1. Rietveld texture analysis of SKAT diffractometer data
R.N. Vasin
STI-2011, 6-9 June, 2011, Dubna, Russia

2. SKAT texture diffractometer
Beamline 7a of IBR-2.
Main objectives: investigation of crystallographic textures of rocks and engineering materials.
Total flight path: m.
Range of d-spacings: Å.
Resolution Δd/d up to 0.55% (d ≈ 2.2 Ǻ).
19 3He detectors on the mounting ring, unique scattering angle of 2θ = 90.

3. Geometry of diffraction experiment on the SKAT
Acquisition of experimental pole figures A S S A S A
Schematic view of the SKAT detector system. Usually, 19 detector modules are used. They are named from A to S, with S in the center of the pole figure.
The line on the unit sphere corresponds to scattering vectors of the detector ring, the line in the XY plane is its stereographic projection.
The grid of the measured pole figure. Small circle corresponds to the plane projection of the scattering vectors, dots shown where the data on pole density are situated.

4. Data processing
Neutron diffraction spectra: 1368 (19 detectors * 72 sample positions) spectra in case of regular 5х5º PF grid
Complete experimental pole figures (measured simultaneously - TOF-method!) in regular 5х5º grid
Recalculation of the ODF
Recalculation of non-measured pole figures using the ODF (absent reflections, overlapped peaks, out of diffractometer’s d-range)
ODF characterization: texture index, entropy, construction of the ODF-histogram and ODF-spectrum
Calculation of bulk physical properties, application in residual stress measurements, etc.

5. Data processing: construction of experimental PF
We have: raw SKAT data
(1368 datafiles: binary, big-endian, 6200 bytes + SKAT protocol file: plain text, contains monitor counts).
Front-end processing.
Conversion to little-endian (from least- to most-significant byte) order, assortment of files into subdirectories, extraction of monitor counts from the protocol file, summation/normalization of spectra are performed.
Quartzite
Quartz, P3221
Sum of 1368 spectra
Diffraction peaks (+ background intervals in vicinity) are selected for PF construction.
What are those peaks?
Determination of the phase/mineral (in case of poly-phase material) and Miller indices for chosen diffraction peaks.

6. Data processing: construction of experimental PF
Quartzite
Quartz, P3221
Determination of the phase and Miller indices for chosen diffraction peaks: comparison with the database.
In general, intensive non-overlapped peaks of the single phase are needed!

7. Data processing: construction of experimental PF
Biotite gneiss: Quartz, P3221, SiO2
Biotite, С2/c, K(Mg,Fe,Ti)3(AlSi3O10)(F,OH)2
Plagioclase, P-1, (Ca,Na)(Al,Si)4O8
Intensive non-overlapped peaks of the single phase?? – maybe at d > 3.5 Å (TOF > 2100)…

8. Data processing: construction of experimental PF
PF visualization, rotation, normalization, ...
Construction of experimental PF from chosen diffraction peaks (in SKAT grid)
Conversion (interpolation) of experimental pole figures into regular 5х5° grid.
Conversion of datafiles with PF corresponding to one phase into some conventional format: structural info is needed (Laue class, cell parameters, ratio of structure factors for overlapped peaks of this phase). For example: short Berkeley program for conversion into standard Berkeley-format (serves as input in BEARTEX).
Repeat for each phase.

9. Orientation distribution function calculation from experimental PF + some other options
BEARTEX (WIMV method)
H.-R. Wenk & S. Matthies
Operations with ODF, PF, inverse PF,
PF modeling, tensor averaging
(calculation of physical properties), …
Single license – 2000$ (academic – 1000$)
Some routines do not function in 64-bit OS!
LABOTEX (ADC method)
K. Pawlik
Operations with ODF, PF, inverse PF, …
Single license – 6000$ (academic – 3000$)

10. Standard data processing procedure
Raw SKAT
data
Front-end processing
Selection of diffraction peaks for use in the construction of experimental PF
Comparison with the database
(containing model spectra)
Are these peaks present in database?
Search for the structural info, load it into database No
ODF of each phase
Yes
Is there enough non-overlapped diffraction peaks for each phase? No No
Is there a good agreement between experimental and recalculated PF?
Yes
Yes
Construction of experimental PF, PF conversion into conventional format, ODF reconstruction

11. Standard data processing procedure: drawbacks
Evident problems with the selection of non-overlapped intensive peaks from diffraction patterns in case of multiphase sample (especially if several low-symmetry phases are present). Usually in this case diffraction peaks are selected at high-d region, where counting statistics are not so good.
Only a small part of acquired diffraction patterns is used (≤ 6 peaks for each phase). And, for example, for Ni (space group Fm-3m) in SKAT d-range at least 12 peaks are easily available, for oligoclase An16 (space group P-1) in interval d > 1.5 Å – more than 400 peaks.
The result of the standard data processing is the ODF, no additional information is retrieved (like cell parameters, phase volume fractions, etc.)
New detector rings for SKAT (at different scattering angles) may add some complexities.
Solution: it is possible to use Rietveld method for simultaneous processing of all (e.g., 1368) SKAT spectra with account for crystallographic texture (this is requirement!).
No need for manual peak selection, most part of available data is used, additional info about crystal structure of the sample is received.

12. MAUD http://www.ing.unitn.it/~maud/
L. Lutterotti, "Total pattern fitting for the combined size-strain-stress-texture determination in thin film diffraction“, Nuclear Inst. and Methods in Physics Research, B, 268, , 2010.
Freeware!
Java-based, needs JVM to work, but
this exists for very much every system.
Versions for Windows, Mac OS,
Linux, Unix (x86 и x64) are available.
User-friendly (fine GUI).
It’s possible to work with X-ray
/synchrotron, electron, neutron diffraction
patterns (TOF is included).
Great options for texture evaluation:
ODF calculation from the set
of diffraction spectra
(several methods are available).

13. MAUD
And what about TOF spectra?

14. SKAT data analysis by MAUD: what do we need?
SKAT instrument parameter file (TOF channel to d conversion: scattering angle, delay, DIFC constant ~ L·sinθ; effective spectrum; peak shape) in GSAS format (.prm).
Calibrations have been made for each of 19 detectors of the SKAT (different calibrations for different reactor cycles!); vanadium spectrum have been fitted by FitSpec routine of GSAS, function №4 has been used (MAUD uses functions № 0…5): Maxvellian term + first 10 Chebyshev polynomials of the first kind; peak shape have been approximated by function №1 TOF (the only one available in MAUD???): Gaussian convoluted with two exponentials, accounts only for the instrument-dependent peak broadening in MAUD.
SKAT datafiles in standard GSAS format (.gda)
It’s not a problem to convert binary file to the formatted ASCII with the proper header. But it’s too complicated and time consuming to perform manually for each of 1368 spectra.
Load all the datafiles into MAUD taking into account the position on the pole figure (two angles!) and monitor counts.
It’s too complicated and time consuming to perform manually for each of spectra.
The fit is not perfect due to some peculiarities of the vanadium spectrum, its better to use “point-to-point” normalization.

15. SKAT2MAUD
«Mass transformation» of spectra and construction of the special script file to automatically load all the data into MAUD.
C++ based.
Ease to use GUI.
Tested in WinXP Pro x86 & Win7 HP x64.
File access is made through Win API functions → it is fast. Conversion + normalization + script creation for 1368 files takes ≈ 15 sec.
A possibility to easily add some other IBR-2 diffractometers.

16. SKAT2MAUD Selection of parameters for the data conversion
Spectra selection
Monitor counts extraction from the SKAT protocol file
Construction of the script file for MAUD and of the protocol.
Options for point-to-point data normalization
Data type selection

17. Ni powder The refinement of diffractometer parameters and peak shapes
(to get unique parameters for each detector!)
Different (most of the time slightly different) parameters for different reactor cycles!
Sum spectrum (detectors from A to S)

18. Ni powder
Detector E
Detector D
Detector C
Detector B
Detector А

19. Ni powder
(111) peak S
(222) & (311) peaks A
Detectors:

20. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Sample: Outokumpu borehole (Finland), 676 m depth. Mineral composition: quartz – 42.6 vol.%, plagioclase – 37.6 vol.%, biotite – 19.8 vol.% (thin sections analysis, Kern, Mengel, Strauss et al. // PEPI, 175, ). Volume of the sample is > 100 cm3.
Lattice spacing range: d = 1.51…4.31 Å → about 700 diffraction peaks/pole figures.
Getting prepared for intensive calculations: MAUD command file is altered – now MAUD exclusively allocates 3 Gb of RAM (should be working on x64 OS or x86 with enabled PAE).
Free parameters: phase volume fractions, individual background for each spectrum (3·1386 parameters), cell parameters of each phase, 1 thermal factor for all atoms (isotropic approximation), crystallite size and microdeformation for each phase (isotropic approximation) – in total 4145 parameters. + ODF calculation for each phase, E-WIMV method, 5° ODF resolution, peaks with intensity less than 1% of maximum for the given phase were not used for the ODF calculation.
1 iteration took ≈ 3 h. 40 min. (Intel Core i5-430M, 4 Gb DDR3-1066(CL7), Win7 HP x64, x64 Java Virtual Machine).

21. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
First 12 spectra, detector A, point-to-point normalized in SKAT2MAUD.

22. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Q(100) + Pl(030)
Pl(-201)
Q(101) + Q(011) + Bi(600) + Bi(402) + Pl(-112) + Pl(-221)
Bi(-411) + Pl(-210)
Pl(002) + Pl(-220) + Pl(-1-22) + Pl(040) + Pl(-202)

23. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
SKAT pole figure coverage for the 676 gneiss sample (different colors correspond to different number of counts of the beam monitor).

24. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Biotite rec. PF, log scale, MAUD (ODF: texture index F2=5.67)
2M1 polymorph (space group C2/c).
Setting 1 is used for the monoclinic biotite here and further.
Biotite rec. PF, log scale, conventional PF analysis (ODF: texture index F2=3.30)

25. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Plagioclase rec. PF, MAUD (ODF: texture index F2=1.27)
Plagioclase rec. PF, conventional PF analysis (ODF: texture index F2=1.23)

26. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Quartz rec. PF, MAUD (ODF: texture index F2=1.24)
Quartz rec. PF, conventional PF analysis (ODF: texture index F2=1.30)
Are indistinguishable in conventional PF analysis because overlapped PF of rombs – (h0l) + (0hl) – have not been selected for ODF calculation.

27. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Is it possible to use less data and get the ODF with acceptable resolution?
PF coverage (1/20 from the available data).
ODF resolution of 7.5° has been chosen in E-WIMV (instead of 5° as it was in the case of full dataset) to account for the decrease in the quantity of data.

28. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Biotite rec. PF, log scale, full coverage (ODF: texture index F2=5.67)
Biotite rec. PF, log scale, reduced coverage, ODF resolution 7.5° (ODF: texture index F2=8.99)

29. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Plagioclase rec. PF, full coverage (ODF: texture index F2=1.27)
Plagioclase rec. PF, reduced coverage, ODF resolution 7.5° (ODF: texture index F2=1.39)

30. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 676
Quartz rec. PF, full coverage (ODF: texture index F2=1.24)
Quartz rec. PF, reduced coverage, ODF resolution 7.5° (ODF: texture index F2=1.37)

31. Outokumpu 676 (a comparison of cell parameters with the American Mineralogist crystal structure database)
Phase
Biotite,
C2/c
Quartz,
P3221
Plagioclase,
P-1
Data from:
SKAT (MAUD)
Database (Mg/Fe+Mg+Mn+Ti)
Database
An16/28/48
a, Å
(1)
19.976
/20.196
(2)
8.1533(1)
8.154/8.169
/8.179
b, Å
5.3599(1)
5.3175
/5.339
(2)
12.823/12.851
/12.880
c, Å
9.2108(2)
9.212
/9.249
(4)
7.1235(1)
7.139/7.124
/7.112
α, ° 90
93.88(1)
94.06/93.63/
93.44
β, °
116.36(1)
116.50/116.40/
116.21
γ, °
94.99(1)
95.09/95.06
120
89.25(1)
88.59/89.46
/90.23

32. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818
Sample: Outokumpu borehole (Finland), 818 m depth. Mineral composition: quartz – 39.9 vol.%, plagioclase – 37.4 vol.%, biotite – 22.6 vol.% (thin sections analysis). Volume of the sample is ≈ 100 cm3.
Outokumpu 676
Two biotite peaks almost disappear from the sum diffraction pattern of the 818 sample. The reason for this is higher crystal symmetry of biotite in 818 sample:
in 676 → C2/c
in 818 → C2/m
Outokumpu 818

33. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818
SKAT pole figure coverage for the 818 gneiss sample.
Full coverage (72 sample positions).
Measurement time: 36 hours.
¼ coverage (18 sample positions).
Measurement time: 9 hours.
ODF resolution of 5° has been used
ODF resolution of 7.5° has been used

34. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818
Biotite rec. PF, log scale, full coverage (ODF: texture index F2=4.69)
1M polymorph (space group C2/m).
Setting 1 is used for the monoclinic biotite.
Biotite rec. PF, log scale, ¼ coverage (ODF: texture index F2=6.19)

35. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818
Plagioclase rec. PF, full coverage (ODF: texture index F2=1.23)
Plagioclase rec. PF, ¼ coverage (ODF: texture index F2=1.20)

36. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818
Quartz rec. PF, full coverage (ODF: texture index F2=1.16)
Quartz rec. PF, ¼ coverage (ODF: texture index F2=1.20)

37. GEOMixSelf elastic properties calculation of the Outokumpu biotite gneiss 818 (spherical grains, no pores)
Full coverage VP
VS splitting
¼ coverage, VP velocities change by about 30 m/s ≈ 0.5%, max VS split increase by ≈ 8%

38. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818: ODF spectra
Full coverage
Biotite
¼ coverage

39. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818: ODF spectra
Full coverage
Biotite
¼ coverage

40. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818: ODF spectra
Plagioclase
Full coverage
Plagioclase
¼ coverage

41. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818: ODF spectra
Quartz
Full coverage
Quartz
¼ coverage

42. Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818
Phase
Quartz
Biotite
Plagioclase
Volume fraction,%
38.65(4) / 38.94(7) / 39.9
23.96(5) / 23.55(9) / 22.6
37.39(5) / 37.51(10) / 37.4
Texture index F2
1.16 / 1.20
4.69 / 6.19
1.23 / 1.20
Rb index (texture refinement quality), %
11.95 / 11.92
17.54 / 16.12
15.93 / 16.12
a, Å
(2) / (4)
(1) / (2)
8.1498(1) / (1)
b, Å
5.3236(1) / (3)
(1) / (3)
c, Å
(5) / (8)
9.2580(2) / (4)
7.1299(1) / (2)
α, ° 90
93.926(5) / (4)
β, °
(1) / (2)
γ, °
120
(5) / (4)
89.073(1) / (3)
Full coverage
¼ coverage
Phase analysis via thin sections
(Kern, Mengel, Strauss et al. //
PEPI, 175, )
Only notable changes are in cell parameters and texture index of the biotite. This may be due to:
Biotite peaks are the least intensive and they are “lost” in the noisy pattern.
Should account for 1M and 2M1 polymorphs coexistence in the sample?

43. Outokumpu 818: comparison with the HIPPO data
HIPPO PF coverage (includes different detectors on different scattering angles) – by courtesy of Prof. H.-R. Wenk.
HIPPO diffractometer (Los-Alamos)
Volume of the sample is about 1 cm3!
4 sample positions have been measured, 2 hours per position, in total 8 hours of measurements.

44. Outokumpu 818: comparison with the HIPPO data
Spectra from 90° detectors of SKAT
Spectra from 144° detectors of HIPPO

45. Outokumpu 818: comparison with the HIPPO data
Biotite rec. PF, log scale, full coverage (ODF: texture index F2=4.69)
Biotite rec. PF, log scale, HIPPO, 10° resolution (ODF: texture index F2=8.90)

46. Outokumpu 818: comparison with the HIPPO data
Quartz rec. PF, full coverage (ODF: texture index F2=1.16)
Quartz rec. PF, HIPPO, 10° resolution (ODF: texture index F2=1.18)

47. Outokumpu 818: comparison with the HIPPO data
Plagioclase rec. PF, full coverage (ODF: texture index F2=1.16)
Plagioclase rec. PF, HIPPO, 10° resolution (ODF: texture index F2=1.22)

48. Neutron diffraction texture analysis of the quartzite sample 26а
PF coverage used. Only 114 spectra (1/12 of the full coverage), sample positions 00 = 0°, 12 = 60°, 24 = 120°, 36 = 180°, 48 = 240°, 60 = 360°.
Range of lattice spacings d = Å (≈ 310 diffraction peaks, i.e., 310 pole figures).
ODF was recalculated by the E-WIMV method, 5° resolution, exp. pole figures (100), (110), ( ).
Complete PF measurements took 15 h. 36 min.
1/12 of full coverage was possible to measure in 1 h. 18 min.

49. Neutron diffraction texture analysis of the quartzite sample 26а
Single spectrum, detector A, sample position 12.
( )
(100)
(110)

50. Neutron diffraction texture analysis of the quartzite sample 26а
Quartz rec. PF, MAUD, 1/12 coverage (ODF: texture index F2=2.24)
Quartz rec. PF, conventional PF analysis, exp. pole figures (100), (110), ( ) & WIMV method via BEARTEX (ODF: texture index F2=2.35)

51. Neutron diffraction texture analysis of the quartzite sample 26а: ODF spectra
1/12 coverage
MAUD
E-WIMV
Quartz
Conventional
PF analysis, 4 PF
WIMV via BEARTEX

52. Quartzite sample 26а: a comparison of cell parameters
SKAT (MAUD)
Quartz powder,
X-ray
SKAT(MRIA, sum spectrum, old calibration)
a, Å
(2)
(3)
b, Å
c, Å
(4)
(7)
α, ° 90
β, °
γ, °
120
Quartz: space group P3221.
X-ray data after:
Antao SM, Hassan I, Wang J, Lee PL, Toby BH. State-of-the-art high-resolution powder x-ray diffraction (HRPXRD) illustrated with Rietveld structure refinement of quartz, sodalite, tremolite, and meionite. // The Canadian Mineralogist. 46 (2008)

53. Zr alloy E-110 samples
Cylindrical plugs of fuel elements of the VVER-1000 reactor, Zr+1%Nb, space group P63/mmc.
d-range used = Å (1 iteration in MAUD ≈ 40 min.).
Sample coordinate system KA
ZA, σ3
YA, σ2
XA, σ1
002
110

54. Zr alloy E-110 samples: texture analysis of the cold-worked sample
PF exp.
PF rec. (WIMV, 6 peaks). F2=3.38.
PF rec. (MAUD, E-WIMV, 22 peaks in the d-range). F2=3.60.

55. Zr alloy E-110 samples: texture analysis of the cold-worked sample
Let’s use ¼ coverage:
, and even a smaller number of diffraction peaks.
Can we still get the ODF with 5° resolution?
PF rec. (MAUD, ¼ coverage, E-WIMV, only 6 peaks! in d-range Å,
axial sample symmetry has not been applied!). F2=3.76. G-space cell hits min. = 10.
PF rec. (MAUD, E-WIMV, 22 peaks in the d-range). F2=3.60.

56. Zr alloy E-110 samples: cold-worked sample
(110) peak
(101) & (002) peaks
Peak position depends on the angle between the corresponding plane normal and the axis of the cylindrical sample, all the peaks are shifted in the direction of smaller d-values with the decrease of this angle.

57. Zr alloy E-110 samples: cold-worked sample
(110) peak
(101) & (002) peaks
Taking into account residual stresses of the 1st order. BulkPathGEOmethod has been applied for the calculation of diffraction elastic moduli using the ODF and single-crystal elastic constants (Voigt coding): C11 = GPa, С12 = 72.5 GPa, С13 = 65.4 GPa, С33 = GPa, С44 = 32.1 GPa, С66 = 0.5(C11 – С12) = 35.5 GPa.

58. Zr alloy E-110 samples: annealed sample
(110) peak
(101) & (002) peaks
After the annealing process:
macroscopic residual stresses → 0;
crystallite size: 1490 → 930 Å;
microdeformation: 2·10-3 → 5·10-5.

59. Zr alloy E-110 samples: texture analysis of the annealed sample
PF rec. (WIMV, 6 peaks). F2=4.04.
PF rec. (MAUD, E-WIMV, 20 peaks in the d-range). F2=4.08.

60. Zr alloy E-110 samples: macroscopic residual stresses
Taking into account axial symmetry of the sample: σ1 = σ2, σ4 = σ5, σ6 = 0 MPa.
Sample
Diffractometer
σ1, MPa
σ3, MPa
σ4, MPa
a0, Å
c0, Å
Number of meas.^1
Cold-worked
E7, Berlin
166.0
-43.0
3.2342
5.1386 23
SKAT, Dubna
141.7(3)
-5.2(1)
-1.4(1)
3.2340
5.1338
19x21=399
HRFD, Dubna
136.0
-5.0
5.1367 17
Annealed
3.2295
5.1463 21
3.2285
5.1467
19x19=361^2
^1 Number of measurements = number of diffraction peaks * number of physically distinguishable directions of the scattering vector in the sample coordinate system KA (taking into account axial symmetry of the sample).
^2 Two peaks at d > 2.5 Å were not used due to poor counting statistics.

61. Current results
The analysis of the SKAT diffractometer data using the Rietveld method (MAUD software) is possible, and now it is easily available. All 1368 spectra could be analyzed in wide d-range even in case of very complex samples (e.g., > 1000 spectra and > 7∙105 diffraction peaks in total…). A number of very different samples measured during different reactor cycles from February 1998 till December 2006 have been processed with MAUD with no problems.
Only 2 programs are needed to get the ODF out of diffraction patterns (SKAT2MAUD → MAUD) instead of 4 (e.g., GeoTOF → AutoIndex → Berkeley → Beartex).
The d-range and the resolution of SKAT are enough to get necessary information for the ODF reconstruction in case of rocks containing several low-symmetry and/or large-cell minerals, e.g. monoclinic 2M1 biotite polymorph (20.2 x 5.4 x 9.2 Å) + triclinic feldspar. But counting statistics should be increased (especially at d > 3.5 Å) due to modernized reactor, new neutron guide, new (cold) moderator or …
by using less sample positions (e.g., 1/6 of full coverage), but increasing the measurement time per position (e.g., 6 times). In some cases utilization of partial experimental PF coverage may drastically (~ 10 times) reduce total measurement time while the ODF reconstruction with 5° resolution will still be possible.
From the SKAT data now its possible to easily get not only ODF but also cell parameters, phase volume fractions, 1st order residual stresses, etc.

62. Some things to do and suggestions
Still there is a lot of space for the method testing/development…
Add a few options to SKAT2MAUD.
In future, it will be great to measure some standard sample with diffraction peaks in wide d-range – e.g., Al2O3 – during each reactor cycle (and also the vanadium standard).
Make a few special test experiments to verify MAUD-processed SKAT data on texture, cell parameters, stresses, crystallite sizes, etc.
Some more experiments, tests and discussions concerning the possibility to measure incomplete PF & reduce measurement time per sample.

63. Acknowledgements I would like to thank
Creators of SKAT and MAUD for the great instrument and the great software
Dr. Tatiana Ivankina (JINR) for the data on ODF of biotite, plagioclase and quartz for the 676 Outokumpu sample (results of the conventional PF analysis of the SKAT data)
Yuri Kovalev (JINR) for the reminder about the GetLastError() function
Prof. Siegfried Matthies (JINR) for the software he made to convert MAUD format ODF into conventional STD format
Dr. Vyacheslav Sumin (JINR) for HRFD and E7 data on E-110 zirconium alloy samples and discussion of the results on these samples
Prof. Hans-Rudolf Wenk (Berkeley university) for the data on the 818 Outokumpu sample measured on HIPPO diffractometer, and his help with the analysis of incomplete PF of 676 Outokumpu sample measured on SKAT

64. Thank you!