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Sample Preparation, Data Collection and Phase-ID using Powder XRD Pamela Whitfield National Research Council, Ottawa 9 th Canadian Powder Diffraction Workshop,

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Presentation on theme: "Sample Preparation, Data Collection and Phase-ID using Powder XRD Pamela Whitfield National Research Council, Ottawa 9 th Canadian Powder Diffraction Workshop,"— Presentation transcript:

1 Sample Preparation, Data Collection and Phase-ID using Powder XRD Pamela Whitfield National Research Council, Ottawa 9 th Canadian Powder Diffraction Workshop, Saskatoon, 23-25 May 2012

2 Horses for courses… Data quality required depends on what you want to do with it Phase-ID has less stringent requirements on both sample prep and data collection Quantitative phase analysis, Rietveld analysis and structure solution require careful sample prep but can require different data collection regimes I’ll mostly cover requirements for phase-ID but will touch on considerations for other techniques.

3 Questions to ask What is in your sample? Organics often better collected in transmission Fluorescence can cause problems in data quality How much have you got? Very small quantities capillary or foil transmission? (not an option for many people) smear mount? We’ll assume conventional reflection geometry unless stated otherwise What kind of instrument have you got access to? If you have a choice which is the best?

4 What matters for phase-ID? Peak positions most important Relative intensities secondary but very important for Rietveld, etc…. If wanting to do search-match it is useful if the phases exist in the PDF database!

5 Where to start? What errors affects peak positions? What affects relative intensities? Preparing the samples Different types of sample holders

6 Peak positions – sources of error Zero point error - is the system properly aligned? use a NIST standard periodically to check it Sample displacement - sample too high/low? (0.1 mm  ~ 0.045°) Note: convention is that –ve sample displacement = sample too high Not an issue for parallel beam systems

7 Sample transparency if X-rays penetrate a long way into the sample can get a ‘sample displacement’ even if the height is perfect not an issue for parallel-beam systems if necessary use a thin sample to avoid transparency peak shifts relative intensities will be affected Diffraction patterns from powdered sucrose as both deep and thin samples Peak positions – sources of error

8 Parallel versus para-focussing The systems don’t look that different but don’t behave the same.. Parallel-beam immune to sample displacement & transparency but has worse peak resolution – twin mirror system excepted Parallel-beam setups with long slits and secondary mirror Divergent-beam without & with secondary graphite monochromator

9 Relative intensities Particle statistics (grain size) Preferential orientation Crystal structure Microabsorption (multiphase samples)

10 Sample-related problems Grainy samples or ‘rocks in dust’ Microabsorption a serious issue for quantitative analysis and could fill a talk by itself! Preferential orientation Extinction

11 “Grainy” samples Issue of graininess relates to particle statistics Particle statistics is what makes a powder a true powder! 600 mesh sieve = <20  m Crystallite size range 15-20  m5-50  m5-15  m<5  m Intensity reproducibility 18.2%10.1%2.1%1.2% Reproducibility of the intensity of the quartz (101) reflection with different crystallite sizes Diameter 40  m10  m1m1m Crystallites / 20mm 3 5.97 × 10 5 3.82 × 10 7 3.82 × 10 10 No. of diffracting crystallites 1276038000 Comparison of the particle statistics for samples with different crystallite sizes

12 “Seeing” particle statistics Playing Russian roulette with a grainy sample Stacking the odds in your favour by micronizing….

13 How to improve particle statistics There are a number of potential ways to improve particle statistics –Increase the area illuminated by X-rays Divergence angle –Rotate samples –Use a PSD –Reduce the particle size (without damaging crystallites!) McCrone mill = good Mortar and pestle = bad 

14 I don’t have a 2D detector – now what? A series of phi-scans can show up problems With a rotation stage phi is a set angle instead of full rotation Phi-scans across 5 fingers of quartz with different samples

15 I don’t have a 2D detector – now what? Can also run repeats after reloading sample each time (get real stats as a bonus) Unmicronized : MgO only appears in 1 sample out of 3 Overlay of 3 repeat patterns from un-micronized cement Overlay of 3 repeat patterns from micronized cement periclase

16 Extreme examples… Occasionally reflections are unexpectedly split Quartz is particularly prone…. Synchrotron data are not immune – in fact it can be worse due to the extremely parallel beam Main 101 reflection of ~100 micron quartz with a fuller pattern inset showing spurious intensities Capillary and rocked reflection data from LaB 6 on a strip heater taken with the Australian synchrotron

17 Microabsorption Microabsorption is the thing that causes most nightmares for analysts doing quantitative phase analysis Caused by a mixture of high and low absorbing phases High absorbers beam absorbed at surface only fraction of grain diffracting relative intensity underestimated QPA too low Low absorbers beam penetrates deeper more diffracting volume relative intensity overestimated QPA too high

18 What can you do about it? Change radiation? Absorption contrast changes with energy Higher energy X-rays often less problematic Use neutrons? Not usually practical but a ‘gold standard’ Use the Brindley correction? Need to know absorption of each phase Need to know particle (not crystallite!) size for each phase Assumes spherical particles with a monodisperse size distribution Usually unrealistic!

19 Effect of particle size Brindley proposed that a maximum acceptable particle size for QPA can be calculated by:  = linear absorption coefficient (LAC) corundummagnetitezircon CuK  LAC (cm -1 ) 1251167380 t max (  m) CoK  LAC (cm -1 ) 195240574 t max (  m)

20 The scale of escalating despair! Brindley also devised a criteria for whether you should be ‘concerned’ about microabsorption  D = linear absorption coefficient x particle diameter Fine powders  D < 0.01 negligible  -absorption Medium powders 0.01 <  D < 0.1  -absorption present – Brindley model applies Coarse powders 0.1 <  D < 1 large  absorption – Brindley model estimates the effect Very coarse powders  D > 1 severe  -absorption – forget it!

21 Radiation dependence of  D CoK  (7 keV) Size  m corundum (Al 2 O 3 )  D magnetite (Fe 3 O 4 )  D zircon (ZrSiO 4 )  D 0.10.002 0.006 0.20.0040.0050.011 0.50.0100.0120.029 10.0190.0240.057 20.0390.0480.115 50.0970.1200.287 100.1950.2400.574 200.3890.4801.148 very coarse  D > 1 coarse 0.1 <  D < 1 medium 0.01 <  D < 0.1 fine  D < 0.01

22 Radiation dependence of  D CuK  (8 keV) Size  m corundum (Al 2 O 3 )  D magnetite (Fe 3 O 4 )  D zircon (ZrSiO 4 )  D 0.10.0010.0120.004 0.20.0030.0230.008 0.50.0060.0580.019 10.0130.1170.038 20.0250.2330.076 50.0630.5840.190 100.1251.1670.380 200.2512.3440.759 very coarse  D > 1 coarse 0.1 <  D < 1 medium 0.01 <  D < 0.1 fine  D < 0.01

23 Radiation dependence of  D MoK  (17 keV) Size  m corundum (Al 2 O 3 )  D magnetite (Fe 3 O 4 )  D zircon (ZrSiO 4 )  D 0.10.0000.0010.000 0.20.0000.0030.001 0.50.0010.0070.002 10.0010.0140.004 20.0030.0280.009 50.0060.0710.022 100.0130.1420.044 200.0250.2840.088 500.0630.7090.219 1000.1261.4180.438 very coarse  D > 1 coarse 0.1 <  D < 1 medium 0.01 <  D < 0.1 fine  D < 0.01 note new rows! {

24 without Brindley correction QXRD Round Robin: CPD #4 unmilled Unmilled grain sizes: Al 2 O 3 28  m, Fe 3 O 4 36  m, ZrSiO 4 21  m Can’t fit intensities very poor particle statistics? (<200 diffracting crystallites per phase) Al 2 O 3  D = 0.345, Fe 3 O 4  D = 4.15!!, ZrSiO 4  D = 0.788 CuK  with graphite monochromator weighed amounts Al 2 O 3 50.5% Fe 3 O 4 19.6% ZrSiO 4 29.9% with Brindley correction 0.1 <  D < 1 large  absorption – Brindley model estimates the effect  D > 1 severe  -absorption – forget it! Thanks to Ian Madsen for the data

25 CPD #4 confirming what we suspected Large grains can be confirmed using 2D detector as before or using a series of scans with different phi angles (no rotation) N.B. Al 2 O 3 may still have preferential orientation CMZZM Thanks to Arnt Kern for the data Al 2 O 3 ZrSiO 4 Fe 3 O 4

26 CuK  with graphite monochromator Micronized CPD #4? Particle statistics no longer a problem Al 2 O 3 and ZrSiO 4 still have some orientation – corrected CoK  doesn’t help much as problem switches from Fe 3 O 4 to ZrSiO 4 How about an SEM? weighed amounts Al 2 O 3 50.5% Fe 3 O 4 19.6% ZrSiO 4 29.9% Thanks to Ian Madsen for the data CoK  with graphite monochromator

27 Al 2 O 3, Fe 3 O 4, ZrSiO 4 - Micronised Corundum Magnetite Zircon Global copyright Ian Madsen!

28 What value of particle size do we choose for the Brindley correction? Wt%CorundumMagnetiteZircon Weighed 50.4619.4629.90 No correction Mean56.5217.0626.42 Bias 6.06 -2.58 -3.48 Brindley model, Ø = 1  m Mean 55.7617.8126.43 Bias 5.30 -1.83 -3.47 Brindley model, Ø = 5  m Mean 52.4921.1826.33 Bias 2.03 1.54 -3.57 Brindley model, Ø = 10  m Mean47.7626.1526.08 Bias -2.70 6.51 -3.82 Thanks to Ian Madsen for the analysis Pick a number, any number…

29 CoK  Al 2 O 3 17  m 40%PD Fe 3 O 4 5  m 40%PD ZrSiO 4 14  m 40%PD What does reality matter anyway? Can fudge the particle size numbers and packing so the Brindley correction gives the right result for CoK  but  D for ZrSiO 4 and Al 2 O 3 well into coarse range CuK  not as good (and  Ds are even worse) weighed amounts Al 2 O 3 50.5% Fe 3 O 4 19.6% ZrSiO 4 29.9% CuK  Al 2 O 3 17  m Fe 3 O 4 5  m ZrSiO 4 14  m if these numbers correct send your McCrone mill and SEM back!

30 Preferential orientation (texture…) Preferential orientation (PO) is most often seen in samples that contain crystallites with a platey or needle-like morphology. Particular culprits Plates mica clays some carbonates, hydroxides e.g. Ca(OH) 2 Needles wollastonite many organics The extent of the orientation from a particular sample depends greatly on how it is mounted

31 Orientation of plate-like samples There’s no getting away from it – they can be a real pain Top-loading is hopeless as you make it worse…. Back-loading the usual approach but not always enough… Breaking up the alignment of the plates by back-loading onto a rough surface such as sandpaper can help…

32 With plate-like samples if you have a capillary stage then use it! If not then spray-drying the sample can be an alternative…. Background-subtracted data from micronized 40S mica in a 0.5mm capillary Top-loaded, spray-dried 40S mica SEM of spray-dried mica 200 001 Going the extra mile…

33 Just to prove the data is usable…. Micas not pleasant to deal with at the best of times and this has some messy anisotropic broadening.. However, the data from the top-loaded, spray-dried sample fits a un-refined literature biotite structure very well with no orientation correction That’s not to say there were no corrections needed at all! Refinement of the top- loaded, spray-dried 40S mica using a literature biotite structure without orientation correction R wp = 11.8% GOF = 1.82

34 Corrections for PO in Rietveld software Two different corrections exist in most software to correct orientation during Rietveld analysis March-Dollase (MD) Single variable but an orientation direction must be supplied by the analyst Spherical Harmonics (SH) VERY powerful approach – can increase SH ‘order’ to fit increasingly complex behaviour No orientation direction required Number of variables increase with reducing cell symmetry Be very careful in quantitative analysis with severe peak overlap (e.g. cements) Negative peaks are very common and very meaningless!

35 Extinction Reduction in the intensity of a Bragg reflection by re-diffraction by the successive planes back in the direction of the incident beam Dependent on size/shape of the coherently-diffracting domains Primary  re-diffraction within a single crystallite Effect minimized by reducing grain size – ideally submicron Normally seen in large, ‘perfect’ crystallites such as silicon or quartz Secondary  mosaic crystals, not seen in powders

36 The different preparation techniques Reflection Top-loading Flat plate Back-loading Side-loading Transmission Capillary Foil transmission

37 Top-loading Simplest but most prone to inducing preferential orientation Special holders often in this category Alternative holders such as cavity zero background silicon or air-sensitive often top- loading as well

38 Flat plate aka: smear mount Used with very small samples (phase-ID , Rietveld  ) Sample adhered to zero background plate using some form of binder/adhesive that doesn’t have any Bragg peaks Vaseline, vacuum grease, hairspray (spray ~12” from holder) Slurry with ethanol or acetone – tricky to get right consistency N.B some quartz plates show a sharp reflection when spun Quartz zero background plate Silicon zero background plate Gem Dugout a commonly used source for zero background plates (

39 Back-loading

40 Side-loading I don’t have one of these! but basic principle….. powder glass slide holder plug sample

41 Capillaries Probably best way to reduce orientation in platey materials Commercially either quartz, borosilicate or soda-glass range in diameter from 2mm to 0.1mm Or use thin-walled polymer tubing of Kapton, PET, etc Most useful where sample absorption is low, e.g. organics Can be extremely fiddly to fill!

42 Capillary instrument setup Capillary setups can be quite specialized Focussing optics specific to transmission geometry Even  systems better run as  in capillary mode Transmission better for low angles Capillary setup on  system at very high 2  angle using detector scan with focussing primary optic, PSD, radial Soller slits and primary slit setup to reduce low angle scatter reaching detector

43 Capillaries – highly absorbing samples Rietveld refinement of ~10 vol% SnO 2 in diamond powder Capillary and reflection data from pure SnO 2 Absorption reduces the peak intensities at low angles Corrections exist but they have limits Smaller capillaries and/or dilution with a ‘light’ phase will help (e.g. diamond, amorphous boron, carbon black, etc)

44 Foil transmission Another approach for small samples Powders can be mounted between films of Kapton, Mylar, etc Not immune to preferential orientation – the plane is just rotated 90° so the peak intensities change accordingly! Quartz powder between Kapton Twin-mirror system set up for foil transmission

45 Foil transmission Sample can be very thin so highly absorbing samples possible without dilution 1/cos(  ) correction required for accurate relative intensities Rietveld refinement of SnO 2 (1400cm -1 )

46 Data collection strategies Rietveld analysis guidelines published by McCusker et al in 1999 Choose beam divergence so the beam doesn’t overspill the sample at low angle remember the under-scan when a PSD is used! 1 st datapoint may be at 10° 2  but the scan may start at 8°! (ENeqV1_0.xls very handy for working out correct divergence) ( Rule of thumb - step size of ~ FWHM/5 to FWHM/8 Too small = wasting time and producing noisy data Too coarse = chopping intensity and peaks not modelled properly

47 Experiment optimization ‘Horses for courses’ – collect data fit for purpose Data for phase-ID does not have to be of the same quality as for structure solution, etc Most common mistake among users too small step size for sample 0.01º step, 1s count R wp = 15.2% 0.02º step, 2s count R wp = 12.0% 2 different datasets from quartz stone – both experiments took 25 seconds Smaller R wp corresponds to a better fit.

48 Peak-to-background A number of things affect the peak-to-background air-scatter at low angles use air-scatter sinks if needed nanoparticles have lower intrinsic peak heights not much you can do here eventually Rietveld results are no longer meaningful capillaries always have higher background subtracting capillary blank can improve this but careful not to distort counting statistics fluorescence is the main cause of poor peak-to-background… Rietveld refinement round robin suggested a minimum P/B value of 50 for accurate structural parameters….

49 Why does background matter? With a high background the uncertainty in the background parameters increase (often use more parameters as well) uncertainty in the extracted peak intensities increases → greater uncertainty in structural parameters and quantitative phase analysis Which line would you choose?

50 Fluorescence Fluorescence even adversely affects phase-ID detection limits a secondary monochromator on conventional system is an effective way to filter out fluorescence CuK  - Li 1.15 Mn 1.85 O 3.9 F 0.1 Lin (Counts) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 2-Theta - Scale 15203040 50607080 No monochromator Properly aligned monochromator/mirror there is a real peak here!

51 Fluorescence – what to do about it? With a PSD a conventional monochromator not possible – data with CoK  Which dataset do you prefer? CoK  - LiMn1.5Ni0.5O4

52 Fluorescence cont. Can improve PSD data significantly by adjusting the detector’s electronic discriminator window Rescaled to normalize background P/B = 13.4 P/B = 4.5 P/B = 4.2 Sacrifice intensity to improve P/B ratio P/B still along way off 50. Change radiation or instrument.

53 Problematic sample: quant analysis FeS + Mg(OH) 2 + SiO 2 CuK  Ground or unground? particle statistics Microabsorption (FeS) ideally switch to CoK  Fluorescence (FeS) high background monochromator, energy-discriminating detector, switch to CoK  Preferential orientation (Mg(OH) 2 ) Extinction? (SiO 2 ) Micronize!!!! All of these problems are reduced by micronizing to sub-micron particle/crystallite size

54 Problematic sample: Rietveld analysis LiMn 1.4 Ti 0.1 Ni 0.5 O 4 (lithium battery cathode material) Mn fluoresces with both CuK  and CoK  ! Use a monochromator or energy discriminating detector Good peak-to-background, but... Fluorescence is still there even if you can’t see it Very high absorption impacts particle statistics (X-rays only penetrate a few 10s of microns) Solution by changing tube? CrK  2.29Å (unusual, high air scatter/attenuation and limits lower d- spacings attainable) FeK  1.94Å (very unusual and low power tubes) MoK  0.71Å (unusual and beta-filter artefacts visible)

55 LiMn 1.4 Ti 0.1 Ni 0.5 O 4 Co P/B = 4.5 Cu P/B = 9.4 Mo A primary monochromator would get rid of this high angle tail P/B = 84 Cr P/B = 87 (P/B = 54 without air-scatter sink to reach angles >100)

56 Variable counting time (VCT) The physics of XRD dictate that intensities drop with angle Most of the information (reflections) is at higher angles Can regain much of the information by counting for longer at higher angles Boehmite (Madsen, 1992) Variable Counting TimeConstant Counting Time I ~ LP * thermal vibration * f 2

57 VCT data - quantitative analysis Also possible to improve detection limits in quant analysis by counting for longer where minor phases expected Fixed count timeVariable count time (normalized) Example from presentation by Lachlan Cranswick

58 VCT data - structure refinement Extract more structural details if reflections still visible at high angles Using a PSD split pattern into sections can also increase step size with angle as well to save some time… Jadarite structure with thermal ellipsoids

59 Phase-ID Phase-ID usually undertaken using vendor-supplied software with the ICDD Database (PDF2 or PDF4) The database is not free so budget accordingly PDF4 requires yearly renewal but has more features PDF2 good enough for search-match and OK for 10 years A free database called the Crystallographic Open Database (COD) exists but there is no quality checking – user beware… The Powder Diffraction File uses XRD ‘fingerprints’ – if they haven’t been deposited they won’t show up Database entries are allocated a ‘quality mark’ but occasionally the newer ones are actually worse! Experimental quality marks ‘*’ > ‘I’ > ‘A’ > ‘N’ > ‘D’ Calculated from ICSD, etc ‘C’ Background subtraction recommended before search-match if it is high but don’t bother with K  2 stripping, etc

60 Phase-ID Improve your odds in the search-match make a sensible guess as to the likely elements does your sample really have plutonium in it?! if you have elemental analysis results then use them but consider possibility of amorphous phases Search-match in EVA on a sample of zircon

61 Be sensible… Use common/chemical sense don’t believe results just because the computer tells you even oxygen has entries in the PDF2! Where software supports it ‘residue’ searches can be very helpful in identifying minor phases

62 Don’t be led astray… Minor peaks - make sure they aren’t K  or tungsten lines vendor software can often identify these (e.g. EVA below) CrK  CrK  WL 

63 No luck – what next? Do you have a large systematic error in the data? your diffractometer alignment should be checked regularly with a standard modern search-match software can cope with a reasonable error but it has limits Look for possible analogues which may appear in the PDF2 LaCoO 3 similar to LaNiO 3 with slightly different lattice parameters analogues may have significantly different relative intensities however: LiMnO 2 (Pmmn) completely different from LiCrO 2 (R-3m) LaCoO 3, R-3c a = 5.449, c = 13.104Å LaNiO 3, R-3c a = 5.456, c = 13.143Å LiMnO 2 LiCrO 2

64 Getting desperate yet? Put the sample under optical microscope does it seem to have the number of phases you expect? If it contains Fe or Co try a magnet! Possible contamination mortar and pestle not clean material from micronizer grinding elements (newer corundum elements not as good as the older ones – use agate) Last possibility to consider…. maybe you have found a new phase then the fun really starts!

65 Conclusions… Use the appropriate sample mounting technique for the sample and the data requirements Graininess, microabsorption and preferential orientation are all related to particle and crystallite size Do yourself a big favour by micronizing your sample if possible! Preferential orientation can be corrected during analysis but the others can’t…… Assumptions of the Brindley correction never met in real life Poor application of Brindley correction worse than no correction

66 Yet more conclusions…. There are times when the newest diffractometer (PSD, etc) isn’t the best one for the job fluorescence can be your #1 enemy! secondary optics can be your friend No such thing as the perfect configuration for everyone VCT data can help in a number of ways improve the detection limit for minor phases significantly improve the quality of a structure refinement If you don’t remember anything else remember this.. think about your samples a one size fits all approach doesn’t work!

67 Acknowledgements Ian Madsen (CSIRO) I couldn’t improve on his explanation of microabsorption so I used it! Responsible for the CPD QPA round robin sample 4 which still give people nightmares Mati Raudsepp (UBC) for spray drying the mica sample and the SEM

68 References G.W. Brindley, “The effect of grain and particle size on X-ray reflections from mixed powders and alloys….”, Philosophical Magazine, 3 (1945), 347-369 Commission on Powder Diffraction webpage commissions/powder- diffraction/projects commissions/powder- diffraction/projects links to all the round- robin information, guidelines and papers (freely available)

69 Questions?

70 OK so you found a new phase…. Before getting to the refinement step you have to figure out a rough idea of the structure There are some different steps in the process Peak fitting (most of the time) Indexing Space group determination Structure determination

71 Indexing…. You need to know whether cubic, monoclinic, etc and what are the lattice parameters The instrument should be as good as you can get it lab data more difficult than synchrotron In the lab it may require a special high resolution dataset over a limited range (usually only use the first 15-25 lines) Accurate peak positions the main goal Software packages TOPAS (LSI and LP Search), Crysfire (Dicvol, Treor, etc), MacMaille, etc

72 Space group determination…. This is where you often need to know a little crystallography…. Conventional way to do this is to study systematic absences (International Tables necessary and Chekcell software useful) Maximum likelihood software Extsym can give a list of probable extinction symbols from a Pawley refinement (not same as SG!) TOPAS makes a guess at extinction symbol and often correct Sample density very useful (buy a pycnometer!) Can then calculate ‘volume per formula unit’ Allows easy exclusion of space groups where the multiplicities are too high With organics a rough guide of 18Å 3 per non-H atom can help

73 Solution…. A number of approaches possible Conventional direct methods (EXPO, SXTL software) Real space methods (DASH, TOPAS, FOX, etc) Charge flipping (Superflip, TOPAS, etc) Real space methods tend to be more reliable with poor resolution data Powder diffraction data often regarded as ‘poor’ by default Charge-flipping a powerful method with higher resolution powder data has been know to work with iffy data, but not mine…..!

74 Example…. aspirin Aspirin tablets usually very pure Done with capillary transmission but… Highly crystalline organic with reflections to high 2  angles Easily indexed to a monoclinic cell Charge flipping does need a space group to work Basic structure solves in a matter of minutes…

75 Example... sucrose Even easier to get hold of than aspirin Also highly crystalline Simulated annealing with a z-matrix works with normal data, charge flipping with VCT data

76 Example... wollastonite An inorganic reflection example…. but a difficult one Wollastonite needles show severe preferential orientation when top-loaded Normally I would say ‘make a better sample’ but sometimes it will still works The basic simulated annealing approach still the same with some tweaks SEM of wollastonite

77 Wollastonite – SA strategy TOPAS input file setup Space group P-1 SiO 4 always tetrahedral – safe to use simple z-matrix Anti-bump for Ca-Ca, Ca-O and Si-Si Octahedrally coordinated Ca-O Too many oxygens with SiO 4 z-matrices Need to merge oxygens to get correct unit cell contents Use “occ_merge O* occ_merge_radius 0.9”

78 Wollastonite – SA strategy TOPAS lets you to use a ‘trick’ to solve badly orientated data for details read the paper! The structure from simulated annealing matches the literature Literature structure Raw structure from SA with 4 th order SH – blue atoms are merging oxygens

79 Wollastonite – SA strategy Just a couple of plots to prove the sample was orientated! Simulated powder pattern from the SA structure without PO correction Fit to the data for the raw SA structure with 4 th order SH

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