Rietveld texture analysis of SKAT diffractometer data

$: Rietveld texture analysis of SKAT diffractometer data$
Rietveld texture analysis of SKAT diffractometer data

R.N. Vasin

STI-2011, 6-9 June, 2011, Dubna, Russia

SKAT texture diffractometer

Beamline 7a of IBR-2.

Main objectives: investigation of crystallographic textures of rocks and engineering materials.

Total flight path: 103.81 m.

Range of d-spacings: 0.6-4.8 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.

Geometry of diffraction experiment on the SKAT

SA AS

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.

Acquisition of experimental pole figures

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.

Data processing: construction of experimental PFWe 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.

Diffraction peaks (+ background intervals in vicinity) are selected for PF construction.What are those peaks?

QuartziteQuartz, P3221Sum of 1368 spectra

Determination of the phase/mineral (in case of poly-phase material) and Miller indices for chosen diffraction peaks.

Data processing: construction of experimental PF

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!

QuartziteQuartz, P3221


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)…


Construction of experimental PF from chosen diffraction peaks (in SKAT grid)

Conversion (interpolation) of experimental pole figures into regular 5х5° grid.

PF visualization, rotation, normalization, ...

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.

Orientation distribution function calculationfrom experimental PF + some other options

BEARTEX (WIMV method)H.-R. Wenk & S. Matthieshttp://eps.berkeley.edu/~wenk/TexturePage/beartex.htmOperations 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. Pawlikhttp://www.labosoft.com.pl/index.htmOperations with ODF, PF, inverse PF, …Single license – 6000$ (academic – 3000$)

http://eps.berkeley.edu/~wenk/TexturePage/beartex.htm

http://www.labosoft.com.pl/index.htm

Standard data processing procedure

Raw SKATdata

Selection of diffraction peaks for use in the construction of

experimental PF

Front-end processing

Comparison with the database(containing model spectra)

Are these peaks present in database?

Search for the structural info, load it into

databaseNo

Is there enough non-overlapped diffraction peaks for each phase?

Yes

Yes

Construction of experimental PF, PF conversion into conventional

format, ODF reconstruction

No

Is there a good agreement between experimental and

recalculated PF?

No

Yes

ODF of each phaseODF of each phase

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.

MAUDhttp://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, 334-340, 2010.

Freeware!Java-based, needs JVM to work, butthis 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 diffractionpatterns (TOF is included).

Great options for texture evaluation:ODF calculation from the setof diffraction spectra(several methods are available).

http://www.ing.unitn.it/~maud/

MAUD

And what about TOF spectra?

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 1368 spectra.

The fit is not perfect due to some peculiarities of the vanadium spectrum, its better to use “point-to-point” normalization.

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.

SKAT2MAUD

Selection of parameters for the data conversion

Spectra selection

Monitor counts extraction from the SKAT protocol file

Data type selection

Options for point-to-point data normalization

Construction of the script file for MAUD and of the protocol.

Ni powder

Sum spectrum (detectors from A to S)

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!

Ni powder

Detector А

Detector B

Detector C

Detector D

Detector E

Ni powderA

SD

etec

tors

:

(111) peak

(222) & (311) peaks

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, 2009. 151-166). 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).


First 12 spectra, detector A, point-to-point normalized in SKAT2MAUD.


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)


SKAT pole figure coverage for the 676 gneiss sample (different colors correspond to different number of counts of the beam monitor).


Biotite rec. PF, log scale, MAUD (ODF: texture index F2=5.67)

Biotite rec. PF, log scale, conventional PF analysis (ODF: texture index F2=3.30)

2M1 polymorph (space group C2/c).Setting 1 is used for the monoclinic biotite here and further.


Plagioclase rec. PF, MAUD (ODF: texture index F2=1.27)

Plagioclase rec. PF, conventional PF analysis (ODF: texture index F2=1.23)


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.


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.


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)


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)


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)

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)

SKAT (MAUD)

Database SKAT (MAUD)

DatabaseAn16/28/48

a, Å 20.2269(1) 19.976/20.196

4.91285(2) 4.91343 8.1533(1) 8.154/8.169/8.179

b, Å 5.3599(1) 5.3175/5.339

4.91285(2) 4.91343 12.8468(2) 12.823/12.851/12.880

c, Å 9.2108(2) 9.212/9.249

5.40451(4) 5.40512 7.1235(1) 7.139/7.124/7.112

α, ° 90 90 90 90 93.88(1) 94.06/93.63/93.44

β, ° 90 90 90 90 116.36(1) 116.50/116.40/116.21

γ, ° 94.99(1) 95.09/95.06 120 120 89.25(1) 88.59/89.46/90.23


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

Outokumpu 818

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/cin 818 → C2/m


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 7.5° has been used

ODF resolution of 5° has been used



Biotite rec. PF, log scale, ¼ coverage (ODF: texture index F2=6.19)

1M polymorph (space group C2/m).Setting 1 is used for the monoclinic biotite.



Plagioclase rec. PF, ¼ coverage (ODF: texture index F2=1.20)



Quartz rec. PF, ¼ coverage (ODF: texture index F2=1.20)

GEOMixSelf elastic properties calculation of the Outokumpu biotite gneiss 818 (spherical grains, no pores)

Full coverage

¼ coverage, VP velocities change by about 30 m/s ≈ 0.5%, max VS split increase by ≈ 8%

VP

VS splitting

Neutron diffraction texture analysis of the Outokumpu biotite gneiss 818: ODF spectra

BiotiteFull coverage

Biotite¼ coverage


PlagioclaseFull coverage

Plagioclase¼ coverage


QuartzFull coverage

Quartz¼ coverage


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 4.91237(2) / 4.91246(4) 10.2347(1) / 10.2363(2) 8.1498(1) / 8.1500(1)

b, Å 4.91237(2) / 4.91246(4) 5.3236(1) / 5.3260(3) 12.8366(1) / 12.8366(3)

c, Å 5.40422(5) / 5.40414(8) 9.2580(2) / 9.2545(4) 7.1299(1) / 7.1297(2)

α, ° 90 90 93.926(5) / 93.920(4)

β, ° 90 90 116.428(1) / 116.427(2)

γ, ° 120 100.068(5) / 100.117(4) 89.073(1) / 89.077(3)

Full coverage¼ coveragePhase analysis via thin sections(Kern, Mengel, Strauss et al. //PEPI, 175, 2009. 151-166)

Only notable changes are in cell parameters and texture index of the biotite. This may be due to:1)Biotite peaks are the least intensive and they are “lost” in the noisy pattern.2)Should account for 1M and 2M1 polymorphs coexistence in the sample?

Outokumpu 818: comparison with the HIPPO data

HIPPO diffractometer (Los-Alamos)

HIPPO PF coverage (includes different detectors on different scattering angles) – by courtesy of Prof. H.-R. Wenk.

Volume of the sample is about 1 cm3!4 sample positions have been measured, 2 hours per position, in total 8 hours of measurements.


Spectra from 144° detectors of HIPPO

Spectra from 90° detectors of SKAT



Biotite rec. PF, log scale, HIPPO, 10° resolution (ODF: texture index F2=8.90)



Quartz rec. PF, HIPPO, 10° resolution (ODF: texture index F2=1.18)



Plagioclase rec. PF, HIPPO, 10° resolution (ODF: texture index F2=1.22)

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 = 0.6-3.4 Å (≈ 310 diffraction peaks, i.e., 310 pole figures).

ODF was recalculated by the E-WIMV method, 5° resolution, exp. pole figures (100), (110), (012+102).

Complete PF measurements took 15 h. 36 min.

1/12 of full coverage was possible to measure in 1 h. 18 min.


Single spectrum, detector A, sample position 12.

(100)

(110)

(012+102)


Quartz rec. PF, MAUD, 1/12 coverage (ODF: texture index F2=2.24)

Quartz rec. PF, conventional PF analysis, exp. pole figures (100), (110), (012+102) & WIMV method via BEARTEX (ODF: texture index F2=2.35)

Neutron diffraction texture analysis of the quartzite sample 26а: ODF spectra

Quartz1/12 coverageMAUDE-WIMV

QuartzConventionalPF analysis, 4 PFWIMV via BEARTEX

Quartzite sample 26а: a comparison of cell parameters

26a,SKAT (MAUD)

Quartz powder,X-ray

26a,SKAT(MRIA, sum spectrum, old calibration)

a, Å 4.91288(2) 4.91343 4.91572(3)

b, Å 4.91288(2) 4.91343 4.91572(3)

c, Å 5.40442(4) 5.40512 5.40639 (7)

α, ° 90 90 90

β, ° 90 90 90

γ, ° 120 120 120

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) 1501-1509.

Zr alloy E-110 samples

002

110

Cylindrical plugs of fuel elements of the VVER-1000 reactor, Zr+1%Nb, space group P63/mmc.d-range used = 0.89-2.89 Å (1 iteration in MAUD ≈ 40 min.).

Sample coordinate system KA

XA, σ1

YA, σ2

ZA, σ3

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.

Zr alloy E-110 samples: texture analysis of the cold-worked sample

Let’s use ¼ coverage:

PF rec. (MAUD, ¼ coverage, E-WIMV, only 6 peaks! in d-range 1.43-2.89 Å,axial sample symmetry has not been applied!). F2=3.76. G-space cell hits min. = 10.


, and even a smaller number of diffraction peaks.

Can we still get the ODF with 5° resolution?

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.

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 = 143.5 GPa, С12 = 72.5 GPa, С13 = 65.4 GPa, С33 = 164.9 GPa, С44 = 32.1 GPa, С66 = 0.5(C11 – С12) = 35.5 GPa.

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.

Zr alloy E-110 samples: texture analysis of the annealed sample

PF rec. (WIMV, 6 peaks). F2=4.04.


Zr alloy E-110 samples: macroscopic residual stresses

Sample Diffractometer σ1, MPa σ3, MPa σ4, MPa a0, Å c0, Å Number of meas.^1

Cold-worked

E7, Berlin 166.0 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 0 -5.0 3.2340 5.1367 17

Annealed E7, Berlin 0 0 0 3.2295 5.1463 21

SKAT, Dubna 0 0 0 3.2285 5.1467 19x19=361^2

Taking into account axial symmetry of the sample: σ1 = σ2, σ4 = σ5, σ6 = 0 MPa.

^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.

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.

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.

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

Thank you!

Rietveld texture analysis of SKAT diffractometer data

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