Rietveld Refinements ppt

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.