rietveld school 01 - durham university...
Post on 30-Apr-2018
228 Views
Preview:
TRANSCRIPT
1
Durham
ChemistryDepartment
DurhamUniversity
Welcome/IntroductionDr John S.O. Evans
Durham, January 2007
john.evans@durham.ac.uk 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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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!
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Tomorrow Morning
• First lecture will be in CG93 (Scarborough lecture theatre)
• Follow somebody!
• Who doesn’t know how to use solver in excel?
4
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
6055504540353025201510
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
0
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
Durham, January 2007
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Acknowledgement
• Alan Coelho (Topas/Topas-Academic author)• http://pws.prserv.net/Alan.Coelho/
‘s
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Topas Graphics
Grid
Zoom
Plot
Run
7
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
jedit interface
8
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Topas/jedit demo
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Refining Parameters
str ‘cell params for an orthorhombic structure
a 7.31192
b 7.53699
c 7.69967
9
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Refining Parameters – Using @
str ‘cell params for an orthorhombic structure
a @ 7.31192
b @ 7.53699
c @ 7.69967
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Refining Parameters – Using names
str ‘cell params for an orthorhombic structure
a lpa 7.31192
b lpb 7.53699
c lpc 7.69967
10
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Refining Parameters – Using Names
str ‘cell params for a cubic structure
a lpa 10.60992
b lpa 10.60992
c lpa 10.60992
str ‘cell params for a cubic structure
Cubic(@ 10.60992)
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Fixing Parameters – Using !
str ‘cell params for a cubic structure
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
User Defined Equations
‘silly(?) example of topas equations
prm zero 0.01
prm var1 0.003
prm !date 21 ‘st of April
th2_offset = zero + var1 * date;
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
User Defined Equations
• 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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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);
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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]
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
6055504540353025201510
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
0
Session 5 – Peak Positions
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
15
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Session 5 – Peak Positions
Bragg’s Law: nλ=2dsinθ
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
d-spacing formulae
• Triclinic
• Cubic
( ) ( ) ( )[ ]βγααγβγβαγβα coscoscos2coscoscos2coscoscos2sinsinsin11 22222222222222222 −+−+−+++= chlabbcklahkabcbalcakcbh
Vd
2
222
2
1a
lkhd
++=
Bragg’s Law: nλ=2dsinθ
16
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
Durham, January 2007
17
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
6055504540353025201510
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
0
Session 6 – Peak Shapes
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Gaussian/Lorentzian Functions
x 2θ-2θhkl – where 2θhkl is position of reflectionfwhm full width at half maximumη mixing parameter for composite function
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
GSAS TCHZ type function
• Modified Thompson-Cox-Hastings pseudo-Voigt
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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)) /(
(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))^2 + 0.1116 (((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))^3; pv_fwhm = (
(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);
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Convolution Approach
( ) ( )θ2YSampleInstrumentSource =⊗⊗
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Contributions to peak shape
24
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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”
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Sample Contributions - Caveat
• Be careful!• See links in tutorial
• http://www.dur.ac.uk/john.evans/topas_workshop/size_strain.htm
26
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Source Profile
N.B. source profile only much sharper then observed peak
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Source ⊗ Equatorial
N.B. peak now considerably broadened by instrument
27
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Source ⊗ Equatorial ⊗ Axial
N.B. peak now has asymmetry
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Source ⊗ Equatorial ⊗ Axial ⊗ Sample
N.B. peak maximum not at calculate 2θ
28
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
Durham, January 2007
30
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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)
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
Durham, January 2007
32
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Fullprof Suite
• Juan Rodriguez-Carvajal• Has a .pcr file (like .inp file) in background• Very widely used• Magnetic refinements• Use winplotr interface
33
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
Durham, January 2007
34
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Data Compression
2-theta
I
(a) (b)
(d)(c)
Single crystal
Four differently oriented single crystals
Polycrystalline material
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
3D Information compressed onto 1D
2θ
2θ
‘…data compressed into one dimension…’
35
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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?
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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 %
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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 %
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Restraints
• Bring in chemical information• Dealt with in least squares in the same way
as data• “Soft Restraints”
restdatatot KK 22
21
2 χχχ +=
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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;
39
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Restraints
• See tutorials
40
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
Constraints
• Force sub-sections of structure to be rigid• Dealt with in least squares in the same way
as symmetry• “Hard Constraints”
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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)
}
41
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
42
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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);
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
43
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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)
44
Durham
ChemistryDepartment
DurhamUniversity
Session 14 – MistakesDr John S.O. Evans
Durham, January 2007
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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!
45
john.evans@durham.ac.uk www.durham.ac.uk/john.evans PCG workshop January 2007
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
top related