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
11
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
14
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
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