MStructprogram/library

for MicroStructure analysisby powder XRD

What is it, how does it work, what is included and what is it useful for?

Zdeněk Matěj

http://xray.cz/mstruct

http://xray.cz/mstruct

Outline

1. What is it? How did it start? What is it based on?

2. How does it work? How can I use it?

3. What can it do? What is included?List of features/effects (~10)

with short description and examples. (possibilities and limitations)

10/14/2009 2

What is it?

• Program/libraryfor analysis of materialsMicroStructureby powder XRD.

– Practically a typical Rietveld program.Rodriguez-Carvajal: FullProf; Larson&VonDreele&Toby: GSAS; Kern: TOPAS, Lutterotti: MAUD; Birkenstock: BRASS; Petříček: Jana; …

– It includes physically relevant models for peak broadeningand shift. Scardi&Leoni: PM2k; Ribárik&Ungár: CMWP-fit

– It accounts for thin film absorption correction and asymmetrical diffraction geometry. Lutterotti: MAUD

10/14/2009 3

History: How did it start? What it is based on?

• FOX: ‘Free Objects for Crystallography’

– free, open-source, program for ab initio structure determination from powder diffraction. Developed by Vincent Favre-Nicolin in collaboration with Radovan Černý.

ref: J.Appl.Cryst. 35 (2002), 734-743

– Written in C++and based on thelibrary ObjCryst++

MStruct-presentation-2009 4

Vincent Favre-Nicolin:http://vincefn.net/Fox/

Fox-1.8.1.2-R1117/Fox-1.8.1.2-R1117.exehttp://vincefn.net/Fox/

Fox – program ©V.Favre-Nicolin, R.Černý

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Fox-1.8.1.2-R1117/Fox-1.8.1.2-R1117.exeFox-1.8.1.2-R1117/Fox-1.8.1.2-R1117.exeFox-1.8.1.2-R1117/Fox-1.8.1.2-R1117.exeFox-1.8.1.2-R1117/Fox-1.8.1.2-R1117.exe

ObjCryst++ Library ©V.Favre-Nicolin, R.Černý

– Library of C++ objects for crystallography computing

– Utilizes cctbx – ‘Computational Crystallography Toolbox’ developed by R. W. Grosse-Kunstleve and P. D. Adams

ref: J.Appl.Cryst43. 35 (2002), 126-136

10/14/2009 6

ObjCryst

cctbx

Fox.cpp

objcryst_doc_html/index.htmlobjcryst_doc_html/index.html

Our contribution: MStruct

– Contains add-on routines for microstructure analysis

– ObjCryst::LSQNumObj used for LSQ data refinement

– What is missing?• xml output (standard for all ObjCryst objects)

• wxWidgets interface -> no GUI availableProgram rus in text-mode(DOS) and external text editor and data

visualization software are necessary.

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ObjCryst

cctbx

MStruct

mstruct.cpp

mstructmstruct

PROGRAM: data and .imput files

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Program:•1) mstruct.exe•2) libfftw3-3.dll•3) structures.xml

Data:•1) my_pattern.xy•2) my_background.bgr

.imput (parametrs) files:•1) my_sample.imp•2) Ihkl_diffData_myPhase.dat

Output:•1) my_pattern.dat•2) my_sample.out•3) Ihkl_diffData_myPhase.dat

PROGRAM: rrunning program (in Matlab enviroment)

• system('mstruct < 64-3-225-05.imp > 64-3-225-05.out'),

• tio2('64-3-225-05');

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program execution input redirection input file output redirectionprogram text output

script to plot refined data

Why use libraries? How it is useful?

Library: including new reflection profile model

– Derive your own (children) class from ObjCryst::ReflectionProfile class• Implement appropriate methods for your class:

– CrystVector_REAL GetProfile (const CrystVector_REAL &x, const REAL xcenter,const REAL h, const REAL k, const REAL l)

– REAL GetFullProfileWidth (const REAL relativeIntensity, const REAL xcenter,const REAL h, const REAL k, const REAL l)

– Or derive fromMStruct::ReflectionProfileComponent class• Implement:

– CrystVector_REAL GetProfile (const CrystVector_REAL &x, const REAL xcenter,const REAL h, const REAL k, const REAL l)

– REAL GetApproxFWHM (const REAL xcenter, const REAL h, const REAL k, const REAL l) const

10/14/2009 10

x-axis values, where the profile should be calculated- in reciprocal space units s = 1/d (1/A)or direct space units L (A)

reflection hkl-indexes

reflection center position – 2Theta (rad)calculated profile

calculated guess of FWHM

x-axis: 2Theta (rad) values

Useful properties

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Can be refined– its parameters can be optimized

•Example 1: How to get the Crystal object from MStruct::ReflectionProfileComponent methodconst ObjCryst::Crystal & crystal = GetParentReflectionProfile().

GetParentPowderPatternDiffraction().GetCrystal();

•Example 2: Wavelengthconst REAL Lambda = GetParentReflectionProfile().

GetParentPowderPatternDiffraction().GetRadiation().GetWavelength()(0);

•Example 3: Convert Miller coordinates into orthonormal coordinates:REAL x = h, y = k, z = l;crystal.MillerToOrthonormalCoords (x, y, z);

•Example 4: Is the crystal hexagonal?// Get cctbx::sgtbx::space_groupconst cctbx::sgtbx::space_group & sg = crystal.GetSpaceGroup().GetCCTbxSpg();// Get Laue group codeconst cctbx::sgtbx::matrix_group::code & LaueCode = sg.laue_group_type();using namespace cctbx::sgtbx::matrix_group;. . .if ( LaueCode == code_6_m || LaueCode == code_6_mmm )

mGroupType = LAUE_HEXAGONAL;

Library:

List of effects/models

1. Instrumental function (PM2k, CMWP-fit, Maud)

2. Arbitrary texture (“PM2k”, “CMWP-fit”, Maud)

3. Texture numerical calculator+ simple models (Maud!!!)

4. pVoigt(A) (PM2k, Maud)

5. SizeLn (PM2k, CMWP-fit)

6. SizeDistrib (PM2k)

7. dislocSLvB (PM2k, CMWP-fit)

8. faultsVfcc (PM2k), faultsBfcc (CMWP-fit)

9. HKLpVoigtA (“PM2k”)

10. ReflProf, DoubleCompReflProf (“PM2k”)

11. Thin film absorption correction (Maud)

12. StressSimple, XECs (Maud)

13. RefractionCorr, Chi0

10/14/2009 12

Instrumental function – pVoigt(A)

• Described by pseudoVoigt function.• Cagliotti polynomial, etc.• Fitted on the measured LaB6 standard.

// Instrumental Parameters0.5 incidence angle (deg)-2Theta scan, negative value-2Theta/Theta scan// X-pert MRD parallel beam - 0.27 deg0.06246 0. 0.009211 instrumental profile params (W,U,V) MPD-Pixcel-variable slits0.002135 0.147385 I nstrumental profile params (Eta0,Eta1)1.0 0.0 0.0 60. instrumental profile params (Asym0,Asym1,Asym2,Asym2ThetaMax(deg))Cu 0.36 wavelength type (Cu,CuA1),linear polarization rate(A=0.8,

f=(1-A)/(1+A)=0.36 graphite mon.,f=0. unmonochromatized)

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)tan()(tan)( 22 VUWradFWHM

)(210 rad

)2(sin)2sin( 221

0 AA

AA

y = 2.30E-03x2 - 5.93E-04x + 1.73E-03R² = 9.99E-01

0.00

0.01

0.02

0.03

0.0 1.0 2.0 3.0 4.0

FWH

M(d

eg)

^2

tan(TH)

FWHM^2

y = 2.381E-03x + 6.249E-01R² = 6.706E-010.0

0.5

1.0

0 50 100 150

h

2Th (deg)

max,22 A

Arbitrary texture (Ihkl_diffData_my_Phase.dat)

• Usually hkl reflections intensities are calculated from crystal structure – atom positions, Biso-factors

• Model useful, if unknown or complicated texture is present• Calculated hkl reflection intensities corrected by arbitrary factors

// Arbitrary texture model

3 1 hkl file(0-don't use,1-generate,2-free all,3-read), print HKLIntensities(0-no,1-yes)

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File: Ihkl_diffData_my_Phase.dat

# h k l 2Theta(deg) |Fhkl|^2 Icor fixed

1 0 1 25.304 2.57e+004 1.00 1

1 0 3 36.975 3.01e+003 0.80 0

0 0 4 37.843 1.28e+004 1.21 0

1 1 2 38.573 3.30e+003 1.08 0

2 0 0 48.026 2.88e+004 0.91 0

2 0 2 51.960 7.71e-011 1.00 1

1 0 5 53.942 2.29e+004 1.07 0

Texture calculator + models• Simple “brute force” algorithm for calculation of the

projection of the ODF function into the diffraction vector direction.

1 number of texture components

1. component scale1. 1. 1. component base hz kz lz (space delimitaded) 1. -1. 0. component base hx kx lx (space delimitaded)

0 force texture symmetry for this component (0,1)1. 0.0 10. th component: weight(0.-1.),th0(deg),dth0 (deg)0. 30.0 10. psi component: weight(0.-1.),psi0(deg),dpsi0(deg)0. 0. tilt: eth0(deg),epsi(deg)

2 number of hkl lines to calculate

1 1 0 h k l (space delimitaded)pf_110-c.dat output filename

0. 75. 5.0 th: min,max,step(deg)0. 360. 5.0 psi: min,max,step(deg)

. . .

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Texture - example

10/14/2009 16

Example: simulation of cubic BST film (on Al2O3 (0001)x(11-20) substrate)

(111) texture axis (perpendicular to sample surface = parallel to Al2O3 (0006))

Y = 0 deg, DY = 10 deg,F = 30 deg, DF = 10 deg, fraction = 0.9

Fibre Texture

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ODF-function model: used for fiber texture modelling(from ref: [Simek, J.Appl.Cryst]) – texture axis direction (HKL) normal to sample surface, pole function:

UN7 (A. Kolomiets)

UN17

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Sample no. UN19: 1e-4 mbar N2, substrate Si at room temperature,5e-5 mbar Ar, 1200 sec

UN:D = (8+/-3) nm, e = (1.6+/-0.3) %, a = (4.9565+/-0.005) A,s = (5.7+/-0.3) GPa - Reuss stress, wFW = (29.1+/-0.8) deg, n = 1

UN2:

D = (8.7+/-0.5) nm, e = (2.2+/-0.1) %, a = (5.3273 +/- 0.002) A,s = (-4.4+/-0.1) GPa - isotropic stress, wFW = (23+/-1) deg, n = (0.64+/-0.03)

pseudoVoigt function – pVoigt(A)

• Reciprocal space:• Real space:• Asymmetry:

• Cagliotit polynomial, etc.• Modelling of micro-deformation/strain effect (e):

// the 1st phase - Strain broadening - modeled by pseudoVoigt function// - only U-Cagliotu param. (W=V=0.) and shape Eta0 (Eta1=0) params. refinedpVoigtA strainProfAnatase broadening component type (pVoigt(A),SizeLn,dislocSLvB,HKLpVoigtA),effect name,comp=20. 0. 0. profile params (W,U,V)0.0 0. profile params (Eta0,Eta1)1. 0. 0. 60. profile params (Asym0,Asym1,Asym2,Asym2ThetaMax(deg))

10/14/2009 19

),2(),2()1()2( ss CGpV

ss

ssss

)/12(4/1

,)/11(2/1,)1(2/1

AA

AA RL

G … Gauss, C … Cauchy/Lorentz

|)|2exp()/exp()1()( 222 xkxkxpV s

/)1)(/(11

GC

k

s .. FWHM/2

UeeradUradFWHMCG

14);tan(4)][2();(tan)][2( 22

/2ln2,/2 GC

U, … strongly correlatede, … almost uncorrelated

Convolution kernel

• Real space effects – convoluted by FT

• Reciprocal space effects – convoluted directly

10/14/2009 20

Size broadening - SizeLn

• Spherical crystallites – size D (diameter) given bylog-normal distribution

// the 1st phase - Size broadening - lognormal distribution of crystals diameter (median M, shape Sigma)

SizeLn sizeProfAnatase broadening component type (pVoigt(A),SizeLn,…),effect name,comp=1

200.0 0.3 M(nm),sigma

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Size broadening - SizeDistrib

• Spherical crystallites defined by refinable probability distribution.

// the 1st phase - Size broadening - refinable Size Distribution model

SizeDistrib sizeProfAnatase broadening component type (pVoigt(A),SizeDistrib,…),effect name,comp=1

wD_vz_380y.dat 1.e2 1.e6 name of file with prescribed weighted distribution, LSQ constraint scale factor, LSQ weight factor

10/14/2009 22

D (nm)

20 40 60 80 100 120 140-4000000

0

4000000

16000000

36000000

64000000

100000000

144000000

2Theta (deg)

Inte

nsity (

arb

itra

ry u

nits)

vz_380y

- 1 0

3-

0 0

4-

1 1

2

- 2 0

0

- 1 0

5-

2 1

1

- 2 1

3-

2 0

4

- 1 1

6-

2 2

0-

1 0

7-

2 1

5-

3 0

1-

0 0

8 - 3 0

3-

2 2

4-

3 1

2

- 2 1

7 - 3 0

5-

3 2

1-

1 0

9-

2 0

8-

3 2

3

- 3 1

6-

4 0

0-

3 0

7-

3 2

5-

4 1

1 - 2 1

9-

1 1

10

- 2 2

8-

4 1

3 - 4 0

4-

3 3

2

- 4 2

0-

1 0

11

- 3 2

7-

4 1

5

Dislocations - dislocSLvB

// the 1st phase - Dislocation Strain broadening (Scardi&Leaoni&van Berkum)

dislocSLvB strainProfCu broadening component type (pVoigt(A),…),effect name,comp=2

20.0 0.002 Re(nm),rou(1/nm^2)

0.30 -2.1 0. Cg0,q1,q2

10/14/2009 23

Stacking faults - faultsVfcc, faultsBfccin fcc materials

// the 1st phase - Stacking Faults - Warren, Velterop2000, Scardi, Leoni

faultsVfcc faultsProfCu broadening component type (pVoigt(A),…),effect name,comp=1

0.00 0.00 alpha, beta(twins)

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// the 1st phase - Stacking Faults - Balogh & Ungar (JAP2006)

faultsBfcc faultsProfCu broadening component type (pVoigt(A),…),effect name,comp=1

twins 0.05 type(intrinsic/twins/extrinsic), alpha

hkl – phenomenological - HKLpVoigtA

// the 1st phase - strange peak position effects

HKLpVoigtA HKLProfEffectCu broadening component type (pVoigt(A),…),effect name,comp=3

8 nb of peaks with preset profiles - phase: 1

1 1 1 0.000 0.00 0.0 000 hkl,d2Theta(deg),fwhm(deg),eta,code(111)?

0 2 0 0.000 0.00 0.0 000 hkl,d2Theta(deg),fwhm(deg),eta,code(111)?

0 2 2 0.000 0.00 0.0 000 hkl,d2Theta(deg),fwhm(deg),eta,code(111)?

. . .

10/14/2009 25

ReflProf, DoubleCompReflProf

10/14/2009 26

DoubleComponentReflectionProfile

AnataseReflProf

ReflProfAnataseProf1

SizeLn (M=5 nm, 0.3)

szieProfAnatase1

ReflProfAnataseProfile2

pVoigtA (U=0, 0=0)

strinProfAnatase

SizeLn (M =25 nm, 0.3)

szieProfAnatase2

Bimodal Size Distribution// the 1st phase - physical line broadening6 number of additional broadening effects (total number - including virtual and unused effects)

// 1 (parent prof) + 2 (child profs) + 3 (2 size and 1 strain comps) = 6

// the 1st phase - Parent Reflection Profile Object - double component broadening effectDoubleCompReflProf AnataseReflProf broadening component typeAnataseReflProf1 name of the first componentAnataseReflProf2 name of the second component0.5 fraction of the second component1 top parent effect (1-yes,0-no)

// the 1st phase - Child Reflection Profile Object 1 - Size + Strain broadenningReflProf AnataseReflProf1 broadening component type2 number of additional broadening effects (components only, instrumental effect already included)sizeProfAnatase1 broadening component namestrainProfAnatase broadening component name0 top parent effect (1-yes,0-no)

// the 1st phase - Child Reflection Profile Object 2 - Size + Strain broadenningReflProf AnataseReflProf2 broadening component type2 number of additional broadening effects (components only, instrumental effect already included)sizeProfAnatase2 broadening component namestrainProfAnatase broadening component name0 top parent effect (1-yes,0-no)

// the 1st phase - Size broadening component 1 - lognormal distribution of crystals diameter (median - M, shape - Sigma)SizeLn sizeProfAnatase1 broadening component type (pVoigt(A),SizeLn,dislocSLvB,HKLpVoigtA),effect name,comp=15.0 0.3 M(nm),sigma

// the 1st phase - Size broadening component 2 - lognormal distribution of crystals diameter (median - M, shape - Sigma)SizeLn sizeProfAnatase2 broadening component type (pVoigt(A),SizeLn,dislocSLvB,HKLpVoigtA),effect name,comp=125.0 0.4 M(nm),sigma

// the 1st phase - Strain broadening component - modeled by pseudoVoigt function// - only U-Cagliotu param. (W=V=0.) and shape Eta0 (Eta1=0) params. refinedpVoigtA strainProfAnatase broadening component type (pVoigt(A),SizeLn,dislocSLvB,HKLpVoigtA),effect name,comp=20. 1. 0. profile params (W,U,V)0.0 0. profile params (Eta0,Eta1)1. 0. 0. 60. profile params (Asym0,Asym1,Asym2,Asym2ThetaMax(deg))

10/14/2009 27

Thin film absorption correction

• Switch presentation

// the 1st phase - thin film absorption correction - TiO2,density=2.49g/cm3

220. 0. 315. absorp corr params:thickness(nm),depth(nm),abs.factor(1/cm)

10/14/2009 28

XRD - TiO2 thin films on ITO.pptx

StressSimple, XECs

• Anatase - XECs

• Switch presentationX

• Stress “zero”

// the 1st phase - Residual stress reflection position correction - simple stress model

StressSimple stressCorrAnatase effect type,effect name,comp=4

Reuss-Voigt 0. XECs model, stress (GPa)

// material C11 C12 C13 C33 C44 C66 constants (in GPa) - in the format: C11 value C12 value etc.

C11 320 C12 151 C13 143 // anatase Cij (GPa)

C33 190 C44 54 C66 60 // ref: M.Iuga,Eur.Phys.J.B(2007)58,127-133

0.3 model weight (0..Reuss,1..Voigt)

10/14/2009 29

nb. T (nm)sTPF

(MPa)Rwp (%)

sRwp (%)s = 0

1 42 760 18.4 20.4

2 100 740 22.5 23.8

3 130 750 24.4 29.8

4 180 510 16.2 21.2

5 300 310 22.4 24.7

6 440 205 22.1 23.4

7 630 280 12.9 15.8

8 800 250 11.2 14.6

0 200 400 600 8000

200

400

600

800

Thickness (nm)

Str

ess (

MP

a)

anatase_ECs_pictures.pptanatase_ECs_pictures.pptanatase_ECs_pictures.pptanatase_ECs_pictures.pptanatase_ECs_pictures.ppttpf-tio2-64-stress.pptxtpf-tio2-64-stress.pptxtpf-tio2-64-stress.pptxtpf-stress-zero.pptx

RefractionCorr, Chi0

• Switch presentation

MStruct::RefractionPositionCorr::GetChi0(...): Chi0 and absolute density computed for Crystal: Anatase

chi0: (-2.3988e-005,-1.2128e-006) (n=1-delata-ii*beta~=1+chi0/2)

critical angle: 0.28 (deg)

density: 3.891 (g/cm3)

10/14/2009 30

// the 1st phase - Refraction reflection position correction

RefractionCorr refractionCorrAnatase effect type,effect name,comp=3

crystal chi0 set directly-value,calculated from-crystal,calculated form chem.-formula

1. relative density

refraction_corr.pptx