Lesson 1 Rietveld Refinement - Profexprofex.doebelin.org/.../07/Lesson-1-Rietveld-refinement.pdf · Lesson 1 Rietveld Refinement and Profex / BGMN Nicola Döbelin RMS Foundation,

Lesson 1

Rietveld Refinementand Profex / BGMN

Nicola Döbelin

RMS Foundation, Bettlach, Switzerland

June 13 – 15, 2018, Bettlach, CH

2

Diffraction Pattern

10 20 30 40 50 60

0

200

400

600

800

1000In

tensity [counts

]

Diffraction Angle [°2]

Diffraction Angle

Absolute Intensity

Relative Intensity

Shape

3

Diffraction Pattern

Diffraction Angle:

Phase Identification

Absolute Intensity:

Phase Quantification

Relative Intensity:

Crystal Structure Determination

Shape:

Crystallite Size and Shape, Lattice Strain

Phase Identification

4

10 20 30 40 50 60

0

200

400

600

800

1000

Inte

nsity [counts

]

Diffraction Angle [°2]

«Pattern Features» originate from crystallographic properties

Feature Origin

Peak positions - Symmetry of the unitcell (space group)

- Dimensions of theunit cell

Relative peak intensities - Coordinates of atomsin unit cell

- Species of atoms

Absolute peak intensities - Abundance of phase

Peak width - Crystallite size- Stress/Strain in crystal

lattice

Usually sufficient for identification

5

Search-Match for Phase Identification

Rietveld Refinement

6

For more than just identification:

Rietveld refinement

Prof. Hugo Rietveld

Extracts much more information from powder XRD data:

- 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

7

Known structure

model

10 20 30 40 50 60

0

1000

2000

3000

4000

Inte

nsity [co

un

ts]

Diffraction Angle [°2]

Calculate theoretical

diffraction pattern

Compare with

measured pattern

Optimize structure model, repeat calculation

10 20 30 40 50 60

0

1000

2000

3000

4000

Inte

nsity [co

un

ts]

Diffraction Angle [°2]

Minimize differences between calculated and observed

pattern by least-squares method

Rietveld Refinement

8

10 20 30 40 50 60

0

1000

2000

3000

4000

5000In

ten

sity [cts

]

Diffraction Angle [°2theta]

Measured Pattern (Iobs)

Calculated Pattern (Icalc)

Difference (Iobs-Icalc)

Rietveld Software Packages

9

Academic Software:

- Fullprof

- GSAS

- BGMN

- Maud

- Brass

- … many more1)

Commercial Software:

- HighScore+ (PANalytical)

- Topas (Bruker)

- Autoquan (GE)

- PDXL (Rigaku)

- Jade (MDI)

- WinXPOW (Stoe)

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

BGMN: Based on Text Files

10

Refinement

Control File

(*.sav)

Geometric

Instrument Data

(*.geq)

Wavelength

Distribution

(*.lam)

Diffraction

Pattern

(*.xy)

Structure

Models 1…n

(*.str)

Refined

Parameters

(*.lst)

Refined

Pattern

(*.dia)

Peak

Parameters

(*.par)

Refined

Structures(*.str, *.res, *.fcf, *.pdb…)

Run BGMN

BGMN

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Profex: A Graphical User Interface for BGMN

12

13

Profex: A Graphical User Interface for BGMN

Developer: Nicola Döbelin (private)

License: GPL v2 or later (open source)

Founded in: 2003

Platforms: Windows 7 / 8 / 8.1 / 10

Linux

Mac OS X 10.9 -10.13 (64bit)

Rietveld Backends: BGMN, Fullprof.2k

Website: http://profex.doebelin.org

Current stable version: 3.13.0

Create and manage refinement projects

Convert raw data files for BGMN

Export results and graphs

Batch refinements

Structure and Instrument

file repositories

+ many more…

Profex Key Features

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Fitting Data

15

𝑓 𝑥 =1

𝜎 2𝜋∙ 𝑒

−𝑥−𝜇 2

2𝜎2

Fitting experimental data requires an adequate mathematical model

𝑓 𝑥 = 𝑎 ∙ 𝑒−𝑥𝑡 + 𝑦0

Fitting Data

16

𝑓 𝑥 =𝐴1

𝜎1 2𝜋∙ 𝑒

−𝑥−𝜇1

2

2𝜎12

𝑔 𝑥 =𝐴2

𝜎2 2𝜋∙ 𝑒

−𝑥−𝜇2

2

2𝜎22

ℎ 𝑥 =𝐴3

𝜎3 2𝜋∙ 𝑒

−𝑥−𝜇3

2

2𝜎32

Fitting Data

17

𝑓 𝑥 𝜎1, 𝐴1, 𝜇1)

𝑔 𝑥 𝜎2, 𝐴2, 𝜇2)

ℎ 𝑥 𝜎3, 𝐴3, 𝜇3)

𝐹 𝑥 = 𝑓 𝑥 + 𝑔 𝑥 + ℎ(𝑥)

Fitting Data

18

𝐹 𝑥 | 𝜎1, 𝐴1, 𝜇1, 𝜎2, 𝐴2, 𝜇2, 𝜎3, 𝐴3, 𝜇3

𝐹 𝑥 | 𝜎, 𝐴1, 𝜇1, 𝐴2, 𝜇2, 𝐴3, 𝜇3

If not all parameters are independent,

(for example constant σ):

Fitting Diffraction Patterns

19

Fit every single peak to determine:

- Position (diffraction angle 2θ)

- Integrated intensity (area)

- Width

Fitting Diffraction Patterns

20

- Diffraction angle lattice plane spacing d

- Lattice type

- Space group

- Unit cell dimensions

- Intensity Structure factor Fhkl

- Atomic species

- Fractional coordinates

- Site occupancies

- Thermal vibration

- Phase quantity

- Width

- Crystallite size

- Micro-strain

Fitting Diffraction Patterns

21

Mathematical model for peaks

in a XRD pattern needed

Fitting Diffraction Patterns

22

2θ = 11.65° 2θ = 35.15°

Modelling the Peak Profile

23

34.8 34.9 35.0 35.1 35.2 35.3 35.4 35.5

Diffraction Angle [°2]

11.3 11.4 11.5 11.6 11.7 11.8 11.9 12.0

Diffraction Angle [°2]

Two Gaussian functions

Modelling the Peak Profile

24

Traditional («Rietveld») Approach:

Pseudo-Voigt curves for Kα1, Kα2 and Kβ

GAUSS LORENTZ PVN05

PVN025

PVN075

PVN0

PVN10

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

𝑉𝑃 𝑥 = 𝑛 ∙ 𝐿 𝑥 + (1 − 𝑛) ∙ 𝐺(𝑥)

Lorentzian Gaussian

Profile functions in FullProf.2k

25

Alternative: Fundamental Parameters Approach (FPA)

26

Origin of peak shape features:

- Wavelength distribution

(radiation spectrum)

- Instrument configuration

2θ = 11.65° 2θ = 35.15°

FPA: Simulate peak shape based on instrument

geometry and wavelength distribution

FPA: Wavelength Contribution

27

Origin of peak shape features:

- Wavelength distribution

(radiation spectrum)

- Instrument configuration

Wavelength

𝐾𝛼1

𝐾𝛼2 2𝜃 = 2 ∙ asin𝜆

2𝑑

2θ = 11.65° 2θ = 35.15°

FPA: Wavelength Contribution

28

2𝜃 = 2 ∙ asin𝜆

2𝑑

5 10 15 20 25 30 35 40

0.00

0.02

0.04

0.06

0.08

0.10

Sp

acin

g b

etw

ee

n C

uK

a1

an

d C

uK

a2

[°2

the

ta]

2Theta [°]

0 20 40 60 80 100 120

0.0

0.1

0.2

0.3

0.4

0.5

Sp

acin

g b

etw

ee

n C

uK

a1

an

d C

uK

a2

[°2

the

ta]

2Theta [°]

2θ = 11.65° 2θ = 35.15°

FPA: Instrument Contribution

29

Origin of peak shape features:

- Wavelength distribution

(radiation spectrum)

- Instrument configuration

Detector window:

FPA: Instrument Contribution

30

0 500 1000 1500 2000 2500

FPA: Instrument Contribution

31

0 500 1000 1500 2000 2500

FPA: Sample Contribution

32

The same crystalline phase, same instrument configuration

Why different peak shape?

Crystallite Size = 560 x 390 nm

Crystallite Size = 45 x 20 nm

Fundamental Parameters Approach FPA

33

Observed peak shape = convolution 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.co

m

Tube Device Configuration Sample

Fundamental Parameters Approach

34

http://www.bgmn.de

Visualize Peak Profiles

35

Visualize Peak Profiles

36