Inorganic materials chemistry and functional …folk.uio.no/ravi/cutn/scm/synthesis/XRD_Method-ANJA...Inorganic materials chemistry and functional materials Helmer Fjellvåg and Anja

Inorganic materials chemistry

and functional materials

Helmer Fjellvåg and Anja Olafsen Sjåstad

Lectures at CUTN spring 2016

X-ray diffraction and structure analysis

Crystal planes - Miller indices ( h k l )

Recipe:

1. Identify the plane that is adjacent

to an equivalent plane that

passes through origin

2. Find intersection of this plane

with unit cell edges (a, b, c)

3. The reciprocals of these values

are the Miller indices of the planes

(1/ 0)

c

a

b

h

(001)

a b c

1

h k l

1/ 1/ 1/1

0 0 1

Crystallographic planes and directions

Crystal planes – Miller indices ( h k l ) – parallell planes

Crystallographic planes and directions

sin2 hkldn

BD = d sin DC = d sin BDC = 2d sin = n

X-ray diffraction; methods and analyses

Bragg’s law

If Bragg’s eq. is NOT satisfied then NO diffraction can occur

If Bragg’s eq. is satisfied then diffraction MAY occur

Diffraction = Reinforced Coherent Scattering

Reflection versus Scattering

Reflection Diffraction

Occurs from surface Occurs throughout the bulk

Takes place at any angle Takes place only at Bragg angles

~100 % of the intensity may be

reflected Small fraction of intensity is diffracted

X-rays can be reflected at very small angles of incidence; X-ray reflectometry


Peak Positions: Miller Indices (hkl)

2 Theta (Degrees)

20 30 40 50 60

Inte

nsity

(111) / d = 3.26Å

(200) / d = 2.82Å

(220) / d = 1.99Å

(400) / d = 1.41Å

(311) / d = 1.70Å

7


sin2 hkldn

Lin

(C

ou

nts

)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

14000

15000

16000

17000

18000

19000

2-Theta - Scale

10 20 30 40 50 60 70 80 90

The powder X-ray diffraction pattern

Diffraction peak

Intensity (relative)

Position (2Q, d)

Peak profile (width)

background


Characteristic features of the pattern

Diffraction peaks

• Intensities

• Position (2theta d-values; Braggs law)

• Profile (width FWHM; Gaussian & Lorentzian contributions)

• Due to ONE or MORE crystalline phases

Background

• Caused by diffuse scattering etc.

• Caused by fluorescence

• Caused by sample holder (capillary); sample prep..

• Caused by amorphous impurities


Information to be analyzed/extracted

• Position (2Q d-values; Braggs law)

– Unit cell dimensions

• Intensities

– Presence/absence symmetry (space group)

– Atomic arrangement = crystal structure; coordinates

– Preferred orientation of crystallites

• Profile (width FWHM; Gaussian & Lorentzian)

– Particle size, strain, stacking disorder

• Intensity+position

– Phase identification; qualitative + quantitative analysis

– Crystal structure


“Fingerprint” phase identification

Bragg’s law shows us that the diffraction pattern is very

characteristic of the crystal lattice for a given phase

We can use the diffraction pattern for phase identification

Visual (if you know the pattern of your phase)

Databases (COD, PDF2, ICDD FindIt)

When we know the phase

we can study it further…

11


2 Theta (Degrees)

20 30 40 50 60

Inte

nsity

Phase ID and quantification from powder

555453525150494847464544434241403938373635343332313029282726252423222120

800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

50

0

-50

-100

-150

-200

-250

Silicon 5.51 %

KCl 8.75 %

Apatite-(CaOH) 34.31 %

Arcanite 15.06 %

Calcite 31.55 %

Quartz low 0.87 %

Periclase 3.96 %

example


State of the sample ?

• Amorphous

• Crystalline (repeating atomic arrangement in 3D)

(inorganic, organic, biomaterials,…..)

• Single crystals

• Powder samples (micron sized particles)

• Nanomaterials (particles, colloids,…)

• Thin films (multilayers, heterostructures)

• Multiphased (composites)

• ...........


0 1 2 3 4 5 60

10

20

Fre

que

ncy %

dimameter / nm

900 W, 5min

DMF, PVP 0.8 gr

mean: 3.3 nm

SD:0.79

Small Spheres mol PVP / mol Precursors = 0.28

2 4 6 8 100

5

10

15

20

25

Fre

qu

en

cy %

diagonal / nm

900 W, 5min

DMF, PVP 0.4 gr

mean: 6.4 nm

SD:1.1

Truncated Cubes mol PVP / mol Precursors = 0.14

Monodisperse Pt-Rh nanoparticles

20 nm

20 nm

5 nm

5 nm

Dr. M. Kalyva, NAFUMA group

Utstyr og brukere Single crystals

Single crystallites = single crystals; but can be extremely small

OK for electron diffraction (very short wave length)

Larger single crystals;

may ”consist of more” mosaicity

may consist of twinned crystals (rooted in the symmetry)

Suitable size for home laboratory: some 50 micron and upwards

Suitable size at synchrotron: a few microns and upwards

Fe Ti

Ni

BF image

EFTEM images

Si substrate

JB1044

NAFUMA @ SMN / KI / UiO

Activities: thematic overview Thin films and multilayers

sin2 hkldn

Lin

(C

ounts

)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

14000

15000

16000

17000

18000

19000

2-Theta - Scale

10 20 30 40 50 60 70 80 90

The sample

Data collection

Theory and tools Results

structure, composition, morphology


Before experiment: what does my sample contain?

Just light elements?

A lot of heavy elements?

Certain transition elements that may give a lot of

fluorescence scattering if Cu-X-rays are used?

Regular particles, or platelets or needles

(impurities; amorphous stuff,….)

Necessary for optimizing the experiment

Transmission (light elements) vs reflection (heavy)

Choice of radiation (wavelength)

Means to reduce preferred orientation

Sample Preparation

Essential for reliable PXRD data!

Bad sample preparation can lead to:

Incorrect peak positions

Bad peak shapes

Incorrect intensities

5 minutes of sample preparation can save hours of

work identifying and fitting phases from bad data!

19


Sample Preparation Sample holder must be full, with powder homogeneously packed

Top of sample must be flat and level with sample holder

“Powder mountain” – Wrong peak positions

– Wrong peak intensities

– Wrong peak shapes

“Powder Valley” – Wrong peak positions

– Wrong peak intensities

– Broad/double peaks

Correct preparation Correct peak positions

Correct peak intensities

Sharp peaks


Sample preparation

2 Theta

30 31 32 33 34 35 36

Correct

2 Theta

20 30 40 50 60 70 80

Powder

valley

Powder

mountain


Preferred orientation issues becomes important when

crystallization gives: needles or platelike crystallites

When preparing a sample for powder X-ray diffraction, it then

becomes difficult to distribute the sample in such a way that all crystal

planes are randomly distributed in space

the diffraction pattern is hence reflecting the orientation of the

crystallites; results in preferred orientation effects

gives systematic enhancement/weakening of certain I(hkl)

May sometimes be helpful to grind the material

along with an inert standard

One may also observe other effects; e.g.

- width of diffraction peaks may vary


Peak Intensity: Preferred Orientation

E.g. mica flakes; tend to lie flat on plate sample holders

23


Peak Intensity: Preferred Orientation

Strong P.O. effects can in the extreme case lead to

peaks being completely absent from the diffractogram

Can be avoided by correct sample preparation

Capillaries

Roughened sample holders

Can also be modelled in profile fits

24

MICA

Operations: Import

MICA - File: COURSE_280311_MICA.raw - Type: 2Th/Th locked - Start: 3.000 ° - End: 40.003 ° - Step: 0.016 ° - Step time: 0.3 s - Temp.: 25 °C (Room) - Time Started: 16 s - 2-Theta: 3.000 ° - Theta: 1.500 ° - Chi: 0.

Lin

(C

ounts

)

0

10000

20000

30000

2-Theta - Scale

3 10 20 30 40

mica

Operations: Import

mica - File: mica_group_II.raw - Type: 2Th/Th locked - Start: 3.000 ° - End: 70.002 ° - Step: 0.008 ° - Step time: 0.5 s - Temp.: 25 °C (Room) - Time Started: 15 s - 2-Theta: 3.000 ° - Theta: 1.500 ° - Chi: 0.00 ° - Phi: 0

Lin

(C

ounts

)

0

100

200

300

400

500

600

700

2-Theta - Scale

3 10 20 30 40 50 60 70


Heat

Incident X-rays

SPECIMEN

Transmitted beam

Fluorescent X-rays Electrons

Compton recoil Photoelectrons Scattered X-rays

Coherent

From bound charges

Incoherent (Compton modified)

From loosely bound charges

X-rays can in addition be refracted and also reflected


http://www.esrf.eu/cms/live/live/en/sites/www/home/about/synchrotron-

science/synchrotron-light-animation.html



A broad range of wavelengths/energies available

Depends on machine and optical elements (magnets)

Selected by monochromators

Allows experiments with fixed wavelength (typically for diffraction)

Allows spectroscopy over selected energy ranges

Hard X-rays: for diffraction/scattering, spectroscopy, imaging...

Soft X-rays: for spectroscopy,...

Brilliance: no. of photons of a given wavelength,

direction focused on an area per unit of time.


Principle of X-ray tube (home lab)

• Electrons are emitted

by heated cathode and

accelerated towards

anode.

• They hit the anode

which leads to – Creation of white radiation

(Bremsstrahlung).

– Emission of characteristic

radiation (cf anode material)

– Heat evolution (98-99% of

the total energy!).

– Hence; cooling by water….

+-

6 V

³15 kV

e-

Emission window (Be)

Anode

Heated cathode

Vacuum

IKa1

KbKa2

Typical anode materials:

Cu, Mo, Cr, Co, Ag


Spectrum consists of both

white (continuous) radiation

and characteristic radiation

Target for use:the strong Ka

In some cases are Ka1 and

Ka2 overlapping (not

resolved). A diffraction

experiment can then result in

only one single peak.

Otherwise partly splitted

peaks will be observed.

The weaker Ka2-radiation can

be removed by means of a

primary monochromator

(a single crystal of e.g. Ge)

White radiation


L K Ka (2p 1s)

M K Kb (3p 1s)

K-shell

Characteristic radiation

The energy difference depends on the element !

Wavelength depends on type of anode in the X-ray tube

Main quantum number

An electron is first kicked out from

the inner level

This hole is then filled by an

outer electron (L, M shell);

and light (Xrays) are emitted

Instrumentation RECX @ KI/NAFUMA

Top of sample

Correct too high too low

Gives rise to height error (shift in observed Bragg positions)

And may after analyses yield incorrect unit cell dimensions

Hence; height correction must (always) be carried out

Helpful; use of internal standard for calibration


Structure factor (F)

Occupation number

Polarization factor

Lorentz factor

Absorption factor

Displacement factor

Scattering from atoms in the unit cell; coordinates

Number of equivalent scattering planes

Effect of wave polarization; instrument dependent

Combination of three geometric factors

Specimen absorption; element dependent

Dynamics of atoms; static displacements

2

1

2

1

SinCos

SinfactorLorentz

21 2CosIP

(hkl) multiplicity

Site occupancy for atoms in the unit cell


Absorption Intensity loss due to sample absorbing the x-ray beam

Wavelength dependent

Sample and geometry dependent

For flat plate absorption is a linear function

For cylindrical sample/Debye-Scherrer transmission geometry

there is angular dependence

For transmission geometry: the absorption should be

calculated prior to data collection, and if needed, the

sample should be diluted

34


linear absorption coefficient [cm-1]

dt thickness

Attenuation (loosing intensity) through collisions with atoms

teII

dtIdI

0


m

miiP

Mass absorption coefficient m = density

If the absorbing sample consists of more elements:

P = weight fraction of the relevant element

Radiation with low energy

(high ) is heavily absorbed

Soft radiation (low energy) will

not penetrate absorbing samples

Radiation with higher energy

is absorbed less

Hard radiation is then useful

1/wavelength

long short

Home lab: Energy defined by

the type of X-ray tube

Synchrotron: all wavelengths

available


energy

Absorption

edge

Fine

structure


L K Ka (2p 1s)

M K Kb (3p 1s)

K-shell

Characteristic radiation

The energy difference depends on the element !

Wavelength depends on type of anode in the X-ray tube

Main quantum number

An electron is first kicked out from

the inner level

This hole is then filled by an

outer electron (L, M shell);

and light (Xrays) are emitted

Linear absorption coefficient

depends on wavelength and sample

increases with increasing (i.e. lower energy)

is discontinuous (due to absorption edges)

Absorption is at maximum at a slightly lower (higher E)

than the absorption edge

For medium heavy elements, the K-absorption edge is in

the range of commonly used for X-ray diffraction

experiments

For heavy atoms, K-electrons are hardly excited and

hence L-edge is more important with respect to

absorption of home-lab X-rays)



Argonne web-page; help to calculate absorption and

dilution of sample with an inert

How to reduce absorption (in transmission geometry):

Sample dilution by mixing in:

Silica (will enhance amorphous background)

MgO; a few additional peaks; well-defined, easy to analyse

KCl: a few additional peaks + increased absorption

Just use a smaller capillary; ...?

Uneven particle distribution

Poor capillary filling


Fluorescence

Fluorescence by Co compared to Ni when using CuKa1 radiation

Fluorescence reduces the signal-to-noise ratio

Can be filtered electronically in many cases

Alternatively: use a different energy for the X-ray radiation

Highly increased background


Cu-Kα

Vacuum level

Energy

levels

KE

1LE

2LE

3LE

K

1L

2L

3L

Emission of

characteristic fluorescent x-rays

Emitted in all directions

Electron kicked out

from inner shell


Fluorescence

Incoming

X-rays


Atoms in an excited state generated by absorption of X-rays, may emit characteristic radiation by outer electrons falling into vacant inner orbitals

Fluorescence has always lower energy (longer wavelength) than the exciting (incoming) X-ray radiation

Atoms are excited more strongly by radiation with wavelength close to the absorption edge

Fluorescence radiation is the basis for X-ray fluorescence spectrometry (XRF)

NB! For X-ray diffraction fluorescence is a nuisance and

experimental conditions should be selected so as to

minimize its impact

Fluorescence

Documents

Inorganic materials chemistry and functional …folk.uio.no/ravi/cutn/scm/synthesis/XRD_Method-ANJA...Inorganic materials chemistry and functional materials Helmer Fjellvåg and Anja