Basics%20of%20Rietveld%20Refinement

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Basics of Rietveld Refinement

• Scott A Speakman
• 13-4009A
• x3-6887
• speakman_at_mit.edu

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Uses of the Rietveld Method

• The Rietveld method refines user-selected
  parameters to minimize the difference between an
  experimental pattern (observed data) and a model
  based on the hypothesized crystal structure and
  instrumental parameters (calculated pattern)
• can refine information about a single crystal
  structure
• confirm/disprove a hypothetical crystal structure
• refine lattice parameters
• refine atomic positions, fractional occupancy,
  and thermal parameter
• refine information about a single sample
• preferred orientation
• refine information about a multiphase sample
• determine the relative amounts of each phase

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Requirements of Rietveld Method

• High quality experimental diffraction pattern
• a structure model that makes physical and
  chemical sense
• suitable peak and background functions

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Obtaining High Quality Data

• issues to consider
• aligned and calibrated instrument
• beam overflow problems
• thin specimen error
• good counting statistics
• appropriate step size
• sample transparency
• surface roughness
• preferred orientation
• particle size
• go to XRD Basics pg 102

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Describing the Crystal Structure

• space group
• lattice parameters
• atomic positions
• atomic site occupancies
• atomic thermal parameters
• isotropic or anisotropic

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The Crystal Structure of LaB6

• LaB6
• Space Group Pm-3m (221)
• Lattice Parameter a4.1527 A

Atom Wyckoff Site x y z B occ.
La 1a 0 0 0 0.00157 1
B 6f 0.1993 0.5 0.5 0.0027 1
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Where to get crystal structure information

• check if the structure is already solved
• websites
• Inorganic Crystal Structure Database (ICSD)
  http//icsd.ill.fr/icsd/index.html
• 4 is available for free online as a demo
• Crystallography Open Database http//www.crystallo
  graphy.net/
• Mincryst http//database.iem.ac.ru/mincryst/index.
  php
• American Mineralogist http//www.minsocam.org/MSA/
  Crystal_Database.html
• WebMineral http//www.webmineral.com/
• databases
• PDF4 from the ICDD
• Linus Pauling File from ASM International
• Cambridge Structure Database
• literature
• use the PDF to search ICSD listings and follow
  the references
• look for similar, hopefully isostructural,
  materials
• index the cell, and then try direct methods or
  ab-initio solutions
• beyond the scope of todays class

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Instrumental Parameters

• background
• peak profile parameters
• cagliotti parameters u, v, w
• pseudo-voigt or other profile parameters
• asymmetry correction
• anisotropic broadening
• error correcting parameters
• zero shift
• specimen displacement
• absorption
• extinction
• roughness
• porosity

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How many parameters can we refine?

• Each diffraction peak acts as an observation
• theoretically, refine n-1 parameters
• refining a tetragonal LaNi4.85Sn0.15 crystal
  structure, there might be
• scale factor
• 2nd order polynomial background 3 parameters
• 2 lattice parameters
• no atomic positions (all atoms are fixed)
• 3 or 5 thermal parameters
• 2 or 4 occupancy factors
• zero shift and specimen displacement
• 5 profile shape parameters
• 22 parameters maximum with 43 peaks (20 to 120
  deg 2theta)
• does this mean we can refine all parameters?

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background functions

• manually fit background
• polynomial
• chebyshev
• shifte chebyshev
• amorphous sinc function
• many others for different programs

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profile functions

• vary significantly with programs
• almost all programs use Cagglioti U, V, and W
• HSP uses pseudo-voigt, Pearson VII, Voigt, or
  pseudo-voigt 3 (FJC asymmetry)
• GSAS uses functions derived more from neutron and
  synchrotron beamlines

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• go to parameters_calc_pattern.pdf

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How do you know if a fit is good?

• difference pattern
• Residuals R
• R is the quantity that is minimized during
  least-squares or other fitting procedures
• Rwp is weighted to emphasize intense peaks over
  background
• Rexp estimates the best value R for a data set
• an evaluation of how good the data are
• RBragg tries to modify the R for a specific phase
• GOF (aka X2)

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Refinement Strategy

• Rietveld methods fit a multivarialbe
  structure-background-profile model to
  experimental data
• lots of potential for false minima, diverging
  solutions, etc
• need to refine the most important variables
  first, then add more until an adequate solution
  is realized
• a correct solution may not result

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Ray Youngs Refinement Strategy

• scale factor
• zero shift or specimen displacement (not both)
• linear background
• lattice parameters
• more background
• peak width, w
• atom positions
• preferred orientation
• isotropic temperature factor B
• u, v, and other profile parameters
• anisotropic temperature factors

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HSP Automatic Refinement Strategy

• Very similar to Prof Youngs recommendations
• a good choice for beginners
• you can set limits on any of these parameters

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Additional Files

• XRD_Basics_HSP_2006.pdf
• large collection of information about X-ray
  diffraction, instrumentation, and different
  techniques
• XPert HighScore Plus Tutorial.pdf
• overview of the different functionality available
  in HighScore Plus
• Introduction.pdf
• overview of Rietveld
• parameters_calc_patterns.pdf
• overview of parameters involved in calculating a
  diffraction pattern

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further reading

• Rietveld refinement guidelines, J. Appl.Cryst.
  32 (1999) 36-50
• R.A. Young (ed), The Rietveld Method, IUCr 1993
• V.K. Pecharsky and P.Y. Zavalij, Fundamentals of
  Powder Diffraction and Structural
  Characterization of Materials, Kluwer Academic
  2003.
• DL Bish and JE Post (eds), Modern Powder
  Diffraction, Reviews in Mineralogy vol 20, Min.
  Soc. Amer. 1989.
• CCP14 website http//www.ccp14.ac.uk/tutorial/tuto
  rial.htm
• prism.mit.edu/xray/resources.htm

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Rietveld Programs

• Free
• GSAS ExpGUI
• Fullprof
• Rietica
• PSSP (polymers)
• Maud (not very good)
• PowderCell (mostly for calculating patterns and
  transforming crystal structures, limited
  refinement)
• Commercial
• PANalytical HighScore Plus
• Bruker TOPAS (also an academic)
• MDI Jade or Ruby

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Examples

• Silicon
• LaB6
• intermetallic LaNi4.85Sn0.15

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Silicon

• Open the datafile in HSP
• Add the structure model
• insert the structure manually
• import (insert) a struture file
• usually use the CIF format the ubiquitous
  standard for crystal structures
• HSP can also import ICSD .cry files and
  structures from other refinement programs
• GSAS can import CIF or PowderCell files
• try the automatic refinement
• manually improve the fit

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Silicon Crystal Structure

• Fd3m
• which setting? (2)
• a5.43 A
• Si at 0.125, 0.125, 0.125

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Lanthanum hexaboride LaB6

• Open the datafile
• insert the crystal structure CIF file
• Note that boron (z5) makes little difference in
  the XRD pattern compared to the lanthanum (z57)
• what can we do to improve the fit

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LaNi4.85Sn0.15

• The data was taken from Chapter 6 of Fundamentals
  of Powder Diffraction and Structural
  Characterization of Materials, by Pecharsky and
  Zavalij
• The structure is a bit more complex that our
  earlier example, which allows us to explore more
  features of HighScore Plus
• The data (Ch6_1.raw) is in GSAS format, which can
  be read into HighScore Plus
• I have also included a CIF file from the ICSD
  (104685) with all the main features of the
  structure described

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Issue to Consider

• How can I work without knowledge of the
  structure?
• Use LeBail or Pawley method to determine lattice
  parameters
• Try indexing and solving the structure using the
  HighScore Plus tools
• You will find that there are 16 possible space
  groups for this material, but picking the most
  common (and simplest) choice, P6/mmm, is the
  right way to go
• Where do I put the atoms?
• You can use a Fourier map to find out wherein the
  structure the electron densities are greatest.
  Put the heaviest atoms (La) at these sites, then
  work your way through the chemistry
• What variables do I refine and in what sequence?
• Take a look at the automatic option in HSP -
  this is not a bad strategy to use. We will go
  through these in detail