Rietveld Refinements:Determination of crystal structure and crystal imperfections
Speaker: Salman-ul-hassanSupervisor: Dr Nikolay. Zotov
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Outline:
• Diffraction methods• What comes before Rietveld method• What is Rietveld Refinement?• Why Rietveld Refinements widely used?• Stages in Rietveld Refinements• Le-bail Method• Fit criteria• Peak shape function
• The background• Refinement parameter• Some common
problems• Software's used in
Rietveld refinements• Summary
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Diffraction Methods:
• Identify crystal structure & quantify the content of crystalline materials.
• Bragg’s Equation: nλ=2dsinθ• Sources: X-ray Neutrons Electrons
1. B.D CULLITY, elements of x-ray diffraction, 2nd edition, Addison-wesley publishing, chapter 3
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What comes before Rietveld method:
• Debye & Paul Scherer
Large and randomly oriented grains
Difficulty in measuring intensities
Increasing complexities2. Fabio pulizzi, powder struggle, nature, (2014), 7.http://
pd.chem.ucl.ac.uk/pdnn/mod1/ip.htm
Figure 1: Debye-Scherrer rings[7]
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What is Rietveld Refinement?• Structure refinement technique• use of least square method: ]
can be expressed by following formation.
3. Eric J. Mittemeijer ,U welzel, Modern Diffraction Methods, Chapter-2, WILEY VCH.
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Figure 2: minimize differences between calculated and observed pattern by least square method
6. profex.doebelin.org/wp-content/.../Lesson-4-Rietveld-Refinement.pdf
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Why Rietveld Refinements widely used?• Computational nature
• Fast calculation
• Uses the entire spectrum (as wide as possible)
• Used in various fields
• Provide information about defects & quantitative phase analysis
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Stages in Rietveld Refinements.
4. McCusker, Von Dreele, D.E.Cox, D.Louer and P.Scardi. (1999).32, 36-50. J.Appl.Cryst
Check model and
closeness of fit
Initial structure
Background
refinement
Unit cell dimension refinement
Refine zero point
correction
Refine peak shape
Refine atomic
coordinates and
thermal parameter
s
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Le-bail Method:• Use for Profile refinement• Crystal structure determination How to use? Modify Rietveld code to set all Extract using Rietveld algorithm Set from extracted Repeat extraction now with
Figure 3: Peak fits of three selected reflections of LaB6.[3]
3. Eric J. Mittemeijer ,U welzel, Modern Diffraction Methods, Chapter-2, WILEY VCH.
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• Residual factors:
• Goodness of fit parameter :
Fit criteria:
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Peak shape function:• Pseudo voigt function• Model over all line broadening
Lorentzian Gaussian Pseudo-voigt
Figure 4: Different peak profile functions
profex.doebelin.org/wp-content/.../Lesson-4-Rietveld-Refinement.pdf
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Figure 5: The observed (circles), calculated (line) and difference (bottom)(a) a good fit of a peak, (b) a calculated intensity that is too high and (c) a calculated intensity that is too low
McCusker, Von Dreele, D.E.Cox, D.Louer and P.Scardi. (1999).32, 36-50. J.Appl.Cryst
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The Background:• Scattering • Bragg peaks• Linearizing the background• Debye formula
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Refinement parameter:• Background coefficients, peak shape parameters• Structural parameters• Unit cell dimension• Atomic coordinates • Thermal parameters• Occupancy parameters.
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Figure 6: PbSO4 X-ray Diffraction, Rietveld Refinement showing structure Refinement
Cu Kα radiation, Pseudo-Voigt profile, h = 0.014*2Q, Rwp = 14% RB = 4.6%
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Some common problems:• Background not fitted well.
• Peak shapes shows poor description.
• Peak position mismatch in calculated and observed patterns
• Missed peaks.
• Relative intensities of few reflections are too high.
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Software’s used in Rietveld Refinements:
Academic software's• Full prof• GSAS• BGMN• MAUD• Brass• Many more
Commercial software's
• High score• Topas• Autoquan• PDXL• Jade• Minx
5. http://www.ccp14.ac.uk/solution/rietveld_software/index.html
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Summary:
• Modern method for extracting structural details.
• Use directly measured intensity points.
• Use of computer software's.
• Best for peak separation.
• Used in different fields.
• Crystal structure determination.
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