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Lesson 4 Rietveld Refinement Nicola Döbelin RMS Foundation, Bettlach, Switzerland October 16 – 17, 2013, Uppsala, Sweden

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### Transcript of Lesson 4: Rietveld Refinement

Lesson 4Rietveld Refinement

Nicola DöbelinRMS Foundation, Bettlach, Switzerland

October 16 – 17, 2013, Uppsala, Sweden

2

Repetition: Powder XRD Patterns

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0

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Inte

nsity

[cou

nts]

Diffraction Angle [°2θ]

Generation of X-rays

Diffraction at crystal structures

Powder samples (Debye rings)

Diffractometers (Types, optical elements)

Sample preparation (errors to avoid)

Phase identification

3

Rietveld Refinement

4

For more than just identification:

Rietveld refinement

Prof. Hugo Rietveld

- Unit cell dimensions

- Phase quantities

- Crystallite sizes / shapes

- Atomic coordinates / Bond lengths

- Micro-strain in crystal lattice

- Texture effects

- Substitutions / Vacancies

No phase identification!

Identify your phases first(unknown phase � no Rietveld refinement)

Needs excellent data quality!

No structure solution(just structure refinement)

Rietveld Refinement

5

Known structuremodel

10 20 30 40 50 600

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Inte

nsity

[cou

nts]

Diffraction Angle [°2θ]

Calculate theoreticaldiffraction pattern

Compare withmeasured pattern

Optimize structure model, repeat calculation

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Inte

nsity

[cou

nts]

Diffraction Angle [°2θ]

Minimize differences between calculated and observedpattern by least-squares method

Rietveld Refinement

6

10 20 30 40 50 60

-1000

0

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Inte

nsity

[cts

]

Diffraction Angle [°2theta]

Measured Pattern (Iobs) Calculated Pattern (Icalc) Difference (Iobs-Icalc)

Beginning of the refinement:

- Phase was identified correctly (peaksat the right position)

- But differences exist:

- Peak width

- Peak positions slightly shifted

- Intensities

Rietveld Refinement

7

10 20 30 40 50 60

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nsity

[cts

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Diffraction Angle [°2theta]

Measured Pattern (Iobs) Calculated Pattern (Icalc) Difference (Iobs-Icalc)

After the refinement:

- Straight difference curve (only noise)

Modelling the Peak Profile

8

27 28 29 30 31 320

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Inte

nsity

Diffraction Angle (°2θ)

CuKβ

CuKα1 & CuKα2 duplet

Remaining Bremsstrahlung

Absorption Edge

CuKα Satellites

(= CuKα3)

All these signals are generatedby one d-spacing.

Mathematical model to describethe profile is needed.

Modelling the Peak Profile

9

Pseudo Voigt curves for Kα1, Kα2 and Kβ

VP(x) = n * L(x) + (1-n) * G(x)

Gaussian curveLorentzian curve

Lorentzian (ω = 1.0) Gaussian (ω = 1.0) Pseudo-Voigt (n = 0.5)

L(x) = 1

1+( )2x-x0ω

G(x) = exp[-ln(2)·( )2]x-x0ω

Pseudo-Voigt Curves

10

n = 0.5

n = 0.25

n = 0.75

n = 0.0

n = 1.0

ω = 1.0

ω = 0.5

ω = 0.25

n = 0.5

Pseudo-Voigt Curves

11

Kα1

Kα2

Fitting n, ω to peaksof a reference material

ω2 = f(θ) = U · tan2(θ) + V · tan(θ) + W

Actually fitting n, U, V, W

Pseudo-Voigt: Problems

12

Asymmetry

Peaks at low 2θ anglesare asymmetric.

Pseudo-Voigt curvesare symmetric.

29.8 30.0 30.2 30.4 30.6 30.8 31.00

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nsity

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Diffraction Angle [°2θ]

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Inte

nsity

[cts

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Diffraction Angle [°2θ]

0.00

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FW

HM

[°2θ

]

Alternative Pseudo-Voigt Functions

13

Alternatives to PV function:

- Pearson VII

- Thompson-Cox-Hastings PV

- Split PV

- PV with axial divergence(Finger-Cox-Jephcoat PV)

FWHM of all these functionsmust be fitted to peaksof a reference material.

Common reference materialsdo not have peaks < 20° 2θ

Fundamental Parameters Approach FPA

14

Calculate the peak profile from the device configuration

Take into account the contributions of:

- Source emission profile (X-ray wavelength distribution from Tube)

- Every optical element in the beam path (position, size, etc.)

- Sample contributions (peak broadening due to crystallite size & strain)

ww

w.b

ruke

r.com

Tube Device Configuration Sample

Fundamental Parameters Approach

15

www.bruker.com

Fundamental Parameters Approach

16

2θ=10° 2θ=30° 2θ=80°

Calculated Peak Profiles

Fundamental Parameters Approach

17

FPA needs:

- Very detailed and complete description ofthe instrument configuration

- Very well aligned instrument

Fundamental Parameters Approach

18

http://www.bgmn.de

Fundamental Parameters Approach

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21.0 21.2 21.4 21.6 21.8

Inte

nsity

[a.u

.]

°2θ

63.0 63.2 63.4 63.6

°2θ

120 121 122

°2θ

If done properly:

Very good description of the peak profile

Fundamental Parameters Approach

20

- Some fundamental parameters are not documented

- Complete configuration can be hard to obtain

Good news:

We created and verified configurations for all instruments involved in the course!

Summary: Rietveld Basics

21

- Calculate XRD pattern from model structure

- Minimize differences between calculated and measured pattern

- Accurate mathematical description of peak profile required:

- Classical Rietveld approach: Fit a peak shape function (PVor similar) to reference pattern

- Fundamental Parameters Approach: Calculate peakprofile from device configuration

Rietveld Software Packages

22

- Fullprof

- GSAS

- BGMN

- Maud

- Brass

- … many more1)

Commercial Software:

- HighScore+ (PANalytical)

- Topas (Bruker)

- Autoquan (GE)

- PDXL (Rigaku)

- WinXPOW (Stoe)

1) http://www.ccp14.ac.uk/solution/rietveld_software/index.html

FPACommercial UI

for BGMN

BGMN

23

BGMN:

- Fundamental Parameters Approach

- Open source (GPL v2 since mid 2013, not officially announced yet)

- Device independent

- Very robust automatic refinement strategy

- Good usability (at least better than most other academic programs)

- Slightly less steep learning curve

- Powerful scripting language

- Multi-Platform

Visit: http://www.bgmn.de for tutorials and documentation

Graphical User Interfaces for BGMN

24

BGMNwin (shipped with BGMN software package)

Graphical User Interfaces for BGMN

25

Profex (developed by Nicola Döbelin)

- Open source

- Multi-Platform

- Device database

- Structure database

- Batch processing

- File conversion

- …

Example Refinement

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1.

2.

3.

Example Refinement

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1.

2.

3.

4.

5.

Example Refinement

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Start Refinement

Example Refinement

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1.

2.

3.

Example Refinement

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Good fit

Summary

Summary: BGMN and Profex

31

- BGMN is the Rietveld kernel

- Fundamental Parameters Approach

- Profex is an editor / graphical user interface to BGMN

- Best-case scenario (example):

- Specify instrument configuration from internal database

- Load structure files from internal database

- Start refinement

- … done

Refinement Strategies

32

10 20 30 40 50 60

-1000

0

1000

2000

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5000

Inte

nsity

[cts

]

Diffraction Angle [°2theta]

Measured Pattern (Iobs) Calculated Pattern (Icalc) Difference (Iobs-Icalc)

Relation

Mismatch – Structural Feature

Refinement Strategies

33

Wrong peak positions:

- Unit cell dimensions

- Sample height displacement

- Zero-shift (instrumentmisalignment)

Refinement Strategies

34

Wrong absolute intensities:

- Weight fraction (scaling)

Refinement Strategies

35

Wrong relative intensities:

- Preferred orientation

- Graininess

- Atomic species

- Atomic coordinates

- Site occupancies

- Thermal displacementparameters

Refinement Strategies

36

Wrong peak width:

- Crystallite size

- Micro-strain in crystal structure

Summary: Refinement Strategy

37

Effect in diffraction pattern Origin in crystal structure model

Wrong peak positions Unit cell dimensions

Sample height displacement

Zero-shift

Wrong absolute intensities Weight fraction (scaling)

Wrong relative intensities Preferred orientation

Atomic species / Substitutions

Atomic coordinates

Site occupancies

Thermal displacement parameters

Wrong peak width Crystallite size

Lattice strain