R.B. Von Dreele, Advanced Photon Source

Argonne National Laboratory

Rietveld Refinement with GSAS

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)

Demonstration – refinement of fluroapatite

Stephens’ Law – “A Rietveld refinement is never perfected,

merely abandoned”

2

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)

3

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

4

Fluoroapatite start – add model (1st choose lattice/sp. grp.)

important – reflection marks match peaks Bad start otherwise – adjust lattice parameters (wrong space group?)

5

2nd add atoms & do default initial refinement – scale & background

Notice shape of difference curve – position/shape/intensity errors

6

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 aboveNB2 – trend with 2(or TOF) important

a – too small LX - too small Ca2(x) – too small

too sharppeak shift wrong intensity

7

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 errorNB – can be “down-up-down” for too “fat” profile

8

Result – much improved!

maybe intensity differences left – refine coordinates & thermal parms.

9

Result – essentially unchanged

Thus, major error in this initial model – peak shapes

CaFPO4

10

So how does Rietveld refinement work?

Exact overlaps - symmetry

Incomplete overlaps

c

coo I

II

LpF

12

Extract structure factors: Apportion Io by ratio of Ic to ic & apply corrections

Io

Ic

2

2

o

cowp wI

)Iw(IR

Residuals:

Rietveld Minimize 2)( coR IIwM

Ic

11

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

)p...,p,p,p(gG n321calc

Given a set of observations Gobs

2co )GG(wM

0pG

)GG(wj

cco

12

Least Squares Theory - continued

Problem - g(pi) is nonlinear & transcendental (sin, cos, etc.)so can’t solve directlyExpand g(pi) as Taylor series & toss high order terms

i

ii

cicic p

pG

)a(G)p(G

Substitute above

ai - initial values of pi

pi = pi - ai (shift)

)a(GGG0pG

ppG

Gw icoj

c

ii

i

c

Normal equations - one for each pi; outer sum over observationsSolve for pi - shifts of parameters, NOT values

13

Least Squares Theory - continued

Rearrange

1

ci

n

1i i

c

1

c

pG

GwppG

pG

w

...

n

ci

n

1i i

c

n

c

pG

GwppG

pG

w

Matrix form: Ax=v

i

cijj

j

c

i

cj,i p

G)G(wvpx

pG

pG

wa

14

Least Squares Theory - continued

Matrix equation Ax=vSolve 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 profilesGcalc - model function for the powder profile (Y elsewhere)

15

Rietveld Model: Yc = Io{khF2hmhLhP(h) + Ib}

Io - incident intensity - variable for fixed 2

kh - scale factor for particular phase

F2h - structure factor for particular reflection

mh - reflection multiplicity

Lh - correction factors on intensity - texture, etc.

P(h) - peak shape function - strain & microstrain, etc.

Ib - background contribution

Least-squares: minimize M=w(Yo-Yc)2

Convolution of contributing functions

Instrumental effects

Source

Geometric aberrations

Sample effects

Particle size - crystallite size

Microstrain - nonidentical unit cell sizes

Peak shape functions – can get exotic!

Gaussian – usual instrument contribution is “mostly” Gaussian

H - full width at half maximum - expressionfrom soller slit sizes and monochromatorangle- displacement from peak position

P(k) = H

k

4ln2 e[-4ln2 k

2/ H

k

2] = G

CW Peak Shape Functions – basically 2 parts:

Lorentzian – usual sample broadening contribution

P(k) = H

k

2 1 + 4

k

2/H

k

21 = L

Convolution – Voigt; linear combination - pseudoVoigt

18

CW Profile Function in GSAS

Thompson, Cox & Hastings (with modifications)

Pseudo-Voigt ),T(G)1(),T(L)T(P

Mixing coefficient j3

1jj )(k

FWHM parameter 5

5

1i

ii5gic

19

CW Axial Broadening Function

Finger, Cox & Jephcoat based on van Laar & Yelon

2Bragg2i2min

Pseudo-Voigt (TCH)= profile function

Depend on slit & sample “heights” wrt diffr. radiusH/L & S/L - parameters in function(typically 0.002 - 0.020)

Debye-Scherrer cone

2 Scan

Slit

H

20

How good is this function?

Protein Rietveld refinement - Very low angle fit1.0-4.0° peaks - strong asymmetry “perfect” fit to shape

21

Bragg-Brentano Diffractometer – “parafocusing”

Diffractometercircle

Sampledisplaced

Receiving slit

X-ray sourceFocusing circle

Divergent beam optics

Incident beamslit

Beam footprintSample transparency

22

CW Function Coefficients - GSAS

Sample shift

Sample transparency

Gaussian profile

Lorentzian profile

36000RS

s s

seff RT

9000

2

22g cos

PWtanVtanU

tanYcos

X

(plus anisotropic broadening terms) Intrepretation?

Shifted difference

2sinTcosST'T ss

Crystallite Size Broadening

a*

b*

d*=constant

dcot

d

d*d 2

sincot2

cosd

d2 2

Lorentzian term - usualK - Scherrer const. "LX"

K180p

Gaussian term - rareparticles same size? "GP"

K180p

Microstrain Broadening

a*

b*

ttanconsdd

cot

*d*d

dd

tand

d22

Lorentzian term - usual effect "LY"180

%100S

Gaussian term - theory?Remove instrumental part

"GU"180

%100S

25

Microstrain broadening – physical model

Stephens, P.W. (1999). J. Appl. Cryst. 32, 281-289.Also see Popa, N. (1998). J. Appl. Cryst. 31, 176-180.

Model – elastic deformation of crystallites

hkhlkllkhMd hkl

hkl654

23

22

212

1

d-spacing expression

j,i ji

ijhkl

MMSM2

Broadening – variance in Mhkl

26

hkM

hlM

klM

lM

kM

hM

654

2

3

2

2

2

1

,,,,,

2222233

2222323

2222332

23342222

32322422

33222224

khklhlhkhklhkkh

klhlhhklhllhklh

lhkhkllkkllkklh

hklhlklllklh

hklhklklkkkh

khlhklhlhkhh

MM

ji

Microstrain broadening - continued

Terms in variance

Substitute – note similar terms in matrix – collect terms

27

42 LKH,lkhSMHKL

LKHHKLhkl

2

1122

1212

211

3013

3301

3130

3031

3103

3310

22022

22202

22220

4004

4040

4400

2

4

2

3

hklSlhkSklhS

klSlhShkSlkShlSkhS

lkSlhSkhSlSkShSM hkl

Microstrain broadening - continued

Broadening – as variance

General expression – triclinic – 15 terms

Symmetry effects – e.g. monoclinic (b unique) – 9 terms

lhkShkSlhS

lkSkhSlhSlSkShSM hkl

2121

3103

3301

22022

22220

22202

4004

4040

4400

2

42

)(33

3 collected terms

Cubic – m3m – 2 terms

222222220

444400

2 3 lklhkhSlkhSM hkl

28

Example - unusual line broadening effects in Na parahydroxybenzoate

Sharp lines

Broad lines

Seeming inconsistency in line broadening- hkl dependent

Directional dependence - Lattice defects?

29

H-atom location in Na parahydroxybenzoateGood F map allowed by better fit to pattern

F contour mapH-atom locationfrom x-ray powder data

30

Macroscopic Strain

hkhlkllkhMd hkl

hkl654

23

22

212

1

Part of peak shape function #5 – TOF & CWd-spacing expression; ij from recip. metric tensor

Elastic strain – symmetry restricted lattice

distortion

TOF:

ΔT = (11h2+22k2+33l2+12hk+13hl+23kl)d3

CW:

ΔT = (11h2+22k2+33l2+12hk+13hl+23kl)d2tanWhy? Multiple data sets under different conditions (T,P, x, etc.)

31

Symmetry & macrostrain

ij – restricted by symmetry

e.g. for cubic

T = 11h2d3 for TOF

'ij

a

1

Result: change in lattice parameters via change in metric coeff.ij’ = ij-2ij/C for TOFij’ = ij-(/9000)ij for CWUse new ij’ to get lattice parameterse.g. for cubic

Bragg Intensity Corrections:

Extinction

Preferred Orientation

Absorption & Surface Roughness

Other Geometric Factors

Affect the integrated peak intensity and not peak shape

Lh

Nonstructural Features

Sabine model - Darwin, Zachariasen & Hamilton

Bragg component - reflection

Laue component - transmission

Extinction

Eh = E

b sin2 + E

l cos2

Eb =

1+x1

Combination of two parts

El = 1 - 2

x + 4x2

- 485x3

. . . x < 1

El = x

2 1 - 8x

1 - 128x2

3 . . . x > 1

Sabine Extinction Coefficient

Crystallite grain size = Ex

2

0%

20%

40%

60%

80%

0.0 25.0 50.0 75.0 100.0 125.0 150.0

Eh

Increasingwavelength(1-5 Å)

2

hx V

FEx

35

Random powder - all crystallite orientations equally probable - flat pole figure

Crystallites oriented along wire axis - pole figure peaked in center and at the rim (100’s are 90º apart)

Orientation Distribution Function - probability function for texture

(100) wire texture(100) random texture

What is texture? Nonrandom crystallite grain orientations

Pole figure - stereographic projection of a crystal axis down some sample direction

Loose powder

Metal wire

36

Texture - measurement by diffraction

Debye-Scherrer cones •uneven intensity due to texture •also different pattern of unevenness for different hkl’s•Intensity pattern changes as sample is turned

Non-random crystallite orientations in sample

Incident beamx-rays or neutrons

Sample(111)

(200)

(220)

Spherical Distribution

Ellipsoidal Distribution -assumed cylindrical

Ellipsoidal particles

Uniaxial packing

Preferred Orientation - March/Dollase Model

Integral about distribution- modify multiplicity

Ro - ratio of ellipsoid axes = 1.0 for nopreferred orientation

2

3n

1j o

222

oh R

sincosR

M

1O

Texture - Orientation Distribution Function - GSAS

f(g) = l=0

m=-l

l n=-l

l C

l

mn T

l

mn (g)

Tlmn = Associated

Legendre functions or generalized spherical harmonics

- Euler angles

f(g) = f()

Probability distribution of crystallite orientations - f(g)

39

• Projection of orientation distribution function for chosen reflection (h) and sample direction (y)

• K - symmetrized spherical harmonics - account for sample & crystal symmetry

• “Pole figure” - variation of single reflection intensity as fxn. of sample orientation - fixed h

• “Inverse pole figure” - modification of all reflection intensities by sample texture - fixed y - Ideally suited for neutron TOF diffraction

• Rietveld refinement of coefficients, Clmn, and 3

orientation angles - sample alignment

Texture effect on reflection intensity - Rietveld model

)()(12

4),(

0

yKhKCl

yhA nl

ml

l

lm

l

ln

mnl

l

Absorption

X-rays - independent of 2 - flat sample – surface roughness effect - microabsorption effects - but can change peak shape and shift their positions if small (thick sample)

Neutrons - depend on 2 and but much smaller effect - includes multiple scattering much bigger effect - assume cylindrical sample Debye-Scherrer geometry

Model - A.W. Hewat

For cylinders and weak absorption onlyi.e. neutrons - most needed for TOF datanot for CW data – fails for R>1

GSAS – New more elaborate model by Lobanov & alte de Viega – works to R>10

Other corrections - simple transmission & flat plate

)ATATexp(A 22B2B1h

Nonuniform sample density with depth from surfaceMost prevalent with strong sample absorptionIf uncorrected - atom temperature factors too smallSuortti model Pitschke, et al. model

Surface Roughness – Bragg-Brentano only

High angle – more penetration (go thru surface roughness) - more dense material; more intensity

Low angle – less penetration (scatter in less dense material) - less intensity

pqp1

q1p1S

2

R

sinsin qq1p

qq1pSR

exp

sinexp

(a bit more stable)

Other Geometric Corrections

Lorentz correction - both X-rays and neutrons

Polarization correction - only X-rays

X-rays

Neutrons - CW

Neutrons - TOF

Lp = 2sin2 cos1 + M cos22

Lp = 2sin2 cos

1

Lp = d4sin

44

Solvent scattering – proteins & zeolites?

Contrast effect between structure & “disordered” solvent region

Babinet’s Principle:Atoms not in vacuum – change form factors

f = fo-Aexp(-8Bsin2/2)

0

2

4

6

0 5 10 15 20

2

fC

uncorrected

Solvent corrected

Carbon scattering factor

Manual subtraction – not recommended - distorts the weighting scheme for the observations& puts a bias in the observations

Fit to a function - many possibilities:

Fourier series - empirical

Chebyschev power series - ditto

Exponential expansions - air scatter & TDS

Fixed interval points - brute force

Debye equation - amorphous background

(separate diffuse scattering in GSAS)

Background scattering

real space correlation functionespecially good for TOFterms with

Debye Equation - Amorphous Scattering

)QB21

exp(QR

)QRsin(A 2

ii

ii

amplitudedistance

vibration

47

Neutron TOF - fused silica “quartz”

48

Rietveld Refinement with Debye Function

7 terms Ri –interatomic distances in SiO2 glass 1.587(1), 2.648(1), 4.133(3), 4.998(2), 6.201(7), 7.411(7) & 8.837(21)Same as found in -quartz

1.60Å

Si

O

4.13Å

2.63Å3.12Å

5.11Å 6.1Å

-quartz distances

Summary

Non-Structural Features in Powder Patterns

1. Large crystallite size - extinction

2. Preferred orientation

3. Small crystallite size - peak shape

4. Microstrain (defect concentration)

5. Amorphous scattering - background

50

Time to quit?

Stephens’ Law –

“A Rietveld refinement is never perfected,

merely abandoned”

Also – “stop when you’ve run out of things to vary”

What if problem is more complex?

Apply constraints & restraints

“What to do when you have

too many parameters

& not enough data”

51

Complex structures (even proteins)

Too many parameters – “free” refinement failsKnown stereochemistry:Bond distancesBond anglesTorsion angles (less definite)Group planarity (e.g. phenyl groups)Chiral centers – handednessEtc.

Choice: rigid body description – fixed geometry/fewer parametersstereochemical restraints – more data

52

Constraints vs restraints

Constraints – reduce no. of parameters

jkjlkil

i p

FSUR

v

F

Rigid body User Symmetry

Derivative vectorBefore constraints(longer)

Derivative vectorAfter constraints(shorter)

Rectangular matrices

Restraints – additional information (data) that model must fitEx. Bond lengths, angles, etc.

53

Space group symmetry constraints

Special positions – on symmetry elementsAxes, mirrors & inversion centers (not glides & screws)Restrictions on refineable parametersSimple example: atom on inversion center – fixed x,y,zWhat about Uij’s?

– no restriction – ellipsoid has inversion center

Mirrors & axes ? – depends on orientation

Example: P 2/m – 2 || b-axis, m 2-fold

on 2-fold: x,z – fixed & U11,U22,U33, & U13 variableon m: y fixed & U11,U22, U33, & U13 variableRietveld programs – GSAS automatic, others not

54

Multi-atom site fractions

“site fraction” – fraction of site occupied by atom“site multiplicity”- no. times site occurs in cell“occupancy” – site fraction * site multiplicity

may be normalized by max multiplicity

GSAS uses fraction & multiplicity derived from sp. gp.Others use occupancy

If two atoms in site – Ex. Fe/Mg in olivineThen (if site full) FMg = 1-FFe

55

If 3 atoms A,B,C on site – problem

Diffraction experiment – relative scattering power of site

“1-equation & 2-unknowns” unsolvable problem

Need extra information to solve problem –

2nd diffraction experiment – different scattering power

“2-equations & 2-unknowns” problem

Constraint: solution of J.-M. Joubert

Add an atom – site has 4 atoms A, B, C, C’

so that FA+FB+FC+FC’=1

Then constrain so FA = -FC and FB = -FC’

Multi-atom site fractions - continued

56

Multi-phase mixtures & multiple data sets

Neutron TOF – multiple detectorsMulti- wavelength synchrotronX-ray/neutron experimentsHow constrain scales, etc.?

p

phphhdbc YSSIII

Histogram scale Phase scale

Ex. 2 phases & 2 histograms – 2 Sh & 4 Sph – 6 scalesOnly 4 refinable – remove 2 by constraintsEx.S11 = -S21 & S12 = -S22

57

Rigid body problem – 88 atoms – [FeCl2{OP(C6H5)3}4][FeCl4]

264 parameters – no constraintsJust one x-ray pattern – not enough data!Use rigid bodies – reduce parameters

P21/ca=14.00Åb=27.71Åc=18.31Å=104.53V=6879Å3

V. Jorik, I. Ondrejkovicova, R.B. Von Dreele & H. Eherenberg, Cryst. Res. Technol., 38, 174-181 (2003)

58

Rigid body description – 3 rigid bodies

FeCl4 – tetrahedron, origin at Fe

z

x

y

Fe - origin

Cl1

Cl2

Cl3Cl4

1 translation, 5 vectorsFe [ 0, 0, 0 ]Cl1 [ sin(54.75), 0, cos(54.75)]Cl2 [ -sin(54,75), 0, cos(54.75)]Cl3 [ 0, sin(54.75), -cos(54.75)]Cl4 [ 0, -sin(54.75), -cos(54.75)]D=2.1Å; Fe-Cl bond

59

PO – linear, origin at P

C6 – ring, origin at P(!)

Rigid body description – continued

P OC1

C5 C3

C4 C2

C6z

x

P [ 0, 0, 0 ]O [ 0, 0 1 ]D=1.4Å

C1-C6 [ 0, 0, -1 ]D1=1.6Å; P-C bondC1 [ 0, 0, 0 ]C2 [ sin(60), 0, -1/2 ]C3 [-sin(60), 0, -1/2 ]C4 [ sin(60), 0, -3/2 ]C5 [-sin(60), 0, -3/2 ]C6 [ 0, 0, -2 ]D2=1.38Å; C-C aromatic bond

DD1D2

(ties them together)

60

Rigid body description – continued

Rigid body rotations – about P atom originFor PO group – R1(x) & R2(y) – 4 setsFor C6 group – R1(x), R2(y),R3(z),R4(x),R5(z)

3 for each PO; R3(z)=+0, +120, & +240; R4(x)=70.55Transform: X’=R1(x)R2(y)R3(z)R4(x)R5(z)X

47 structural variables

P

O

C

C C

C C

C

z

x

y

R1(x)

R2(y)R3(z)

R5(z) R4(x)

Fe

61

Refinement - results

Rwp=4.49%Rp =3.29%RF

2 =9.98%Nrb =47Ntot =69

62

Refinement – RB distances & angles

OP(C6)3 1 2 3 4R1(x) 122.5(13) -76.6(4) 69.3(3) -158.8(9) R2(y) -71.7(3) -15.4(3) 12.8(3) 69.2(4)R3(z)a 27.5(12) 51.7(3) -10.4(3) -53.8(9)R3(z)b 147.5(12) 171.7(3) 109.6(3) 66.2(9)R3(z)c 267.5(12) 291.7(3) 229.6(3) 186.2(9)R4(x) 68.7(2) 68.7(2) 68.7(2) 68.7(2)R5(z)a 99.8(15) 193.0(14) 139.2(16) 64.6(14)R5(z)b 81.7(14) 88.3(17) 135.7(17) -133.3(16)R5(z)c 155.3(16) 63.8(16) 156.2(15) 224.0(16)P-O = 1.482(19)Å, P-C = 1.747(7)Å, C-C = 1.357(4)Å, Fe-Cl = 2.209(9)Å

z

x

R1(x - PO)

R2(y- PO)R3(z)

R5(z) R4(x)

Fe

}Phenyl twist

− C-P-O angle

C3PO torsion(+0,+120,+240)

} PO orientation

}

63

Packing diagram – see fit of C6 groups

64

Stereochemical restraints – additional “data”

4

2

2

4

2

4

2

2

2

)( ciiR

cioiix

cioiih

cioiiv

ciip

ciit

cioiid

cioiia

cioiiY

Rwf

xxwf

hhwf

vvwf

pwf

twf

ddwf

aawf

YYwfM

Powder profile (Rietveld)*

Bond angles*

Bond distances*

Torsion angle pseudopotentials

Plane RMS displacements*

van der Waals distances (if voi<vci)

Hydrogen bonds

Chiral volumes**

“” pseudopotentialwi = 1/2 weighting factorfx - weight multipliers (typically 0.1-3)

65

For [FeCl2{OP(C6H5)3}4][FeCl4] - restraints

Bond distances: Fe-Cl = 2.21(1)Å, P-O = 1.48(2)Å, P-C = 1.75(1)Å, C-C = 1.36(1)ÅNumber = 4 + 4 + 12 + 72 = 92Bond angles:O-P-C, C-P-C & Cl-Fe-Cl = 109.5(10) – assume tetrahedralC-C-C & P-C-C = 120(1) – assume hexagonNumber = 12 + 12 + 6 + 72 + 24 = 126Planes: C6 to 0.01 – flat phenylNumber = 72Total = 92 + 126 + 72 = 290 restraints

A lot easier to setup than RB!!

66

Refinement - results

Rwp=3.94%Rp =2.89%RF

2 =7.70%Ntot =277

67

Stereochemical restraints – superimpose on RB results

Nearly identical with RB refinementDifferent assumptions – different results

68

New rigid bodies for proteins (actually more general)

Proteins have too many parameters

Poor data/parameter ratio - especially for powder data

Very well known amino acid bonding –

e.g. Engh & Huber

Reduce “free” variables – fixed bond lengths & angles

Define new objects for protein structure –

flexible rigid bodies for amino acid residues

Focus on the “real” variables –

location/orientation & torsion angles of each residue

Parameter reduction ~1/3 of original protein xyz set

69

txyz

Qijk

Residue rigid body model for phenylalanine

3txyz+3Qijk++1+2 = 9 variables vs 33 unconstrained xyz coordinates

70

Qijk – Quaternion to represent rotations

In GSAS defined as: Qijk = r+ai+bj+ck – 4D complex number – 1 real + 3 imaginary components

Normalization: r2+a2+b2+c2 = 1

Rotation vector: v = ax+by+cz; u = (ax+by+cz)/sin(/2)

Rotation angle: r2 = cos2(/2); a2+b2+c2 = sin2(/2)

Quaternion product: Qab = Qa * Qb ≠ Qb * Qa

Quaternion vector transformation: v’ = QvQ-1

71

How effective? PDB 194L – HEWL from a space crystallization; single xtal data,1.40Å resolution

X-Plor 3.1 – RF = 25.8% ~4600 variables

GSAS RB refinement – RF=20.9% ~2700 variables

RMS difference - 0.10Å main chain & 0.21Å all protein atoms

21542 observations; 1148 atoms (1001 HEWL)

RB refinement reduces effect of “over refinement”

72

194L & rigid body model – essentially identical

73

Conclusions – constraints vs. restraints

Constraints required space group restrictionsmultiatom site occupancy

Rigid body constraintsreduce number of parametersmolecular geometry assumptions

Restraintsadd datamolecular geometry assumptions (again)

74

GSAS - A bit of historyGSAS – conceived in 1982-1983 (A.C. Larson & R.B. Von Dreele)1st version released in Dec. 1985

•Only TOF neutrons (& buggy) •Only for VAX•Designed for multiple data (histograms) & multiple phases from

the start•Did single crystal from start

Later – add CW neutrons & CW x-rays (powder data)SGI unix version & then PC (MS-DOS) versionalso Linux version (briefly HP unix version)

2001 – EXPGUI developed by B.H. TobyRecent – spherical harmonics texture & proteins

New Windows, MacOSX, Fedora & RedHat linux versionsAll identical code – g77 Fortran; 50 pgms. & 800 subroutinesGrWin & X graphics via pgplotEXPGUI – all Tcl/Tk – user additions welcome

Basic structure is essentially unchanged

75

Structure of GSAS

1. Multiple programs - each with specific purposeediting, powder preparation, least squares, etc.

2. User interface - EXPEDTedit control data & problem parameters forcalculations - multilevel menus & help listingstext interface (no mouse!)visualize “tree” structure for menus

3. Common file structure – all named as “experiment.ext”experiment name used throughout, extensiondiffers by type of file

4. Graphics - both screen & hardcopy5. EXPGUI – graphical interface (windows, buttons, edit boxes,

etc.); incomplete overlap with EXPEDT but with useful extra features – by B. H. Toby

76

PC-GSAS – GUI only for access to GSAS programs

pull down menus for GSAS programs

(not linux)

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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 screenKeyboard input – text & numbers1 letter commands – menu helpLayers of menus – tree structureType ahead thru layers of menusMacros (@M, @R & @X commands)

GSAS – EXPEDT (and everything else):

Numbers – real: ‘0.25’, or ‘1/3’, or ‘2.5e-5’ all allowedDrag & drop for e.g. file names

78

GSAS & EXPGUI interfaces

EXPGUI:

Access to GSASTypical GUI – edit boxes,buttons, pull downs etc.Liveplot – powder pattern

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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

80

Powder pattern display - liveplot

Zoom

(new plot)

cum. 2 onupdates at end of genles run – check if OK!

81

Powder pattern display - powplot

“publication style” plot – works OK for many journals; save as “emf”can be “dressed up”; also ascii output of x,y table

Io-Ic

Refl. pos.

Io

Ic

82

Powplot options – x & y axes – “improved” plot?

Sqrt(I)

Q-scale (from Q=/sin)rescale y by 4x

Refl. pos.

co II

83

Citations:

GSAS:

A.C. Larson and R.B. Von Dreele, General Structure Analysis System (GSAS), Los Alamos National Laboratory Report LAUR 86-748 (2004).

EXPGUI:

B. H. Toby, EXPGUI, a graphical user interface for GSAS, J. Appl. Cryst. 34, 210-213 (2001).