FEATURE ARTICLE www.rsc.org/materials | Journal of Materials Chemistry

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Advanced electron microscopy and its possibilities to solvecomplex structures: application to transition metal oxides

Gustaaf Van Tendeloo,*a Joke Hadermann,a Artem M. Abakumovab and Evgeny V. Antipovb

Received 13th October 2008, Accepted 12th December 2008

First published as an Advance Article on the web 4th February 2009

DOI: 10.1039/b817914j

Design and optimization of materials properties can only be performed through a thorough knowledge

of the structure of the compound. In this feature article we illustrate the possibilities of advanced

electron microscopy in materials science and solid state chemistry. The different techniques are briefly

discussed and several examples are given where the structures of complex oxides, often with

a modulated structure, have been solved using electron microscopy.

1. Introduction

When Ernst Ruska and Max Knoll built their first transmission

electron microscope (TEM) in 1931, they probably had no idea

of the impact of their invention. Their initial goal was to obtain

a resolution better than that of the optical microscope. They

easily succeeded, but their application to biological materials was

a disaster; the samples carbonised under the electron beam. Only

after the Second World War did electron microscopy become

a scientific technique, available in some specialised laboratories.

The spatial resolution gradually improved and in 1971 Hashi-

moto and Formanek showed independently the first direct

images of gold atom columns.1,2 For a long time the resolution of

the instruments seemed to be hampered by the aberration of the

lenses in the electron microscope, but about 10 years ago, this

problem was tackled and aberration corrected electron micro-

scopes have been developed.3,4 Now in 2008 a resolution of 0.05

Gustaaf Van Tendeloo

Gustaaf Van Tendeloo was

educated as a physicist. In 1974

he obtained his Ph.D. at the

University of Antwerp on

ordering phenomena in alloys.

He had several research periods

at the University of California

(Berkeley), University of Illi-

nois (Champaign-Urbana) and

the Universit�e de Caen. He is

a co-author of over 600 papers

and his h-index is 50. Presently

he is the head of the EMAT

research group and the NANO

Centre of Excellence of the

University of Antwerp. His current interest is in advanced electron

microscopy and nanostructured non-metallic materials.

aEMAT, University of Antwerp, Groenenborgerlaan 171, B-2020, Antwerp,Belgium. E-mail: staf.vantendeloo@ua.ac.be; Fax: +3232653257; Tel:+3232653262bDepartment of Chemistry, Moscow State University, Moscow, 119992,Russia

2660 | J. Mater. Chem., 2009, 19, 2660–2670

nm (50 pm) can been achieved by the most advanced instruments

(http://ncem.lbl.gov/TEAM-project).

2. Advanced electron microscopy

‘‘Resolution’’ however should not be confused with ‘‘precision’’.

Resolution is determined by the instrument and is classically

defined as the minimum distance between two objects that are

separately reproduced in a real space image. The instrumental

resolution of an electron microscope however is better defined in

reciprocal space through the information limit in the Fourier

transform of the high resolution image. ‘‘Precision’’ in a high

resolution image is defined as a measure of how accurately one

can define the position of the peak corresponding to a projected

atom column; it is not only determined by the instrument, but

also by the statistics, i.e. the noise on the measurement. Although

the resolution of modern instruments is 50 to 100 pm, the

precision to determine projected atom positions through high

resolution microscopy can be down to 1 or a few pm. An

example is shown in Fig. 1 for a complex oxichloride with the

nominal composition Bi4Mn1/3W2/3O8Cl. The figure shows

a phase reconstructed image5 based on 20 images taken with

Joke Hadermann

Dr Joke Hadermann studied

physics at the University of

Antwerp, where she received her

Ph.D. in 2001 and obtained

a position as lecturer in 2002.

Her research interests are new

materials, electron crystallog-

raphy and aperiodic crystals.

She is a co-author of more than

50 publications in international

journals.

This journal is ª The Royal Society of Chemistry 2009

Table 1 Projected interatomic distances obtained from X-raypowder diffraction and the phase of the reconstructed wave forBi4Mn1/3W2/3O8Cl

X-ray powder diffraction (�A) Phase of reconstructed wave (�A)

d1 1.79(2) 1.83(5)d2 2.07(2) 2.08(6)d3 1.70(2) 1.8(1)d4 2.17(5) 2.10(3)d5 0.96(7) 1.04(4)d6 2.14(5) 2.29(5)d7 1.63(3) 1.43(5)d8 2.57(3) 2.6(1)

Fig. 1 Phase of the reconstructed exit wave for Bi4Mn1/3W2/3O8Cl. The

bright dots correspond to the starting projected positions of the different

atoms. The scheme at the bottoms indicates the refined projected

distances corresponding to Table 1.

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very small defocus difference. The individual images were

taken with an instrument having an information limit of 110

pm, but the position of the oxygen atoms (weakly visible and

indicated in Fig. 1 by white circles) could be determined with

a precision of 3–5 pm. This precision is of the same order of

magnitude as can be reached by powder XRD (Table 1).

Details can be found in ref. 6.

However, one should not forget that this information is only

two dimensional. Indeed, a TEM image is only a projection of the

three dimensional structure and therefore a single high resolution

image is generally unable to solve a three dimensional structure.

In the case of a crystalline material, TEM images along different

zone axes and prior compositional knowledge of the material can

overcome this problem. The major advantage of electron

microscopy over other diffraction techniques such as XRD or

neutron diffraction is that even nanosize crystallites or highly

faulted materials do not form an obstacle. In this sense electron

Artem Abakumov

Dr Artem Abakumov received

his Ph.D. in 1997 at the

Department of Chemistry of

Moscow State University and

obtained a scientific researcher

position at the Inorganic Crystal

Chemistry Laboratory. He

spent three years as a post-

doctoral fellow and as invited

professor at the Electron

Microscopy for Material

Research (EMAT, University of

Antwerp) laboratory and joined

EMAT as a professor in 2008.

His research interests are

crystal chemistry and properties of mixed oxides, modulated

structures, local structure determination by electron microscopy.

He is a co-author of more than 100 articles, 2 patents and more

than 60 contributions to international conferences.

This journal is ª The Royal Society of Chemistry 2009

microscopy (including electron diffraction and different imaging

techniques) is very complementary to more bulk-oriented tech-

niques of structure characterization.

In conventional TEM all incident electrons are parallel and the

image is recorded in one single shot with an exposure time of the

order of a second. However there is another way to form an

image! One can focus the electron beam into a fine spot on the

sample, scan the beam over the sample and record the trans-

mitted image point by point; this is the so-called scanning

transmission electron microscopy (STEM) mode. This technique

attracted a lot of attention since Browning et al. proved that

atomic resolution could be obtained.7 Since the inelastic scat-

tering strongly depends on the atomic number Z, this technique

also showed possibilities for chemical analysis on an atomic

scale. Images recorded in dark field, eliminating the transmitted

beam as well as the elastically scattered electrons (using a high

angle annular detector), are therefore also called ‘‘Z-contrast’’

images. At present the resolution in HAADF (high angle annular

dark field) STEM is comparable to the resolution in TEM. Most

important for the materials scientist however is that the infor-

mation in both techniques is complementary: TEM mainly

provides information on the lattice, the symmetry and the pro-

jected atom positions; STEM contains information on the lattice,

Evgeny Antipov

Evgeny Antipov is professor

at the Department of Chemistry

of Moscow State University,

head of the Electrochemistry

Department, Inorganic Crystal

Chemistry Laboratory and

Laboratory for Basic Research

in Aluminum Production. His

research interests are crystal

chemistry of inorganic com-

pounds, synthesis of new inor-

ganic materials with important

physical properties and X-ray

diffraction. He is a co-author of

more than 240 papers in refereed

journals and over 60 invited talks. He was awarded the Karpinskij

Award of the Alfred Toepfer Foundation, Russian State Award,

Lomonosov Award of the Moscow State University and the Award of

the World Congress on Superconductivity.

J. Mater. Chem., 2009, 19, 2660–2670 | 2661

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but also provides a map of scattering density that is strongly

correlated with the local composition.

The strength of ‘‘electron microscopy’’ however is that this

local information in real space can be combined with information

in reciprocal space. Electron diffraction is in many respects

complementary to X-ray diffraction and neutron diffraction. The

scattering by X-rays or neutrons is kinematic while the scattering

for electrons is dynamic. The interaction between matter and

electrons is about 104 times stronger than the scattering of X-

rays, therefore an electron can be scattered more than once

during its trajectory through the material. As a consequence the

scattered intensity is no longer proportional to the squared

modulus of the structure factor and strongly depends on the

crystal orientation and the local sample thickness. Particularly

the latter is difficult to access. However, the strong electron–

matter interaction also has its advantages: electron diffraction

patterns can be obtained from nanometer small regions and weak

modulations are much more easily detected, as we will illustrate

below.

The strength of electron microscopy for the materials science

and inorganic chemistry society also benefits from complemen-

tary techniques such as EDX (energy dispersion of X-rays) and

EELS (electron energy loss spectroscopy). While EDX is more

reliable in composition determination for heavy elements, EELS

is more quantitative, particularly for lighter elements. Analysing

the energy loss of the transmitted electron beam provides infor-

mation on the local composition as well as on the local band

structure of the material.8 The combination of (S)TEM and

EELS has existed for a few decades, but only recently have

improvements in instrumentation and software made it a user

friendly and more quantitative technique. A major difficulty is

the fact that one is interested in weak excitation peaks, super-

imposed on a huge background. Using the EELSMODEL soft-

ware9 reliable chemical information can be obtained on a local

scale. This is particularly interesting to analyse chemical diffu-

sion or valence changes at interfaces or grain boundaries. An

example of the power of EELS in obtaining electronic structure

information is the study of the multilayer LaAlO3 (LAO)–SrTiO3

(STO) heterostructure. Since the discovery by Ohtomo and

Hwang10 that the LAO/STO interface becomes conducting, while

the STO/LAO interface remains insulating, there has been

speculation on the origin of this effect and the valency change of

the different elements.11,12 Recent measurements of the fine

structure of the EELS spectrum indicate a clear difference in the

oxygen K edge between both interfaces.13

Fig. 2 Crystal structure of Sr4Fe6O13. The iron atoms are in green

octahedra and yellow five-fold polyhedra, the Sr atoms are shown as large

blue spheres.

3. TEM analysis of complex modulated structures

We will illustrate the power of electron microscopy for the study

of different families of complex transition metal oxides. All

selected compounds are modulated structures; the modulation is

induced by a combination of displacive and occupational

modulation waves, composite structure formation or periodic

translational interfaces. The analysis of these materials through

conventional bulk diffraction techniques failed because of

intrinsic disorder or structural inhomogeneities originating from

either:

– chemical inhomogeneity resulting in local variations of the

modulation vector related to compositional fluctuations;

2662 | J. Mater. Chem., 2009, 19, 2660–2670

– structural disorder resulting from a weak interaction

between the modulated fragments, such as chains or layers;

– intergrowth of interface modulated structures with similar

chemical compositions and/or different crystallographic orien-

tation of the interfaces.

3.1 Modulated structures in Sr4Fe6O12+d with local variation

of the oxygen content

The Sr4Fe6O13 perovskite-type oxide (Fig. 2) and its anion-

deficient derivatives Sr4Fe6O12+d (d < 1) demonstrate a complex

mechanism of anion non-stoichiometry through compositional

and displacive modulations in the double NaCl-like Fe2O2+a

blocks.14–17 These blocks consist of two iron–oxygen (FeO) layers

where the oxygen and iron atoms are arranged according to the

motif of a face-centered cubic lattice (Fig. 3, top). There are

tetrahedral voids between these layers and they can be occupied

by extra oxygen atoms. Alternation of the filled and empty voids

gives rise to occupational modulations. However, such idealized

atomic arrangement does not satisfy the local crystal chemistry

requirements and inappropriate interatomic distances should be

optimized by cooperative atomic displacements which results in

displacive modulations (Fig. 3, bottom).

Due to the ability of iron atoms to acquire a variable oxidation

state between +2 and +3, bulk powder samples of Sr4Fe6O12+d

strongly suffer from local oxygen inhomogeneity.15 Because the

oxygen content is directly related to the wavelength of the

occupational modulation, the positions of the satellite reflections

change substantially for different crystallites of Sr4Fe6O12+d. It

makes conventional X-ray powder diffraction useless to inves-

tigate the modulated structure of this material because only

reflections from the basic structure are observed on the

powder XRD patterns.15 The relationship between the

This journal is ª The Royal Society of Chemistry 2009

Fig. 3 The structure of the Fe2O2+a layer. Top: the idealized NaCl-like

arrangement with extra oxygen atoms in tetrahedral voids; bottom: the

structure modified by displacive modulations. Extra oxygen atoms are

shown by arrows.

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modulation vector and the oxygen content, as well as the struc-

ture models for the commensurately modulated cases, have been

determined from electron diffraction and high resolution elec-

tron microscopy data; this was done for Sr4Fe6O12+d with

different oxygen contents in bulk as well as in thin film

materials.13,15

The electron diffraction data were interpreted using the (3 +

1)-dimensional superspace formalism. Analysis of the geometry

of the electron diffraction patterns provides valuable informa-

tion required for further structure modelling: 1) orientation and

length of the modulation vector; 2) (3 + 1)D superspace group

for the modulated structure; 3) lattice parameters and possible

atomic arrangement for the basic structure; 4) a set of possible

3D space groups for commensurately modulated structures. The

electron diffraction patterns of Sr4Fe6O12+d (Fig. 4) were indexed

with the diffraction vector g ¼ ha* + kb* + lc* + mq, q ¼ aa*,

where a*, b*, c* are the reciprocal lattice vectors of the basic

structure. The hkl0 reflections correspond to a face-centered

orthorhombic basic unit cell with a z apO2, b z 20.6�A, c z apO2

(ap is the a parameter of the perovskite subcell). From the

observed reflection conditions the superspace group was deter-

mined as Xmm2(a00)0s0 with centering vectors (0, ½, ½, ½), (½,

0, ½, 0), (½, ½, 0, ½). If a is rational (i.e. it can be expressed as

Fig. 4 [001] ED patterns of the Sr4Fe6O12+d compounds and their

indexation schemes for a ¼ 1/3 (a, b) and a ¼ 0.39 (c, d).

This journal is ª The Royal Society of Chemistry 2009

p/q where p, q are integers with reasonably small numbers), the

modulation can be considered as commensurate and can be

equally described as a superstructure with the lattice parameters

qa, b, c. For the commensurately modulated structure, the actual

3D symmetry of the superstructure depends on the choice of the

initial ‘‘phase’’ of the modulation t (the underlying theory is

described in International Tables for Crystallography18 and in

a recent book of Van Smaalen19). For different choices of t and

a the 3D symmetry is derived from the (3 + 1)D space group by

restricting it to a subgroup which leaves the physical 3D space

invariant (see Table 1 from ref. 15). For example, for Sr4Fe6O13

with a¼ 1/2, the 3D space group Iba2, as determined from single

crystal X-ray diffraction data,20 corresponds to t ¼ (2n + 1)/8

(n ¼ integer).

The next step in building the structure model should consist of

determining the exact shape of the occupational and positional

modulation functions. The intensities of the satellite reflections

normally provide this information, but in the case of electron

diffraction these intensities are significantly affected by dynam-

ical scattering that hampers the quantitative estimation of the

coefficients of the modulation functions.21–23 A qualitative idea of

the origin of the modulations can be obtained from HREM

images and knowledge of the crystal structures of the commen-

surate members that were refined using other diffraction tech-

niques, such as X-ray diffraction from a single crystal (Sr4Fe6O13

in the present case).22 Two [001] HREM images of Sr4Fe6O12+d

with very similar defocus and thickness conditions, correspond-

ing to a ¼ 1/3 and a ¼ 0.39, and their corresponding Fourier

transforms (FT) are shown in Fig. 5. The average visible repeat

period along the b axis corresponds to the –SrO–FeO2–SrO–

Fe2O2+d–SrO– sequence of alternating layers. A comparison of

the simulated and experimental images shows that the thicker

bright layers correspond to the Fe2O2+d layers. These layers

demonstrate a (quasi)periodic variation of the contrast related to

the modulations. Assuming that the average repeat period along

the Fe2O2+d layers is equal to the average distance between the

tetrahedral voids filled with extra oxygen atoms, and that

the spacings between the filled voids form a uniform sequence,

the average spacing n between the filled voids can be calculated as

n¼ 2/a¼ x{n} + (1� x)({n} + 1), where {n} is the integer part of

n, x stands for the fractional part of the spacing with a width

of n, and 1 � x is the fractional part of the n + 1 spacing. The

compound composition can therefore be written as

Sr4Fe6O12+2a. This dependence between a and the oxygen

content was subsequently confirmed by the single crystal XRD

structure solution of Sr4Fe6O12.9217 and by the preparation of the

isostructural Ba4In4+4aMg2�4aO12+2a solid solutions,24 where the

oxygen content is fixed by the degree of heterovalent replacement

of In3+ by Mg2+.

Unfortunately, the parameters of the positional modulation

functions for the Fe and O atoms in the Fe2O2+d layers can not be

reliably determined from the HREM images. A tentative model

of the atomic displacements and local coordination of the Fe

atoms was proposed by comparison with the known Sr4Fe6O13

crystal structure. Therefore the structure models were constructed

for the commensurately modulated compounds with a ¼ 2/5 and

1/3. The proposed atomic arrangement in the Fe2O2+d layers

qualitatively reproduces the main aspects found experimentally in

the Sr4Fe6O12.92 and Ba4In4+4aMg2�4aO12+2a structures.17,24

J. Mater. Chem., 2009, 19, 2660–2670 | 2663

Fig. 5 [001] HREM images of the Sr4Fe6O12 + d phases showing (a)

a commensurate modulation with a ¼ 1/3 and (b) an incommensurate

modulation with a ¼ 0.39; (c) and (d) are the corresponding FT patterns

of (a) and (b), respectively. The commensurate 3a0, b0 supercell is out-

lined by a white rectangle for a ¼ 1/3. White brackets mark the sequence

of spacings between the filled tetrahedral voids for a ¼ 0.39.

Fig. 6 Examples of naturally occurring frameworks built up from MnO6

octahedra, a) pyrolusite, b) ramsdellite, c) hollandite, d) todorokite

(shown is the synthetic todorokite [SrF0.82(OH)0.18]2.5[Mn6O12] discussed

in this paper, with four mixed cation–anion columns inside the tunnels;

natural todorokite contains only one).

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3.2 Occupational and positional modulations in tunnel

manganites AxMnO2

A large family of complex Mn-based oxides are the so-called

‘‘tunnel’’ manganites with general formula AxMnO2. The struc-

tures within this family have a framework constructed from

MnO6 octahedra, which are connected into infinite chains by

edge sharing. These chains themselves are connected either by

edge- or by corner-sharing, forming the walls of tunnels of

different shapes.27 Some examples of well known tunnel frame-

works are shown in Fig. 6. The larger tunnels can accommodate

chains of A cations inside. In such a case, the positive charge of

these cations in the tunnels is compensated by a partial reduction

of Mn4+ to Mn3+, often followed by charge ordering, as was

found for example in the case of hollandite,28 romanechite,29 and

todorokite (in contrast to other tunnel oxides, the tunnels in

todorokites are occupied by [A(H2O)6] octahedral strings with

water molecules at the corners of the octahedra and the alkali

2664 | J. Mater. Chem., 2009, 19, 2660–2670

and/or alkali-earth cations A at the centers of these octahedra).30

All tunnel frameworks have a characteristic cell parameter along

the tunnels of approximately 2.9 �A, which corresponds to the

Mn–Mn distance across the common edge of two adjacent MnO6

octahedra. However, the preferred spacing for the A cations

along the chains is not necessarily the same as the spacing

between the stacked MnO6 octahedra. The average distance

between the A cations is related to their overall content and the

positions of the A cations correspond to a minimum in the free

energy of their electrostatic repulsion and their interaction with

the periodic electrostatic potential of the tunnel walls. Since the

framework is rigid and keeps its characteristic repeat period

along the tunnels, two different periodicities arise leading to

a modulated structure. The modulated structure can alterna-

tively be described as a composite structure consisting of the

MnO2 (framework) subsystem and the Ax (cation chains)

subsystem.31

The problem in the characterization of tunnel structures is

related to the weak correlation between the A-cation chains in

neighbouring tunnels, which are effectively shielded from each

other by the tunnel walls. Even if perfect order of the A cations

occurs along one chain, the neighbouring chains can be displaced

in a disordered manner along the tunnel direction. The structure

then represents 1D order with corresponding sheets of diffuse

intensity in reciprocal space, perpendicular to the tunnel direc-

tion32,33 (Fig. 7). The structural analysis of these compounds can

be separated into two parts: 1) the determination of the shape of

the tunnels and how they are arranged into the framework; 2) the

determination of the ordering pattern of the A cations within the

tunnels.

On a projection along the tunnel direction, the tunnels often

form a two-dimensional lattice with a nearly rectangular mesh,

so that there is no specific feature of the geometry of the electron

diffraction patterns that can be used to reveal the framework

structure. However, the tunnel framework can be easily

This journal is ª The Royal Society of Chemistry 2009

Fig. 7 [010] Electron diffraction pattern of the todorokite-type

compound [SrF0.82(OH)0.18]2.5[Mn6O12] demonstrating diffuse intensity

sheets perpendicular to c*.

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distinguished using direct space imaging in TEM or STEM. This

is illustrated in Fig. 8 for the compounds SrMn3O634 and

CaMn3O635 where the electron diffraction patterns along the

tunnel direction are shown together with the corresponding

HRTEM images. The electron diffraction patterns have very

similar geometry: a rectangular mesh with nearly the same ratio

between the lengths of the shortest reciprocal lattice vectors, 1.25

for CaMn3O6 and 1.32 for SrMn3O6. On both HRTEM images

the dark areas correspond to the projected positions of the cation

columns, the black dots to Mn and the grey ones to the A (¼Ca,

Sr) cations. A set of Mn columns forming a single tunnel is

indicated by connected white dots. In SrMn3O6 the tunnels have

the shape of an ‘‘8’’, while for CaMn3O6 the tunnels are six-sided.

The HRTEM clearly reveals the different structures of the tunnel

frameworks: CaMn3O6 is a marokite type structure with six-

sided tunnels, whereas SrMn3O6 has’’8’’-shaped tunnels, similar

to those found in NaxFexTi2�xO423,24 and BaPb1.5Mn6Al2O16

38

(see Fig. 8).

Fig. 8 Electron diffraction patterns (top) and HREM images along the

tunnel directions (bottom) for SrMn3O6 (left) and CaMn3O6 (right). The

positions of the cation columns forming the tunnels are marked on the

HREM images.

This journal is ª The Royal Society of Chemistry 2009

In addition to the reflections from the tunnel framework, extra

reflections induced by the order between the A cations and cation

vacancies appear on the electron diffraction patterns. The final

interpretation of the reciprocal lattice actually depends on the

strength of the interaction between the A cations along the chains

and between the A cations and the tunnel walls. If the A cations

are tightly bonded to the walls and this interaction overcomes the

electrostatic repulsion between the A cations, then the displace-

ment of the A cations from their basic positions in the tunnels can

be considered as small. The order of the A cations can then be

described as an alternation of filled and vacant sites obeying a step-

like occupational modulation function. In this case the structure is

represented as a modulated structure with the diffraction vector

given as g ¼ ha* + kb* + lc* + mq, where a*, b*, c* are the

reciprocal basic vectors of the lattice of the tunnel framework

which can be considered as the basic structure. On the other hand,

at the limit of strong repulsion, it can be expected that the A

cations will tend to distribute themselves as evenly as possible

along the tunnels, i.e. they should be subjected to large longitu-

dinal displacements. The structure is then better described as

a composite structure consisting of two mutually modulated

subsystems. The first subsystem is the tunnel framework MnO2

with lattice vectors a, b, c1 and the second subsystem is Ax with

lattice vectors a, b, c2, where the c axis is oriented along the tunnels.

The indexation is performed with g ¼ ha* + kb* + lc1* + mq, q ¼gc1*¼ c2*. The real situation often lies between these two limiting

cases. For example, in the crystal structure of CaMn3O6, 1/3 of the

A sites are empty and the vacant and occupied sites are distributed

in an ordered manner giving rise to a commensurate modulation

with q ¼ 2/3a* + 1/3c*.35 The g component of q is responsible for

the order along the A-cation chain, whereas the a component

arises due to a shift of the occupational modulation wave on going

from tunnel to tunnel. SrMn3O6 with q ¼ 0.52a* + 0.31c* also

demonstrates a step-like occupancy modulation of the Sr posi-

tions, but in this case it is superimposed with linear displacements,

which are adequately described with a saw-tooth function.34 The

todorokite-type [SrF0.82(OH)0.18]2.5[Mn6O12], on the other hand,

is better described as an incommensurate composite structure.39

The octahedral tunnel walls compose subsystem I with a [Mn6O12]

composition and a periodicity c1 ¼ 2.84�A while the [Sr(F,OH)]4columns belong to subsystem II with a periodicity c2 ¼ c1/g ¼4.49�A, resulting in a [Sr(F, OH)]4g[Mn6O12] composition (Fig. 9).

Fig. 9 An enlarged part of the [010] ED pattern of [SrF0.82(OH)0.18]2.5-

[Mn6O12] and the indexation scheme. White squares mark the reflections

common for subsystems I and II. Black and grey squares stand for the

main reflections of subsystems I and II, respectively. The small black circles

are the satellites.

J. Mater. Chem., 2009, 19, 2660–2670 | 2665

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The [Mn6O12] framework, shown in Fig. 5d, consists of walls built

up of three edge-sharing rutile-type strings of MnO6 octahedra

forming large square tunnels. The interior space in the tunnels is

filled with rock-salt type [Sr(F,OH)]4 columns. The periodicity of

the rock-salt fragment along the tunnel is significantly larger than

the periodicity of the tunnel walls. This expansion of the rock-salt

subsystem is required to achieve appropriate Sr–(F,OH) separa-

tions and gives rise to a composite structure. The composite

modulated structure representation was also proposed for hol-

landites33 and for the Ba6Mn24O48 manganite.31

The A cation composition in the tunnels (x in the AxMnO2

formula) can be directly deduced from the modulation vector

obtained from the ED patterns if the ratio between the number of

A-cation chains in the tunnels (r) and the number of chains of

MnO6 octahedra in the tunnel walls (p) is known; this r/p ratio

depends on the structure of the framework, and can be deduced

from the HRTEM and STEM images. The r/p ratio changes from

2/3 in Na4Mn9O1840 and Na1.1Ca1.8Mn9O18,41 1/2 in CaMn2O4,42

AMn3O6 (A ¼ Ca, Sr),34,35 CaMn4O843 to 5/12 in Ba6Mn24O48,31

2/7 in woodruffite Znx/2(Mn4+1–xMn3+

x)O2$yH2O,44 1/4 in hol-

landite BaxMn8O1645 and 1/6 in todorokites (Na, Ca, K, Ba,

Sr)0.3–0.7(Mn, Mg, Al)6O12$3.2–4.5H2O46 (Fig. 6 and 10). The

amount of A cations relative to MnO2 can be evaluated from the

g component of the modulation vector as x ¼ (1 � g)r/p, or x ¼c1r/c2p if the structure is represented as a composite one. Because

of this relation between g and the cation composition, a (local)

cation inhomogeneity can induce a displacement of the satellite

reflections on the electron diffraction patterns. For example, in

the sample with nominal composition SrMn3O6 domain forma-

tion occurs with neighbouring domains exhibiting slight

Fig. 10 Frameworks of a) SrMn3O6, b) CaMn3O6 (marokite-type), c)

Na1.1Ca1.8Mn9O18 (orange spheres Ca and green spheres Na).

2666 | J. Mater. Chem., 2009, 19, 2660–2670

differences in chemical composition and, hence, in the modula-

tion vector.34 ED patterns from different domains are shown in

Fig. 11. They correspond to a variation of the g value in the

range of g ¼ 0.28 to 1/3 and compositions ranging from

Sr1.08Mn3O6 to SrMn3O6. These variations could not be detected

in the XRD or NPD data.

3.3 Perovskites modulated by translational interfaces.

Perhaps the most famous examples of structures modulated by

periodically arranged translational interfaces are the crystallo-

graphic shear (CS) structures in anion-deficient oxides derived

from ReO3 or rutile (TiO2) type structures.47–51 The shear oper-

ation consists of: a) cutting the parent structure into parallel

blocks along lattice planes (hkl) equally spaced by ndhkl, where n

is an integer and dhkl is the interplanar spacing of the (hkl) lattice

planes; b) eliminating a layer of material with a thickness that is

a fraction of dhkl: gdhkl, with 0 < g < 1; c) closing the gap by

displacing the blocks relative to each other over a vector R with

a component R0 ¼ �gdhkl perpendicular to the (hkl) planes.52

The shear operation eliminates the oxygen vacancies and changes

the connectivity scheme of the metal–oxygen octahedra, so that

along the CS plane the octahedra share edges or faces instead of

corners or edges as in the parent structure. When applied to the

perovskite ABO3 structure, the shearing operation generates

a homologous series of ferrites A4p+3qFe4(p+q)O10p+9q (A ¼ Pb,

Sr, Ba)53–55 and the manganite ‘‘PbMnO2.75’’.56 These different

phases are all formed using the same building principles, where

the R ¼ 1/2[110]p shear vector is applied along the (h0l)p lattice

plane (subscript p denotes the perovskite subcell). CS planes with

CaMn4O8, d) Ba6Mn24O48 and e) Na4Mn9O18 (all spheres Na) and

This journal is ª The Royal Society of Chemistry 2009

Fig. 11 ED patterns along the [010] direction of different domains in SrMn3O6 with different types of A-cation order in the tunnels. A rectangle

connecting the same four basic reflections has been drawn on each pattern as a guide to the eye, and the modulation vector q is indicated, and is slightly

different for each pattern. The modulation vector and composition derived from the pattern are, from left to right: q¼ 2/3a* + 1/3c* giving Sr1.00Mn3O6,

q ¼ 0.52a* + 0.31c* giving Sr1.04Mn3O6, q ¼ 0.54a* + 0.28c* giving Sr1.08Mn3O6.

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high (h0l)p index can formally always be considered as a combi-

nation of fragments of low-index CS interfaces, such as 1/

2[110](�101)p, 1/2[110](100)p and 1/2[110](001)p (Fig. 12).57 Along

the interfaces, edge-sharing metal–oxygen polyhedra are formed,

instead of corner-sharing octahedra in the parent perovskite

structure. The chemical composition of the final structure

depends on the crystallographic orientation of the CS plane as

well as on the block thickness between successive CS planes. For

example, the compounds belonging to the A4p+3qFe4(p+q)O10p+9q

(A ¼ Pb, Sr, Ba) homologous series contain the (p0(p + q))p ¼p{101}p + q{001}p CS planes that gives the A4p+3qFe4(p+q)O10p+9q

¼ pA2Fe2O4 + qAFe2O3 + 2(p + q)AFeO3 composition when

Fig. 12 Schematic representation of the structures of the low-index

interfaces of the CS planes in perovskites: a) 1/2[110](�101)p; b) 1/

2[110](100)p; c) 1/2[110](001)p. The edge sharing polyhedra are coloured

blue.

This journal is ª The Royal Society of Chemistry 2009

combined with a perovskite block 2(p + q)AFeO3, the thickness

of which is determined by the Fe oxidation state of +3.

In contrast to CS planes in binary oxides, the orientation and

interplanar spacing of CS planes in perovskites influence both the

cation and anion content. Changing the orientation of the CS

planes and the thickness of the parent structure block between

the CS planes requires long range cation migration that is

possible only at elevated temperatures. Thus, the nucleation of

CS planes in perovskites occurs at the stage of the solid state

reaction. The preparation of a single-phase compound with

a single type of 1/2[110](h0l)p CS plane is hampered even by small

cation inhomogeneity. This results in a number of defects in these

compounds, such as twinned microdomains related by a mirror

plane and numerous coherent intergrowths of the 1/2[110](h0l)p

CS structures with different (h0l)p.58 Moreover, the CS structures

can demonstrate incommensurability due to slight orientation

and spacing anomalities of the translational interfaces. This

makes TEM virtually the only tool for revealing and analysing

the structure of such materials.

Analysis of the geometry and (qualitatively) the intensity

distribution of the electron diffraction patterns provides a useful

set of data. The reciprocal lattice of structures modulated by

periodic translational interfaces demonstrates specific features

compared to displacive or composition modulated structures.

For the latter structures, there is a set of strong reflections

associated with the basic structure, accompanied by a set of

generally weaker satellite reflections related to the periodic

perturbation of that basic structure. The reflection positions are

defined by g¼G + mq, where G is a reciprocal vector of the basic

structure and q ¼ aa* + bb* + gc* is the modulation vector, m is

an integer. For the interface modulated structures this expression

can be modified to g ¼ G + [m + G$R]q, where q ¼ e/d is the

modulation vector, e is a unit vector normal to the interface

plane, d is the interplanar distance for the interfaces, and R is the

displacement vector for the interfaces, which cannot be a lattice

translation of the basic structure, but only a fraction of it.52,59

The product G$R results in a ‘‘fractional shift’’ of the array of

satellites with respect to the position of the basic spots (even

when they are extinct). The fractional shift method defines the

projection of R onto G; measurements for three independent G

reflections therefore determine the complete displacement vector

R. In the kinematical approximation, the intensity of the satellite

depends on how closely it is located to the basic node and varies

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as a slit function sin(pud)/pud, centred at the basic spot G, where

u is the reciprocal distance between the basic node G and the

satellite g. Thus, the position of the basic lattice node is revealed

by the centre of mass of the intensity of the satellite reflections

assigned to this basic spot.

The [010] electron diffraction pattern of the Pb15Fe16O39 CS

structure, with a grid of basic reflection positions and a scheme of

the fractional shift determination superimposed, is shown in

Fig. 13. The direction of the satellite rows provides the crystal-

lographic orientation of the CS planes, the spacing between the

satellites gives the interplanar spacing of the CS planes, and the

fractional shift gives the components of the displacement vector.

In Fig. 13 the CS planes are parallel to (104)p and are spaced by

approximately 14.8�A. The q vector (marked by brackets) is

directed along the row of satellite reflections. The u and w

components of the displacement vector R ¼ [u v w] can be

determined from Fig. 12. The first non-extinct basic spots along

a* and c* are 200 and 003, respectively, which result in u ¼ 1/2

and w¼ 1/3 since the fractional shift for these reflections is 0. The

fractional shifts for other hkl reflections are in agreement with R

¼ 1/2 + v + 1/3. The v ¼ 1/2 component can be deduced in the

same way from the [001] electron diffraction pattern (not shown).

This determines R ¼ [1/2 1/2 1/3] ¼ 1/2[110] + 1/3[001], from

which the first term corresponds to the pure shear vector and the

second term is a relaxation part.58

Fig. 13 Application of the fractional shift method for the [010] ED

pattern of the Pb15Fe16O39 CS structure: a) the basic reciprocal lattice

where the lattice nodes are located at centres of mass of the intensity of

the satellites; b) derivation of the fractional shifts h$R for the satellite

arrays. Squares stand for the positions of the basic nodes. Brackets mark

the modulation vector q.

2668 | J. Mater. Chem., 2009, 19, 2660–2670

The atomic structure at the CS plane can be deduced from

real space information. Imaging in HRTEM is unable to

provide reliable information on the locations of the Fe and Pb

cations. HAADF-STEM imaging along the direction parallel

to the CS plane however will provide the required chemical

information.53 An unfiltered [010] HAADF-STEM image of

Pb15Fe16O39 is presented in Fig. 14a. Two types of dots with

significantly different brightness can be recognized. Based on

the Z dependence, and verified by the calculated image (shown

as inset), the brighter dots are associated with the Pb columns

(forming the prominent pattern on the image) whereas the less

bright dots (hardly visible in the image) correspond to the Fe

columns. Image distortions due to microscope instabilities

while scanning the focused electron probe hamper precise

determination of the atomic coordinates of the projected

columns. The atomic coordinates are therefore calculated using

the transformation matrix from the perovskite subcell to the

monoclinic supercell of a commensurate approximant, and

then the types of atomic columns (either Pb or Fe) are assigned

according to the spot brightness on the HAADF-STEM image.

The resulting atomic arrangement is shown at the bottom of

Fig. 14, along with a complete structure derived from crystal

chemistry considerations and subsequently confirmed by

comparison of experimental and calculated HREM images

(Fig. 15).

Fig. 14 (a) [010] HAADF-STEM image of the Pb15Fe16O39 CS struc-

ture. The unit cell is marked with white lines; the image simulation (inset)

is outlined by a white border. (b) Location of the Pb and Fe columns in

the monoclinic unit cell. The perovskite blocks (dashed rectangles) are

marked with a fat broken line. The thin dotted lines mark the CS planes.

This journal is ª The Royal Society of Chemistry 2009

Fig. 15 The perspective view of the Pb15Fe16O39 CS structure. The FeO5

tetragonal pyramids are blue, the Pb atoms are yellow and green. The

corresponding HREM image is shown below. The calculated [010] image

(Df ¼ �275 �A, t ¼ 30 �A) is superimposed on the experimental image

(outlined by a fine white border). The superstructure unit cell is outlined.

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Conclusions

The evolution of electron microscopy over the last few years has

been such that structural, chemical as well as electronic infor-

mation is available on a local scale. This is extremely important

for materials science in general and for the development of new

materials in particular. Electron microscopy is therefore very

complementary to bulk characterization techniques such as

XRD and neutron diffraction.

Since direct imaging allows the positioning of atoms with

picometer precision and since EELS data are able to provide

band structure sections with a resolution of 0.1 eV, electron

microscopy is, finally, at a stage where a comparison with

theoretical results from modeling is no longer a dream. Beyond

any doubt, in the near future, this will be possible not only for

simple structures, but also for more complex inorganic

materials.

Acknowledgements

The authors are grateful to S. Bals, S. Van Aert, J. Verbeeck, M.

G. Rozova, S. Ya. Istomin, L. Gillie, C. Martin, O. P�erez, E.

Suard and M. Hervieu for the use of common results. A.M.A.

and E.V.A. are grateful to Russian Foundation of Basic

Research (RFBR grants 07-03-00664-a, 06-03-90168-a).

This journal is ª The Royal Society of Chemistry 2009

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