Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), …w3.esfm.ipn.mx/~fcruz/ADR/Cristalografia/Roisnel... · 2004. 6. 30. · pseudo-Voigt function with the Ikeda-Carpenter

MéridaNovember 2003 Taller intensivo: El método de Rietveld, FullProf

Juan Rodríguez-CarvajalLaboratoire Léon Brillouin (CEA-CNRS), CEA/Saclay

FRANCE

Introduction to the programFullProf


A program for analysis of diffraction patterns: FullProf

• A program for : Simulation of powder diffraction patternsPattern decomposition integrated intensities Structure refinementPowder and single crystal data

• Crystal and magnetic structures • Multiple data sets: simultaneous treatment of several

powder diffraction patterns (CW X-rays & neutrons, Energy dispersive X-rays, TOF neutron diffraction)

• Combined treatment of single crystal and powder data• Crystal and magnetic Structure determination capabilities:

simulated annealing on integrated intensity data


The Rietveld Method for refinement of crystal and

magnetic structures


profileThe model to calculate a powder diffraction pattern is:

( )h hh

ci i iy I T T b= Ω − +∑( ) 1x dx

+∞

−∞Ω =∫

Profile function characterized by its full width at half maximum (FWHM=H)and shape parameters (η, m, ...)

( ) ( ) ( )x g x f x instrumental intrinsic profileΩ = ⊗ = ⊗

The profile of powder diffraction patterns


The profile of powder diffraction patterns

( )h hh

c i iiy I T T b= Ω − +∑Contains structural information: atom positions, magnetic moments, etc( )h h II I= β

( , )h PixΩ = Ω β Contains micro-structural information: instr. resolution, defects, crystallite size, ..

( )Bi ib b= β Background: noise, diffuse scattering, ...


, ,h

( )h hci i iy s I T T bφ φ φφ

= Ω − +∑ ∑

Several phases (φ = 1,nφ) contributing to the diffraction pattern

, ,h

( )h h

p p p p pci i iy s I T T b

φφ φφ

= Ω − +∑ ∑

Several phases (φ = 1,nφ) contributing to several (p=1,np) diffraction patterns


The Rietveld Method consist of refining a crystal (and/or magnetic) structure by minimising the weighted squared difference between the observed and the calculated pattern against the parameter vector: β

22

1( )

n

i i ciiw y yχ β

=

= −∑

21i

iw σ=

2iσ : is the variance of the "observation" yi


The conventional method for refining a crystal (and/or magnetic) structure consist of minimising the weighted squared difference between the observed and the calculated integrated intensities or structure factors against the parameter vector: β

2 2 2, ,( ( ))n obs n calc k

n k

M w G G β= −∑ ∑

2

1n

n

wσ

=

: is the variance of the "observation" 2,obs nG2

nσ


Least squares: Gauss-Newton (1)Minimum necessary condition:

A Taylor expansion of around allows the application of an iterative process. The shifts to be applied to the parameters at each cycle for improving χ2 are obtained by solving a linear system of equations (normal equations)

2

0∂=

∂χβ

( )icy β 0β

0

0 0

0

( ) ( )

( )( )

A b

ic ickl i

i k l

ick i i ic

i k

y yA w

yb w y y

β β

β

=

∂ ∂=

∂ ∂∂

= −∂

∑

∑

βδ

β β

β


Least squares: Gauss-Newton (2)

The new parameters are considered as the starting ones in the next cycle and the process is repeated until a convergence criterion is satisfied. The variance of the adjusted parameters are calculated by the expression:

The shifts of the parameters obtained by solving the normal equations are added to the starting parameters giving rise to a new set

01 0= + ββ β δ

1( ) ( )Ak kk

N - P+C

2 2ν

22ν

σ β χ

χχ

−=

=


Least squares: a local optimisation method

• The least squares procedure provides (when it converges) the value of the parameters constituting the local minimum closest to the starting point

• A set of good starting values for all parameters is needed

• If the initial model is bad for some reasons the LSQ procedure will not converge, it may diverge.


FullProf

Outputfiles,Plot

diffr. patterns

Minimal input:Input control file (extension ‘ .pcr ’): PCR-fileModel, crystallographic/magnetic information

PCR file

DAT file(s)Eventually, experimental data

How works FullProf


Many variables and options Complex to handlePCR file

Format depending on the instrument, usually simpleDAT file(s)

Hint: copy an existing (working) PCR-file and modify it for the user case, or...

USE the new GUI: EdPCR

The PCR file: steep learning curve


--------------------------------------------------------------------------In this file new features, as well as discovered bugs, of FullProf.2kare periodically documented. For details consult the manual of FullProf.From 10 May 2003, comments on the programs constituting the FullProf suiteare also provided.

Juan Rodriguez-Carvajal (Laboratoire Leon Brillouin, Saclay)--------------------------------------------------------------------------

---------------28 July 2003

---------------- An updated version of FullProf.2k is now available.

. . . . . . . . .- Some changes have been introduced for treating the background:

(1) The polynomial background of 12 coefficients, for constant wavelength case, has beenchanged so that the last three coefficients correspond to inverse powers of 2theta.. . . . . . .

(2) Now there is the possibility to include several previously calculated profiles ascontributing, through a linear combination, to the background of a powder diffractionpattern. The individual profiles are read in input files named "filedat_n.bac". Where"filedat" is the code of the data file corresponding to a diffraction pattern and theindex "n" is the number of the contributing profile. The additional contribution tothe background is calculated as:

Last minute changes in FullProfDocumented in “fp2k.inf”


- Reorganization of the TOF peak shapes and derivatives. The refinement of the instrumental parameters is now much more stable. . . . . . The new peak shape INSTR=13 (thanks to Laurent Chapon!) consisting in the convolution of a pseudo-Voigt function with the Ikeda-Carpenter function is now working.

The TOF peak shapes used in FullProf and the meaning of each refinable parameter is now documented in the note: TOF_FullProf.PDF

Last minute changes in FullProfDocumented in “fp2k.inf”


A button on WinPLOTR gives access to EdPCR

Within EdPCR you have access to a series of programs of the FullProf_Suite

Open WinPLOTR

BasIreps: Irreducible representations of space groups

GFourier: Fourier maps

In construction: Moment, Similar, CrystCalc

How to use the FullProf Suite

Execute WinPLOTR


Automatic mode for handling refinementcodes and symmetry constraints

The use of distances and angles restraints

New facilities concerning symmetry

Changes in the format of the file containingthe Instrumental Resolution Function

Special form factors

Simulated Annealing

The treatment of micro-structural effects

Some recent features in FullProf


⇒ New output files with full information of crystallographic symmetry are produced (extension: sym)

⇒ The symmetry used within FullProf is totally based in the Crystallographic Fortran 95 Modules Library (CrysFML)

⇒ These modules provide better crystallographic information to the user of the program. In particular automatic calculation of the multiplicity of each site is now performed after reading the atoms as well as the calculation of the appropriate coefficients for automatic quantitative analysis of mixture of phases.

New facilities concerning symmetry in FullProf


⇒ The user may combine the manual mode with the automatic mode for making the desired constraints. The program automatically renumber the codes, suppress the holes in the matrix and takes care of user-defined constraints.

⇒ The user may select between the traditional modechanging by hand the codewords controlling the refinement, or select the automatic mode.

⇒ If the automatic mode is selected, a code of the type “1.00” means that the corresponding parameter should be refined. The symmetry constraints in atom positions and anisotropic temperature factors are automatically applied.

The automatic mode for handling refinement codes and symmetry constraints in FullProf


In automatic mode two keywords have been introduced in order to facilitate the handling of refinement codes.

This two keywords are VARY and FIX (both in uppercase). They should be inserted in the "name of the phase" line starting farther than column 41.

If both keywords are used VARY should appears before FIX. Both may be accompanied by character values (directives) indicating what to do. At present the available directives are 'xyz','cell','b' (all in lower case and without quotes).

The automatic mode for handling refinement codes and symmetry constraints in FullProf


VARY xyz b FIX b : All positions varied but thermal parameter will be fixed. The appearance of 'b' accompanying the FIX keyword supersedes the previous VARY instruction.

VARY xyz : means that all position parameters should be refined

VARY xyz 0.1 : as before but a multiplier 0.1 will be used to limit the shift of parameters during refinement. This affect only to those parameters that have no codeword at the moment of the run

VARY xyz cell b : means that all positions, cell and thermal parameters are to be refined.

FIX xyz : fix all atom positions (all refinement codes are put to zero)

The program takes care of symmetry constraints automatically. If two atoms of different species occupy the same position the program attributes the same refinement codes to the coordinates and displacement parameters. The user must perform explicit constraints for occupation parameters (if refined!).

The automatic mode for handling refinement codes: examples of VARY and FIX directives


Several types of special form factors are included in FullProf, among them the Symmetry Adapted Spherical Harmonics (SASH) as special form-factors are now fully implemented.

F m 3 m <--Space group symbol!Atom Typ X Y Z Biso Occ In Fin N_t Spc/CodesC SASH 0.00000 0.00000 0.00000 1.49934 1.00000 0 0 4 0

0.00 0.00 0.00 21.00 0.00! Form-factor refinable parameters! f1 f2 f3 f4 f5 f6 f7

3.53862 60.00000 1.00000 -0.01809 0.01335 0.00453 0.0274231.00 0.00 0.00 41.00 51.00 61.00 71.00

! f8 f9 f10 f11 f12 f13 f14-0.01328 0.00617 -0.00220 0.02042 0.00000 0.00000 0.00000

81.00 91.00 101.00 111.00 0.00 0.00 0.00klj 9

0 1 6 1 10 1 12 1 12 2 16 1 16 2 18 1 18 2

Piece of PCR file adapted for the refinement of a diffraction pattern containing C60 in

its nearly free rotator phase.

Special form factors in FullProf


Free rotators: Symmetry Adapted Spherical/Cubic Harmonics

( ) ( )4 ( , )s llmp l s s lmp

slmp

f c i j Qr b yπ θ ϕ= ∑Q

( ) ( )4 ( , )s llj l s s lj

slj

f c i j Qr b Kπ θ ϕ= ∑Q

Special form factors in FullProf


Plot of the observed (red) versus calculated (black) square structure factors in a region of sinθ/λ, after refining the C60 (C60) molecule using a SASH form factor.

C60Number of independentreflections: 141

=> RF2-factor : 3.49=> RF -factor : 3.01

Documents

Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), …w3.esfm.ipn.mx/~fcruz/ADR/Cristalografia/Roisnel... · 2004. 6. 30. · pseudo-Voigt function with the Ikeda-Carpenter