Welcome/Introduction

Transcription

1 Durham University Chemistry Department Welcome/Introduction Dr John S.O. Evans Durham, January 2007 Durham 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 1

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 Durham University 2

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? 3

4 Information in a Powder Pattern 1. Peak positions determined by size, shape, symmetry of unit cell internal structure 3. Peak widths influenced by size/strain of crystallites - microstructure. 2θ 2. Peak Intensities determined by where atoms sit in unit cell internal structure 45,000 40,000 Counts 35,000 30,000 25,000 20,000 15, ,000 5, θ - degrees Timetable 09:00 09:45 11:00 11:30 13:00 14:00 14:30 16:00 16:30 18:00 18:30 19:00 20:00 Sunday Monday Tuesday Wednesday 3. Introduction to powder diffraction 8.Structure factors, peak intensities 13. Question and Answer session and data collection. and Rietveld refinement 4. jedit/topas academic/rietveld 9. Pawley and Rietveld refinement 14. Spot the errors refinement Coffee Coffee Coffee 5. Peak positions - indexing/cell refinement exercises 10. Intro to gsas/fullprof then examples 15. Free problems then wrap up Lunch - Musgrave Room Lunch - Musgrave Room Departure 6. Peak shapes lecture 7. Peak shape tutorial 11. Restraints, Constraints, Rigid Bodies and Structure Solution 12. Structure solution and rigid body refinements Registration in Trevelyan Tea Tea 7. Peak shape tutorial 12. Structure solution and rigid body refinements Dinner - Trevelyan Close Close 0.Welcome/Introduction 1.Symmetry lecture Dinner - Trevelyan Dinner - Trevelyan 2. Symmetry bar quiz Pub Quiz Free evening Lecture slot Food/Drink Problems/Workshop 4

5 Durham University Chemistry Department Introduction to Software/Problems Dr John S.O. Evans Durham, January 2007 Durham 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 5

6 Acknowledgement Alan Coelho (Topas/Topas-Academic author) s Topas Graphics Grid Run Zoom Plot 6

7 Software Interface Command file driven for flexibility/speed jedit free customisable java editor Interacts directly with software Helps with formatting jedit interface 7

8 Topas/jedit demo Refining Parameters str cell params for an orthorhombic structure a b c

9 Refining Parameters str cell params for an orthorhombic structure Refining Parameters Using names str cell params for an orthorhombic structure a lpa b lpb c lpc

10 Refining Parameters Using Names str cell params for a cubic structure a lpa b lpa c lpa str cell params for a cubic structure Cubic(@ ) Fixing Parameters Using! str cell params for a cubic structure a!lpa b!lpa c!lpa N.B. jedit column editting hold down ctrl key and type all! s at once 10

11 Refining Parameters - Macros Zero_Error(, 0) fixed zero point 0.013) refine zero point Zero_Error(!zero, 0) Zero_Error( zero, 0.013) fixed zero point 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 prm corr th2_offset = corr2*x^2 + thcorr*x + zero; 11

12 User Defined Equations silly(?) example of topas equations prm zero 0.01 prm var prm!date 21 st of April th2_offset = zero + var1 * date; User Defined Equations Flexible system for defining your own equations Fully programmable program e.g. gsas vs topas: zero 0.01 y shft y shft = 3600*height/π*radius 2θ obs = 2θ calc + 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; 12

13 Simulated Annealing Flexible Simulated Annealing approach for complex structures: topas annealing expression in input file val_on_continue = Val + Val * Rand(-0.1,0.1); val_on_continue = ideal_coord + Rand(-0.1,0.1); Flexible definition of restraints, constraints, rigid bodies, etc 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 13

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] Session 5 Peak Positions 1. Peak positions determined by size, shape, symmetry of unit cell internal structure 3. Peak widths influenced by size/strain of crystallites - microstructure. 2θ 2. Peak Intensities determined by where atoms sit in unit cell internal structure 45,000 40,000 Counts 35,000 30,000 25,000 20,000 15, ,000 5, θ - degrees

15 Session 5 Peak Positions Bragg s Law: nλ=2dsinθ d-spacing formulae Triclinic [ ] = h b c sin α + k a c sin β + l a b sin γ + 2hkabc ( cosα cos β cosγ ) + 2kla bc( cos β cosγ cosα ) + 2hlab c( cosα cosγ cos β ) 2 2 d V Cubic 1 d 2 = h 2 + k a l 2 Bragg s Law: nλ=2dsinθ 15

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 (Counts) dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= Lin (Counts) dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= Theta dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= dsp= , 2th= Theta Durham University Chemistry Department Session 6 Peak Shapes Dr John S.O. Evans Durham, January 2007 Durham 16

17 Session 6 Peak Shapes 1. Peak positions determined by size, shape, symmetry of unit cell internal structure 3. Peak widths influenced by size/strain of crystallites - microstructure. 2θ 2. Peak Intensities determined by where atoms sit in unit cell internal structure 45,000 40,000 Counts 35,000 30,000 25,000 20,000 15, ,000 5, θ - degrees Peak Shapes View 1 Peak shapes are a nuisance. For Rietveld refinement we only fit peaks to get an good agreement between y obs and y calc 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 17

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 18

19 Gaussian/Lorentzian Functions x fwhm η 2θ-2θ hkl where 2θ hkl is position of reflection full width at half maximum mixing parameter for composite function Gaussian vs Lorentzian 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 19

20 Gaussian, Lorentzian, Pseudo Voigt Counts Counts 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, ,000-1, ,500 7,000 6,500 6,000 5,500 5,000 4,500 2Th Degrees Gauss wrp=30.5% Lorentz wrp=19.9% 4,000 3,500 3,000 2,500 2,000 1,500 1, , Th Degrees 7,500 7,000 6,500 6,000 Counts 5,500 5,000 4,500 4,000 3,500 3,000 2,500 2,000 1,500 1, , Th Degrees η=0.68 wrp=17.6% 57.8 Individual peak fitting on simulated Y 2 O 3 data 3/2/ fwhm vs 2θ 2 Gauss: ( ) 1 2 fwhm = U tan θ + V tanθ + W Lorentz: X fwhm = + Y cosθ tanθ U, V, W, X, Y Refineable Parameters fwhm theta 20

21 GSAS TCHZ type function Modified Thompson-Cox-Hastings pseudo- Voigt GSAS/Topas topas TCHZ peak shape function TCHZ_Peak_Type( pku, `,pkv, `, pkw, `,!pkx, , pky, `,!pkz, ) 21

22 Look in topas.log to see what s happening TCHZ_Peak_Type(pku, `,pkv, `,pkw, `,pkx, `,pky, `,pkz, `) prm pku ` min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pkv ` min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pkw ` min = Max(- 1, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pkx min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pky ` min = Max(0.0001, Val-.1); max = Min(2, Val+.1); del 1.0e-4 prm pkz min = Max(0.0001, Val-.1); max = Min(2, Val+.1); del 1.0e-4 peak_type pv pv_lor = (((pky) Tan(Th) + (pkz) /Cos(Th)) /( ( Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^ Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^4 ((pky) Tan(Th) + (pkz) /Cos(Th)) Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^3 ((pky) Tan(Th) + (pkz) /Cos(Th))^ Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^2 ((pky) Tan(Th) + (pkz) /Cos(Th))^ 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 )) (((pky) Tan(Th) + (pkz) /Cos(Th)) /( ( Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^ Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^4 ((pky) Tan(Th) + (pkz) /Cos(Th)) Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^3 ((pky) Tan(Th) + (pkz) /Cos(Th))^ Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^2 ((pky) Tan(Th) + (pkz) /Cos(Th))^ 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 ))^ (((pky) Tan(Th) + (pkz) /Cos(Th)) /( ( Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^ Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^4 ((pky) Tan(Th) + (pkz) /Cos(Th)) Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^3 ((pky) Tan(Th) + (pkz) /Cos(Th))^ Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^2 ((pky) Tan(Th) + (pkz) /Cos(Th))^ 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 ) )^ Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^4 ((pky) Tan(Th) + (pkz) /Cos(Th)) Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^3 ((pky) Tan(Th) + (pkz) /Cos(Th))^ Sqrt( Sqrt( ((pku) Tan(Th)^2 + (pkv) Tan(Th) + (pkw) + (pkx) /Cos(Th)^2)^2 ) )^2 ((pky) Tan(Th) + (pkz) /Cos(Th))^ 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 ); Fundamental Parameters Approach Peak Widths depend on X-ray source Instrument Sample Convolution or folding blends one function with another Y ( 2θ ) = ( Source Instrument) Sample (or empirical instrumental function) f () t g() t = f ( τ ) g( t τ ) dτ = g( τ ) f ( t τ d )τ 22

23 Convolution Approach ( Source Instrument) Sample = Y ( 2θ ) Contributions to peak shape 23

24 Sample Contributions - Size Scherrer formula β full width half maximum; k a constant L Vol is volume weighted mean column height; only for cubic crystals and h00 reflections is it equal to L 0 in figures below Sample Contributions - Strain d-spacings of d+ d and d- d e 0 = d/d Assume Braggs law gives different 2θ for different d-spacings 24

25 X-ray Particle Size from peak shape Intensity Size: 324(110) nm Strain: (40) Size: 20.4(8) nm Strain: 0.138(7) Broadening /cos(th) 3.5 tan(th) size strain theta theta Size broadening broad over whole 2-theta range Strain broadening narrow at low 2-theta Sample Contributions - Caveat Be careful! See links in tutorial 25

26 Source Profile N.B. source profile only much sharper then observed peak Source Equatorial N.B. peak now considerably broadened by instrument 26

27 Source Equatorial Axial N.B. peak now has asymmetry Source Equatorial Axial Sample N.B. peak maximum not at calculate 2θ 27

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, ) size term nm Strain_G(strain_g, ) 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 tan 2 θ + V tanθ + W fwhm = U 2θ 2 + 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 fwhm theta 28

29 Semi Empirical Size/Strain See: tutorial 9 - Size/Strain Analysis: Shows how size/strain can be determined in topas using the CeO 2 round robin data and an empirical instrumental function tutorial 10 determining the size of nanoparticles Durham University Chemistry Department Session 9 Pawley/Rietveld Problems Dr John S.O. Evans Durham, January 2007 Durham 29

30 Tomorrow s Programme Wednesday morning open questions session Either submit questions on paper before hand or ask on the morning Will limit to 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) 30

31 Rietveld/Pawley Problems Tutorial 1 TiO 2 Rietveld Tutorial 2 TiO 2 Pawley Tutorial 3 ZrW 2 O 8 X-ray/neutron/neutron time of flight Tutorial 10.5 Jeremy s PbSO 4 data in.xye format for you to try in topas Gsas 2 (later) Jeremy s PbSO 4 data Tutorial 11 Combined X-ray and neutron refinement (also gsas3/gsas4) Tutorial 12 Multiphase Rietveld refinement Durham University Chemistry Department Session 10 Other Software Dr John S.O. Evans Durham, January 2007 Durham 31

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 32

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 University Chemistry Department Session 11 Constraints, Rigid Bodies and Structure Solution Dr John S.O. Evans Durham, January 2007 Durham 33

34 Data Compression (a) (b) Single crystal Four differently oriented single crystals Polycrystalline material (c) I 2-theta (d) 3D Information compressed onto 1D data compressed into one dimension 2θ 2θ 34

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 step 3750 observations 530 hkl reflections in 2θ range 10,000 9,000 8,000 7,000 STR(P_-1, AlVO4) ` ` ` ` AlVO % ` ` 6,000 Counts 5,000 4,000 3,000 2,000 1, , Th Degrees

36 How many peaks? 10,000 AlVO % 9,000 8,000 7,000 6,000 Counts 5,000 4,000 3,000 2,000 1, , Th Degrees Counts 3,500 3,000 2,500 2,000 1,500 1, AlVO % Th Degrees 19 How many peaks? 10,000 AlVO % 9,000 8,000 7,000 6,000 Counts 5,000 4,000 3,000 2,000 1, , Th Degrees ,000 AlVO % 4,000 Counts 3,000 2,000 1, Th Degrees

37 How many peaks? 10,000 AlVO % 9,000 8,000 7,000 6,000 Counts 5,000 4,000 3,000 2,000 1, , Th Degrees AlVO % 1,500 Counts 1, Th Degrees 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 37

38 Restraints Bring in chemical information Dealt with in least squares in the same way as data Soft Restraints 2 2 χ tot = K1χ data + K 2 χ 2 rest 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; 38

39 Topas bond lengths/angles O1 Zr1 append_bond_lengths O1: Zr1:0 O1: O1: O1: O2: O2: O2: Restraints See tutorials 39

40 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 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) } 40

41 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 P 2 O 7 groups are well understood 2 parameters per P 2 O 7? Typically 1.5 Å P-O-P Angle P-O(-P) Distance

42 Structure Solution Simulated annealing type approach Refine, randomise, refine topas annealing expression in input file val_on_continue = Val + Val * Rand(-0.1,0.1); val_on_continue = ideal_coord + Rand(-0.1,0.1); Tutorials Restraints/Constraints Tutorial 3 ZrW 2 O 8 GSAS 4 restraints/combined refinement oxide GSAS 5 Rigid bodies Sc 2 (WO 4 ) 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 42

43 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) 43

44 Durham University Chemistry Department Session 14 Mistakes Dr John S.O. Evans Durham, January 2007 Durham 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! 44

45 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 45