Gsas intro rvd (1)
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Rietveld refinement is a technique for determining crystal structures from powder diffraction data. It involves minimizing the difference between observed and calculated powder diffraction patterns through least squares refinement of structural and instrumental parameters. GSAS is a software package that performs Rietveld refinement across multiple diffraction data types. It allows refinement of parameters related to lattice constants, atomic positions, thermal motion, and instrumental profile shapes. EXPGUI provides a graphical user interface for GSAS, while EXPEDT is the text-based interface that allows access to all GSAS capabilities.
Gsas intro rvd (1)
- 1. Introduction to GSAS and Rietveld Refinement R.B. Von Dreele, Advanced Photon Source Argonne National Laboratory Recent Quote seen in Rietveld e-mail: “Rietveld refinement is one of those few fields of intellectual endeavor wherein the more one does it, the less one understands.” (Sue Kesson) Stephens’ Law – “A Rietveld refinement is never perfected, merely abandoned”
- 2. GSAS – General Structure Analysis System A.C. Larson & R.B. Von Dreele 1985-present •! Multidata/multiradiation crystal structure refinement –! Originally neutron time-of-flight(TOF); for LANSCE powder & single crystal instruments (VAX Fortran) –! Expanded to include CW neutron & x-ray data •! Data sets – “histograms” in GSAS parlance – upper limit of 99! •! Other “data sets” – restraints (bonds, angles, etc.) •! Powder patterns – multiple phases – upper limit of 9 •! Language – Fortran 77 (>100K lines) •! Platforms – MS Windows (XP – Win7), linux (unix), Mac OSX •! Graphics – •! Distribution – free from CCP14 & now ANL (some development still in progress)
- 3. Where is GSAS in grand scheme? Thanks to Lynn McCusker for maze Includes: -!Results -!Powder pattern plots -!For publication -!Bond lengths & angles -!Other geometry -!CIF (& PDB) files of result -!Fourier maps & (some) display -!Texture (polefigures) -!Utilities Missing: -!Indexing -!Structure solution Must go elsewhere for these.
- 4. Structure of GSAS 1. Multiple programs (~50) - each with specific purpose editing, powder preparation, least squares, etc. 2. User interface - EXPEDT edit control data & problem parameters for calculations - multilevel menus & help listings text interface (no mouse!) visualize “tree” structure for menus 3. Common file structure – all named as “experiment.ext” experiment name used throughout, extension differs by type of file 4. Graphics - both screen & hardcopy 5. EXPGUI – graphical interface (windows, buttons, edit boxes, etc.); incomplete overlap with EXPEDT but with useful extra features – by B. H. Toby
- 5. PC-GSAS – GUI only for access to GSAS programs pull down menus for GSAS programs (not linux or Mac OSX)
- 6. GSAS & EXPGUI interfaces EXPEDT data setup option (<?>,D,F,K,L,P,R,S,X) > EXPEDT data setup options: <?> - Type this help listing D - Distance/angle calculation set up F - Fourier calculation set up K n - Delete all but the last n history records L - Least squares refinement set up P - Powder data preparation R - Review data in the experiment file S - Single crystal data preparation X - Exit from EXPEDT On console screen Keyboard input – text & numbers 1 letter commands – menu help Layers of menus – tree structure Type ahead thru layers of menus Macros (@M, @R & @X commands) GSAS – EXPEDT (and everything else): Numbers – real: ‘0.25’, or ‘1/3’, ‘2.5e-5’ or ‘s25’ (for sin25) all allowed Drag & drop for e.g. file names Macro files: add comments after !
- 7. GSAS & EXPGUI interfaces EXPGUI: Access to GSAS Typical GUI – edit boxes, buttons, pull downs etc. Liveplot – powder pattern NB: not all features of GSAS can be accessed from EXPGUI Must use EXPEDT to get to them
- 8. Unique EXPGUI features (not in GSAS) •! CIF input – read CIF files (not mmCIF) •! widplt/absplt •! coordinate export – various formats •! instrument parameter file creation/ edit Gauss FWHM (instrument) Lorentz FWHM (sample) Sum widplt
- 9. Powder pattern display - liveplot Zoom (new plot) cum. !2 onupdates at end of genles run – check if OK!
- 10. Powder pattern display - powplot “publication style” plot – works OK for many journals; save as “emf” In Windows; can be “dressed up”; also ascii output of x,y table Io-Ic Refl. pos. Io Ic
- 11. Powplot options – x & y axes – “improved” plot? Sqrt(I) Q-scale (from Q="#/sin$) rescale y by 4x Refl. pos.
- 12. Citations: •!GSAS: A.C. Larson and R.B. Von Dreele, General Structure Analysis System (GSAS), Los Alamos National Laboratory Report LAUR 86-748 (2005). •!EXPGUI: B. H. Toby, EXPGUI, a graphical user interface for GSAS, J. Appl. Cryst. 34, 210-213 (2001). Distribution kits include both GSAS & EXPGUI To date: GSAS >5000 citations, EXPGUI >1000 citations Demonstration – refinement of fluroapatite from lab CuKa data
- 13. •! Result from fluoroapatite refinement – powder profile is curve with counting noise & fit is smooth curve •! NB: big plot is sqrt(I) Rietveld refinement is multiparameter curve fitting Iobs + Icalc | Io-Ic | ) Refl. positions (lab CuK% B-B data)
- 14. So how do we get there? •! Beginning – model errors ! misfits to pattern •! Can’t just let go all parameters – too far from best model (minimum !2) !2 parameter False minimum True minimum – “global” minimum Least-squares cycles !2 surface shape depends on parameter suite
- 15. Fluoroapatite start – add model (1st choose lattice/sp. grp.) •! important – reflection marks match peaks •! Bad start otherwise – adjust lattice parameters (wrong space group?)
- 16. 2nd add atoms & do default initial refinement – scale & background •! Notice shape of difference curve – position/shape/intensity errors
- 17. Errors & parameters? •! position – lattice parameters, zero point (not common) - other systematic effects – sample shift/offset •! shape – profile coefficients (GU, GV, GW, LX, LY, etc. in GSAS) •! intensity – crystal structure (atom positions & thermal parameters) - other systematic effects (absorption/extinction/preferred orientation) NB – get linear combination of all the above & trend with 2& important a – too small LX - too small Ca2(x) – too small too sharppeak shift wrong intensity
- 18. Difference curve – what to do next? •! Dominant error – peak shapes? Too sharp? •! Refine profile parameters next (maybe include lattice parameters) •! NB - EACH CASE IS DIFFERENT!! Characteristic “up-down-up” !!profile error NB – can be “down-up- down” for too “fat” profile
- 19. Result – much improved! •! maybe intensity differences left – refine coordinates & thermal parms.
- 20. Result – essentially unchanged "!Thus, major error in this initial model – peak shapes Ca F PO4
- 21. So how does Rietveld refinement work? Exact overlaps - symmetry Incomplete overlaps Io 'Ic Residual: Rietveld Minimize Ic
- 22. Rietveld refinement - Least Squares Theory and a function then the best estimate of the values pi is found by minimizing This is done by setting the derivative to zero Results in n “normal” equations (one for each variable) - solve for pi Given a set of observations Yobs
- 23. Least Squares Theory - continued Problem - g(pi) is nonlinear & transcendental (sin, cos, etc.) so can’t solve directly Expand g(pi) as Taylor series & toss high order terms Substitute above ai - initial values of pi (pi = pi - ai (shift) Normal equations - one for each (pi; outer sum over observations Solve for (pi - shifts of parameters, NOT values
- 24. Least Squares Theory - continued Rearrange . . . Matrix form: Ax=v
- 25. Least Squares Theory - continued Matrix equation Ax=v Solve x = A-1v = Bv; B = A-1 This gives set of (pi to apply to “old” set of ai repeat until all xi~0 (i.e. no more shifts) Quality of fit – “!2” = M/(N-P) ! 1 if weights “correct” & model without systematic errors (very rarely achieved) Bii = )2 i – “standard uncertainty” (“variance”) in (pi (usually scaled by !2) Bij/(Bii*Bjj) – “covariance” between (pi & (pj Rietveld refinement - this process applied to powder profiles Ycalc - model function for the powder profile - Next