihilation lifetimes have been measured with a
fast-fast coincidence assembly consisting of two constant fraction differential
discriminators (Fast ComTech Model number 7029A). The detectors are 25-mm-long
× 25-mm tapered to 13 mm – diameter cylindrical BaF2 scintillators optically coupled
to Philips XP2020Q photomultiplier tubes. The resolving time (full width at half
maximum, FWHM), measured with a 60Co source and with the proper energy window
(700 keV to 1320 keV for the start channel and 300 keV to 550 keV for the stop
channel) of the fast-fast coincidence assembly is 180 ps [19]. During the
measurement, temperature was kept constant at 300 K. Altogether 20 measurements
have been carried out (each positron annihilation lifetime spectrum of about 5 × 106
coincidence counts) to ensure the repeatability of the measurements. Measured
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 96 ~
positron annihilation lifetime spectra have also been analyzed by computer
programme PATFIT-88 [20] with necessary source corrections. The details of the
lifetime set up have been shown in the block diagram of Fig.2.2, chapter-2.
Fig.3.6 The plot of the channel shift of the 60Co prompt coincidence peak for different known values of the delay.
By using by using 60Co source the lifetime spectrometer has been calibrated.
The 60Co source emits two prompt γ ray of energy 1173.2 keV and 1332.5 keV in a
time gap of 0.7 ps. To calibrate the TAC some known delay is given to the stop pulse
so that the centroid of the 60Co prompt coincidence spectrum shifts by a number of
channels in the MCA. The time per channel of the TAC has been calculated from the
slope of the peak channel shift vs. time delay curve (Fig.3.6).
Fig.3.7 A typical positron lifetime spectrum. The prompt time resolution of the system using 60Co is also shown in the figure.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 97 ~
The delay per channel in this coincidence assembly is 26.2 ps. Fig.3.7 shows a
typical positron annihilation lifetime spectrum in some material at room temperature.
3.7.2 Positron Annihilation Lifetime Data Analysis For each lifetime spectrum 106 or more coincidence counts has been recorded
with 8000:1 random ratio. The system stability has been checked frequently during
the progress of the experiment.
3.7.2 (a) Mathematical analysis of the positron annihilation lifetime data The positron annihilation lifetime spectrum is an exponential spectrum (in the
form e-λt where λ is the annihilation rate in the material). The time dependent positron
annihilation decay spectrum F(t) for N discrete state is given by
(3.4)
where τi ( = 1/λi) is the positron lifetime in the ith state and Ii is the relative intensity.
Due to the spectrometer contribution in the measured spectra with the resolution
function R(t), the lifetime spectrum is modified as
(3.5)
The contents of channel n of the experimental lifetime spectrum is expressed as
(3.6) where C is the constant background due to random coincidence.
The positron annihilation lifetime component can be obtained from the
measured spectrum either by using the least square method or by the integral
transform method. In the integral transform method, the lifetime spectrum is
considered as the Laplace transform and the lifetime component is obtained by its
inverse. The positron lifetime components have been evaluated here by using the
widely used least square method.
To evaluate the lifetime parameters from the measured spectrum computer
programs (PATFITT – 88) have been used here. This program consists of two parts:
RESOLUTION and POSITRONFIT.
The shape of the resolution function has been evaluated by using
RESOLUTION program.
The shape of the resolution function is determined by the sums of the shifted
Gaussians. The output of the RESOLUTION program describes the width of this
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 98 ~
Gaussians. POSITRONFIT program has been used to evaluate the lifetime
components. It is necessary to perform the source correction before evaluating the
lifetime components. The contribution of the source component in the lifetime
spectrum has been subtracted from the measured spectra. Then, by fixing the shape
parameters of the resolution function the positron annihilation lifetime components
have been evaluated from the measured spectra by using the POSITRONFIT program.
3.7.2 (b) Positron annihilation lifetime data analysis The positron lifetime component τi and its relative intensity Ii can be evaluated
from the measured positron annihilation lifetime spectrum N(t) vs. t. In case of single
crystal only one lifetime component exists whereas for polycrystalline samples the
number of lifetime states will be different depending upon the sample property. In the
two state trapping model [21] it is assumed that the smallest lifetime component, τ1, is
due to the positron annihilation in the bulk of the material and the longer lifetime
component, τ2, is due to the positron annihilation at the defect sites in the material.
We can calculate the annihilation lifetime in the Bloch state (called τB), and the mean
positron lifetime (τav) from the equation (2.14) and equation (2.15) in chapter-2
respectively.
3.8 Doppler Broadening of the Electron Positron Annihilation Radiation Measurement After entering a material positrons get thermalized and then annihilate with
electron. In the center of mass frame, the energy of the annihilating photon is exactly
moc2 = 511 keV (mo is the rest mass of the electron or the positron) and the two
photons are moving exactly in the opposite direction. But due to the electron-positron
pair momentum, p, the 511 keV annihilation γ-rays are Doppler shifted by an amount
± ∆E in the laboratory frame with
± ∆E = pLc/ (3.7)
Fig.3.8: Schematic representation of Doppler shift of the annihilating γ- rays along the detector direction.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 99 ~
pL (p cos θ) is the component of the electron momentum, p, along the direction of the
detection of the annihilating γ-rays. Fig. 3.8 represents the Doppler shift of the
electron positron pair along the detector direction due to non-zero momentum of the
electron positron pair. So by measuring the Doppler shift of these 511 keV γ-photons
one can study the momentum distributions of the electrons at the positron annihilation
site.
3.8.1 Coincidence Doppler broadening of the electron positron annihilation radiation measurement One can measure the Doppler broadening of the electron positron annihilation
γ-radiation (DBEPAR) spectrum using a high resolution HPGe detector. The central
portion of the DBEPAR spectrum (as shown in Fig.3.9) represents those 511 keV γ-
rays, which are less Doppler shifted, i.e., coming from the annihilation of positrons
with the lower momentum electrons. Similarly, the wing portion of the DBEPAR
spectrum represents those 511 keV γ-rays, which are more Doppler shifted, i.e.,
coming from the annihilation of positrons with the higher momentum electrons, e.g.,
core electrons. Now it is very important to study the annihilation of positrons with the
core electrons in a particular material. Hence it is very important to increase the
statistics of the counts in the DBEPAR spectrum, particularly in the wing portion.
Unfortunately, the Compton part of the 1.274 MeV γ-ray is always present in the
photo-peak of the 511 keV γ-rays and is more prominent as a background in the wing
portion of the DBEPAR spectrum. The typical peak to background ratio is ~ 50:1.
Using two HPGe detectors in opposite direction one can increase the peak to
background ratio better than 105:1 [22]. For the coincidence Doppler broadening
(CDB) measurement, two identical HPGe detectors (Efficiency: 12 % ; Type : PGC
1216sp of DSG, Germany) having energy resolution of 1.1 keV at 514 keV of 85Sr
have been used as two 511 keV γ- ray detectors, while the CDB spectra have been
recorded in a dual ADC based - multi parameter data acquisition system (MPA-3 of
FAST ComTec., Germany). The peak to background ratio of this CDB measurement
system [22] with ± ∆E selection is ~ 105:1. The CDB spectrum has been analyzed by
evaluating the ratio curve analysis [15].
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 100 ~
Fig.3.9: A typical Doppler broadening spectrum with two detectors in coincidence [one HPGe and another NaI(Tl) detectors].
3.8.2 The coincidence Doppler broadening of the electron positron annihilation radiation (CDBEPAR) spectrometer The block diagram of such a Coincidence DBEPAR (CDBEPAR)
spectrometer used, is shown in Fig.2.3 in chapter-2, which is discussed earlier.
A total of ~ 6 × 106 to 107 coincidence counts have been recorded under the
photo-peak of the 511 keV γ-ray CDBEPAR spectrum at a rate of 110 counts per
second. The CDBEPAR spectrum is recorded in a PC based 8k multi-channel
analyzer. The energy per channel of the multichannel analyzer is kept at 22 eV (as
shown in Fig. 3.10).
Background has been calculated from 607 keV to 615 keV energy range of the
spectrum. The achieved peak to background ratio in the present case is ~ 14000:1.
The system stability has been checked frequently during the progress of the
experiment. For the energy calibration of the set up, the 383.7 keV γ-ray from 133Ba,
411.1 keV and 444 keV γ-ray from 152Eu and 661.6 keV γ-ray from 137Cs source have
been used.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
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Fig.3.10: Calibration of the coincidence Doppler broadening spectrometer using standard monoenergetic γ-rays.
3.8.3 The Doppler broadening data analysis
3.8.3 (a) Line shape analysis The coincidence Doppler broadening of the electron positron annihilated 511
keV γ-ray spectrum has been analyzed by evaluating the so called line-shape
parameters [23] (S-parameter) and (W-parameter). The S-parameter is calculated as
the ratio of the counts in the central area of the 511 keV photo peak ( | 511 keV - Eγ |
≤ 0.85 keV ) and the total area of the photo peak ( | 511 keV - Eγ | ≤ 4.25 keV ). The
S-parameter represents the fraction of positron annihilating with the lower momentum
electrons with respect to the total electrons annihilated. During all measurements, the
value of the S parameter is kept fixed around 0.45 to 0.5 by suitable selecting the
energy range. The W-parameter represents the relative fraction of the counts in the
wings region (1.6 keV ≤ |Eγ -511 keV| ≤ 4 keV) of the annihilation line with that
under the whole photo peak ( | 511 keV - Eγ | ≤ 4.25 keV ). The W-parameter
corresponds to the positrons annihilating with the higher momentum electrons. The
schematic representations of the S parameter and W-parameter are shown in Fig.2.4 &
Fig.2.5 in chapter-2 respectively. The statistical error is 0.2% on the measured line-
shape parameters.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 102 ~
3.8.3 (b) Ratio-curve analysis Ratio curve analysis [16,24] have been followed to identify the contributions
of the valence and the core electron momentum involved in the annihilation process.
Ratio-curve is defined as point to point ratio of area normalized CDBEPAR spectrum
of the material under study with an area normalized CDBEPAR spectrum of reference
sample. Reference sample should be a highly pure defects free sample. We have been
taken defects free 99.9999% pure Al single crystal and 99.9999% pure Cu single
crystal as reference samples.
3.9 An outline of Mössbauer spectroscopy experiment The Mösbauer spectroscopy represents one of the great achievements in
experimental physics. I first describe the principle of energy modulation using
Doppler velocity, which is a key step in observing a Mössbauer spectrum. This
technique is well developed and well documented in the literature [25,26]. Next, I
describe the Mössbauer radiation sources and the γ -ray detectors. These sources and
detectors must possess certain particular properties and are specially prepared. The
data acquisition system is relatively simple, which I briefly deal with.
3.9.1 The Mössbauer Spectroscopy The Mösbauer spectroscopy is a recoilless γ- ray emission and subsequent
absorption spectroscopy. To obtain the resonance curve of a nucleus absorbing γ-rays,
the energy of the incoming γ-ray must be modulated. This is achieved using the
Doppler effect, in which the perceived frequency of a wave is different from the
emitted frequency if the source is moving relative to the receiver. Suppose the source
and the receiver have a relative velocity of v, then the perceived frequency of the γ-
radiation is
(3.8)
where f0 is the frequency of the radiation when the source is at rest, c is the speed of
light, and θ is a small angle between the relative velocity and the γ-ray direction.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 103 ~
To obtain a typical Mössbauer spectrum, vmax< 1 m s-1, thus v/c << 1 and a very good
approximation of the above equation is
, or, (3.9) Mössbauer spectrometer has a velocity transducer based on equation (3.9)
modulating the γ -ray energies in order to observe the resonance curve. In most cases,
the source undergoes a mechanical motion, whereas the absorber is at rest so that it is
easier to change its temperature or to apply an external magnetic field to the absorber.
The velocity transducers are generally operated in two modes: constant
velocity and velocity scan. The first is the simplest, developed in the early 1960s. In
this case the spectrum is recorded ‘‘point by point’’ throughout the selected velocities
provided that the measurement time interval at each velocity is fixed. The Mössbauer
spectrometers used at the present time are almost exclusively constructed using the
second mode, in which the source scans periodically through the velocity range of
interest. If every increment/decrement in velocity between adjacent points is the same,
the source motion must have a constant acceleration, and the velocity-scanning
spectrometer becomes a constant-acceleration one. For recording the transmitted γ -
rays, each velocity has its own register (usually called a channel) which is
sequentially held open for a fixed, short time interval synchronized with the velocity
scan. The number of channels, i.e., the number of velocity points, is usually chosen to
be 256, 512, or sometimes 1024, etc.
Fig.3.11 shows a block diagram of a velocity-scanning spectrometer in
transmission geometry. It consists of a radiation source, an absorber, a detector with
its electronic recording system, a clock signal and a function generator, a drive circuit,
and a transducer.
The radiation source is not monochromatic. For example, in addition to
emitting the 14.4-keV γ-rays, a 57Co source also emits γ-rays and x-rays of other
energies. In order to pick out the signal due to the 14.4-keV radiation, a single-
channel analyzer (SCA) is placed behind the amplifier. Fig.3.12 shows various control
signals and an observed spectrum.
The clock generates a synchronizing signal, which sets the starting moment
(t =0) for velocity scanning. A triangular wave from the waveform generator begins to
increase (decrease) from its minimum (maximum), and the first channel also begins to
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 104 ~
open. After that, each channel is opened in turn by an advance pulse alone. The
velocity of the transducer is scanned linearly from –vm to + vm
Fig.3.11 Block diagram of a Mössbauer spectrometer in transmission geometry. Fig.3.12 Various control signals in a constant-acceleration spectrometer and an absorption spectrum. and a spectrum taken during the linear ramp is stored in one half of the total channels.
Then, the velocity decreases from +vm back to -vm, completing a backward scan,
during which the measured data are stored in the other half of the available channels.
Therefore, in one scan period, a multiscaler or a computer will record two spectra,
which are mirror images of each other. In order to obtain a spectrum with a good
signal-to-noise ratio, hundreds of thousands of scans are usually necessary. An
occasional synchronization problem would have no impact, because it recovers at the
next scan period. One obvious advantage of using a constant-acceleration
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 105 ~
spectrometer is that the stability requirement is not as strict as in a constant-velocity
spectrometer. If instability, such as a discrimination voltage drift at SCA, should
cause a decrease in the absorbed line intensities during one scan or several scans, it
has a small effect on the absolute intensities but no effect on the positions and the
shape of the spectral lines because this process is equivalent to shortening the
experiment duration slightly. Another advantage is that this mode can make full use of
digital technology, improving the properties of the spectrometer and allowing
automatic data acquisition.
3.9.2 Radiation Sources Among the isotopes in which the Mössbauer effect has been observed, 40K is
the lightest one. 57Fe and 119Sn are the most popular Mössbauer isotopes, whose decay
schemes are shown in Fig.3.13. 57Fe is by far the most important one, for more than
69% of research work involves 57Fe.
Fig.3.13 Nuclear decay schemes of 57Co and 119Sn. 3.9.3 The Absorber In Mössbauer spectroscopy, the absorber is usually the sample to be
investigated. In transmission geometry, the thickness of the absorber significantly
affects the quality of the spectrum and must be carefully chosen.
3.9.4 Detection and Recording Systems If we take the 57Co source, it emits γ-rays of 136, 122, and 14.4 keV and x-
rays of 6.3 keV (Fig.3.14), with an approximate intensity ratio of 1:10:1:13.
Therefore, the 14.4 keV Mössbauer radiation is only a small part of the total radiation,
and what is worse is that the flux of 14.4 keV γ-rays is attenuated considerably after
going through a typical sample, but the flux of the 122 keV γ-rays will be decreased
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 106 ~
0 50 100 150 200 2501x105
2x105
3x105
4x105
8.568
5.273
1.784-0.835
-4.337
-8.025Cou
nts
Channel Number
very little. Consequently, the detector must be highly efficient for the 14.4 keV γ-rays,
but be as insensitive as possible to the 122 keV γ-rays. As to the γ-rays with energies
below 14.4 keV, they will be discriminated against by the single-channel analyzer if
they have been detected. The most widely employed detectors are proportional
counters and NaI(Tl) scintillation counters, followed by semiconductor detectors [27].
Fig.3.14 Schematic diagram showing various processes of secondary radiation as γ-rays from a 57Co source travel through the absorber towards the detector. 3.9.5 Experimental set up of Mössbauer spectroscopy Mössbauer spectroscopy has been successfully employed in our laboratory on
different system. Mössbauer spectra have been recorded using a CMTE constant
acceleration drive (Model-250) with a 5 mCi 57Co source in Rh matrix. A Xe filled
proportional counter was used as detector.
The sample was made vibration free using home made arrangements. Recoil
spectral analysis [28] software was used for quantitative evaluation of Mössbauer
spectra. The isomer shift was calculated with respect to metallic iron (α-Fe) at room
temperature.
Fig.3.15 Room temperature Mössbauer spectra for standard enriched 57Fe2O3 sample
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 107 ~
0 50 100 150 200 250-12
-8
-4
0
4
8
12
Velo
city
(mm
/sec
)
Channel Number
Zero Channel = 128.8Velocity/Channel = 0.096
Fig.3.16 Velocity per channel calibration curve of the Mössbauer spectrometer
Room temperature 57Fe Mössbauer spectra for all the samples have been
recorded in the transmission configuration with constant acceleration mode. A gas
filled proportional counter has been used for the detection of 14.4 keV Mössbauer γ -
rays, while a 10 mCi 57Co isotope embedded in an Rh matrix has been used as the
Mössbauer source. The Mössbauer spectrometer has been calibrated with 95.16%
enriched 57Fe2O3 and standard α-57Fe foil. Fig.3.15 and Fig.3.16 show the spectrum of
the 57Fe2O3 and the velocity per channel calibration curve of the Mössbauer
spectrometer respectively. The Mössbauer spectra have been analyzed by a standard
least square fitting program (NMOSFIT).
3.10 References [1] E. Ermakov, E.E. Yurchikov, V.A. Barinov, Phys. Met. Metallogr., 52(6)
(1981) 50.
[2] C.C. Koch, O.B. Cavin, C.G. McKamey, J.O. Scarbrough, Appl. Phys. Lett.,
43 (1983) 1017.
[3] C.C. Koch, In: R.W. Cahn editor. Processing of metals and alloys of Materials
Science and Technology-a comprehensive treatment, Weinheim, Germany:
VCH Verlagsgesellschaft GmbH, 15 (1991) 193.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 108 ~
[4] C. Suryanarayana, Bibiography on mechanical alloying and
milling,Cambridge, UK: Cambridge International Science Publishing, 1995.
[5] C. Suryanarayana, Metals and Materials, 2 (1996) 195.
[6] M.O. Lai, and L. Lu, Mechanical alloying, Boston, MA: Kluwer Academic
publishers, 1998.
[7] B.S. Murty, S. Ranganathan, Internat. Mater. Rev., 43 (1998) 101.
[8] G. Heinicke, Tribochemistry, Berlin, Germany: Akademie Verlag, 1984.
[9] P.G. McCormick, Mater. Trans. Japan Inst. Metals, 36 (1995) 161.
[10] D.R. Maurice, T.H. Courtney, Metall. Trans., A21 (1990) 289.
[11] P.R. Soni, Mechanical Alloying: Fundamentals and Applications, Cambridge
International Science Publishing, Cambridge (2000).
[12] E. Gaffet, Materials Science and Engineering A, (1990)
[13] M. Chakrabarti, A. Sarkar, S. Chattopadhyay, D. Sanyal, In: Martins BP (ed)
New topics in superconductivity research. Nova Science, New York, (2006).
[14] M. Chakrabarti, D. Sanyal, A. Chakrabarti, J Phys Condens Matter, 19 (2007)
236210.
[15] D. Sanyal, M. Chakrabarti, T.K. Roy, A. Chakrabarti, Phys Lett A, 371 (2007)
482.
[16] Hautojarvi P, Corbel C (1995) In: Dupasquier A, Mills AP Jr (eds) Positron
spectroscopy of solids. IOS Press, Amsterdam, p 491; In: Krause-Rehberg R,
Leipner HS (eds) Positron annihilation in semiconductors, Springer Verlag,
Berlin, 1999.
[17] K.G. Lynn, A.N. Goland, Solid State Commun., 18 (1976) 1549.
[18] W. Brandt, R. Paulin, Phys. Rev. B, 15 (1977) 2511.
[19] D. Sanyal, M. Chakrabarti, A. Chakrabarti, Solid State Communications, 150
(2010) 2266.
[20] P. Kirkegaard, N.J. Pedersen and M. Eldrup: Report of Riso National Lab,
(Riso- M-2740), 1989.
[21] W. Brandt and A. Dupasquier (Eds.), Positron Solid State Physics, North-
Holland, Amsterdam, 1983.
[22] N. Kumar, D. Sanyal, and A. Sundaresan: Chem. Phys. Lett., 477 (2009) 360.
[23] P. Hautojarvi (Eds.), Positron in Solids, Springer-Verlag, Berlin, (1979) 4.
[24] R.S. Brusa, W. Deng, G.P. Karwasz and A. Zecca: Nucl. Instr. & Meth. B, 194
(2002) 519.
EXPERIMENTAL CONSIDERATIONS CHAPTER-3
~ 109 ~
[25] R.L. Cohen and G.K. Wertheim. Experimental methods in Mössbauer
spectroscopy. In Methods of Experimental Physics, vol. 11, R.V. Coleman
(Ed.), pp. 307–369 (Academic Press, New York, 1974).
[26] G. Longworth. Instrumentation for Mössbauer spectroscopy. In Advances in
Mössbauer Spectroscopy: Applications to Physics, Chemistry and Biology,
B.V. Thosar and P.K. Iyengar (Eds.), pp.122–158 (Elsevier, Amsterdam,
1983).
[27] Yi-Long Chen and De-Ping Yang, Mössbauer Effect in Lattice Dynamics,
Experimental Techniques and Applications.
[28] Z.Q. Chen, M. Maekawa, S. Yamamoto, A. Kawasuso, X.L. Yuan, T.
Sekiguchi, R. Suzuki, T. Ohdaira: Phys. Rev. B, 69 (2004) 035210.
PART: II
Experimental investigations on some nanomaterials
CHAPTER-4
Nanophase iron oxides by ball-mill grinding and their Mössbauer characterization
CHAPTER-4
~ 111 ~
4.1 Introduction
In the recent years nanocrystalline materials have been extensively
investigated due to their unusual properties as well as application potentials [1]. The
iron oxides, α-Fe2O3 (hematite) and Fe3O4 (magnetite), for example, are important
electrical and magnetic materials. Mössbauer spectra [2] of fine particles of α-Fe2O3,
produces by a chemical impregnession process and supported on a high area silica, in
different sizes, have been recorded before the name nanophase was coined. Among
various methods of producing nanomaterials, ball-milling [3] has potential for large
scale production and is being further developed. Particle size reduction and possible
chemical transformation of the sample during ball-milling are believed to be
influenced by ball-to-powder mass ratio (BPMR), duration of milling time, milling
environment, milling speed etc. as well as type of ball-mill itself. Recently, Zdujic et
al. [4] reported the results of ball milling of α-Fe2O3 powder in air and in ‘closed
atmosphere’ milling conditions using a planetary ball mill and showed that the
mechanochemical treatment of iron oxides was very sensitive to milling conditions.
Recently, structural and magnetic properties of nanophase materials have been
investigated by X-ray powder diffraction [1,5,6,14] and Mössbauer spectroscopic
[1,7-9] techniques. The present work is devoted to X-ray powder diffraction line
profile analysis and Mössbauer studies on differently ball-milled α-Fe2O3 fine
particles. It is noted that the nature of the Mössbauer spectrum depends on the relation
between the time of measurement and that of the magnetization vector relaxation. If
the time of observation is much less than the relaxation time, the particles exhibit
ferromagnetism, while in the opposite case one observes superparamagnetism. Also,
the relaxation time of superparamagnetic particles increases with particle volume, as
detailed later. Therefore, in ferromagnetic samples consisting mainly of nanoparticles,
the Mössbauer spectrum is usually a superposition of a superparamagnetic doublet,
corresponding to particles of smaller size, and a Zeeman sextet, corresponding to
large ferromagnetic particles [10,11].
4.2 Experimental details
Analytical grade α-Fe2O3 powder was used as the starting material for milling
in Fritsch Pulverisette 5 planetary ball mill. Two hardened-steel vials of 80 cm3
volume, each charged with 30 hardened-steel balls of 10 mm diameter were used for
CHAPTER-4
~ 112 ~
milling, keeping the angular velocity of the supporting disc at 31.42 (300 rpm) rad s-1.
The powder was milled in air atmosphere without any additives (dry milling) under
‘closed’ milling conditions, i.e., the vials were not opened during all the milling
periods. In all the experiments, the ball-to-powder mass ratios (BPMR) of 30:1 and
35:1.have been tried.
The X-ray powder diffraction (XRD) step scan data (0.020 2θ) were collected
on a Philips PW 1710 automatic diffractometer with CuKα radiation. The Mössbauer
spectra have been recorded in transmission geometry using a constant acceleration
type. Mössbauer spectrometer with a 5mCi Co57 source in a Pd matrix. A Xe-filled
proportion counter has been used as detector. The data have been acquired in the
MCS mode in a multichannel analyzer. Mössbauer spectra of α-Fe2O3 fine particles
produced by ball-milling have been recorded at room temperature.
4.3 Method of X-ray line profile analysis
In the present study, the Scherrer formula [12] has been used only for grain
size (D) determination and Warren-Averbach method of Fourier analysis of line
profile [12] for estimation of both the particle size (coherently diffracting domain)
(De) and r.m.s strain (<ε2>1/2) of unmilled and all the ball-milled α-Fe2O3 samples.
Mössbauer spectra for all the samples are fitted by least-square fitting programme
with Lorentzian line shape. The isomer shift (IS), line width, quadrupole splitting
(QS) internal hyperfine field (Hn) are obtained from best fitted Mossbauer spectra
lines.
4.4 Results and discussion
We have considered the most prominent reflections of α-Fe2O3 (012), (104),
(110), (113), (024), (116), (214) and (030) for X-ray line profile analyses (XRLPA).
The reflections of transformed Fe3O4 and Fe1-xOx are very weak and/or completely
overlapped with α-Fe2O3 reflections and are not considered for XRLPA. As some of
the peaks of α-Fe2O3 are partially overlapping [Fig. 4.1], it is prime necessity to
estimate the correct background of the X-ray spectra in the vicinity of overlapping
region in order to obtain the accurate values of peak-position maxima, peak
intensities, full-width at half-maxima (FWHM) and Gaussianity of the experimental
profiles. The Scherrer formula [12] for grain size (D) estimation or Warren-Averbach
CHAPTER-4
~ 113 ~
20 30 40 50 60 70
0
100
200
300
400
500
2θ (degree)
3= FeO2= Fe3O41= α-Fe2O3
112
12
12
1131
(030
)(2
14)
(116
)
(024
)
(113
)(110
)
(104
)
(012
)
1
123
0h
20h
15h
10h
5h
Inte
nsity
(arb
.uni
t)method of Fourier analysis of line shapes [12] for determination of particle size (De)
and r.m.s. strain, <ε2> 2/1 have been used after the correction for background by a
standard profile fitting procedure [13]. For peak fitting, the most suited pseudo-Voigt
peak shape function has been used, as recommended by Young and Wiles [14]. The
said function has the following refinable parameters: peak-height (I), peak area (S),
peak maximum position (2θmax), full width at half maxima (FWHM), an asymmetry
parameter (A) and gaussianity of the peak (G) and background parameters (linear/non
linear). Two weighting schemes can be used during the profile fitting: (a) unweighted
refinement (wI =1) and (b) weight equals to the reciprocal of the standard deviation.
Refinement uses the Marquardt minimization algorithm. The adopted software [13]
allows simultaneous fittings of upto 15 overlapping peaks of mixed Gaussian and
Lorenzian type. For both the Scherrer equation and Warren-Averbach analyses and a
specially prepared polycrystalline Si is used as ‘instrumental standard’ [15]. The
results of X-ray powder diffraction line profile analysis on differently ball-milled
samples of α-Fe2O3 is presented in Table 4.1.
Fig. 4. 1 X-ray powder diffraction patterns for different periods of ball-milling of α-Fe2O3
CHAPTER-4
~ 114 ~
Table 4.1 Results of X-ray powder diffraction line profile analysis on differently ball-milled samples with α-Fe2O3 (0h) denoting the as-supplied or the starting material.
Sample (milling time)
hkl
Lattice
parameter
(nm)
Particle size (nm) R.m.s. strain (103) Scherrer Warren-Averbach Warren-Averbach
(D)hkl (D)av (D)hkl (D)av 2/12hkl⟩⟨ε 2/12
av⟩⟨ε
Fe2O3 (0hrs.)
012 104 110 113 024 116 214 030
a=0.50250 c=1.36838
57.05 54.91 61.61 53.12 62.69 62.40 80.94 65.38
62.26 29.8 32.4 30.1 59.8 35.3 27.6 36.7 30.0
35.2 1.71 1.37 1.03 1.32 0.79 0.58 0.41 0.47
0.96
Fe2O3 (5hrs.)
BPMR= 30:1
012 104 110 113 024 116 214 030
a=0.50281 c=1.37402
8.08 8.04 9.56 6.93 6.85 7.59 6.74 7.84
7.70
5.02 3.01 6.54 3.29 3.20 3.62 3.00 3.21
3.86
9.97 7.60 6.16 6.06 5.09 4.21 4.25 3.81
5.89
Fe2O3 (10hr)
BPMR= 35:1
012 104 110 113 024 116 214 030
a=0.50320 c=1.37751
8.16 10.70 9.69 9.64 7.75 10.21 7.72 9.10
9.12
6.16 4.67 3.93 3.85 3.15 4.85 5.46 3.62
4.46
10.38 4.99 5.44 4.82 4.93 3.15 4.44 3.38
5.19
Fe2O3 (15hr)
BPMR= 35:1
012 104 110 113 024 116 214 030
a=0.50380 c=1.37638
8.20 9.91 10.41 11.66 10.83 8.87 12.59 10.72
10.39
3.27 3.95 5.89 6.41 4.37 4.25 5.12 5.26
4.81
9.53 5.76 5.04 3.79 3.56 3.61 2.44 2.58
4.53
Fe2O3 (20hr)
BPMR= 30:1
012 104 110 113 024 116 214 030
a=0.50391 c=1.37664
10.39 9.27 9.02 9.97 7.45 9.95 6.96 12.29
9.41
5.00 5.17 3.61 7.93 4.11 4.04 2.85 5.01
4.71
6.92 4.94 5.89 2.36 4.92 3.54 4.39 2.45
4.42
CHAPTER-4
~ 115 ~
Table 4.2 Mössbauer parameters for differently ball-milled α-Fe2O3
.Sample (milling time)
IS (mm/s)
a( 5612 ∆−∆ ) (mm/s)
QS (mm/s)
Hn (Tesla)
FWHM Γ(mm/s)
Relative Intensity(%)
Fe2O3(0h) Six-finger Doublet Single line
0.41
– –
0.22
– –
-0.08
– –
51.82
– –
0.34
– –
100 0 0
Fe2O3(5h) Six-finger Doublet
0.37 0.38
0.197
–
0.15 2.33
49.467
–
–
0.71
84.09 15.91
Fe2O3(10h) Six-finger Doublet Single line
0.48 0.40
–
0.008 – –
0.087 1.79
–
49.13 – –
– 2.27
–
80.52 19.48
0 Fe2O3(15h) Six-finger Doublet Single line
0.37 0.40
–
0.01 – –
0.27 1.69
–
48.89 – –
– 1.22
–
77.18 22.82
0 Fe2O3(20h) Six-finger Doublet Single line
0.35 0.64
–
0.167 – –
0.038 2.33
–
49.867 – –
– 1.89
–
74.22 25.78
0
)( 5612 ∆−∆a is the energy difference between lines 1 and 2 of the sextet, minus the energy difference between lines 5 and 6 of the sextet (line 1 is at extreme left). All the values of Mössbauer parameters have been calculated using α-Fe as standard. Mössbauer spectra for all the samples (Table 4.2) are fitted by least-square
fitting programme [16] with Lorentzian profiles to determine the line positions, line
width and peak-intensities. The continuous lines represent the computer fitted data,
where as the dot represents the experimental data. The isomer shift (IS), quadrupole
splitting (QS), internal hyperfine field (Hn), obtained from best fitted Mössbauer
spectra lines are presented in Table 4.2. Two typical spectra of bulk or as-supplied α-
Fe2O3 and 5h ball-milled α-Fe2O3 powder samples are shown in the Fig.4.2(a),(b),
respectively. The Mössbauer spectra of different ball-milled α-Fe2O3 samples consist
of a sextet and doublet.
Mössbauer spectrum of the bulk α-Fe2O3 sample, having particle size 35.2 nm
according to Warren-Averbach calculations, shows a six-finger pattern having
IS=0.41 mm/s and Hn=51.82 Tesla, which is in agreement with earlier findings [2].
Kundig and Bommel [2] have obtained only a central doublet with samples having
CHAPTER-4
~ 116 ~
particle size ~18nm or lower. They attributed the doublet to the superparamagnetic
state. In our case,
Mössbauer spectrum consisted of a sextet (predominating in intensity) and a
broad central doublet for particle sizes much smaller than 18nm (Table 4.2).
However, the Mössbauer spectra of the 5h milled sample is best fitted with a sextet, a
doublet and a single line of very weak relative intensity (0.01%). This single line
having an IS=0.64mm/s can be attributed to Fe1-xOx phase. It is interesting that the
relative intensity of the doublet increases as particle size decreases (corresponding to
longer milling time). So the doublet is attributed to the superparamagnetic behaviour
of ferromagnetic fine particles. One still needs an explanation for the additional
presence of the sextet that obviously indicates a ferromagnetic ordering in the
samples. Appearance of this ferromagnetic ordering can be explained either from the
theory of superparamagnetic relaxation or from a presence of larger particles (at
least>18nm) in high proportion. However, XRD analysis does not detect such high
proportion of larger particles. Therefore the only option remaining is to explain the
appearance of sextet from the theory of superparamagnetic relaxation. The
superparamagnetic relaxation time is given by
)/exp(0 kTKVττ = (4.1)
where 0τ depends only slightly on temperature and is of the order of 10-9-10-12, k is
Boltzman constant, T is the temperature, K is the magnetic anisotropic energy
constant, and V is the volume of the particle.
Now the time of relaxation τ at a fixed temperature depends both on the
particles volume V and anisotropy energy constant K. The nature of the Mössbauer
spectrum of magnetic nano-particles depends on the correlation between the time of
observation (τobs) and that of magnetization vector ralaxation (τ). For all the samples
we have obtained complex Mössbauer spectra consisting of a sextet and a doublet,
implying that obsττ ≅ . The time of relaxation τ at a fixed temperature depends both
on particle volume V and anisotropic phase constant K. In our case, particle sizes
smaller than that in the experiments of Kundig and Bommel [2], which should lead to
a predominant superparamagnetic doublet. Predominance of the sextet in our patterns
can be explained through a possible variation of the anisotropy constant K for
deferently ball-milled samples presumably due to internal strain (Table 4.1). It is
CHAPTER-4
~ 117 ~
noted that according to the model of collective magnetic excitations, the hyperfine
magnetic field of small magnetic
Fig.4.2 (a) Mössbauer spectrum of bulk or as supplied α-Fe2O3. And (b) Mössbauer spectrum of 5h ball-milled α-Fe2O3. particles depends on particles size and broadening of the Mössbauer lines can be
explained by a particle size distribution [17,18]. The magnetic splitting in a
Mössbauer spectrum of small magnetic particles is generally smaller than that found
in a microcrystal and if the samples contain a broad size distribution, the magnetic
splitting of the spectra of those particles will be different. Superposition of all these
spectra gives rise to asymmetric and broadened Mössbauer pattern. In the present
experiment, hyperfine field (Hn) obtained for the fine particle is ~49 Tesla, that for
bulk sample H is ~51.8 Tesla, and the lines are asymmetric and broadened. The
reduction in Hn, broadening of lines and asymmetry of line shape suggest not only a
CHAPTER-4
~ 118 ~
broad particle size distribution but also a fluctuation of the magnetization vector in a
direction close to the easy direction leading to the so-called collective magnetic
excitations.
4.5 Conclusions The particle size of α-Fe2O3 reduces to nanometric order within a few hours of
ball milling and becomes almost constant after 5h of milling. From X-ray line profile
analysis, the lattice strain has been estimated which is considerably high for all ball-
milled samples. Mössbauer spectra of all the ball-milled sample consists of a doublet
which is attributed to the superparamagnetic behaviour of ferromagnetic fine particles
and a broad sextet which is presumably due to high internal strain. The decrease in
hyperfine field, broadening of lines and asymmetry of line shape implies a broad
particle size distribution in the ball-milled sample.
4.6 References [1] E. Jartych, J.K. Zurawicz, D. Oleszak, M. Pekala, J. Mag. Mat., 208 (2000)
221.
[2] W. Kundig, H. Bommel. Phys. Rev. B ,142 (1966) 327.
[3] A.S. Edelslein, R.C. Camurata (Eds.), ‘Nanomaterials’, IOP, Bristol, (1994).
[4] M. Zdujic, C. Jovalekic, Lj. Karanovic, M. Mitric, D. Poleti, D. Skala, Mat.
Sci. Engg., A245 (1998) 109.
[5] S.K. Shee, S.K. Pradhan, M. De, J. Alloys and Compounds, 265 (1998) 249.
[6] H. Pal, S.K. Pradhan, M. De, Jpn. J. Appl. Phys., 35 (1996) 1836.
[7] S. Kumar, K. Roy, K. Maity, T.P. Sinha, D. Banerjee, K.C. Das, R.
Bhattacharya, Phys. Stat. Sol. A, 167 (1998) 12.
[8] S. Kumar, K. Roy, K. Maity, T.P. Sinha, D. Banerjee, K.C. Das, R.
Bhattacharya, Phys. Stat. Sol. A, 175 (1999) 927.
[9] E. Jartych, J.K. Zurawicz, D. Oleszak, M. Pekala, Nanostructured Mater., 12,
(1999).
[10] M.A. Polikarpov, I.V. Trushin, S.S. Yakimov, J. Magn. Magn. Mater, 116
(1992) 372.
[11] D.H. Jones, Hyperfine Interactions, 47 (1989) 289.
[12] B.E. Warren, X-ray diffraction, Addision-Wesley, (1969) 264.
CHAPTER-4
~ 119 ~
[13] A. Benedetti, G. Fagherazzi, S. Enzo and M. Battagliarin, J. Appl. Cryst., 21
(1988) 543.
[14] R A. Young, D.B. Wiles, J. Appl. Cryst., 15 (1982) 430.
[15] J.G.M. Van Berkum, Ph.D. Thesis, Delft University of Technology, The
Netherlands, (1994).
[16] E. von Meerwall, Comput, Phys. Commun. 9 (1975) 430.
[17] S. Morup, J.A. Dumesic, H. Topsoe, in: R.L. Cohen (Ed.), Application of
Mossbauer Spectroscopy, Vol. II, Academic Press, New York, (1980) 1.
[18] S. Morup, M.B. Madsen, J. Franck, J. Magn. Magn. Mater, 40 (1983) 163.
CHAPTER-5
Annealing effect on nano-ZnO powder studied from positron lifetime and optical absorption spectroscopy
CHAPTER-5
~ 121 ~
5.1 Introduction Nanocrystalline materials, semiconductors in particular, are being widely
investigated at present because of their interesting electronic and optical properties
which may find applications in devices such as solar cells, light emitting diodes,
ultraviolet (UV) lasers, fluorescent displays etc.[1-4]. Surface phenomena dominate
nanomaterial properties over their respective bulk features due to high surface to
volume ratio. Grain surfaces are defect rich and engineering on these defects offer a
scope to tune the useful material properties [5]. Here, we employ mechanical milling
or ball milling technique to reduce the grain size of powder ZnO material. This
technique is advantageous for large scale and cost effective production of
nanocrystalline materials without any effect of chemical contamination [6].
Recently, room temperature UV lasing has been reported in ZnO samples
with grain size few tens of a nanometer[7,8]. It has also been found that
incorporation of low density defects in ZnO lattice sometimes helps to obtain
improved crystalline quality through proper choice of annealing environment and
temperature [9]. In this way, the extent of disorderness and so also the characteristic
emission from the material can effectively be controlled. A better understanding on
the generation and recovery of defects in ZnO, particularly defects at grain surfaces,
has thus of immense potential to reach optimized annealing conditions. Suitable
defect characterization technique like positron annihilation lifetime spectroscopy has
been proved to be helpful [3,10-13] in this regard. Usually, positrons injected inside
a solid from a radioactive source (here 22Na) get thermalized and annihilate with an
electron. It is well known that positrons preferentially populate in the regions where
electron density, compared to the bulk of the material, is lower (e. g., vacancy type
defects, vacancy clusters, micro-voids). For materials with nanometer scale grain
size, positrons diffuse [14,15] to the surface region of the grains, which are rich in
open volume defects. Hence the electron-positron annihilated γ-rays bear the
lifetime of positrons, which provides information regarding the nature and
abundance of defects at the grain surface[3,13,15,16]. Simultaneous investigation of
UV-VIS (ultraviolate-visible) photon absorption by the sample elucidate, as detailed
later, the defect dependent optical processes in such technologically important
semiconductors.
CHAPTER-5
~ 122 ~
5.2 Experiment and data analysis
As supplied polycrystalline ZnO powder (purity 99.9 % from Sigma-Aldrich,
Germany) samples have been ball-milled (ball : mass = 35:1) by a Fritsch Pulverisette
5 planetary ball-mill grinder for 3 hours and then annealed at ten different
temperatures (between 210-1200 °C) for 4 hours followed by slow cooling (30 °C/h)
in air. Henceforth, the milled but unannealed sample will be termed as nano-ZnO. X-
ray diffraction (XRD) of all the samples have been recorded in a Philips PW 1710
automatic diffractometer with CuKα radiation. The average grain size of the powdered
samples has been determined by Scherer’s formula [17]:
Dhkl = Kλ/β cosθ (5.1)
where Dhkl is the average grain size, K the shape factor (taken as 0.9), λ is the x-ray
wavelength, β is the line width at half maximum intensity (here 101 peak of the ZnO
spectrum fitted with a gaussian) and θ is the Bragg angle. Standard method [17] to
deduct the contribution of instrumental broadening in β has been taken into account.
Different sets of samples have been pressed into pellets (~1 mm thickness
and 10 mm diameter) for positron annihilation lifetime (PAL) study. A 10-µCi 22Na
positron source (enclosed in thin mylar foils) has been sandwiched between two
identical plane- faced pellets. The PAL spectra have been measured with a fast-slow
coincidence assembly [18] having 182±1 ps [12] time resolution. Measured spectra
have been analyzed by computer program PATFIT-88 [19] with necessary source
corrections to evaluate the possible lifetime components τi, and their corresponding
intensities Ii. The two state trapping model [20] predicts a two-component fitting of
the spectrum, the shorter one (τ1) from free annihilation of positrons and the other
(τ2) from trapped positrons at defects. One can also construct, without assuming any
model, the average positron lifetime (τav = (τ1I1+τ2I2)/(I1+I2)), which represents the
defective state of the sample as a whole [19,21]. It is to be noted that τav is free from
errors, if any, arising from particular fitting procedure.
The electronic absorption spectra of the ZnO samples have been recorded on
a Hitachi U-3501 spectrophotometer in the wavelength range of 300–1100 nm. The
spectral absorption coefficient α(λ) has been evaluated [3,22] from the spectral
extinction coefficient, k(λ), using the following expression:
α(λ) = 4πk(λ)/λ (5.2)
CHAPTER-5
~ 123 ~
where λ is the wavelength of the absorbed photon.
5.3 Results and discussion The XRD spectra of the ZnO samples, ball milled and subsequently annealed
at 600° C and 1200° C, have been shown in Fig.5.1.
Fig.5.1 X-ray diffraction patterns for the nano-ZnO and annealed ZnO samples. Insets show the corresponding full width at half maximum FWHM) for (002) peak.
Mechanical milling reduces the average grain size from 76±1 nm (as-supplied
ZnO) to 22±0.5 nm (nano-ZnO). Annealing at elevated temperatures induce an
agglomeration of grains in the sample however, appreciable grain growth occurs only
above 425 °C (Fig.5.2). It is interesting to note that the average grain size of the
samples annealed higher than 776±8 °C (as estimated from Fig.5.2) becomes larger
than that of the as supplied or non-milled material. Chen et al.[9] have reported
similar
CHAPTER-5
~ 124 ~
Fig.5.2 Variation of grain size with annealing temperature. The annealing temperature of nano-ZnO sample has been taken as 30 °C (room temperature). The solid line is a guide to the eyes, and the dotted line is the reference line indicating the grain size for the nonmilled (as-supplied) sample.
observation in single crystalline ZnO where initial amorphization by energetic Al+
irradiation and subsequent heat treatment dramatically improve the crystalline quality
and so also the band edge emission. Increase of average grain size, in our case,
continues up to 1100 °C annealing temperature and reaches to 139±2 nm. Reduction
of the grain size for ~ 15 nm in 1200 °C annealed sample is, probably, due to
thermally generated defects at both Zn and O sites [23].
PAL analysis reveals a three-component lifetime fit, the third (τ3) and the
longest (~ 1400 ps with intensity 3-4 %) being due to the positron annihilation from
positronium [21] like atoms. Formation of positroniums generally occurs in the form
of ortho-positronium inside large voids in the material. Ortho-positroniums
subsequently decay as para-positronium by pick-off annihilation giving rise to such
a long lifetime ~ 1200 – 3000 ps. In polycrystalline samples there always exist void
spaces where positronium formation is favourable [12]. To note, positronium
formation in the material is a separate physical process not related to positron
trapping at defects. τ1 is generally attributed to the free annihilation of positrons
[21,24]. However in disordered systems, smaller vacancies [9,16] (like
monovacancies etc.) or shallow positron traps (like oxygen vacancies [25] in ZnO)
may be mixed with τ1. In the present investigation, τ1 from different ZnO samples
show considerable variation with annealing temperature (Table 5.1). τ1, here, is
indeed a weighted average of free and trapped positrons. But these sites are not
CHAPTER-5
~ 125 ~
major positron traps and their correlation with the material properties is not yet
conclusive. The most important lifetime component is the second one (τ2), which
indicates qualitatively the nature and size of the vacancy [20] and its relative
intensity (I2) quantifies the abundance of that vacancy with respect to some standard
of the same material. Here, τ2 increases from 326±3 ps to 343±3 ps due to
mechanical milling (Fig.5.3(a)).
Table 5.1. Table showing the c-axis lattice parameter (from XRD), band tailing parameter, E0 (from optical absorption) and part of the PAL parameters for the ZnO samples. For comparison the corresponding values of the as-supplied (nonmilled) material has been shown. The annealing temperature of nano-ZnO sample has been taken to be room temperature (RT) ~ 30 oC.
Sample Annealing
temperature (oC)
c-axis
(Å)
E0
(meV)
τ1
(ps)
I1
(%)
I2
(%) as-supplied
ZnO RT 5.160 92 147±2 38.0±0.5 58.0±0.5
nano- ZnO RT 5.242 316 173±2 32.3±0.2 64.5±0.2 210 5.172 320 181±2 29.8±0.2 66.4±0.3 250 5.168 300 214±2 47.0±0.2 49.4±0.2 300 5.166 255 201±2 41.3±0.2 55.0±0.2 350 5.182 201 184±2 36.4±0.2 60.2±0.3 425 5.197 226 186±2 40.9±0.2 55.2±0.2 600 5.177 214 159±2 31.6±0.2 64.1±0.3 800 5.258 258 163±2 50.4±0.2 46.0±0.2 900 5.264 386 151±2 57.9±0.3 38.3±0.2 1100 5.272 523 151±2 59.7±0.3 35.8±0.2 1200 5.279 676 153±2 61.5±0.3 34.2±0.2
CHAPTER-5
~ 126 ~
Fig.5.3 Variation of (a) τ2 (positron lifetime at defects) and (b) τav (average positron lifetime) with annealing temperature. The dotted lines are the reference lines corresponding to the error bars of the average positron lifetime and positron lifetime at defects (indicated by solid line) for nonmilled ZnO sample. The annealing temperature of nano-ZnO sample has been taken as 30 °C (room temperature). The inset of lower panel shows the variation of I2 with grain size. The same parameters of the nonmilled ZnO are representedby the dashed lines in the inset.
Enhanced vacancy clustering near the grain surfaces as a result of milling can
be understood. While annealing the nano-ZnO material an increase of τ2 with initial
annealing up to ~ 300 °C has been found. This is similar to what we have observed for
as-supplied ZnO [12]. Probably, the supply of small thermal energy helps intra-grain
zinc vacancies to migrate towards the grain surfaces, which are universal sink of
defects. In this way, small size Zn vacancies (monovacancies etc.) assemble near the
grain surfaces and τ1 grows accordingly (Table 5.1). Part of such vacancies
agglomerate to form larger size vacancy clusters causing and increase of τ2 also. Such
process can be understood as an intrinsic feature of granular ZnO systems that causes
the increase of positron lifetime up to some annealing temperature ~ 300 °C. The
variation of average lifetime (τav) with annealing temperature is more or less similar
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with that of τ2 (Fig.5.3(b)). τav starts to decrease above annealing temperature of 425
°C, interestingly, which is very close to the temperature from where XRD spectrum
shows a substantial grain growth. One should note here that positrons have a specific
affinity towards cationic defect sites, which are generally negatively charged in these
II-VI semiconductors [10,24]. So, the reduction of τ2 as well as τav above 425 °C
annealing represents a lowering of Zn vacancy defects at the grain boundaries and
consequently grain growth occurs. Mobility of interstitial Zn defects above 425 °C
may be the reason of Zn vacancy annihilation [26]. It can be estimated from figure
5.3(b) that above 700±50 °C annealing temperature the annealed sample becomes less
defective compared to the non-milled one. Similar conclusion has been reached while
discussing the grain size variation of the annealed samples and the related temperature
zone is also close to that have been estimated from the variation of grain size (776±8
°C). In view of the qualitative probing by two different techniques such consistency is
remarkable. Alternatively, our results altogether confirm the clustering of cationic
vacancies at grain boundaries in ZnO nanocrystals. At the same time, it can also be
concluded that majority of such cation vacancies, incorporated artificially either by
particle irradiation [9,26] or by mechanical milling (present case), in ZnO gets
recovered in between 700-800 oC. Compared to 1100 °C annealed sample, the defect
lifetime (τ2) has been found to be increased for 1200 °C annealed sample. Chen et
al.[27] have also found an increase of positron lifetime above 1000 °C in single
crystal ZnO. Such increase of positron lifetime is due to the enhancement of cationic
vacancy sites. A reflection of the large number of thermal vacancy generation, anionic
as well as cationic, is also evident from the lower grain size of the 1200 °C annealed
sample with respect to the 1100 °C annealed one (Fig.5.2). Here we should briefly
mention the variation of I2 (i.e., the relative intensity of τ2) due to annealing. I2 is
related (but not proportional) to the abundance of defects in the material that gives
rise to a positron lifetime of τ2. It has been mentioned earlier that in materials with
few tens of nanometer grain size, most of the defects reside near the grain surfaces
where positrons annihilate. With annealing induced grain growth the ratio of surface
to bulk region decreases in the material. Hence, in our nano-ZnO system also, we
should expect a correlation [15] between I2 and the grain size and that has been
plotted in the inset of Fig.5.3 (a). A general trend of lowering I2 with increasing grain
size can be identified although below 38 nm, there exists some subtle features which
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are not understood at this stage. Below certain grain size, other type of defects such as
dislocations, microstrain etc., which are very much likely in such mechanically milled
nano-systems, may partly contribute to I2.
The photon energy dependence of the optical absorption coefficients of the
milled and annealed samples has been shown in Fig.5.4.
Fig.5.4 (Color online) Absorption coefficients near the UV edge as a function of photon energy for the ZnO samples annealed at different temperatures. The optical band gap (Eg) of the samples have been estimated from the well
known expression [28] for direct transition
αE = A(E - Eg)1/2 (5.3)
where E(=hc/λ) is the photon energy and A is a constant. Standard extrapolation of
absorption onset [28] to αE = 0 (where E = Eg) has been figured for selected samples
(Fig.5.5) along with the modification of band gap due to annealing (inset of Fig.5.5).
The nano-ZnO has a lower optical band gap (3.11 eV) compared to the nonmilled or
as-supplied one (3.22 eV), which is probably due to its more granular nature [29].
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Fig. 5.5 (Color online) Plots of (αhν)2 vs photon energy for (a) as-supplied ZnO sample, (b) nano-ZnO sample, (c) sample annealed at 600 °C, and (d) sample annealed at 1200 °C. The inset shows the variation of band gap withannealing temperature.
Annealing above 900 °C temperature induces a red-shift in the band gap,
which is consistent with earlier reports [24,30,31]. Possible reason may be the
increase of oxygen vacancy related disorder for annealing at high temperature.
Enhanced oxygen vacancy in ZnO lattice is also evident from the expansion [12,32]
of c-axis lattice parameter above 800 °C annealing as shown in Table 5.1.
Fig.5.6 (Color online) Plots of ln(α) vs photon energy for (a) as supplied nonmilled ZnO sample, (b) nano-ZnO sample, (c) sample annealed at 350 °C, and (d) sample annealed at 1200 °C to show the linear variation of the respective curves. The inset shows the same curves in a broader region.
CHAPTER-5
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We further plotted for all the samples ln (α) vs. E graph (Fig.5.6) just below
the band edge (E < Eg) to understand the band tailing effect due to
enhancement/reduction of defects with annealing. According to the theory [28], α(E)
should follow
α(E) = α0 exp(E/E0) (5.4)
with α0 is a constant and E0 is an empirical parameter. E0 has been estimated from
reciprocal of the slope by fitting the linear part of the respective ln(α) vs. E curves.
Any defect or disorder in the lattice gives rise to localized states within the band gap
(band tailing) and E0 describes the width of such localized states [29]. Enhancement
of E0 indicates the increase of disorder in the system. It has been found that the 350
°C annealed sample shows a lowest E0 value (Table 5.1). Interestingly, we have also
observed a reduced E0 due to annealing of as supplied ZnO near the same temperature
zone [33]. However, the degree of disorderness as reflected from the value of E0 is
higher for nano-ZnO along with its annealed counterparts than the as-supplied
material. E0 starts increasing steeply with the increase of annealing temperature from
and 800 oC. In contrast, the PAL investigation reveals (discussed earlier) a
considerable lowering of defects due to annealing above 700±50 oC. This is due to the
fact that relative trapping probability of positrons at an oxygen vacancy is much
weaker compared to that of a zinc vacancy. Within 700-800 oC most of the zinc
vacancies are recovered but at this stage thermally generated oxygen vacancies
become dominant defects in ZnO lattice. Oxygen vacancy and its related disorder
create localized defect states within the band gap resulting an increase of the band
tailing parameter E0 and a red shift of the band gap.
5.4 Conclusions
We have studied the effect of mechanical milling and subsequent annealing in
air at temperatures between 210-1200 °C on high purity ZnO by XRD, PAL and
optical absorption spectroscopy. The grain size has been reduced to 22±0.5 nm (nano-
ZnO) from the 76±1 nm (as-supplied ZnO) due to milling. The XRD analysis reveals
a substantial grain growth in nano-ZnO above 425 °C temperature. Distinct decrease
of the average lifetime of positrons also starts from the same temperature. This
indicates a lowering of defect concentration, mostly cationic, due to annealing above
425 °C. Such a reduction of defects continues up to 1100 °C annealing and little
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above 700 °C the sample becomes less defective, even better than the as supplied
ZnO. However, the band tailing parameter (E0), which has contributions from all
possible disorder, does not reflect a lowering of defects for high temperature
annealing (>700 °C). Enhanced oxygen vacancy concentration is responsible for such
an increase of E0. These oxygen vacancies are less sensitive to positron spectroscopic
measurements. Only increase or decrease of the zinc vacancies is reflected in the PAL
results. The annealing induced grain growth occurs due to the recovery of such zinc
vacancies the majority of which reside near the grain surfaces. PAL results, thus, bear
a qualitatively similarity with the findings from XRD analysis. Oxygen vacancy
related disorder (>800 °C) mainly contributes to the modification of UV-VIS
absorption spectrum and thus positron lifetime and optical absorption spectroscopy
provide different scenario regarding the defective state of the material.
5.5 References [1] Shalish, H. Temkin, and V. Narayanamurti, Phys. Rev. B, 69 (2004) 245401.
[2] X.T. Zhou, P.S.G. Kim, T.K. Sham, and S.T. Lee, J. Appl. Phys., 98 (2005)
024312.
[3] M. Chakraborty, S. Dutta, S. Chattopadhyay, A. Sarkar, D. Sanyal, and A.
Chakrabortyi, Nanotechnology, 15 (2004) 1792.
[4] M. Bredol, and H. Althues, Solid State Phenom., 99-100 (2004) 19.
[5] Y.S. Wang, P.J. Thomas, and P. O’Brien, J. Phys. Chem. B, 110 (2006) 4099.
[6] A. Urbieta, P. Fernández, and J. Piqueras, J. Appl. Phys., 96 (2004) 2210.
[7] G. Tobin, E. McGlynn, M.O. Henry, J.P. Mosnier, J.G. Lunney, D.
O’Mahony, and E. dePosada, Physica B, 340-342 (2003) 245.
[8] U. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V.
Avrutin, S.-J. Cho, and H. Morkoç, J. Appl. Phys., 98 (2005) 041301.
[9] Z.Q. Chen, M. Maekawa, S. Yamamoto, A. Kawasuso, X.L. Yuan, T.
Sekiguchi, R. Suzuki, and T. Ohdaira, Phys. Rev. B, 69 (2004) 035210.
[10] R. Krause-Rehberg, and H. S. Leipner, Positron Annihilation in
Semiconductors, (Springer, Berlin, 1999), Chap. 3, pp. 61.
[11] F. Tuomisto, V. Ranki, K. Saarinen, and D.C. Look, Phys. Rev. Lett., 91
(2003) 205502.
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~ 132 ~
[12] S. Dutta, M. Chakrabarti, S. Chattopadhyay, D. Sanyal, A. Sarkar, and D.
Jana, J. Appl. Phys., 98 (2005) 053513.
[13] M. Chakraborti, D. Bhowmick, A. Sarkar, S. Chattopadhayay, and S.
DeChoudhuri, D. Sanyal, A. Chakraborti, J. Mater. Sci., 40 (2005) 5265.
[14] A. Dupasquier, and A. Somoza, Mater. Sci. Forum, 175-178 (1995) 35.
[15] V. Thakur, and S.B. Shrivastava, M.K. Rathore, Nanotechnology, 15 (2004)
467.
[16] P.M.G. Nambissan, C. Upadhyay, and H.C. Verma, J. Appl. Phys., 93 (2003)
6320.
[17] B.D. Cullity, Elements of X-ray Diffraction (Addison-Wesley Publishing
Company, Inc., Philippines, 1978), Chap. 9, 284.
[18] A. Banerjee, A. Sarkar, D. Sanyal, P. Chatterjee, D. Banerjee, and B.K.
Chaudhuri, Solid State Commun., 125 (2003) 65.
[19] P. Kirkegaard, N. J. Pedersen, and M. Eldrup, Report of Riso National Lab
(Riso-M-2740), 1989.
[20] P. Hautojarvi, and C. Corbel, Positron Spectroscopy in Solids, edited A.
Dupasquier, A.P. Millis Jr. (IOS Press, Ohmsha, Amsterdam, 1995), 491.
[21] D. Sanyal, D. Banerjee, and U. De, Phys. Rev. B, 58 (1998) 15226.
[22] A.A. Dakhel, and F.Z. Henari, Cryst. Res. Technol., 38 (2003) 979.
[23] Z.Z. Zhi, Y.C. Liu, B.S. Li, X.T. Zhang, D.Z. Shen, and X.W. Fan, J. Phys. D:
Appl. Phys., 36 (2003) 719.
[24] R.M. de la Cruz, R. Pareja, R. Gonzalez, L.A. Boatner, and Y. Chen, Phys.
Rev. B, 45 (1992) 6581.
[25] F. Tuomisto, K. Saarinen, D.C. Look, and G.C. Farlow, Phys. Rev. B, 72
(2005) 085206.
[26] Z.Q. Chen, M. Maekawa, A. Kawasuso, S. Sakai, and H. Naramoto, Physica
B, 376-377 (2006) 722.
[27] Z.Q. Chen, S. Yamamoto, M. Maekawa, A. Kawasuso, X.L. Yuan, and T.
Sekiguchi, J. Appl. Phys., 94 (2003) 4807.
[28] J. Pancove, Optical Processes in Semiconductors (Prentice-Hall, Englewood
Cliffs, New Jersey, 1979).
[29] V. Srikant, and D.R. Clarke, J. Appl. Phys., 81 (1997) 6357.
CHAPTER-5
~ 133 ~
[30] N.R. Aghamalyan, I.A. Gambaryan, E.Kh. Goulanian, R.K. Hovsepyan, R.B.
Kostanyan, S.I. Petrosyan, E.S. Vardanyan, and A.F. Aerrouk, Semicond. Sci.
Technol., 18 (2003) 525.
[31] R. Hong, J. Huang, H. He, Z. Fan, and J. Shao, Appl. Surf. Sci., 242 (2005)
346.
[32] H. Kim, A. Piqué, J.S. Horwitz, H. Murata, Z.H. Kafafi, C.M. Gilmore and
D.B. Chrisey, Thin Solid Films, 377-378 (2000) 798.
[33] S. Dutta, S. Chattopadhyay, A. Sarkar, M. Sutradhar, and D. Jana, (to be
submitted).
CHAPTER-6
Particle size dependence of optical and defect parameters in mechanically milled Fe2O3
CHAPTER-6
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6.1 Introduction Presently, oxides in its nanocrystalline phase become very important due to
their wide applications. The large surface-to- volume ratio of these nanomaterials
makes them different from the bulk of the material [1]. Among them,magnetic
nanomaterials have received special attention as they can be used in different fields
like magnetic resonance imaging, drug delivery agents, etc. [2]. Further, the
observation of peculiar characteristics like superparamagnetism [3] in the nanoparticle
phase of such materials makes these materials objects of great interest for
fundamental studies. Among different magnetic nanoparticles, α-Fe2O3 has large
applications in chemical industry [4]. It can be used as catalyst, gas sensing material
to detect combustible gases [5] like CH4 and C3H8 etc. α-Fe2O3, generally a
rhombohedrally centered hexagonal structure [6], is the most stable polymorph in
nature under ambient condition and can be easily found in mineral hematite.
Nanocrystalline oxides can be prepared by different methods, e.g., sol–gel [7],
hydrothermal [8], chemical vapor phase deposition [9], calcinations of hydroxides
[10], radio frequency sputtering [11], gas condensation technique [12], high-energy
ball-milling process [13, 14], etc. Among these the high-energy ball-milling process
has many potential advantages. The main advantage is large quantities of samples can
be produced in a very short time, and the process is relatively simple and inexpensive.
In the present work, ball-milling process has been adapted to prepare nanocrystalline
Fe2O3 samples. The optical and defect properties of the prepared nanocrystalline
samples have been studied by employing UV spectroscopy and coincidence Doppler
broadening of the electron positron annihilation γ-radiation (CDBEPAR)
spectroscopy, respectively. Employing the UV absorption spectroscopic method [15]
the changes in the band gap for direct transitions for all the samples (milled and
unmilled Fe2O3) have been measured. The defect parameter in the band gap has also
been estimated from the optical absorption data. During the preparation of
nanocrystalline oxides by the ball-milling process, large numbers of defects are
introduced in the material [14–16]. In the nanocrystalline phase the surface-to-volume
ratio is very high, hence the surface defects play important role in determining the
optical, magnetic, and electronic properties of the material. Thus it is very important
to study these defects. Presently, CDBEPAR spectroscopic technique, a powerful
technique to study the defects in a material [17, 18], has been employed to study the
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defects in the different hour ball milled as well as the unmilled samples. In the
CDBEPAR spectroscopic technique, positron from the radioactive (22Na) source is
thermalized inside the material under study and annihilate with an electron emitting
two oppositely directed 511 keV γ -rays. Depending upon the momentum of the
electron (p) these 511 keV γ-rays are Doppler shifted by an amount ±∆E in the
laboratory frame, where ∆E = pLc/2; pL being the component of the electron
momentum p toward the detector direction. By using two identical high-resolution
HPGe detectors one can measure the Doppler shifts of these 511 keV γ -rays [18]. The
wing part of the 511 keV photo peak carries the information about the annihilation of
positrons with the higher momentum electrons, e.g., core electrons of different atoms.
Thus by measuring the Doppler broadening of the 511 keV γ -ray and proper analysis
of the CDBEPAR spectrum [14] one can identify the electrons with which positrons
are annihilating.
6.2 Experimental outline α-Fe2O3 of purity 99.998% (Alfa Aesar, Johnson Matthey, Germany) has been
milled in a Fritsch Pulverisette 5 planetary ball mill grinder with agate balls for
different hours to achieve lower particle size. The ball-to-powder mass ratio has been
fixed to 12:1. The powder X-ray diffraction (XRD) data has been collected in a
Philips PW 1710 automatic diffractometer with CuKα radiation. In each case scanning
has been performed in between the 2θ range 20–90˚ in a step size of 0.02˚. The
average particle size of the sample has been calculated from Williamson–Hall plot
[19]
(6.1)
where D is the average particle size, β is the full width at half maximum (FWHM), K
is a constant (= 0.89), λ is the wavelength; θ is the Bragg angle, and ε is the strain
introduced inside the sample. The XRD patterns (Fig.6.1) for differently milled and
unmilled samples show α-Fe2O3 lines only, implying that none of the other oxide
phases have been developed during ball milling. Transmission electron microscopy
(TEM) with TECNAI S-TWIN (FEI Company) electron microscope operating at 200
kV has been used to estimate the average particle size of the different hour ball-milled
Fe2O3 samples. Powder ultrasonically dispersed in alcohol was put on a standard
microscope grid for the TEM work.
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Fig.6.1 X-ray diffraction pattern for the unmilled and milled samples
For the CDBEPAR measurement, two identical HPGe detectors (Efficiency:
12%; Type: PGC 1216sp of DSG, Germany) having energy resolution of 1.1 keV at
514 keV of 85Sr have been used as two 511 keV γ-ray detectors, while the CDBEPAR
spectra have been recorded in a dual ADC-based multiparameter data acquisition
system (MPA- 3 of FAST ComTec., Germany). A 10 µCi 22Na positron source
(enclosed in between thin Mylar foils) has been sandwiched between two identical
and plane faced pellets [20]. The peak-to-background ratio of this CDBEPAR
measurement system, with ± ∆E selection, is ~105:1 [21, 22]. The CDBEPAR
spectrum has been analyzed by evaluating the so-called lineshape parameters [17, 21]
(S parameter). The S parameter is calculated as the ratio of the counts in the central
area of the 511 keV photo peak (|511 keV − Eγ | ≤ 0.85 keV) keV_and the total area of
the photo peak (|511 keV − Eγ | ≤ 4.25 keV) The S parameter represents the fraction of
positron annihilating with the lower momentum electrons with respect to the total
electrons annihilated. The statistical error is ~0.2% on the measured lineshape
parameters. The coincidence DBEPAR spectra for the unmilled and the milled
samples have been also analyzed by constructing the ‘‘ratio-curves’’ [18, 21, 22] with
respect to defects-free 99.9999% pure Al single crystal (reference sample). The
electronic absorption spectra [23] of the Fe2O3 nanoparticles have been recorded on
HitachiU-3501 spectrophotometer in the wavelength range of 200–1,500 nm.
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6.3 Results and discussion
Figure 6.1 represents the XRD pattern for the unmilled, 1, 6, 10, and 20 h
milled samples. Particle size as calculated from the Williamson–Hall plot for the
unmilled sample is 120 nm. Figure 6.2 shows the Williamson–Hall plot for 2 h milled
sample. Particle size and the strain introduced inside the samples due to ball milling
have been calculated from the intercepts and slope of the straight line fitted curve as
shown in Fig. 6.2. Table 6.1 represents the particle sizes and strain values for the
unmilled and the milled samples (calculated from the Williamson–Hall plot). From
Table 6.1 it is clear that the strain increases with increasing milling hour. Increase of
strain with the milling hour suggests the formation of defects in the milled sample.
Figure 6.3 shows the variation of particle size with milling hour. From Fig. 6.3 it is
clear that with the ball-milling process the particle size cannot be lowered
continuously, rather it becomes saturated after some specific milling hour. Figure
6.4(a)–(c) represents the TEM micrographs for the unmilled, 10 and 20 h milled
samples, respectively. From the TEM pictures the measured particle sizes are 206, 14,
and 10 nm for unmilled, 10 h milled, and 30 h milled
Fig.6.2 Willamson–Hall plot for 1 h milled sample
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Table 6.1 Value of strain for the unmilled and different hour ball milled samples
Fig.6.3 Variation of particle size (estimaetd from Scherrer formula and Williamson–Hall plot) with milling hour samples, respectively. The lattice parameters ‘‘a’’ and ‘‘c’’ for the unmilled and
milled samples have been calculated from different diffraction lines of the XRD
pattern (Fig.6.1). Figure 6.5 shows the variation of the lattice parameters ‘‘a’’ and
‘‘c’’ with milling hour. From Fig. 6.5 it is observed that both the lattice parameters
(‘‘a’’ and ‘‘c’’) decrease with increasing milling hour. This clearly indicates that with
milling, large number of defects have been introduced inside the milled samples. To
observe the effect of milling in the band gap, the optical absorption spectroscopic
technique has been used. The spectral absorption coefficient, α, is defined as [24]
(6.2)
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where k(λ) is the spectral extinction coefficient obtained from the absorption curve
and λ is the wavelength. Figure 6.6 represents the absorbance curve for unmilled, 8 h
milled, and 20 h milled samples. The inset of Fig. 6.6 shows the absorbance curve in
some specific wavelength region. From Fig. 6.6 it has been observed that in case of
ball-milled (8 and 20 h) samples the absorption maxima occur at 303 and 306 nm,
whereas for the unmilled sample the absorption maximum is at 304 nm. Thus the
position of the absorption maxima remains almost the same for the unmilled and the 8
h milled samples, whereas for the 20 h milled sample it is on the longer wavelength
side (306 nm). The band gap, Eg (for a direct transition between the valence and
conduction band), is obtained by fitting the experimental absorption data with the
following equation
αhν ~ A(hν - Eg)1/2 (6.3)
for a direct transition, [25] where hν is the photon energy, a is the absorption
coefficient Eg is the band gap, and A is a characteristic parameter independent of
photon energy.
Fig.6.4 TEM micrographs for (a) unmilled (b) 10 h milled and (c) 30 h milled Fe2O3 samples, respectively
CHAPTER-6
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Fig.6.5 Variation of lattice parameters (‘‘a’’ and ‘‘c’’) with milling Hour
Fig.6.6 Absorbance curve for unmilled, 8 h, and 20 h milled samples
Figure 6.7(a), (b) represent the absorption curves of different ball-milled
Fe2O3 powder for direct transition. The value of band gap Eg (for direct transition) has
been obtained from the intercept of the extrapolated linear part of the (αhν)2 versus hν
curve with the energy (hν) axis. The band gap for direct transition (estimated from
Fig. 7a, b) for the unmilled sample is 2.62 eV at the wavelength 473 nm, whereas for
1, 4, 6, 8, 10, and 20 h milled samples it is 2.59, 2.56, 2.54, 2.52, 2.49, and 2.49 eV at
479, 485, 489, 493, 497, and 498 nm, respectively. The variation of the band gap (for
direct transition) with the inverse of particle size (D) follows a linear fit with a
negative slope (Fig.6.8). The decrease of band gap with decreasing particle size may
be due to the enhanced band bending effect [26, 27] at the particle boundaries or may
be due to the defects introduced in the milled samples.
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Fig.6.7 (a) Absorption spectra for unmilled and 4 h milled samples for direct transition. (b) Absorption spectra for 8 and 20 h milled samples for direct transition
In the energy region hν < Eg, i.e. near the band edge, the absorption coefficient follow
the relation [23]
α = α0exp(hν / E0) (6.4)
where α0 is a constant and E0 is an empirical parameter which represents the width of
the band tail states. E0 may be considered as the defect parameter in the band gap
energy value [26]. E0 can be obtained from the slope of the linear part of ln(α) versus
E curve in the E<Eg region. Figure 6.9 shows the ln(α) versus E curve for the
unmilled, 8 h, and 20 h milled samples. The values of E0 as calculated from the
intercept of the extrapolated linear part of the ln(α) versus hν curve with the energy
(hν) axis are plotted in Fig.6.10 with inverse of the particle size (D). It is clear from
Fig.6.10 that with lowering the particle size (by increasing milling hour) the defect
parameter E0 increases linearly. This confirms that lowering the particle size by
increasing milling hour, a large number of defects have been introduced inside the
samples
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Fig.6.8 Variation of band gap (Eg) with the inverse of particle size (1/D)
Fig.6.9 Plots of ln(α) versus photon energy (E) for unmilled, 8 h, and 20 h milled
samples
Fig.6.10 Variation of E0 with the inverse of particle size (1/D)
.
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To identify the defects, CDBEPAR measurement technique has been employed. In
case of nanocrystalline materials, the positron diffusion length plays an important
role, as after entering a material the positron becomes thermalized and diffuses inside
the material. The typical positron diffusion length is ~100 nm [28], which is larger
than the average particle size of the milled samples. Therefore, compared to the
unmilled sample (particle size ~120 nm), positrons annihilate more at the grain
surfaces in the milled samples. Figure 6.11 represents the variation of S parameter
with milling hour, where S parameter increases with milling hour. In general, the
increase of the S parameter suggests either the positrons are less annihilating with the
core electrons or an increase of the number of lower momentum electrons at the
positron annihilation site [17, 20–22]. Thus from the variation of S parameter with
milling hour it can be concluded that either positrons are less annihilating with the
core electrons of Fe and O or more annihilating with the lower momentum electrons.
To identify the nature of defects in the milled samples, the CDBEPAR spectra for the
unmilled and ball milled Fe2O3 have been analyzed by constructing the ratio curve
[20, 29] with the CDBEPAR spectrum of the defect-free 99.9999% pure Al single
crystal (Fig.6.12). From Fig.6.12 it is clear that there is a peak at ~10 x 10-3 m0c and a
flat region at ~20 x 10-3 m0c for unmilled, 1 h, and 20 h milled samples. Using the
relation E = p2/4m0 the kinetic energies of the electrons corresponding to momentum
pL ~ 10 x 10-3 m0c and 20 x 10-3 m0c comes out to be ~ 13 and 51 eV, respectively.
The annihilation of positrons
Fig.6.11 Variation of S parameter with milling hour
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Fig.6.12 Ratio of the experimental electron positron momentum distributions for unmilled, 1, 20, and 30 h milled Fe2O3 samples to the electron positron momentum distributions for the defect-free 99.9999% pure Al single crystal
with 2p core electrons of oxygen and 3d core electrons of Fe are mainly contributing
to the peak at 10x10-3 m0c, while the annihilation of positrons with the 3p core
electrons of Fe contribute to the flat region (pL ~ 20 x 10-3 m0c).
Fig.6.13 Ratio of the experimental electron positron momentum distributions for 1 and 20 h milled Fe2O3 samples to the electron positron momentum distributions for the unmilled Fe2O3 samples
Figure 6.13 represents the ratio curve for the ball-milled Fe2O3 with respect to
unmilled Fe2O3. A broad dip from the momentum range ~ 7 x 10-3 m0c to ~ 22 x 10-3
m0c is prominent (Fig.6.13) in the 20 h milled sample. Thus from Figs. 12 and 13 it
can be concluded that positrons annihilation with the core electrons (both 3d and 3p)
of Fe decreases with increasing milling hour. This indicates the formation of cation
CHAPTER-6
~ 146 ~
type of defects (Fe vacancy) at the grain surface of the milled Fe2O3 system, which is
in agreement with the earlier observation of formation of cation type of defects in
different oxide samples due to the ball-milling process [14, 15].
6.4 Conclusions
Nanocrystalline Fe2O3 samples have been prepared by the ball-milling
process. Particle sizes of the milled and the unmilled samples have been estimated
from XRD pattern and TEM micrographs. The strain introduced inside the sample
increases with ball milling hour. Ratio curve analysis of the CDBEPAR spectra for
the different hour milled and unmilled samples indicates the formation of cation type
of defects at the grain surfaces due to the ballmilling process. Direct optical band gap
decreases with decreasing particle size but the defect parameter (as calculated from
the band tail near the absorption edge of the absorption spectra) increases linearly
with milling hour (or decreasing particle size). Finally, it has been concluded that due
to ball milling the average particle size of the Fe2O3 decreases, but due to the
formation of cation type of defects the optical band gap decreases.
6.5 References
[1] Henglin, Chem Rev., 89 (1989) 1861.
[2] K.A. Hinds et al, Blood, 102 (2003) 867; S.R. Rudge, T.L. Kurtz, C.R
Vessely, L.G. Catterall, D.L. Williamson, Biomaterials, 21 (2000) 1411.
[3] D.H. Jones, Hyperfine Interact, 47 (1989) 289.
[4] N. Mimura, I. Takahara, M. Saito, T. Hattori, K. Ohkuma, M. Ando, Catal
Today, 45 (1998) 61.
[5] L. Huo, W. Li, L. Lu, H. Cui, S. Xi, J. Wang, B. Zhao, Y. Shen, Z. Lu, Chem
Mater, 12 (2000) 790.
[6] R. Zboril, M. Mashlan, D. Petridis, Chem Mater, 14 (2002) 969.
[7] R. Pascual, M. Sayer, C.V.R.V. Kumar, L. Zou, J Appl Phys, 70 (1991) 2348.
[8] X. Wang, X. Chen, X.C. Ma, H. Zheng, M. Ji, Z. Zhang, Chem Phys Lett., 384
(2004) 391.
[9] E.T. Kim, S.G. Yoon, Thin Solid Films, 227 (1993) 7.
CHAPTER-6
~ 147 ~
[10] X. Bokhimi, A. Morales, M. Portilla, A. Gracia-Ruiz, Thin Solid Films, 12
(1999) 589.
[11] W.G. Luo, A.L. Ding, H. Li, Integr Ferroelectr, 9 (1995) 75.
[12] R. Birringer, H. Gleiter, H.P. Klein, P. Marquardt, Phys Lett A, 102 (1984)
365.
[13] D. Michel, E. Gaffet, P. Berther, Nanostruct Mater, 6 (1995) 667.
[14] M. Chakrabarti, D. Bhowmick, A. Sarkar, S. Chattopadhyay, S. Dechoudhury,
D. Sanyal, A. Chakrabarti, J Mater Sci, 40 (2005) 5265. doi:10.1007/s10853-
005-0743-3.
[15] M. Chakrabartii, S. Dutta, S. Chattopadhyay, A. Sarkar, D. Sanyal, A.
Chakrabarti, Nanotechnology, 15 (2004) 1792.
[16] B.Q. Zhang, L. Lu, MO. Lai, Physica B, 325 (2003)120.
[17] Hautojarvi P, Corbel C (1995) In: Dupasquier A, Mills AP Jr (eds) Positron
spectroscopy of solids. IOS Press, Amsterdam, p 491; In: Krause-Rehberg R,
Leipner HS (eds) Positron annihilation in semiconductors, Springer Verlag,
Berlin, 1999.
[18] K.G. Lynn, A.N. Goland, Solid State Commun, 18 (1976) 1549.
[19] G.K. Williamson, W.H. Hall, Acta Metall, 1 (1953) 22.
[20] M. Chakrabarti, A. Sarkar, S. Chattopadhyay, D. Sanyal, (2006) In: Martins
BP (ed) New topics in superconductivity research. Nova Science, New York.
[21] M. Chakrabarti, D. Sanyal, A. Chakrabarti, J Phys Condens Matter, 19 (2007)
236210.
[22] D. Sanyal, M. Chakrabarti, T.K. Roy, A. Chakrabarti, Phys Lett A, 371 (2007)
482.
[23] J. Pancove (1979) Optical processes in semiconductors. Prentice- Hall,
Englewood Cliffs, NJ.
[24] A.A. Dakhel, F.Z. Henari, Cryst Res Technol, 38 (2003) 979.
[25] J. Tauc, Mater Sci Bull, 5 (1970) 72.
[26] S. Dutta, S. Chattopadhyay, M. Sutradhar, A. Sarkar, M. Chakrabarti, D.
Sanyal, D. Jana, J Phys Condens Matter, 19 (2007) 236218.
[27] V. Srikant, D.R. Clarke, J Appl Phys, 81 (1997) 6357.
[28] M.J. Puska, R.M. Nieminen, Rev Mod Phys, 66 (1994) 841.
[29] U. Myler, P.J. Simpson, Phys Rev B, 56 (1997) 14303.
CHAPTER-7
Microstructure, Mössbauer and optical characterizations of nanocrystalline α-Fe2O3
synthesized by chemical route
CHAPTER-7
~ 149 ~
7.1. Introduction
Nanostructured materials (oxides) nowadays attract lots of attention as their
structure and properties can be manipulated by changing the surface to volume ratio
[1], preparation process [2], annealing temperature [3], and by changing the crystallite
size [4]. Properties of the nanomaterials can also be controlled by incorporating
different types of defects inside nanocrystals [5]. Nanocrystalline magnetic metal
oxides have received special attention as they can be used in different fields, for
example, magnetic resonance imaging [6], drug delivery agents [7], and so forth.
Further, an unusual characteristic like superparamagnetism [8] in nanocrystalline state
of these materials makes them object of great interest for fundamental studies. Among
different magnetic nanoparticles, α-Fe2O3 is a very common magnetic material as it
has potential applications in chemical industry [9]. It can be used as catalyst, gas
sensing material to detect combustible gases [10] like CH4 and C3H8, and so forth.
Among different iron oxides, α-Fe2O3 is the most stable polymorph in nature under
ambient condition and can be easily found as mineral hematite. Hematite has a
rhombohedrally centered hexagonal structure of the corundum type with a
closepacked oxygen lattice in which two-thirds of the octahedral sited are occupied by
Fe (III) ions [11]. Nanocrystalline α-Fe2O3 powders have been prepared by different
preparation techniques like sol-gel [12], hydrothermal [13], chemical vapor phase
deposition [14], calcinations of hydroxides [15], radio frequency sputtering [16], gas
condensation technique [17], and high-energy ball-milling process [18, 19]. K¨undig
et al. [20] measured the Mössbauer spectra of Fe57 in α-Fe2O3 as a function of particle
size and temperature and noticed that bulk α-Fe2O3 changed in the sign of the
quadrupole interaction in going through the Morin transition temperature, 263 K.
They reported the superparamagnetic behavior of α-Fe2O3 when the particle size is
less than 13 nm and as the particle size gradually increased, it became ferromagnetic.
Giri et al. [21] prepared single-phased α-Fe2O3 nanoparticles using a hydrothermal
synthesis method in aqueous-organic microemulsion under mild alkaline condition.
They confirmed the uniformity of nanocrystalline α-Fe2O3 particles both by XRD and
HRTEM studies and obtained sextet pattern for these crystallites from the Mössbauer
study. Lemine et al. [22] studied the effect of high-energy ball milling on α-Fe2O3
particles and characterized the ball-milled powders by the Rietveld analysis based on
XRD patterns and Mössbauer spectroscopy and revealed that the magnetic hyperfine
CHAPTER-7
~ 150 ~
field was affected by the grain size. Sahu et al. [23] noticed the phase transformation
reaction in nanocrystalline α-Fe2O3 powder induced by ball milling under both air and
oxygen atmospheres. They revealed that the transformation of α-Fe2O3 to Fe3O4 and
finally to FeO occurs in both atmospheres depending upon the oxygen partial
pressures. In none of the above cases, detailed microstructure characterization and
oxygen vacancies in α-Fe2O3 lattice have been estimated by the Rietveld method of
structure refinement, and magnetic structures have been corroborated to the
microstructure parameters and oxygen vacancies. The purposes of the present work
are to (i) establish a correlation in between microstructure parameters and oxygen
vacancies with magnetic properties of nanocrystalline α-Fe2O3 and postannealed
powders and (ii) estimate the optical band gaps of nanocrystalline α-Fe2O3 under the
influence of lattice distortion. Optical band gaps of as-prepared and postannealed
samples have been measured by the UV-Vis absorption spectroscopic method. Goyel
et al [24] measured the direct band gap 2.5 eV of nanocrystalline Fe2O3 powder
synthesized by modified CVD technique. Fu et al. [25] reported that the α-Fe2O3
nanoparticles exhibited n-type semiconducting (SC) properties under ambient
conditions with a band gap of 2.2 eV. Sahana et al. [26] reported that the band gap for
α-Fe2O3 nanoparticle was 2.3 eV, and bandgap increases by the decreasing size of
Fe2O3 crystallites which was manifested in terms of the quantum confinement effect.
7.2. Experimental outline
In the present study, reagent grade Fe(NO3)3, 9H2 O has been used as
precursor for the preparation of nanocrystalline α-Fe2O3 powder by chemical route.
Initially, a solution of Fe(NO3)3, 9H2 O is made with distilled water. A few drops of
concentrated nitric acid have been added to keep the pH level of the solution in acidic
range. This solution is then stirred for 1 h and then poured into a plastic flat-bottomed
container and left for three days in ambient atmosphere for gelation. The gel is then
evaporated to obtain “as-prepared” sample in powder form [27]. The dry powder is
then annealed in open air at different temperatures, 300C, 350C, and 500C for 1 h
in a precisely controlled furnace.
The X-ray powder diffraction data of as-prepared and annealed samples have
been recorded in a Philips PW 1830 X-ray powder diffractometer using Ni-filtered
CuKα radiation. In each case, step-scan data have been obtained in the 20–80 2θ in a
CHAPTER-7
~ 151 ~
step size of 0.02 and 5 sec/step counting time. All experimental patterns are fitted
very well and the structure and microstructure parameters like crystallite size, lattice
parameters, oxygen concentration, and displacement of oxygen atoms in α-Fe2O3
lattice are obtained from the Rietveld analysis [22–26].
Transmission electron microscopy with TECNAI STWIN (FEI Company)
electron microscope operating at 200 kV has been used to estimate the average
crystallite size of different nanocrystalline α-Fe2O3 samples. A pinch of powder was
ultrasonically dispersed in alcohol, and a drop of the solution was put on a 300 mesh
copper grid for the transmission electron microscopy work.
Room temperature 57Fe Mössbauer spectra for all samples have been recorded
in the transmission configuration with constant acceleration mode. A gas filled
proportional counter has been used for the detection of 14.4 keV Mössbauer γ-rays,
while a 10mCi 57Co isotope embedded in an Rh matrix has been used as the
Mössbauer source. The Mossbauer spectrometer has been calibrated with 95.16%
enriched 57Fe2O3 and standard α-57Fe foil. The Mossbauer spectra have been analyzed
by a standard least square fitting program (NMOSFIT).
The UV-Vis absorption spectra of all samples have been recorded in a Hitachi
U-3501 spectrophotometer in the wavelength range 200–800 nm.
7.3. Method of microstructure analysis by Rietveld refinement In the present study, we have adopted the Rietveld’s powder structure
refinement analysis [28–33] of X-ray powder diffraction data to obtain the refined
structural parameters, such as atomic coordinates, occupancies, lattice parameters,
thermal parameters, and so forth, and microstructure parameters, such as crystallite
size and r.m.s. lattice strain. The Rietveld’s software MAUD 2.06 [31] is specially
designed to refine simultaneously both the structural and microstructure parameters
through least-squares method. The instrumental broadening for the present
experimental setup has been obtained using a specially prepared Sistandard, free from
all kinds of lattice imperfections. The peak shape is assumed to be a pseudo-Voigt
(pV) function with asymmetry because it takes individual care for both the crystallite
size and strain broadening of the experimental profiles. The background of each
pattern is fitted by a polynomial function of degree 4. The theoretical X-ray powder
diffraction pattern is simulated containing all structure and a trial set of microstructure
CHAPTER-7
~ 152 ~
parameters of rhombohedral α-Fe2O3 phase. A detailed mathematical description of
the Rietveld analysis has been reported elsewhere [28–31]. Considering the integrated
intensity of the peaks as a function of structural and microstructure parameters, the
Marquardt least-squares procedures are adopted for the minimization of the difference
between the observed and simulated powder diffraction patterns and the minimization
was monitored
Fig.7.1 X-ray powder diffraction patterns for different α- Fe2O3 sample.
Fig.7.2 Variation of lattice parameter with temperature of α-Fe2O3 samples.
using the reliability index parameters, Rwp (weighted residual error), and Rexp
(expected error) defined respectively as
CHAPTER-7
~ 153 ~
(7.1)
where I0 and Ic are the experimental and calculated intensities, wi(= I/I0) and N are the
weight and number of experimental observations, and P the number of fitting
parameters. This leads to the value of goodness of fit (GoF) [28–31].
(7.2)
Refinement continues till convergence is reached with the value of the quality factor,
GoF very close to 1 (varies between 1.1 and 1.7), which confirms the goodness of
refinement.
Fig.7.3 Variation of crystallite size of α-Fe2O3 samples with temperature.
7.4. Results and Discussion 7.4.1. Microstructure Characterization Using XRD and HRTEM The nanocrystalline α-Fe2O3 powder is prepared from the ferric-nitrate
solution and then annealed at 300C, 350C, and 500C in open air. Figure 7.1 shows
the X-ray powder diffraction patterns of these samples. It is evident from the figure
that all strong α-Fe2O3 reflections appear clearly in the XRD pattern of as-prepared
CHAPTER-7
~ 154 ~
sample with significant peak broadening. The peak broadening reduces, and intensity
of all reflections increases continuously with increasing annealing temperature up to
500C. The intensity ratios of all reflections agree well with the reported pattern
(JCPDS File # 33-0664, Space group: R3-cH (hexagonal setting)). For microstructure
characterization of these samples, the Rietveld structure and microstructure
refinement method has been adopted in the present study, and all experimental data
are fitted with the simulated XRD patterns containing only the α-Fe2O3 phase. All
experimental patterns are fitted very well and the structure and microstructure
parameters are obtained from the Rietveld analysis. Both the “a” and “c” lattice
parameters of α-Fe2O3 lattice are significantly large in “as-prepared” sample than the
reported values (a = 5.0356 A° , c =13.7489 A° ) [34] and decrease continuously
(Figure 7.2) towards the reported values with increasing annealing temperature up to
500C. It signifies that the lattice of the “as-prepared” sample contains a significant
amount of lattice strain and almost strain-free α-Fe2O3 lattice is obtained after
annealing the powder at 500C for 1hr. Considering all reflections the Rietveld
analysis reveals that the shape of α-Fe2O3 crystallites is isotropic in nature and their
size variation with increasing annealing temperature is shown in Figure 7.3. The
crystallite size of the “as-prepared” powder is ~18nm and remains almost unchanged
up to 300C and then increases sharply to ~54nm after annealing the powder at 500C
for 1 h. Figures 7.4(a) and 7.4(b) depict the HRTEM image of as-prepared powder
sample. It is evident from the image that particles are almost spherical in shape, and
average particle size is ~18nm which is very close to that obtained from X-ray
analysis. The as-prepared lattice is highly strained which is clearly evidenced by the
presence of Moire fringe in the HRTEM image.
The Rietveld analysis reveals that the “as-prepared” α-Fe2O3 powder is not
completely stoichiometric, and there are significant amount of oxygen vacancies
present in the α-Fe2O3 lattice and oxygen atoms are displaced from their stable
position. The variation of oxygen concentration with increasing annealing temperature
is shown in Figure 7.5. In as-prepared lattice, ~20 mol% oxygen positions remain
unoccupied and with increasing annealing temperature, most of the positions are
occupied and the lattice approaches towards the stoichiometric oxygen concentration
and after annealing at 500C, it becomes saturated and only 4 mol% oxygen positions
CHAPTER-7
~ 155 ~
remain unfilled. It seems that all oxygen positions in α-Fe2O3 powder may not be
completely filled up even after annealing the powder sample at higher temperatures.
Fig.7.4(a) HRTEM image of Fig.7.4(b) HRTEM image of α-Fe2O3 α-Fe2O3 crystallites in unannealed. crystallites in 300C annealed sample.
Fig.7.5 Variation of oxygen concentration with temperature.
Fig.7.6 Variation of displacement of oxygen with temperature.
CHAPTER-7
~ 156 ~
From the analysis it is also revealed that the displaced oxygen atoms in the
nonstoichiometric “as-prepared” sample (z = 0.29) approach towards their normal
positions (z = 0.32) as in the bulk α-Fe2O3 (ICSD Code No. 82904) (Figure 7.6).
These observations indicate that the nonstoichiometric and heavily distorted as-
prepared α-Fe2O3 lattice approaches gradually towards stoichiometric and perfect
lattice configuration with increasing annealing temperature.
7.4.2. Magnetic Characterization Using Mössbauer Spectroscopy Figures 7.7(a) and 7.7(b) show the room temperature Mössbauer spectra for
the as-prepared and 350C annealed samples, respectively. It is clear from these
figures that the as-prepared sample shows a doublet type of Mössbauer spectra, and
no ferromagnetic nature (six line pattern of Mössbauer spectra) has been observed.
This clearly indicates that the as-prepared α-Fe2O3 powder is superparamagnetic in
nature. The 350C annealed sample and all other annealed samples (300C and 500C)
show sextet patterns in Mössbauer spectra confirming the appearance of
ferromagnetic nature in these annealed samples From the experimental Mössbauer
spectra both isomer shift (IS), quadrupole splitting (QS), and hyperfine field (HF)
have been calculated by a standard leastsquare fitting program, NMOSFIT. Values of
the IS, QS, and HF for as-prepared and 500C annealed samples are summarized in
Table 7.1.
Table 7.1 Values of the Mössbauer parameters, IS, QS, and HF for the “as-prepared”
and 500C annealed Fe2O3 samples.
Sample IS (mm/sec) Line width (mm/sec) HF (Tesla) QS (mm/sec)
Nanocrystalline Fe2O3
0.42 10.41±0.482 - 0.7934
5000C annealed Fe2O3
0.36 3.95±0.23 78.8 -0.1250
From Table 7.1 it has been observed that the nanocrystalline as-prepared sample
shows enhanced IS, line width, and QS values in comparison to the annealed sample.
In the as-prepared sample there are two components. The first one is the grain
consisting of all atoms located in the lattice of the crystallites, and the second one is
CHAPTER-7
~ 157 ~
the interfacial component consisting of all the atoms situated in the grain boundaries
of the crystallites.
Fig.7.7 (a) Room temperature Mössbauer spectrum “as-prepared”α-Fe2O3 sample
Fig.7.7 (b) Room temperature Mössbauer spectrum for the for annealed α-Fe2O3
sample.
The enhanced IS, line width, and QS for the as-prepared sample may be due to
the reduction of the electron density at the interfacial site in presence of lattice
imperfections. The HF value for the 350C annealed sample is also higher than that of
the standard α-Fe2O3 sample (52 T). This enhanced HF value may be due to the low
electron density at the interfacial site in this annealed sample compared to the bulk
standard α-Fe2O3 sample. From the Rietveld analysis it has been shown that the
oxygen concentration increases gradually with annealing temperature, and displaced
oxygen atoms approach towards their equilibrium positions during annealing. It
CHAPTER-7
~ 158 ~
suggests that the as-prepared distorted lattice contains significant amount of lattice
imperfections, and the enhancement in all magnetic parameters may be attributed to
the high density of point defects in the as-prepared sample.
Fig.7.8 Variation of ratio of superparamagnetic fraction of α-Fe2O3 particles to the ferromagnetic fraction with the crystallite size.
Figure 7.8 represents the variation of ratio of superparamagnetic fraction of α-Fe2O3
particles to the ferromagnetic fraction with increasing crystallite size. This fraction
has been calculated by directly integrating the absorptions lines. It indicates that both
superparamagnetism and ferromagnetism persist in these nanoparticles. From
Mössbauer spectroscopy measurements It has been reported earlier [22] that there are
two kinds of particles which coexist in the sample: nanostructured and micrometric
hematite. Nanostructured particles result in superparamagnetism, and relatively bigger
particles having less lattice imperfections are responsible for ferromagnetism. This
nature of change in magnetic behaviour with change in particle size is already noticed
by several researchers [20–22, 24–26]. It is evident from the variation that
superparamagnetism in as-prepared sample caused mainly due to lattice imperfections
in α-Fe2O3 lattice for the following possible reasons. (i) Oxygen vacancy in the lattice
reduces the Fe-O dipoles; (ii) displacement of oxygen atoms from their equivalent
positions enhances the Fe-O bond lengths; (ii) magnetic dipoles are randomly oriented
in presence of lattice imperfections.
CHAPTER-7
~ 159 ~
7.4.3. Optical Characterization Using UV-Vis Spectroscopy
Optical band gaps of as-prepared and all annealed samples have been
measured using UV-Vis absorption spectroscopic technique. The spectral absorption
coefficient, α, is defined as [35]
(7.3)
where k(λ) is the spectral extinction coefficient obtained from the absorption
curve and λ is the wavelength. Figure 7.9 represents the absorbance curve for as-
prepared and all annealed samples. It is clearly observed that the absorption maxima
occur around ~ 475nm for all the samples. Thus the position of the absorption maxima
remains almost the same for the nanocrystalline as-prepared and the annealed
samples.
Fig.7.9 UV-Vis absorption spectra for different α-Fe2O3 samples.
The band gap, Eg (for a direct transition between the valence and conduction
band), is obtained by fitting the experimental absorption data with the following
equation:
(7.4)
for a direct band gap transition, [35] where hν is the photon energy, α is the
absorption coefficient, Eg is the band gap, and A is a characteristic parameter
independent of photon energy. Figures 7.10(a) and 7.10(b) represent the absorption
curves of as-prepared and 500C annealed powders for direct transition.
CHAPTER-7
~ 160 ~
Fig. 7.10(a) Band gap estimation for unannealed (as-prepared) sample.
Fig. 7.10(b) Band gap estimation for annealed sample.
The value of band gap Eg (for direct transition) has been obtained from the intercept
of the extrapolated linear part of the (αhν)2 versus hν curve with the energy (hν) axis.
The band gap for direct transition (estimated from Figures 7.10(a) and 7.10(b)) for the
as-prepared nanocrystalline sample is 2.65 eV at the wavelength 468 nm, whereas for
the annealed sample the value reduces to 2.50 eV. Thus the as-prepared and annealed
α-Fe2O3 nanoparticles are n-type semiconductor which was already noticed earlier
[24–26] and there is a red shift in the band gap with annealing of the samples.
CHAPTER-7
~ 161 ~
7.5. Conclusions Nanocrystalline α-Fe2O3 crystallites of size ranging 18 to 54nm have been
prepared by chemical synthesis. The Rietveld analysis reveals that the “as-prepared”
α-Fe2O3 powders are not completely stoichiometric, and significant oxygen vacancies
are noticed in the α-Fe2O3 lattice. With increasing annealing temperature the lattice
approaches towards the stoichiometric oxygen concentration. The “asprepared”
sample shows superparamagnetic behavior at the Mössbauer spectra whereas the
annealed samples show both superparamagnetic and ferromagnetic behaviors. From
Mössbauer spectra it has been observed that the nanocrystalline as-prepared sample
shows enhanced IS, line width, and QS values compared to the annealed samples
which may be due to the reduction of the electron density at the interfacial site. From
UV-Vis absorption spectra it has been observed that the band gaps of the annealed
samples are lower than the as-prepared samples and all samples belong to n-type
semiconductors.
7.6 References [1] Henglein, Chemical Reviews, 89 (1989) 1861.
[2] J. Drbohlavova, R. Hrdy, V. Adam, R. Kizek, O. Schneeweiss, and J. Hubalek,
Sensors, 9 (2009) 2352.
[3] S. Volden, A.L. Kjøniksen, K. Zhu, J. Genzer, B. Nystr¨om, and W.R.
Glomm, ACS Nano, 4 (2010) 1187.
[4] M. Chakrabarti, S. Dutta, S. Chattapadhyay, A. Sarkar, D. Sanyal, and A.
Chakrabarti, Nanotechnology, 15 (2004) 1792.
[5] M. Chakrabarti, A. Banerjee, D. Sanyal, M. Sutradhar, and A. Chakrabarti,
Journal of Materials Science, 43 (2008) 4175.
[6] H. Basti, L. Ben Tahar, L.S. Smiri et al., Journal of Colloid and Interface
Science, 341 (2010) 248.
[7] K.A. Hinds, J.M. Hill, E.M. Shapiro et al., Blood, 102 (2003) 867.
[8] D.H. Jones, Hyperfine Interactions, 47-48 (1989) 289.
[9] N. Mimura, I. Takahara, M. Saito, T. Hattori, K. Ohkuma, and M. Ando,
Catalysis Today, 45 (1998) 61.
[10] L. Huo, W. Li, L. Lu et al., Chemistry of Materials, 12 (2000) 790.
CHAPTER-7
~ 162 ~
[11] R. Zboril, M. Mashlan, and D. Petridis, Chemistry of Materials, 14 (2002)
969.
[12] R. Pascual, M. Sayer, C.V.R.V. Kumar, and L. Zou, Journal of Applied
Physics, 70 (1991) 2348.
[13] X. Wang, X. Chen, X. Ma, H. Zheng, M. Ji, and Z. Zhang, Chemical Physics
Letters, 384 (2004) 391.
[14] E.T. Kim and S.G. Yoon, Thin Solid Films, 227 (1993) 7.
[15] X. Bokhimi, A. Morales, M. Portilla, and A. Garc´ıa-Ruiz, Nanostructured
Materials, 12 (1999) 589.
[16] W.G. Luo, A.L. Ding, X.T. Chen, and H. Li, Integrated Ferroelectrics, 9
(1995) 75.
[17] R. Birringer, H. Gleiter, H.P. Klein, and P. Marquardt, Physics Letters A, 102
(1984) 365.
[18] D. Michel, E. Gaffet, and P. Berthet, Nanostructured Materials, 6 (1995) 667.
[19] M. Chakrabarti, D. Bhowmick, A. Sarkar et al., Journal of Materials Science,
40 (2005) 5265.
[20] W. K¨undig, H. B¨ommel, G. Constabaris, and R.H. Lindquist, Physical
Review, 142 (1966) 327.
[21] S. Giri, S. Samanta, S. Maji, S. Ganguli, and A. Bhaumik, Journal of
Magnetism and Magnetic Materials, 285 (2005) 296.
[22] O.M. Lemine, M. Sajieddine, M. Bououdina, R. Msalam, S. Mufti, and A.
Alyamani, Journal of Alloys and Compounds, 502 (2010) 279.
[23] P. Sahu, M. De, and M. Zduji´c, Materials Chemistry and Physics, 82 (2003)
864.
[24] R.N. Goyal, A.K. Pandey, D. Kaur, and A. Kumar, Journal of Nanoscience
and Nanotechnology, 9 (2009) 4692.
[25] X. Fu, F. Bei, X. Wang, X. Yang, and L. Lu, Journal of Raman Spectroscopy,
40 (2009) 1290.
[26] M.B. Sahana, C. Sudakar, G. Setzler et al., Applied Physics Letters, 93 (2008)
Article ID 231909.
[27] A.E. Gash, T.M. Tillotson, J.H. Satcher, J.F. Poco, L.W. Hrubesh, and R.L.
Simpson, Chemistry of Materials, 13 (2001) 999.
[28] H.M. Rietveld, Acta Crystallographica, 22 (1967) 151.
[29] H.M. Rietveld, 2 (1969) 65.
CHAPTER-7
~ 163 ~
[30] R.A. Young and D.B. Willes, Journal of Applied Crystallography, 15 (1982)
430.
[31] L. Lutterotti, “Maud Version 2.14,” 2009, http://www.ing
.unitn.it/~Luttero/maud.
[32] B. Ghosh and S.K. Pradhan, Journal of Alloys and Compounds, 477 (2009)
127.
[33] S. Patra, B. Satpati, and S.K. Pradhan, Journal of Applied Physics, 106 (2009)
Article ID 034313.
[34] S. Dutta, S. Chattopadhyay, A. Sarkar, M. Chakrabarti, D. Sanyal, and D.
Jana, Progress in Materials Science, 54 (2009) 89.
[35] J. Tauc, Materials Research Bulletin, 5 (1970) 721.
CHAPTER-8
Microstructural changes and effect of variation of lattice strain on positron annihilation lifetime
parameters of zinc ferrite nanocomposites prepared by high energy ball-milling
CHAPTER-8
~ 165 ~
8.1 Introduction Ferrites are a group of technologically important materials used in magnetic,
electronic and microwave fields. Magnetic nanocrystalline materials hold great
promise for atomic engineering of materials with functional magnetic properties [1-3].
Many magnetic nanocrystals show superparamagnetism in single domain particles
below a certain critical size. Magnetic nanocrystals have been extensively applied in
magnetic recording medium, information storage, bio-processing and magneto-optical
devices [4-5]. The sulfur absorption capacity of milled zinc ferrite increases with
decreasing crystallite size due to structure–reactivity relationship at high temperature.
Crystalline ZnFe2O4 (cubic, a = 0.8441nm, space group: Fd−
3 m, Z = 8; ICDD
PDF #22-1012) is a normal spinel at room temperature. Spinel structure is made up by
a cubic close-packed array of oxygen atoms with tetrahedral (T) and octahedral (O)
cavities. In the normal 2–3 spinels, one-eighth of the T sites and one-half of the O
sites are filled by the divalent (A) cations (Mg2+, Zn2+, Mn2+, Cd2+, etc.) and the
trivalent (B) cations (Al3+, Fe3+, Cr3+ etc.), respectively, in the ratio AB2O4. The
structural formula of zinc ferrite is usually written as (Zn1−δ2+Feδ3+)[Znδ2+Fe2−δ
3+]O42−,
where round ( ) and square [ ] brackets denote T and O sites of co-ordination,
respectively, and δ represents the degree of inversion (defined by the fraction of the T
sites occupied by B cations). There are two ordered configuration stable at low
temperature, the one with δ = 0 (normal spinel) and the other with δ = 1 (inverse
spinel). When the temperature increases, disorder takes place, since A and B cations
undergo increasing intersite exchange over the three cation sites per formula unit (one
T and two O sites). The completely random distribution of A and B cations over the
three cation sites corresponds to δ = 2/3, which is asymptotically approached at very
high temperatures. Same type of cation distribution is also observed in ball-milled
samples [6-7]. The change in temperature or the change in milling parameter may
result in change in the degree of inversion. It has been found that a metastable
nanoscale structural state of mechanosynthesized ZnFe2O4 is characterized by a
substantial displacement of Fe3+ cations to tetrahedral sites and of Zn2+ cations into
octahedral sites. The inverse–normal transition in mechanosynthesized zinc ferrite
proceeds rapidly in the temperature range 885–1073K and the activation energy of the
transition is E ~72 kJ mol-1 [6].
CHAPTER-8
~ 166 ~
Formation of nanocrystalline ZnFe2O4 as normal and inverse spinel structures
was noticed after ball-milling the stoichiometric mixture of ZnO and α-Fe2O3
powders in open air for different lengths of time. Formation of nanocrystalline
materials in the process of ball-milling leads to significant amount of structural and
microstructural defects which can be characterized by X-ray diffraction and positron
annihilation spectroscopy studies.
The powder patterns of almost all the ball-milled materials, milled at different
milling time are composed of a large number of overlapping reflections of α-Fe2O3,
ZnO and ZnFe2O4 (normal and inverse spinel) phases. The Rietveld analysis based on
structure and microstructure refinement [8-9] was adopted for precise determination
of several microstructural parameters as well as relative phase abundance of such
multiphase material.
The purpose of the present work is to characterize defect states of the zinc
ferrite nanocomposites by positron annihilation lifetime spectroscopy (PALS) and
establish their relationship with microstructure parameters obtained from X-ray
analysis. PALS is a powerful technique to characterize defects in solid materials [10].
A nanostructured material contains unlimited grain boundaries and these boundaries
are rich in lattice defects. Thus, PALS method can be effectively used to characterize
nanostructures in terms of lattice imperfections. To the best of our knowledge, this
type of analysis will help to understand the nature of deformation generated in the
process of mechanical alloying in nanocrystalline ferrite powders.
8.2 Experimental method High-energy ball-milling of ZnO (M/s Merck, 99% purity) and α-Fe2O3 (M/s Glaxo,
99% purity) mixture in 1:1 mol% was conducted in a planetary ball mill (Model P5,
M/S Fritsch, GmbH, Germany). The time of milling was varied from 30 min to 10 h
depending upon the rate of formation of zinc ferrite phase. The step-scan data (of step
size 0.020 2θ and counting time 5 s) for the entire angular range (15–800 2θ) of the
unmilled mixture and all ball-milled samples were recorded using Ni-filtered CuKα
radiation from a highly stabilized and automated Philips X-ray generator (PW 1830)
operated at 35 kV and 25 mA.
For PALS measurements, about 12 µCi 22Na activity was deposited and dried
on a thin aluminium foil and was covered with an identical foil. This assembly was
CHAPTER-8
~ 167 ~
used as the positron source. The source correction was determined using a properly
annealed defect- free aluminium sample. The PALS system used was a standard fast-
fast coincidence set-up with two identical 1-inch tapered off BaF2 scintillator
detectors fitted with XP 2020Q photomultiplier tubes. The time resolution obtained
using 60Co source with 22Na gates was 285 ps. All lifetime spectra were analysed
using PATFIT 88 [11] programme.
8.3 Method of analysis The Rietveld’s powder structure refinement analysis [12-15] of X-ray powder
diffraction data using the Rietveld software MAUD 2.26 [9] revealed the refined
structural parameters, such as atomic coordinates, occupancies, lattice parameters,
thermal parameters etc. and microstructural parameters, such as crystallite size and
r.m.s. lattice strain etc The experimental profiles were fitted with the most suitable
pseudo-Voigt (pV) analytical function15 because it takes individual care for both the
crystallite size and strain broadening of the experimental profiles. Positron
annihilation lifetime data were deconvoluted with three lifetime components using the
PATFIT programme. A total source correction of 10 % had been deducted while
analysing the spectra.
8.4 Results and discussion
8.4.1 X-ray diffraction analysis: Figure 8.1 shows the X-ray powder diffraction patterns of unmilled and ball milled
mixture of ZnO and α-Fe2O3 powders milled for different durations. The powder
pattern of unmilled mixture contained only the individual reflections of ZnO and α-
Fe2O3 phases and the precursors were free from impurities. It was noticed that in the
course ball milling the mixture, ZnFe2O4 phase was formed and its amount increased
gradually with increasing milling time. After 30 min milling, the formation of
ZnFe2O4 was noticed clearly with the appearance of (220) (2θ = 29.950) and strongest
(311) (2θ = 35.30) reflections in the XRD pattern.
CHAPTER-8
~ 168 ~
Fig.8.1. X-ray powder diffraction patterns of unmilled and ball milled ZnO - α-Fe2O3 mixture (1:1mol%) at BPMR 40:1.
It may also be noticed that the content of ZnO phase was reduced to a large
extent in comparison to α-Fe2O3 phase. It indicated that the ZnO phase was much
prone to deformation fault as all the reflections were sufficiently broadened due to
reduction in particle size and accumulation of lattice strain in the course of milling.
As a result, solid-state diffusion between ZnO and α-Fe2O3 nanoparticles enhanced
extensively with increasing milling time. In the course of further milling, broadening
as well as degree of overlapping of neighbouring reflections were increased with
increasing milling time. After 2.5h of milling, except the strongest (104) (2θ = 33.180)
reflection, all other reflections of α-Fe2O3 were disappeared completely in the XRD
pattern. It was the indication of either (i) significant reduction in content of the phase
or (ii) significant increase in peak-broadening due to reduction in particle size and
accumulation of lattice strain aroused from the high energy impact of milling or due
to both these effects. Concurrently, an incredible change in intensities of ZnFe2O4
reflections was observed in the XRD pattern. The rate of mechanosynthesis of
ZnFe2O4 was then increased rapidly in course of milling. After 6.5h milling, all
reflections of starting precursors were completely disappeared and it appeared that the
CHAPTER-8
~ 169 ~
ZnFe2O4 phase was completely grown up as the intensity distribution of the XRD
pattern resembled perfectly in accordance with the ICDD PDF # 22-1012. It was
reported earlier that the present process of mechanosynthesis of zinc ferrite at room
temperature by ball milling may also lead to the formation of a metastable inverse
spinel structure. The inverse spinel zinc ferrite was derived by a substantial
displacement of Fe3+ cations to tetrahedral (T) sites and equal amount of Zn2+ cations
into octahedral (O) sites of the cubic close-packed anionic sublattice. After 2.5h
milling, when the formation of ZnFe2O4 was almost completed, verification for
formation of inverse spinel structure along with normal spinel was made because
without considering the inverse spinel, fitting quality of XRD powder data was poor.
Figure 8.2 shows the comparison of the quality of profile fitting in the 2.5h and
10h-milled samples with and without consideration of inverse spinel structure of
ZnFe2O4.
Fig.8.2. Calculated (-) and experimental( )X-ray powder diffraction patterns of ball milled ZnO - α- Fe2O3 (a) for 2.5h without inverse spinel (b) for 2.5h with inverse spinel (c) for 10h without inverse spinel (d) for 10h with inverse spinel revealed by Rietveld powder structure refinement analysis.
CHAPTER-8
~ 170 ~
It is evident that from the figure that the inclusion of the inverse spinel with
normal one improved the profile fitting quality significantly. It indicated towards the
coexistence of both the normal and inverse spinel structures of ZnFe2O4 in the
samples prepared with higher milling time.
Figure 8.3 shows the dependence of relative phase abundances of different
phases with increasing milling time.
Fig.8.3. Variation of phase content (wt.%) of different phase with increasing milling time
The content (wt.%) of ZnO decreased rapidly but that of α-Fe2O3 decreased
slowly with increasing milling time. After 2.5 and 6.5 h milling, ZnO and α-Fe2O3
phases disappeared completely from the respective XRD patterns. The formation of
normal spinel phase was noticed after 30 min of milling and its content increased
continuously (9.4–41.3 wt.%) up to 2.5 h milling. Simultaneously, almost equal
amount (40.1 wt.%) of inverse spinel phase was noticed to form. Content of normal
phase remained almost unchanged up to 10 h milling but that of inverse phase
increased to a large extent after 6.5h milling when α-Fe2O3 was completely utilized
for making exact stoichiometric (1:1 mol%) Zn-ferrite phase. This sudden increase in
CHAPTER-8
~ 171 ~
inverse phase content was essentially due to occupancy of octahedral vacancies by
Fe3+ cations of inverse spinel structures [16].
The nature of variation of crystallite sizes (D) of ZnO, α-Fe2O3 and ferrite
phases are shown in figure 8.4(a).
Fig.8.4(a). Variation of crystallite size of ZnO, Fe2O3, ZnFe2O4 and inverse ZnFe2O4 with increasing milling time.
Crystallite sizes of all the phases were considered to be isotropic. The
crystallite size of ZnO decreased rapidly to ~11nm within 30min milling and then
decreased slowly with increasing milling time. Crystallite size α-Fe2O3 phase was
reduced from ~75nm to ~13nm within 30min ball milling and then decreased slowly
to a saturation value ~7nm. Normal ZnFe2O4 phase was formed after 30min of milling
with ~19nm crystallite size and then reduced to ~10nm after 2.5h of milling. This
decrease in normal spinel crystallite size was manifested in the growth very small
crystallite size of ~6nm of inverse spinel phase after 2.5h of milling. After complete
formation of both spinel phases, heat energy produced by high energy impacts was
utilised to release the accumulated strain inside the nanoparticles and as a result, the
crystallite size increased to a small extent. This effect may also be explained as the
agglomeration of nanometric particles by re-welding mechanism.
CHAPTER-8
~ 172 ~
The nature of variation of r.m.s lattice strain with increasing milling time is
shown in figure 8.4(b).
Fig.8.4(b). Variation of r.m.s strain of ZnO, Fe2O3, ZnFe2O4 and inverse ZnFe2O4 with increasing milling time.
It is obvious that the strain value of normal spinel lattice increased very
rapidly within 30 min and then increased very slowly with increasing milling time,
but after 2.5 h milling, lattice strain suddenly started to release and after 5h milling it
reached a saturation value and remained almost unchanged with increasing milling
time. This nature of variation corroborates the variation of particle size with
increasing milling time.
8.4.2 Positron Annihilation Spectroscopy:
Positron annihilation lifetime spectra (PALS) all the ball-milled samples were
deconvoluted using three lifetime-components τ1, τ2 and τ3 with corresponding
intensities I1, I2 and I3 respectively. In general, for bulk polycrystalline samples, the
shortest positron lifetime (τ1) is assigned to the free annihilation of positrons at
defect-free sites, the intermediate lifetime (τ2) is assigned to the lifetime of positrons
trapped at the defect sites (mono or di-vacancies) and the longest one (τ3) to the pick-
off annihilation of o-Ps atoms formed inside large voids. But, in the case of
polycrystalline samples with crystallite size of the order of a few tens of nanometers,
CHAPTER-8
~ 173 ~
the assignments of lifetime parameters are different. When crystallite sizes become
smaller compared to the mean positron diffusion length (~100 nm), positrons pass
through the grains and annihilate mainly in the grain boundary regions. In this case,
the shortest lifetime (τ1) represents the weighted average of positron lifetimes at the
grain boundary defects (mono or di-vacancies) and the lifetime corresponding to
annihilation with free electrons residing at the grain boundaries. The intermediate
lifetime τ2 corresponds to annihilations at the triple junctions. Triple junctions are
open volumes present at the intersection of three or more grain boundaries and their
size is of the order of 8-10 missing atoms. The fraction of positrons that gets
annihilated inside a grain depends on the positron ‘trapping capability’ of the defects
present at the grain boundaries. The more is the positron trapping at grain boundary
defects, the less is the probability of annihilation with free electrons inside a grain.
Fig.8.5. Variation of mean-lifetime (τm) for ZnO + α-Fe2O3 nanocomposites as a function of ball-mill duration.
Figure 8.5 shows the variation of mean positron lifetime (τm) for ZnO + α-
Fe2O3 nanocomposites as a function of ball-milling duration. τm is related to average
defect density and is defined as
321
332211
IIIIII
m ++++
=ττττ . (8.1)
CHAPTER-8
~ 174 ~
For a given type (size) of defect, higher the defect density larger will be the
value of τm. It is clear that τm remains more or less constant throughout the ball-
milling process. This implies that the overall defect density, as seen by the positrons
remains more or less constant although ball-milling is expected to introduce several
changes in structure and phase content of the nanocomposite. To obtain an insight into
the positron capture mechanism at various trapping centers, the variation of the
individual lifetime parameters with ball-milling duration is to be seen.
Figure 8.6 shows the variation of positron lifetimes τ1, τ2 and intensity I2 with
milling duration. Before milling, i.e. at milling duration t = 0 h, lifetime τ1 may be
ascribed to free annihilation of positrons in the bulk α-Fe2O3 and ZnO crystals.
Fig.8.6. Variation of τ1, τ2 and I2 for ZnO + α-Fe2O3 nanocomposites as a function of ball-mill duration. Positron trapping can be also expected in the grain boundary defects of α-Fe2O3 as its
average crystallite size is ~75 nm (Figure 8.4(a)), which is less than positron diffusion
length in solids. τ2 may be ascribed to the lifetime of positrons trapped at the defect
sites viz., grain boundary defects in ZnO and triple-junctions of α-Fe2O3 nanocrystals.
After 30min of milling, the XRD analysis shows that the sample contains nanocrystals
of ZnO, α-Fe2O3 and ZnFe2O4 (Figures 8.1 and 8.3). Hence the shortest lifetime (τ1)
after milling the mixture for 30min, may be assigned to the mixed lifetime of
positrons trapped at defects (mono or di-vacancies) present at the grain boundaries of
all the nanocrystals (ZnO, α-Fe2O3 and ZnFe2O4) present in the sample and also to the
CHAPTER-8
~ 175 ~
free annihilation inside these nanocrystalline grains. The intermediate lifetime (τ2) has
been assigned to the lifetime of positrons trapped at the triple junction formed at the
intersection of three or more nanocrystalline grains. Similar assignment of lifetimes
was seen to successfully explain the results obtained in case of ZnO nanocrystals [17].
τ1 and τ2 in this case can be expressed as follows
( )∑ +=1i
BiiGBii nn τττ (8.2)
and,
( )∑=i
TPiinττ 2 (8.3)
where i stands for species of nanocrystalline grains viz., ZnO, α-Fe2O3 or ZnFe2O4,
GB stands for grain-boundary, B stands for bulk i.e. the defect free sites inside a grain,
n stands for the fraction of positrons annihilating in a particular site (GB or B) of a
particular type of grain i, and TP stands for triple junction.
Upto a milling duration of 3.5 h, τ1 shows a slight increasing trend. This is
because of the fact that the crystallite sizes become smaller as the ball-milling
duration is increased which in turn increases the surface area to volume ratio. As a
result of this, the contribution from the annihilation at grain boundary increases
resulting in the increase in the value of τ1. However τ2 shows a decreasing trend as
milling hour changes from 30 min to 2.5 h and remains more or less same up to
milling time 3h. The fall in τ2 may be ascribed to the decrease in weight percentage of
α-Fe2O3 (from 58.6 to 14.9 %) with increase in milling time. Disappearance of α-
Fe2O3 from the sample in the course of milling indicates decrease in the contribution
of triple junctions to τ2. It can also be seen that the corresponding intensity I2, which
gives an idea of the defect concentration related to τ2, maintains a steady value up to
3.5 h of milling. Another point to be noted is that though the wt% of α-Fe2O3 phase
changes, τ1 still remains more or less constant in the region of 2.5 to 3.5 h of milling.
A decrease in wt% could have decreased the contribution of annihilation at triple
junction of α-Fe2O3 nanocrystals. This may be explained as following manner. Since
the crystallite size of α-Fe2O3 was also seen to decrease in this region, the fraction of
positrons annihilating at the grain boundaries becomes more, thereby compensating
CHAPTER-8
~ 176 ~
the decrease in the value of τ1. However τ1 was seen to decrease after milling the
sample for 5 h. The phase content of the sample at this stage includes α-Fe2O3,
normal spinel ZnFe2O4 and inverse spinel ZnFe2O4 phases. Their content and grain
sizes do not change much in this milling stage compared to the previous milling stage
(3.5 h). The only change is a substantial decrease in r.m.s. strain value of the normal
spinel ZnFe2O4 structure [18]. Lattice strain depends on the lattice imperfection and
lattice imperfections may arise from the non-stoichiometric composition of the crystal
structure. In this case, decrease in r.m.s. strain value of the normal spinel ferrite
structure strongly indicates the removal of vacancy type defects, which arises out of
non-stoichiometric composition in the ferrite structure. The removal of defects, from
the normal spinel structure, leads to a decrease in contribution of defect related
lifetime to the lifetime component τ1, leading to a reduction in its value. After 6.5 h of
milling, τ1 again increases. At this milling stage, it was seen that the α-Fe2O3 phase
completely vanishes from the composite sample. Simultaneously, the wt.% of inverse
spinel component also increases after milling the sample for 6.5 h. This indicates a
reduction in the contribution of the free annihilation of positrons in the α-Fe2O3
crystals as well as of the annihilation at the grain boundary defect sites in the inverse
spinel structure resulting in an overall increase in τ1 value. However, as the complete
solid solution of α-Fe2O3 results in increase the wt.% of inverse spinel ZnFe2O4, the
value of τ2 did not change at this stage.
Fig.8.7 Variation of τ3 and I3 for ZnO + α-Fe2O3 nanocomposites as a function of ball-mill duration.
CHAPTER-8
~ 177 ~
Figure 8.7 shows the variation of τ3 and I3 as a function of ball-mill duration.
Except an initial increase, value of τ3 remains more or less steady. However, I3 shows
some fluctuations in its behavior. These fluctuations do not correlate themselves
anyhow to the structural changes and hence are not discussed in this article.
8.5. Conclusions The quantitative analysis of the XRD data evaluated on the basis of Rietveld’s
powder structure refinement method yielded detailed information about the structure
and microstructure of mechanosysthesized nanoscale zinc ferrite as well as the
distribution of cations in the spinel ferrite. The main feature of the structural disorder
of mechanosynthesized zinc ferrite was the defect induced inverse spinel phase
transition. The degree of inversion increased rapidly with increasing milling time and
then wt% of inverse phase approached towards a saturation value. Positron
annihilation lifetime data shows that the mean lifetime τm does not change much with
ball milling durations. This implies that the overall defect density, as seen by the
positrons remains more or less constant during milling. The variation of individual
lifetimes τ1 and τ2 and corresponding intensities I1 and I2 shows evaluation of different
phases with milling duration and confirms the formation of inverse spinel ferrite
structure.
8.6 References [1] A.Goldman, Modern Ferrite Technology, Van Nostrand Reinhold, New York;
(1990).
[2] B.M. Berskovsky, V.F. Mcdvcdcv and M.S. Krakov , Magnetic Fluids:
Engineering Applications, Oxford: Oxford University Press, (1993).
[3] R.E. Ayala and D.W. Marsh, Industrial & Engineering Chemistry Research,
30, (1991), 55.
[4] L.A. Bissett and L.D. Strickland , Industrial & Engineering Chemistry
Research, 30 (1991), 170.
[5] R.O. Sack and M.S. Ghiorso, Contributions to Mineralogy and Petrology, 106
(1991), 474.
CHAPTER-8
~ 178 ~
[6] P. Druska, U. Steinike and V. Sepelak. Journal of Solid State Chemistry, 146
(1999), 13.
[7] C.N. Chinnasamy, A. Narayanasamy, N. Ponpandian, K. Chattopadhyay, H.
Guerault, and J-M. Greneche, Journal of Physics Condensed Matter, 12 (2000)
7795.
[8] L. Lutterotti, P. Scardi and P.Maistrelli, Journal of Applied Crystallography,
25 (1992) 459.
[9] L. Lutterotti. MAUD version 2.26. 2011; http://www.ing.unitn.it/~maud/.
[10] R. Krause-Rehberg and H.S. Leipner, Positron Annihilation in
Semiconductors. Solid-State Sciences, Berlin, Springer, (1999) 127.
[11] P. Kirkegaard and M.Eldrup, Computer Physics Communications, 3 (1972)
240.
[12] H. M. Rietveld. Acta Crystallographica, 22 (1967) 151.
[13] H. M. Rietveld, Journal of Applied Crystallography, 2 (1969) 65.
[14] S. Sain, S. Patra and S.K. Pradhan, Journal of Physics D,44 (2011) Article ID
075101, 8 pages.
[15] R.A. Young and D.B. Willes, Journal of Applied Crystallography, 15 (1982)
430.
[16] Q-M. Wei, J-B. Li and Y-J. Journal of Materials Science. 36 (2001) 5115.
[17] A.K. Mishra, S.K. Chaudhuri, S. Mukherjee, A. Priyam, A. Saha and D.Das,
Journal of Applied Physics, 102 (2007) 103514.
[18] S. Bid and S.K. Pradhan, Materials Chemistry and Physics, 82 (2003) 27.
CHAPTER-9
Microstructure and positron annihilation studies of mechanosysthesized CdFe2O4
CHAPTER-9
~ 180 ~
9.1 Introduction The synthesis of nanocrystalline spinel ferrite has been investigated intensively
in recent years due to their potential applications in high-density magnetic recording,
microwave devices and magnetic fluids [1, 2]. High-energy milling is a very suitable
solid-state processing technique for preparation of nanocrystalline ferrite powders
exhibiting new and unusual properties [3–6]. Reports on synthesis of nanocrystalline
cadmium ferrite by high-energy ball milling of CdO and α-Fe2O3 mixture are very
few [7, 8]. The phase transformation kinetics and microstructure characterization of
ball-milled ferrites have been studied in detail in our previous work. Crystalline
CdFe2O4 (Cubic, a = 0.86996 nm, space group: Fd−
3 m, Z = 8; ICDD PDF #22-1063)
is normal spinel at room temperature. Spinel structure consists of a cubic close-
packed array of oxygen atoms with tetrahedral (A) and octahedral (B) cavities. In the
normal 2–3 spinels, one eighth of the A sites and one half of the B sites are filled by
the divalent cations (Mg2+, Zn2+, Mn2+, Cd2+ etc.) and the trivalent cations (Al3+, Fe3+,
Cr3+ etc.) respectively in the ratio AB2O4. When the temperature increases above a
critical limit, disorder takes place, since A and B cations undergo increasing intersite
exchange over the three cation sites per formula unit (one A and two B sites). Lattice
imperfections and phase transformations kinetics of ball-milled nanocrystalline
materials can be resolved by X-ray characterization technique based on structure and
microstructure refinement [9–13]. The powder patterns of almost all the ball-milled
materials, milled at different milling time are composed of a large number of
overlapping reflections of α-Fe2O3, CdO and CdFe2O4 phases. Rietveld’s analysis
based on structure and microstructure refinement [11, 14] has been adopted in the
present analysis for precise determination of several microstructural parameters as
well as relative phase abundance of individual phases.
The purpose of the present work is: (i) to prepare nanocrystalline CdFe2O4
from the stoichiometric mixture (1:1mol%) of powdered reactants containing α-Fe2O3
and CdO by high energy ball-milling at room temperature (ii) to determine the
relative phase abundances of spinel ferrite and other phases (iii) to characterize the
prepared materials in terms of several structural/microstructural defect parameters
(changes in lattice parameters, particle sizes, r.m.s. lattice strains) employing
Rietveld’s powder structure refinement method [9, 10, 12–14] and (iv) to study the
CHAPTER-9
~ 181 ~
defects and microstructural evolution of different phases with milling time by positron
annihilation lifetime spectroscopy[15, 16].
9.2 Experimental Accurately weighed starting powders of CdO (55.43 wt%) (M/s Merck, 99%
purity) and α-Fe2O3 (44.57 wt%) (M/s Glaxo, 99% purity) were hand-ground by an
agate mortar- pestle in a double-distilled acetone medium for more than 30 min. High-
energy ball-milling of unmilled stoichiometric homogeneous powder mixture(1: 1
mol%) was conducted in a planetary ball mill (Model P5, M/S Fritsch, GmbH,
Germany). Milling of powder mixture was done at room temperature in hardened
chrome steel vial using hardened chrome steel balls. The time of milling varies from
30 min. to 25 h depending upon the rate of formation of cadmium ferrite phase.
The X-ray powder diffraction profiles of the unmilled mixture and ball-milled
samples were recorded using Ni-filtered CuKα radiation from a highly stabilized and
automated Philips X-ray generator (PW 1830) operated at 35 kV and 25 mA. The
generator is coupled with a Philips X-ray powder diffractometer consisting of a PW
3710 mpd controller, PW 1050/37 goniometer, and a proportional counter. The step-
scan data (of step size 0.020 2θ and counting time 5 s) for the entire angular range
(15–800 2θ) of the experimental samples were recorded and stored in a PC, coupled
with the diffractometer.
For PALS measurements, about 12 µCi 22Na activity was deposited and dried
on a thin aluminium foil and was covered with an identical foil. This assembly was
used as the positron source. The source correction was determined using a properly
annealed defect free aluminium sample. The PALS system used was a standard fast-
fast coincidence set-up with two identical 1-inch tapered off BaF2 scintillator
detectors fitted with XP2020Q photomultiplier tubes. The time resolution obtained
using 60Co source with 22Na gates was 285 ps. All lifetime spectra were analysed
using PATFIT 88 [17] programme.
9.3 Method of analysis In the present study, we have adopted the Rietveld’s powder structure
refinement analysis [9-13] of X-ray powder diffraction data to obtain the refined
structural parameters, such as atomic coordinates, occupancies, lattice parameters,
CHAPTER-9
~ 182 ~
thermal parameters etc. and microstructural parameters, such as particle size and
r.m.s. lattice strain etc. The Rietveld software MAUD 2.33 [14] is specially designed
to refine simultaneously both the structural and microstructural parameters through a
least-squares method. The peak shape was assumed to be a pseudo-Voigt function
with asymmetry. The background of each pattern was fitted by a polynomial function
of degree 4. In the present study, refinements were conducted without refining the
isotropic atomic thermal parameters.
Microstructure characterization of unmilled and all the ball milled powder
samples has been made by employing the Rietveld’s whole profile fitting method
based on structure and microstructure refinement [9-14]. The experimental profiles
were fitted with the most suitable pseudo-Voigt (pV) analytical function [12] because
it takes individual care for both the particle size and strain broadening of the
experimental profiles. Positron annihilation lifetime data were deconvoluted with
three lifetime components using the PATFIT programme. A total source correction of
10 % had been deducted while analysing the spectra.
9.4 Results and Discussion 9.4.1 X-ray diffraction analysis The fitted XRD powder patterns of unmilled CdO+α-Fe2O3 (1:1mol %)
homogeneous mixture and some of the selected patterns of ball-milled mixture
powders are presented in Fig.9.1. The powder pattern of unmilled mixture contains
only the individual reflections of CdO (ICDD PDF #5-0640) and α-Fe2O3 (ICDD
PDF #33-0664) phases. The intensity ratio of individual reflections is in accordance
with the stoichiometric composition of the mixture. It is evident from the figure that
in the course of ball milling, the peak broadening increases and CdO peaks are much
broaden in comparison to α-Fe2O3, implies that particle size of CdO reduces faster
than α-Fe2O3 phase. The formation of CdFe2O4 phase is first noticed clearly in the
XRD pattern of 5h milled powder with the appearance of isolated (220) (2θ = 29.040;
I/I0 = 60%) and (440) (2θ = 60.170; I/I0 = 35%) reflections.
CHAPTER-9
~ 183 ~
2 0 3 0 4 0 5 0 6 0 7 0 8 0
5 0 0 0
1 0 0 0 0
1 5 0 0 0
I o - I c
I o - I c
I o - I c
I o - I c
7 h
C d OF e 2 O 3
C d F e2O
4
I o - I c
2 5 h
5 h
P u r e
2 h
Inte
nsity
(arb
. uni
t)
2 θ ( d e g r e e )
Fig. 9.1 X-ray powder diffraction patterns of unmilled and ball milled CdO-α-Fe2O3 mixture (1:1mol%) The content of CdO phase has been reduced more rapidly in comparison to α-
Fe2O3 phase and except the isolated (200) (2θ = 38.3180; I/I0 = 88%) reflection, all
other reflections of CdO do not appear apparently in the XRD pattern of 5h milling
sample, because (i) small CdO particles contain huge amount of lattice strain arising
from high energy milling and (ii) the wt% of CdO has been reduced significantly
within this period of milling. As the milling goes on, peak broadening as well as
degree of overlapping of neighbouring reflections increases gradually. After 7 h of
milling, intensities of all CdFe2O4 reflections have been increased and relatively
strong (220), (311), (511) and (440) reflections are distinctly appeared in the XRD
pattern. In the mean time, all the reflections of CdO have been completely
disappeared and the peak intensities of α-Fe2O3 reflections have been reduced further.
Up to 10 h of milling, intensities of CdFe2O4 and α-Fe2O3 reflections increase and
decrease respectively. After 15 h of milling, wt% of α-Fe2O3 phase increases in
expense of CdFe2O4 phase and this trend continues upto 25 h of milling. The above
observations about phase transformation kinetics of nonstoichiometric ball milled
CHAPTER-9
~ 184 ~
powder mixture clearly reveals the following facts: (i) particle sizes of both the
starting materials reach a critical size within 5 h of milling and through the solid state
diffusion of highly active particles of both the phases the particles of CdFe2O4 phase
has been formed (ii) a significant amount of α-Fe2O3 phase does not take part in
ferrite formation and as a result the prepared ferrite is a non-stoichiometric one (iii)
increase in α-Fe2O3 content in expense of ferrite phase at higher milling due to
formation of nanocrystalline α-Fe2O3–CdFe2O4 solid solution.
0 4 8 12 16 20 240
15
30
45
60
75
90 CdO Fe2O3
CdFe2O4
Wt%
Milling time (h)
Fig. 9.2 Variation of phase content (wt.%) of different phase with increasing milling time.
Figure 9.2 shows the variation of relative phase abundances of different phases
with increasing milling time. The content (wt%) of CdO decreases very rapidly
whereas the wt% of α-Fe2O3 increases almost with the same rate with increasing
milling time. After 5h of milling, the wt% of α-Fe2O3 phase drops suddenly, this in
turn, results in formation of considerable amount of CdFe2O4 phase. After 7h of
milling when reflections of CdO phase completely disappear from XRD pattern (Fig.
1), the wt% of CdFe2O4 phase increased considerably at the expense of both the CdO
and α-Fe2O3 phases. Further milling in between 10-15h reveals that the wt% of α-
Fe2O3 phase increases at the expense of the CdFe2O4 phase. This trend of wt%
variation of these two phases continues till the end of ball milling up to 25h. The
CHAPTER-9
~ 185 ~
phase transformation kinetics of ferrite phase formation clearly reveals the following
facts: (i) increase in wt% of α-Fe2O3 up to 3h of milling is due to solid state diffusion
of CdO into α-Fe2O3 matrix (ii) the CdFe2O4 phase is formed from CdO-α-Fe2O3 solid
solution (iii) the increase in wt% of α-Fe2O3 phase at the expense of CdFe2O4 phase is
due to the formation of α-Fe2O3-CdFe2O4 solid-solution phase and (iv) the prepared
CdFe2O4 phase is a non-stoichiometric one because a considerable amount of α-Fe2O3
phase does not take part in CdFe2O4 phase formation even after 25h of ball milling.
5 10 15 20 25
2
3
4
5
6
0 5 10 15 20 254
6
8
10
60.0
60.5
61.0
61.5
0 1 2 3 4 52
4
6
220
222
224
(c) CdFe2O
4
L KPa
rticl
e si
ze (n
m)
Milling time (h)
(b) α-Fe2O
3Pa
rticl
e si
ze (n
m)
Milling time (h)
(a) CdO
Par
ticle
siz
e (n
m)
Milling time (h)
Fig. 9.3 Variation of particle size of CdO, α-Fe2O3 and CdFe2O4 with increasing milling time.
The natures of variations of particle size (D) of CdO, α-Fe2O3 and CdFe2O4
phases are shown in Fig.9.3. Except CdFe2O4 phase, particle sizes of other two phases
are found to be isotropic. Particle size of CdO phase decreases sharply from ~224nm
to ~7nm (Fig.9.3a) within 30min of ball milling and then slowly to ~3nm within 5h of
CHAPTER-9
~ 186 ~
milling. Particle size of α-Fe2O3 phase reduces less rapidly (Fig.9.3b) than CdO phase
and within 30min of milling it drops from ~61nm to ~11nm and reaches lowest value
of ~6nm within 2h of milling. It is then interesting to note the particle size of this
phase increases constantly with increasing milling time. The initial reduction and then
expansion of particle size value with increasing milling time is due to the well-known
fracture and re-welding mechanism of nanocrystalline particles [18, 19]. It is obvious
that during size reduction, particle fracture and during expansion (particle
agglomeration) re-welding of nanoparticles has been manifested. In contrast to the
particle size variation of these phases, the CdFe2O4 particles grow with a very small
isotropic size (~5nm) after 5h of milling (Fig.9.3c). Within 10h of milling, the particle
size becomes anisotropic and the degree of anisotropy increases with increasing
milling time. Particle size along the two major reflection directions [311] and [220]
has been estimated and their variation with increasing milling time is shown in Fig.
9.3c. It is evident from the figure that the particle size along [311] remains almost
constant but along [220] decreases continuously up to 25h of milling indicates that
(220) plane is more prone to deformation fault than most dense (311) plane of cubic
CdFe2O4 phase. It indicates that the oxygen vacancies have been created during ball-
milling on the (220) plane and one filled up by the substitution of the Cd atoms and
the mismatch in atomic size of these atoms may result in reduction in particle size
along [220]. All these observations regarding the particle size variation of all three
phases suggest that CdFe2O4 phase has been formed when particle size of α-Fe2O3
solid solution phase reduces to a minimum value of ~6nm, because the initial particle
size of Cd-ferrite is ~5 nm and it grows with growing oxygen vacancy with increasing
milling time.
9.4.2 Positron Annihilation Spectroscopy All the lifetime spectra of the samples were deconvoluted using three lifetime-
components τ1, τ2 and τ3 with corresponding intensities I1, I2 and I3 respectively.
Since the particle sizes of the constituents becomes less than the mean positron
diffusion length (~100 nm) within a short time during milling, positrons pass through
the grains and annihilate mainly in the grain boundary regions. In this case the
shortest lifetime (τ1) represents the weighted average of positron lifetimes at the grain
boundary defects (mono or di-vacancies) and the lifetime corresponding to
CHAPTER-9
~ 187 ~
annihilation with free electrons residing at the grain boundaries. The intermediate
lifetime τ2 corresponds to annihilations in the triple junctions. Triple junctions are
open volumes present at the intersection of three or more grain boundaries and their
size is of the order of 8-10 missing atoms. The fraction of positrons that gets
annihilated inside a grain depends on the positron ‘trapping capability’ of the defects
present at the grain boundaries. The more is the positron trapping at grain boundary
defects, the less is the probability of annihilation with free electrons inside a grain.
Therefore τ1 and τ2 in the present case may be expressed as follows.
( )∑ +=1i
BiiGBii nn τττ (9.1)
and,
( )∑=i
TPiinττ 2 (9.2)
where i stands for species of nanocrystalline grains viz., CdO, α-Fe2O3 or CdFe2O4,
GB stands for grain-boundary, B stands for bulk i.e. the defect free sites inside a grain,
n stands for the fraction of positrons annihilating in a particular site (GB or B) of a
particular type of grain i, and TP stands for triple junction.
The longest lifetime τ3 is attributed to the pick-off annihilation of ortho-
positroniums formed in the air trapped at the junction of sample-source sandwich.
0 5 10 15 200.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
Mea
n Li
fetim
e (n
s)
Ball - Mill Duration (h)
Fig. 9.4. Variation of mean-lifetime for CdO + α-Fe2O3 nanocomposites as a function of ball-mill duration.
CHAPTER-9
~ 188 ~
Figure 9.4 shows the variation of mean lifetime of cadmium ferrite nano-
composite as a function of ball-mill duration. τm is related to average defect density
and is defined as
321
332211
IIIIII
m ++++
=ττττ . (9.3)
For a given type (size) of defect, higher the defect density larger will be the
value of τm. The mean lifetime was seen to increase up to a ball-milling duration of 5
hrs. This is in good agreement with the XRD results where it was shown that the grain
size of the both CdO and α-Fe2O3 nanocrystals decrease. This might have resulted in
an increase in the surface to volume ratio, which in turn led to an increased trapping
of positrons at the grain boundaries. For rest of the ball milling process the mean
lifetime maintains a more or less same value indicating that the defect density remains
same thereafter.
To obtain an insight into the positron capture mechanism at various trapping
centers, the variation of the individual lifetime parameters with ball-milling duration
is to be seen.
0 5 10 15 200.1520.1600.1680.1760.1840.192
0.3000.3150.3300.3450.360
3035404550
τ1
Life
time
(ns)
Ball Mill Duration (hrs)
τ2
Life
time
(ns)
I2
Inte
nsity
(%)
Fig 9.5 Variation of τ1, τ2 and I2 for CdO + α-Fe2O3 nanocomposites as a function of ball-mill duration.
Figure 9.5 shows the variation of lifetime parameters viz., τ1, τ2 and I2. The
shortest lifetime component τ1 is seen to increase up to 5 hour milling duration . This
CHAPTER-9
~ 189 ~
increase is due to creation of defects associated with the reduction in grain size of
both CdO and α-Fe2O3. τ2 and I2 remain more or less constant up to 5 hour milling
duration. This indicates that the size and volume fraction of triple junctions remain
more or less same in that period of milling. During 5 to 10 hour ball milling duration
both τ1 and τ2 were seen to decrease. XRD results showed that CdO at this stage no
more exists in the composite whereas CdFe2O4 has formed. So contribution of CdO to
positron annihilation at grain surfaces, triple junctions or in the grain itself has
disappeared leading to a decrease in the value of τ1 and τ2. It may also be noted that
XRD results have indicated an upward trend for the size of α-Fe2O3 particles after 5
hour ball milling. This creates a reduction of the size of the triple junctions associated
with this component, which may also cause reduction of τ2. The increase of I2 after 5
hour ball milling is attributed to formation of CdFe2O4 phase and creation of
associated triple junctions. After 10 hour ball milling, the increase in τ1 is assigned to
lattice defects in the CdFe2O4 phase which is supported by the observed increasing
trend of r.m.s strain in the 311 direction (Table 9.1) as deduced from the XRD
analysis.
Table 9.1. Microstructure parameters of ball-milled CdO-Fe2O3 (1:1mol.%) powder revealed from Rietveld’s X-ray powder structure refinement method.
The slight increase of τ2 and decrease of I2 after 10 hour milling are attributed
to formation of larger vacant spaces at the triple junctions at the cost of smaller spaces
because of continuous reduction of size of the CdFe2O4 phase.
Milling time(h)
CdFe2O4
Lattice para- meter (nm)
Particle size (nm)
r.m.s.strain<ε2>1/2 X 103
Wt.%
[220] [311] [220] [311]
5 0.8663 5.1 5.1 6.68 6.68 45.8 7 0.8657 5.5 5.5 7.848 7.848 58.5 10 0.8652 4.3 5.4 7.448 8.968 59.4 15 0.8646 3.3 5.6 8.336 12.07 55.1 20 0.8641 2.5 5.8 8.951 18.213 41.3 25 0.8639 2.2 5.7 7.986 23.397 36.0
CHAPTER-9
~ 190 ~
0 5 10 15 201.8
1.9
2.0
2.1
2.2
2.3
2.4
1.2
1.4
1.6
1.8
2.0
τ3
Life
time
(ns)
Ball mill duration (h)
I3
Inte
nsity
(%)
Fig 9.6 Variation of τ3 and I3 for CdO + α-Fe2O3 nanocomposites as a function of ball-mill duration The fluctuations in the values of τ3 and I3 (Fig.9.6) is not connected to the structural changes and hence are not discussed. 9.5 Conclusions Microstructure characterization and phase transformation kinetic studies of
high-energy ball milled stoichiometric (1:1 mol%) CdO + α-Fe2O3 powder mixture
have been investigated by Rietveld analysis of X-ray powder diffraction data. The
experimental results reveal that the ball milled prepared Cd-ferrite phase is a non-
stoichiometric one.
The microstructure characterization of ball milled samples in terms of lattice
imperfections lead to the following important conclusions:
(i) the nanocrystalline Cd-ferrite phase is formed after 5h of milling from the
nanocrystalline CdO - α-Fe2O3 solid-solution.
(ii) the increase in α-Fe2O3 phase at higher milling time in expense of Cd-ferrite
phase is due to the formation α-Fe2O3 – CdFe2O4 solid solution.
(iii) a stoichiometric Cd-ferrite phase can not be prepared by just ball milling the
stoichiometric powder mixture even for a longer duration (25h).
CHAPTER-9
~ 191 ~
(iv) the anisotropy in particle size and lattice strain of ball milled Cd-ferrite phase
arises due to continuous creation of oxygen vacancies and occupation of these
vacant sites by smaller Cd atoms on (220) plane during milling.
(v) variation of positron annihilation mean lifetime with milling time indicates
increase of defect density in the composite up to 5 h milling , beyond that the
defect density remains more or less same. The variation of individual lifetime
parameters indicate disappearance of CdO phase from the composite and
formation of CdFe2O4 phase after 5 h milling. It also shows enhancement of
α-Fe2O3 particle size after 5h milling and formation of lattice defect in
CdFe2O4 after 10 h milling.
9.6 References [1] Goldman, Modern Ferrite Tech, Nostrand Reinhold, New York, 1990.
[2] B.M. Berskovsky, V.F. Mcdvcdcv, M.S. Krakov, Magnetic Fluids:
Engineering Applications, Oxford University Press, Oxford, 1993.
[3] V. Sepelak, A.Yu. Rogachev, U. Steinike, D. Chr. Uccker, F. Krumcich, S.
Wibmann, K.D. Becker, The synthesis and structure of nanocrystalline spinel
ferrite produced by high-energy ball-milling method, Mater. Sci. Forum 235-
238 (1997) 139.
[4] V. Sepelak, A. Yu, Rogachev, U. Steinike, D. Chr. Uccker, S. Wibmann, K.D.
Becker, Structure of nanocrystalline spinel ferrite produced by high-energy
ball-milling method, Acta Crystallogr. Suppl. A52 (1996) C367.
[5] S.J. Stewart, M.J. Tueros, G. Cernicchiaro, R.B. Scorzelli, Magnetic size
growth in nanocrystalline copper ferrite, Solid State Commun. 129 (2004)
347.
[6] M. Sinha, H. Dutta, S. K. Pradhan, Phase Stability of Nanocrystalline Mg–Zn
Ferrite at Elevated Temperatures, Japn. J .Appl. Phys. 47 (2008) 8667.
[7] C.N. Chinnasamy, A. Narayanasamy, N. Ponpandian, R. Justin Joseyphus, K.
Chattopadhyay, K. Shinoda, B. Jeyadevan, K. Tohji, K. Nakatsuka, H.
Guérault, J.-M Greneche, Structure and magnetic properties of nanocrystalline
ferrimagnetic CdFe2O4 spinel, Scripta Mater. 44 (2001)1411.
[8] N.M. Deraz, M.M. Hessien, Structural and magnetic properties of pure and
doped nanocrystalline cadmium ferrite, J. Alloys Compd. 475 (2009) 832.
CHAPTER-9
~ 192 ~
[9] H.M. Rietveld, Line profiles of neutron powder-diffraction peaks for structure
refinement, Acta Cryst. 22 (1967) 151.
[10] H.M. Rietveld, A profile refinement method for nuclear and magnetic
structures, J. Appl. Crystallogr. 2 (1969) 65.
[11] L. Lutterotti, P. Scardi, P. Maistrelli, LSI- a computer program for
simultaneous refinement of material structure and microstructure, J. Appl.
Crystallogr. 25 (1992) 459.
[12] R.A. Young, D.B. Wiles, Profile shape functions in Rietveld refinements, J.
Appl. Crystallogr. 15 (1982) 430.
[13] R.A Young, The Rietveld Method, Oxford University Press/IUCr, Oxford,
1996, pp. 1.
[14] L. Lutterotti, Maud version 2.33, 2011 <http://www.ing.unitn.it/~maud/>.
[15] A.K. Mishra, S.K. Chaudhuri, S. Mukherjee, A. Priyam, A. Saha, D. Das, Characterization of defects in ZnO nanocrystals: Photoluminescence and
positron annihilation spectroscopic studies, J.Appl. Phys. 102 (2007) art.
no.103514.
[16] R. Krause-Rehberg, H.S. Leipner, Positron Annihilation in Semiconductors,
Solid-State Sciences, Springer, Berlin, 1999.
[17] P. Kirkegaard, M. Eldrup, POSITRONFIT: A versatile program for analysing
positron lifetime spectra, Comput. Phys. Commun. 3 (1972) 240.
[18] S Bid, S. K. Pradhan, Preparation and microstructure characterization of ball-
milled ZrO2 powder by the Rietveld method: monoclinic to cubic phase
transformation without any additive, J. Appl. Crystallogr. 35 (2002) 517.
[19] N. J. Welham, Room temperature reduction of scheelite (CaWO4), J. Mater.
Res. 14 (1999) 619.
~ 193 ~
General conclusions
In the present dissertation, industrially important nanomaterials have been
prepared by (i) high energy ball-milling technique and (ii) sol-gel method. Different
kinds of characterization have been made employing X-ray powder diffraction,
positron annihilation technique, transmission electron microscopy, Mossbauer
spectroscopy and band gap measurement by UV-Vis spectrometer. Microstructure
characterization in terms of several lattice imperfections like change in lattice
parameters, particle size, r.m.s. lattice strain, dislocation density etc. has been made
employing basically the modified Warren-Averbach’s method of X-ray line profile
analysis and the Rietveld’s X-ray powder structure refinement method. Both the
Warren-Averbach and Rietveld methods of analysis indicate the anisotropy in particle
size and lattice strain values. Again the particle sizes have been calculated by the
transmission electron microscope (TEM) experiment. The point defects, voids,
cluster, have been detected by the positron annihilation experiments. Super
paramagnetic state of the nanocrystalline Fe2O3 has been identified by the Mossbauer
experiment In the band gap experiment the value of band gap energy Eg (for direct
transition) has been obtained from the intercept of the extrapolated liner part of the
(αhν)2 versus hν curve with the energy (hν) axis. However , the following most
important findings can be treated as general conclusions of the present dissertation:
(1) From X-ray line profile analysis, the lattice strain has been estimated which is
considerably high for all ball-milled α-Fe2O3 samples. Mössbauer spectra of α-
Fe2O3 ball-milled sample consists of a doublet which is attributed to the
superparamagnetic behaviour of ferromagnetic fine particles and a broad sextet
which is presumably due to high internal strain. The decrease in hyperfine field,
broadening of lines and asymmetry of line shape implies a broad particle size
distribution in the ball-milled sample.
(2) The XRD analysis reveals a substantial grain growth in nano-ZnO above 425 °C
temperature. Distinct decrease of the average lifetime of positrons also starts
from the same temperature. This indicates a lowering of defect concentration,
mostly cationic, due to annealing above 425 °C. Such a reduction of defects
continues up to 1100 °C annealing and little above 700 °C the sample becomes
less defective, even better than the as supplied ZnO. However, the band tailing
~ 194 ~
parameter (E0), which has contributions from all possible disorder, does not
reflect a lowering of defects for high temperature annealing (>700 °C).
(3) The strain introduced inside the nanocrystalline Fe2O3 samples increases with
ball milling hour. Ratio curve analysis of the CDBEPAR spectra for the
different hour milled and unmilled samples indicate the formation of cation type
of defects at the grain surfaces due to the ball milling process. Due to ball
milling, the average particle size of the Fe2O3 decreases, but due to the
formation of cation type of defects the optical band gap decreases.
(4) From Mössbauer spectra it has been observed that the nanocrystalline α-Fe2O3
as-prepared by chemical synthesis sample shows enhanced isomer shift (IS), line
width, and quadrupole splitting (QS), and hyperfine field (HF) values compared
to the annealed samples which may be due to the reduction of the electron
density at the interfacial site. From UV-Vis absorption spectra it has been
observed that the band gaps of the annealed samples are lower than the as-
prepared samples and all samples belong to n-type semiconductors.
(5) The quantitative analysis of the XRD data evaluated on the basis of Rietveld’s
powder structure refinement method yields detailed information about the
structure and microstructure of mechanosysthesized nanoscale zinc ferrite as
well as the redistribution of cations from the spinel ferrite. The main feature of
the structural disorder of mechanosynthesized zinc ferrite is the mechanically
induced inversion spinel structure. Positron annihilation lifetime data shows that
the mean lifetime τm does not change much with ball milling durations. This
implies that the overall defect density, as seen by the positrons remains more or
less constant during milling. In the positron annihilation lifetime data the
variation of individual life times τ1 and τ2 and corresponding intensities I1 and I2
shows evaluation of different phases with milling duration and confirms the
formation of inverse spinel ferrite structure.
(6) The nanocrystalline Cd-ferrite phase is formed after 5h of milling from the
nanocrystalline CdO - α-Fe2O3 solid-solution. The experimental results reveal
that the ball milled prepared Cd-ferrite phase is a non-stoichiometric one. The
variation of individual lifetime parameters indicate disappearance of CdO phase
from the composite and formation of CdFe2O4 phase after 5 h milling. It also
~ 195 ~
shows enhancement of α-Fe2O3 particle size after 5h milling and formation of
lattice defect in CdFe2O4 after 10 h milling.
Future plan of research work
In completing the present dissertation, I acquired knowledge about the
characterization of lattice imperfections in nano-crystalline materials by positron-
annihilation, x-ray diffraction and other methods. I have got interest in preparation of
nanocrystalline materials by high-energy ball milling because the materials change
their different properties with the different milling time. I wish to prepare
nanocrystalline multiphase materials. The microstructure characterization and
measurement of physical properties would be helpful to establish correlation between
microstructure and property.
~ 196 ~
List of publications
(1) “Nanophase iron oxides by ball-mill grinding and their Mössbauer
characterization”, S. Bid, Abhijit Banerjee, S. Kumar, S.K. Pradhan, Udayan
De, D. Banerjee,
Journal of Alloys and Compounds, 326, 292-297, (2001).
(2) “Annealing effect on nano-ZnO powder studied from positron lifetime and
optical absorption spectroscopy”, Sreetama Dutta, S. Chattopadhyay, and D.
Jana, Abhijit. Banerjee, S. Manik, and S. K. Pradhan, Manas Sutradhar, A.
Sarkar
Journal of Applied Physics, 100, 114328 (2006).
(3) “Particle size dependence of optical and defect parameters in mechanically
milled Fe2O3”, Mahuya Chakrabarti , Abhijit. Banerjee , D. Sanyal, Manas
Sutradhar, Alok Chakrabarti
J Mater Sci, 43, 4175–4181, (2008).
(4) “Microstructure, Mössbauer and Optical Characterizations of
Nanocrystalline α-Fe2O3 Synthesized by Chemical Route”, Abhijit
Banerjee, Soumitra Patra, Mahuya Chakrabarti, Dirtha Sanyal, Mrinal Pal,
Swapan Kumar Pradhan,
ISRN Ceramics, Volume 2011, Article ID 406094, 8 pages, (2011).
(5) “Microstructural changes and effect of variation of lattice strain on positron
annihilation lifetime parameters of zinc ferrite nanocomposites prepared by
high enegy ball-milling”, Abhijit.Banerjee, S. Bid, H. Dutta, S. Chaudhuri,
D. Das and S. K. Pradhan ,
Material Research (in press) (2012).
~ 197 ~
(6) “Microstructure and positron annihilation studies of mechanosysthesized
CdFe2O4”, Abhijit. Banerjee, S. Bid, H. Dutta, S. Chaudhuri, D. Das and
S.K. Pradhan,
Communicated to Acta Physica Polonica
Recommended