rietveld school 01 - Durham University...

1

Durham

ChemistryDepartment

DurhamUniversity

Welcome/IntroductionDr John S.O. Evans

Durham, January 2007

[email protected] www.durham.ac.uk/john.evans PCG workshop January 2007

Welcome

• Health and Safety/Fire procedures• Course will be lectures followed by

hands on practical• Emphasis on understanding not

learning a package• Please submit pre-course questionnaire

with name/pseudonym

2


Teachers/Tutors

• Jeremy Cockcroft UCL/Birkbeck• John Evans Durham Chemistry• Ivana Evans Durham Chemistry

• Will Bisson UCL• Sarah Lister Durham• Graham Stinton Durham• Lars Peters Durham


Thanks

• Tutors for time• Sponsors for cash• Alan Coelho for Topas software• Bob von Dreele/Alan Larson for gsas• Juan Rodriguez-Carvajal for fullprof

DurhamUniversity

3


Legalities

• By using ITS account you’re agreeing to University policy on use of the web

• You each have your own login id. Don’t change the password!!!

• Don’t try stealing the software! It won’t work anywhere else plus is time limited!

• All timetabled sessions are compulsory!


Tomorrow Morning

• First lecture will be in CG93 (Scarborough lecture theatre)

• Follow somebody!

• Who doesn’t know how to use solver in excel?

4


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Information in a Powder Pattern

2θ - degrees

Cou

nts

1. Peak positions determined by size, shape, symmetry of unit cell – internal

structure

2 9 .52 95

2. Peak Intensities determined by

where atoms sit in unit cell – internal

structure

3. Peak widths influenced by size/strain of crystallites -

microstructure.

2θ


Timetable

Sunday Monday Tuesday Wednesday

09:003. Introduction to powder diffraction

and data collection.8.Structure factors, peak intensities

and Rietveld refinement13. Question and Answer session

09:454. jedit/topas academic/Rietveld

refinement9. Pawley and Rietveld refinement 14. Spot the errors

11:00 Coffee Coffee Coffee

11:305. Peak positions - indexing/cell

refinement exercises10. Intro to gsas/fullprof then

examples15. Free problems then wrap up

13:00 Lunch - Musgrave Room Lunch - Musgrave Room Departure

14:00 6. Peak shapes lecture 11. Restraints, Constraints, Rigid Bodies and Structure Solution

14:30 7. Peak shape tutorial 12. Structure solution and rigid body refinements

16:00 Registration in Trevelyan Tea Tea

16:30 7. Peak shape tutorial 12. Structure solution and rigid body refinements

18:00 Dinner - Trevelyan Close Close

18:30 Dinner - Trevelyan Dinner - Trevelyan

19:000.Welcome/Introduction

1.Symmetry lecture

20:00 2. Symmetry bar quiz Pub Quiz Free evening

Lecture slot Food/Drink Problems/Workshop

5

Durham

ChemistryDepartment

DurhamUniversity

Introduction to Software/ProblemsDr John S.O. Evans



Topas Academic

• Useful for teaching as can input equations, see everything in file very quickly

• Powder and single crystal• X-ray, neutron• Constant λ, time of flight, energy dispersive• Structural models, Pawley fitting, peak fitting• Restraints, constraints, penalty only fitting• Multi phase, multi histogram• Non crystallographic applications• Simulated Annealing for structure solution

6


Acknowledgement

• Alan Coelho (Topas/Topas-Academic author)• http://pws.prserv.net/Alan.Coelho/

‘s


Topas Graphics

Grid

Zoom

Plot

Run

7


Software Interface

• Command file driven for flexibility/speed• jedit – free customisable java editor• Interacts directly with software• Helps with formatting

http://www.dur.ac.uk/john.evans/topas_academic/topas_main.htmhttp://www.dur.ac.uk/john.evans/topas_workshop/pcg_workshop_menu.htm


jedit interface

8


Topas/jedit demo


Refining Parameters

str ‘cell params for an orthorhombic structure

a 7.31192

b 7.53699

c 7.69967

9


Refining Parameters – Using @


a @ 7.31192

b @ 7.53699

c @ 7.69967


Refining Parameters – Using names


a lpa 7.31192

b lpb 7.53699

c lpc 7.69967

10


Refining Parameters – Using Names

str ‘cell params for a cubic structure

a lpa 10.60992

b lpa 10.60992

c lpa 10.60992


Cubic(@ 10.60992)


Fixing Parameters – Using !


a !lpa 10.60992

b !lpa 10.60992

c !lpa 10.60992

• N.B. jedit column editting – hold down ctrl key and type all !’s at once

11


Refining Parameters - Macros

Zero_Error( , 0) ‘fixed zero point

Zero_Error( @ , 0.013) ‘refine zero point

Zero_Error( !zero, 0) ‘fixed zero point

Zero_Error( zero, 0.013) ‘refined zero point


User Defined Equations

‘topas zero point correction in input file

prm zero 0.01

th2_offset = zero;

‘topas zero point correction in input file

prm zero 0.01

prm corr 0.003

prm corr2 0.001

th2_offset = corr2*X^2 + thcorr*X + zero;

12



‘silly(?) example of topas equations

prm zero 0.01

prm var1 0.003

prm !date 21 ‘st of April

th2_offset = zero + var1 * date;



• Flexible system for defining your own equations• Fully “programmable program”• e.g. gsas vs topas:

• shft = 3600*height/π*radius • 2θobs = 2θcalc + zero – 2*shft*Cos(θ)

‘topas height/zero point correction in input file

prm zero 0.01

prm height 0.15

th2_offset = zero - 2*height*Cos(Th)/radius;

zero 0.01 y shft -10.00 y

13


Simulated Annealing

• Flexible Simulated Annealing approach for complex structures:

• Flexible definition of restraints, constraints, rigid bodies, etc

‘topas annealing expression in input fileval_on_continue = Val + Val * Rand(-0.1,0.1);val_on_continue = ideal_coord + Rand(-0.1,0.1);


Running Tutorial Problems – Session 4

• You should all be able to log in to computer• Work on the j: drive where you have full read/write

privileges• Use folder j:\school_work• Run jedit from icon on desktop• Launch topas-academic from inside jedit• Access tutorials

14


Initial Software Setup

• First time you log in you’ll need to double click on:

• I:\licence\rietveld\rietveld_setup.bat• Wait a few minutes for software to be

copied• Use desktop icons created

• [For fullprof will need to double click on rietveld_setup.bat each time you log in]


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Session 5 – Peak Positions

2θ - degrees

Cou

nts


structure

2 9 .52 95



structure


microstructure.

2θ

15


Session 5 – Peak Positions

Bragg’s Law: nλ=2dsinθ


d-spacing formulae

• Triclinic

• Cubic

( ) ( ) ( )[ ]βγααγβγβαγβα coscoscos2coscoscos2coscoscos2sinsinsin11 22222222222222222 −+−+−+++= chlabbcklahkabcbalcakcbh

Vd

2

222

2

1a

lkhd

++=

Bragg’s Law: nλ=2dsinθ

16


Indexing Tutorials – Session 5

• Folders should contain print outs of powder patterns for tutorials 4 and 5

• Try to index powder pattern for tutorial 4 by hand/with excel

• Use excel to refine cell parameter of diffraction pattern for tutorial 5

Lin

(Cou

nts)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

110000

120000

2-Theta11 20 30 40 50 60 70

dsp=

5.31

391,

2th

=16.

669

°

dsp=

4.33

307,

2th

=20.

480

°

dsp=

3.06

375,

2th

=29.

123

°

dsp=

2.83

540,

2th

=31.

527

°

dsp=

2.65

292,

2th

=33.

758

°

dsp=

2.50

084,

2th

=35.

879

°

dsp=

2.37

171,

2th

=37.

904

°

dsp=

2.26

181,

2th

=39.

822

°

dsp=

2.16

404,

2th

=41.

703

°

dsp=

2.07

998,

2th

=43.

472

°

dsp=

1.93

575,

2th

=46.

897

°ds

p=1.

8742

6, 2

th=4

8.53

3 °

dsp=

1.81

849,

2th

=50.

122

°ds

p=1.

7675

9, 2

th=5

1.67

0 °

dsp=

1.71

986,

2th

=53.

215

°ds

p=1.

6763

9, 2

th=5

4.70

8 °

dsp=

1.63

639,

2th

=56.

162

°ds

p=1.

5985

9, 2

th=5

7.61

3 °

dsp=

1.56

335,

2th

=59.

038

°ds

p=1.

5303

7, 2

th=6

0.44

1 °

dsp=

1.49

953,

2th

=61.

818

°ds

p=1.

4702

4, 2

th=6

3.19

0 °

dsp=

1.44

305,

2th

=64.

523

°ds

p=1.

4167

9, 2

th=6

5.86

9 °

dsp=

1.34

650,

2th

=69.

788

°ds

p=1.

3251

4, 2

th=7

1.08

1 °

dsp=

1.30

495,

2th

=72.

353

°ds

p=1.

2855

7, 2

th=7

3.62

1 °

dsp=

1.26

716,

2th

=74.

873

°

Lin

(Cou

nts)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

2-Theta

11 20 30 40 50 60 70

dsp=

3.24

505,

2th

=27.

463

°

dsp=

2.48

511,

2th

=36.

113

°

dsp=

2.29

395,

2th

=39.

241

°

dsp=

2.18

518,

2th

=41.

281

°

dsp=

2.05

272,

2th

=44.

079

°

dsp=

1.68

599,

2th

=54.

371

°

dsp=

1.62

283,

2th

=56.

674

°

dsp=

1.47

801,

2th

=62.

820

°ds

p=1.

4516

7, 2

th=6

4.09

4 °

dsp=

1.42

278,

2th

=65.

557

°

dsp=

1.35

899,

2th

=69.

055

°ds

p=1.

3456

2, 2

th=6

9.84

0 °

Durham

ChemistryDepartment

DurhamUniversity

Session 6 – Peak ShapesDr John S.O. Evans


17


6055504540353025201510

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Session 6 – Peak Shapes

2θ - degrees

Cou

nts


structure

2 9 .52 95



structure


microstructure.

2θ


Peak Shapes – View 1

• Peak shapes are a nuisance. For Rietveld refinement we only fit peaks to get an good agreement between yobs and ycalc to give us an accurate structural model

• We’re therefore not interested in the mathematical details of the peak shape model

• Failure to fit the finest details of the peak shape (e.g. tails of the peaks) aren’t very important

18


Peak Shapes – View 2

• Peak shapes in a powder diffraction pattern result from a combination of instrumental effects (the optics you use) and sample effects (size/strain)

• There is a wealth of fascinating information contained in experimental peak shapes


Peak Shapes – 3 Approaches

• Empirical Peak Shapes– Used by most Rietveld packages– Whatever function fits the data is good

• Fundamental Parameters– Instrumental contribution to peak shape– Sample contribution to peak shape– Excellent fits with very few parameters

• Semi Empirical– Define instrument with empirical function– Convolute with sample contribution

19


Gaussian/Lorentzian Functions

x 2θ-2θhkl – where 2θhkl is position of reflectionfwhm full width at half maximumη mixing parameter for composite function


Gaussian vs Lorentzian

www.phys.unsw.edu.au/~mgb/pics/gausscauchy.gif

• Lorentz sharp near maximum but has long tails away from peak

• Gauss smaller tails but rounded maximum

• PV mixes two functions

• Mixing η 0 to 1

20


Gaussian, Lorentzian, Pseudo Voigt

2Th Degrees58.458.458.3558.358.2558.258.1558.158.055857.9557.957.8557.857.7557.757.6557.657.5557.557.4557.457.3557.357.2557.257.1557.157.055756.9556.956.85

Cou

nts

7,500

7,0006,5006,0005,5005,0004,5004,000

3,5003,0002,5002,0001,5001,000

500

0-500

-1,000-1,500

2Th Degrees58.458.458.3558.358.2558.258.1558.158.055857.9557.957.8557.857.7557.757.6557.657.5557.557.4557.457.3557.357.2557.257.1557.157.055756.9556.956.85

Cou

nts

7,500

7,000

6,500

6,000

5,500

5,000

4,500

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0

-500

-1,000

2Th Degrees58.458.458.3558.358.2558.258.1558.158.055857.9557.957.8557.857.7557.757.6557.657.5557.557.4557.457.3557.357.2557.257.1557.157.055756.9556.956.85

Cou

nts

7,500

7,000

6,500

6,000

5,500

5,000

4,500

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0

-500

-1,000

Gauss wRp=30.5%

Lorentz wRp=19.9%

η=0.68 wRp=17.6%Individual peak fitting on simulated Y2O3 data 3/2/07


fwhm vs 2θ

Gauss: ( ) 212 tantan WVUfwhm ++= θθ

Lorentz: θθ

tancos

YXfwhm +=

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 20 40 60 80 100 120 140 160

2-theta

fwhm

U, V, W, X, YRefineableParameters

21


GSAS TCHZ type function

• Modified Thompson-Cox-Hastings pseudo-Voigt


GSAS/Topas

‘topas TCHZ peak shape function

TCHZ_Peak_Type( pku,-0.15636`,pkv, 0.24248`, pkw, -.16266`, !pkx, 0.00000, pky, 0.03861`, !pkz, 0.0000)

22


Look in topas.log to see what’s happening

TCHZ_Peak_Type(pku,-0.02510`,pkv, 0.03611`,pkw, -0.01238`,pkx, 0.00000`,pky, 0.16545`,pkz, 0.00010`)

prm pku -0.02510` min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pkv 0.03611` min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pkw -0.01238` min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pkx 0.0000 min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pky 0.16545` min = Max(0.0001, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pkz 0.0000 min = Max(0.0001, Val-.1); max = Min(2, Val+.1); del 1.0e-4 peak_type pv pv_lor = 1.36603 (((pky) Tan(Th) + (pkz) /Cos(Th)) /(

(Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^5 +2.69269 Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^4 ((pky) Tan(Th) + (pkz) /Cos(Th)) +2.42843 Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^3 ((pky) Tan(Th) + (pkz) /Cos(Th))^2 +4.47163 Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^2 ((pky) Tan(Th) + (pkz) /Cos(Th))^3 +0.07842 Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) ) ((pky) Tan(Th) + (pkz) /Cos(Th))^4 +((pky) Tan(Th) + (pkz) /Cos(Th))^5

)^0.2)) - 0.47719 (((pky) Tan(Th) + (pkz) /Cos(Th)) /(


)^0.2))^2 + 0.1116 (((pky) Tan(Th) + (pkz) /Cos(Th)) /(


)^0.2))^3; pv_fwhm = (


)^0.2);


Fundamental Parameters Approach

• Peak Widths depend on– X-ray source– Instrument– Sample

• Convolution or folding “blends” one function with another

( ) ( ) ( ) ( ) ( ) ( ) ττττττ dtfgdtgftgtf −=−=⊗ ∫∫∞

∞−

∞

∞−

( ) ( ) SampleInstrumentSourceY ⊗⊗=θ2(or empirical instrumental function)

23


Convolution Approach

( ) ( )θ2YSampleInstrumentSource =⊗⊗


Contributions to peak shape

24


Sample Contributions - Size

• Scherrer formula• β full width half maximum; k a constant• LVol is volume weighted mean column height; only for

cubic crystals and h00 reflections is it equal to L0 in figures below


Sample Contributions - Strain

• d-spacings of d+∆d and d-∆d• e0=∆d/d• Assume Braggs law gives different 2θ for different

d-spacings

25


Inte

nsity

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

110000

2-theta10 20 30 40 50 60 70 80 90 100 110 120 130 140

X-ray Particle Size from peak shape

Size: 324(110) nmStrain: 0.1637(40)

Size: 20.4(8) nmStrain: 0.138(7)

0.00.51.01.52.02.53.03.54.04.5

0 20 40 60 80 100 120 140 160 180

2-theta

Broa

deni

ng

1/cos(th)tan(th)

sizestrain

• Size broadening – “broad over whole 2-theta range”• Strain broadening – “narrow at low 2-theta”


Sample Contributions - Caveat

• Be careful!• See links in tutorial

• http://www.dur.ac.uk/john.evans/topas_workshop/size_strain.htm

26


Source Profile

N.B. source profile only much sharper then observed peak


Source ⊗ Equatorial

N.B. peak now considerably broadened by instrument

27


Source ⊗ Equatorial ⊗ Axial

N.B. peak now has asymmetry


Source ⊗ Equatorial ⊗ Axial ⊗ Sample

N.B. peak maximum not at calculate 2θ

28


Topas Language

Radius(217) ‘diffractometer radius

Divergence(1) ‘divergence slit deg

axial_conv

filament_length 12

sample_length 15

receiving_slit_length 12

primary_soller_angle 5.1

secondary_soller_angle 5

Slit_Width(0.1) ‘receiving slit

CS_L(size_lor, 329.49186) ‘size term nm

Strain_G(strain_g, 0.04939) ‘strain term


The tutorial (hard!)

• Take an experimental data set• Determine fwhm for all peaks and plot in excel• Use excel to fit fwhm=f(2θ) functions

– fwhm = U tan2θ + V tanθ + W– fwhm = U 2θ2 + V 2θ + W

• Try these same functions in a Rietveld refinement in topas• Try a fundamental parameters approach in topas and get

a better fit with fewer parameters.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 20 40 60 80 100 120 140 160

2-theta

fwhm

29


Semi Empirical Size/Strain

• See:– tutorial 9 - Size/Strain Analysis: Shows how

size/strain can be determined in topas using the CeO2 round robin data and an empirical instrumental function

– tutorial 10 – determining the size of nanoparticles

Durham

ChemistryDepartment

DurhamUniversity

Session 9 – Pawley/Rietveld ProblemsDr John S.O. Evans


30


Tomorrow’s Programme

• Wednesday morning open questions session– Either submit questions on paper before hand

or ask on the morning– Will limit to 30-45 minutes

• Spot the errors tutorials– Deliberate errors in data for trouble shooting

• Free problems/play with your data• Wrap up session (if required)


Today’s Programme

• Next – workshop tutorials• After coffee

– Gsas demonstration– Workshop tutorials

• Split into “fullprof-bias” room (on the right)?• After lunch

– intro to problems lecture– Restraints/rigid bodies– Structure solution problems (simple)

31


Rietveld/Pawley Problems

• Tutorial 1 – TiO2 Rietveld• Tutorial 2 – TiO2 Pawley• Tutorial 3 – ZrW2O8 X-ray/neutron/neutron time of

flight• Tutorial 10.5 – Jeremy’s PbSO4 data in .xye

format for you to try in topas• Gsas 2 (later) – Jeremy’s PbSO4 data• Tutorial 11 – Combined X-ray and neutron

refinement (also gsas3/gsas4)• Tutorial 12 – Multiphase Rietveld refinement

Durham

ChemistryDepartment

DurhamUniversity

Session 10 – Other SoftwareDr John S.O. Evans


32


GSAS

• General Structural Analysis System• Bob Von Dreele/Alan Larson• Very widely used• Magnetic refinements• Run via expedt/expgui• Actually has a .exp file (like .inp file) in

background


Fullprof Suite

• Juan Rodriguez-Carvajal• Has a .pcr file (like .inp file) in background• Very widely used• Magnetic refinements• Use winplotr interface

33


Mistakes

• Hardest thing in practice is spotting mistakes• You don’t know what the “right” answer is• Are there errors in model or data?

• mistake_02 to mistake_08 contain data with “errors” in them – solve the errors and win a prize!

• Stick to isotropic temperature factors• Stick to a TCHz analytical peak shape function• Fix pkx and pkz at 0

Durham

ChemistryDepartment

DurhamUniversity

Session 11 – Constraints, Rigid Bodies and Structure Solution

Dr John S.O. Evans


34


Data Compression

2-theta

I

(a) (b)

(d)(c)

Single crystal

Four differently oriented single crystals

Polycrystalline material


3D Information compressed onto 1D

2θ

2θ

‘…data compressed into one dimension…’

35


Insufficient information

• Powder pattern 3D diffraction data compressed onto 1D

• Loss of “information” relative to a single crystal experiment

• Single crystal people like 10 observations (10 hkl reflections) per refined parameter

• How many “observations” do we have in a powder pattern?


alvo4_tch.inp

• 5-80 0.02 step 3750 observations• 530 hkl reflections in 2θ range

2Th Degrees8075706560555045403530252015105

Cou

nts

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

-1,000

AlVO4 100.00 %

STR(P_-1, AlVO4)a @ 6.54138`b @ 7.75971`c @ 9.13591`al @ 96.18561`be @ 107.23757`ga @ 101.40086`

36


How many peaks?

2Th Degrees1918171615

Cou

nts

3,5003,0002,5002,0001,5001,000

5000

AlVO4 100.00 %

2Th Degrees8075706560555045403530252015105

Cou

nts

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

-1,000

AlVO4 100.00 %


How many peaks?

2Th Degrees2524.824.624.424.22423.823.623.423.2

Cou

nts

5,000

4,000

3,000

2,000

1,000

0

AlVO4 100.00 %

2Th Degrees8075706560555045403530252015105

Cou

nts

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

-1,000

AlVO4 100.00 %

37


How many peaks?

2Th Degrees62.56261.56160.560

Cou

nts

1,500

1,000

500

0

AlVO4 100.00 %

2Th Degrees8075706560555045403530252015105

Cou

nts

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

-1,000

AlVO4 100.00 %


Information in a powder pattern

• How much information is there in a powder pattern?

• Rarely enough

• See literature by e.g. Giacovazzo/David/Di Sivia

38


Restraints

• Bring in chemical information• Dealt with in least squares in the same way

as data• “Soft Restraints”

restdatatot KK 22

21

2 χχχ +=


Restraints

• e.g. you might know that Zr1-O2 distance should be ~2.075 Å

• Apply a “penalty” if it’s not that value• Penalty = (value-2.075)2

Distance_Restrain(Zr1 O1, #ideal_dist, #actual dist, #tolerance, #weight)

Distance_Restrain(Zr1 O1, 2.075, 2.037, 0.01, 1)

Angle_Restrain(O1 Zr2 02, 90, 91, 1, 1)

Penalty = weight * (2.075-2.037)^2;

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Topas bond lengths/angles

append_bond_lengths

Zr1:0 O1:3 0 1 0 2.12510 O1:10 0 0 0 2.12510 90.053 O1:7 -1 0 1 2.12510 90.053 90.053 O2:7 -1 1 1 2.12575 179.898 89.897 90.036 O2:3 0 1 -1 2.12575 90.015 89.897 90.036 179.898

O2:10 -1 0 0 2.12575 90.015 90.015 90.036 179.898 89.897

Zr1

O1

O1:3 0 1 0


Restraints

• See tutorials

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Constraints

• Force sub-sections of structure to be rigid• Dealt with in least squares in the same way

as symmetry• “Hard Constraints”


Constraints/Rigid Bodies

• e.g. force the Zr1-O2 bond to be exactly 2.075 Å• e.g. rigid body• How many parameters?

macro Octahedra(Zr1, o1, o2, o3, o4, o5, o6, 2.075)

{

Point_for_site(s0, 0, 0, 0)

Point_for_site(s1, r, 0, 0)

Point_for_site(s2, -r, 0, 0)

Point_for_site(s3, 0, r, 0)

Point_for_site(s4, 0, -r, 0)

Point_for_site(s5, 0, 0, r)

Point_for_site(s6, 0, 0, -r)

}

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TLS Matrices

• Atoms on both sides of a rigid group ought to vibrate in related ways

• Atoms/adps independently – how many parameters?

• Rigid body/TLS e.g. 8 parameters


Rigid Bodies

• P2O7 groups are well understood – 2 parameters per P2O7?

Typically1.5 Å

1.55 1.65

180

120

P-O

-P A

ngle

P-O(-P) Distance

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Structure Solution

• Simulated annealing type approach• Refine, randomise, refine

‘topas annealing expression in input fileval_on_continue = Val + Val * Rand(-0.1,0.1);val_on_continue = ideal_coord + Rand(-0.1,0.1);


Tutorials – Restraints/Constraints

• Tutorial 3 – ZrW2O8

• GSAS 4 – restraints/combined refinement oxide • GSAS 5 – Rigid bodies Sc2(WO4)3 using TLS matrices• GSAS 7 – organic using restraints• GSAS 9 – Ni coordination polymer using restraints• Tutorial 14 – refining an organic using restraints then as a

rigid group

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Tutorials – Structure Solution

• Tutorial 13 – Structure solution of an inorganic oxide

• Tutorial 15 – Organic structures and structure solution

• Tutorial 3 – data suitable for structure solution


Guided Tours?

• Bragg-Brentano/Transmission instruments• Incident beam mono/no mono• d8’s/d5000’s• High temperature furnace/cryostat• Vantec/Lynx-Eye psd’s• Sol-X energy dispersive

• Single crystal instruments (Judith’s)

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Durham

ChemistryDepartment

DurhamUniversity

Session 14 – MistakesDr John S.O. Evans



Group Refinement

• Group discussion of order of refining parameters• e.g. if you refine just scale parameter when peak

positions are wrong the peaks will “disappear”• Look at obs/calc patterns before thinking what to

refine• Don’t be afraid to e.g. fix scale parameter to a

sensible value at the start• Never refine a parameter if you don’t understand

its meaning!

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Mistakes

• Hardest thing in practice is spotting mistakes• You don’t know what the “right” answer is• Are there errors in model or data?• Ivana’s “Rietveld Crimes”

• mistake_02 to mistake_08 contain data with “errors” in them – solve the errors and win a prize!

• Stick to isotropic temperature factors• Stick to a TCHz analytical peak shape function• For this instrument you can fix pkx and pkz at 0

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