# Changeset 4961 for Tutorials/2DTexture

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Timestamp:
Jun 17, 2021 11:46:44 AM (6 months ago)
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update this tutorial

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Tutorials/2DTexture
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• ## Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II.htm

 r4949 Von DreeleVon Dreele, Robert B.62779829532021-06-08T17:35:00Z2021-06-09T22:13:00Z404431252572021-06-17T16:44:00Z1470926844Argonne National Laboratory2105929629223623149116.00 Print 188 Clean Clean font-weight:bold;} h2 {mso-style-noshow:yes; mso-style-priority:9; {mso-style-priority:9; mso-style-qformat:yes; mso-style-link:"Heading 2 Char"; span.Heading2Char {mso-style-name:"Heading 2 Char"; mso-style-noshow:yes; mso-style-priority:9; mso-style-unhide:no; src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png" v:shapes="_x0000_i1025">coefficients is sufficient to describe the effect on the diffraction patterns due to texture. The crystal to describe the effect on the diffraction pattern due to texture. The crystal harmonic factor, , and the three sample orientation angles, Ws, , and the three sample orientation angles, Ws, Cs, Fs, all of which can be adjustable parameters of the refinement. Once the to accommodate the two possible uses of this correction. In one, a suite of spherical harmonics coefficients is defined for the texture of a phase in the sample; this can have any of the possible sample symmetries and is the usual result desired for texture analysis. The other is the suite of spherical harmonics terms for cylindrical sample symmetry for each phase in each powder pattern (histogram) and is usually used to accommodate preferred orientation effects in a Rietveld refinement. The former description allows refinement of the sample orientation zeros, Ws, sample; this can have any of the possible sample symmetries and is the usual result desired for texture analysis. The other is the suite of spherical harmonics terms for cylindrical sample symmetry for each phase in each powder pattern (histogram) and is usually used to accommodate preferred orientation effects in a Rietveld refinement. The former description allows refinement of the sample orientation zeros, Ws, Cs, Fs, but the latter description does not (they are assumed to be zero and not refinable). The sample orientation angles, (Fs, but the latter description does not (they are assumed to be zero and not refinable). The sample orientation angles, (W, C, F) are specified in the Sample Parameters table in the GSAS-II data tree structure and are applied for either description.

Some useful examples:

1) Bragg-Brentano laboratory powder diffractometer

The conventional arrangement of this experiment is to have a flat sample with incident and diffracted beams at equal angles (theta) on opposite sides of the sample. The sample is frequently spun about its normal to improve powder statistics and impose cylindrical symmetry on any preferred orientation (texture). Thus, the diffraction plane (source, diffraction vector & detector) contains the K-vector which is parallel to the diffraction vector and W, C, F = 0.

2) Debye-Scherrer diffractometer with point detector(s)

The usual arrangement here is to have a capillary sample perpendicular to the diffraction plane. The capillary may be spun about its cylinder axis for powder averaging and to impose cylindrical symmetry on the texture which is perpendicular to the diffraction plane. Thus, W, F = 0 and C =90.

3) Debye-Scherrer diffractometer with 2D area detector

The area detector is presumed to be directly behind the sample with the incident beam somewhere near the center of the detector. The detector axes are defined (for a synchrotron) with the X-axis toward the synchrotron ring and the Y-axis vertical up; one views the detector image as if looking from the x-ray source. The sample is assumed to be a capillary (which may be spun to impose cylindrical symmetry), although other sample shapes may be used, and is aligned with the cylinder axis horizontal. Integration of the image from a series of caked slices gives a set of powder patterns, each assigned an azimuthal angle where zero is along the X-axis. Thus, this diffraction plane is horizontal and contains the cylinder axis so W, C, F = 0.

alt="GSAS-II plots: <unnamed project>" v:shapes="_x0000_i1081">

and the The detector was previously calibrated and the coefficients are stored in a file found by doing ParmsParms/Load Controls from the Image Controls menu. A file selection popup will appear showing NDC5.imctrl; select it and press Open. The /Load Controls from the Image Controls window will be repainted with the new values and the image will be redrawn.

Controls menu. A file selection popup will appear showing NDC5.imctrl; select it and press Open. The Image Controls window will be repainted with the new values and the image will be redrawn.

mm symmetry so that the unique part of this intensity variation covers 0-90° of azimuth. In addition the ring intensity variation is such that using 10° slices will capture it reasonably well. However, we want to include both 0° and 90° as slice centers. Thus there will be 10 slices beginning at -5° and ending at 95°. Check the Show integration limits? box and uncheck the Do full integration? box, enter 10 in the No. azimuth bins, enter -5 in the Start azimuth box (it will change to 355) and enter 455 in the End azimuth box. In addition, recall that the sample was mounted vertically and thus is aligned with the defined laboratory I axis. Thus, the sample coordinate system needs to be rotated by 90° to match the sample axis with the K axis; this can be done by making the Show integration limits? box and uncheck the Do full integration? box, enter 10 in the Sample goniometer axis Chi = No. azimuth bins, enter -5 in the Start azimuth box (it will change to 355) and enter 455 in the End azimuth box. In addition, recall that the sample was mounted vertically and thus is aligned with the defined laboratory I axis. Thus, the sample coordinate system needs to be rotated by 90° to match the sample axis with the K axis; this can be done by making the Sample goniometer axis Chi = 90. The plot will change with each entry and at the end should look like

minor-latin;mso-hansi-theme-font:minor-latin'>90. The plot will change with each entry and at the end should look like

to 2500; the image will be redrawn reflecting this mask. By zooming in you may see isolated red pixels; these are excluded points. Make sure the diffraction rings do not have any excluded points. For example, with the level set to 2200 the plot shows

alt="GSAS-II plots: NiTi.gpx" v:shapes="Picture_x0020_59">

for one ring. histogram has a set of parameters (e.g. phase fraction, size, mustrain & hydrostatic strain) in addition to the ones for each histogram (e.g. background & scale factor). Consequently the total number of parameters can build up very quickly in this method of analysis. The other two methods seek to reduce this problem by splitting the fitting into a sequential refinement (histogram by histogram) step followed by a texture fitting step.

& scale factor). Consequently, the total number of parameters can build up very quickly in this method of analysis. The other two methods seek to reduce this problem by splitting the fitting into a sequential refinement (histogram by histogram) step followed by a texture fitting step.

It is evident that there remains intensity differences due to texture. We can increase the harmonic order to more closely fit these, however one should only do this carefully. Select the Texture tab for the B2 phase; the Texture tab will show

that there remain intensity differences due to texture. We can increase the harmonic order to more closely fit these, however one should do this carefully. Select the Texture tab for the B2 phase; the Texture tab will show

001 pole figure will be drawn. This is the very typical bulls eye for cylindrical texture; of much more use is an inverse pole figure. Select that from the Texture plot type; the plot will be redrawn

more use is an inverse pole figure. Select that from the Texture plot type; the plot will be redrawn

This shows the probability of reflection vectors coinciding with the sample wire axis the high spots are the 111 family of reflections. We should try the next higher Harmonic probability of reflection vectors coinciding with the sample wire axis; the high spots are the 111 family of reflections. We should try the next higher harmonic order (10).

Next go to the Texture tab for the B19 phase. Again, a bullseye pole figure is drawn; change that to an Inverse pole figure.

Texture tab for the B19 phase. Again, a bullseye pole figure is drawn; change that to an Inverse pole figure.

Calculate/Refine from the main menu; the Rwp has dropped to ~10.4%. One can add the atom Uiso for the Ni and Ti atoms in o:spid="_x0000_i1056" type="#_x0000_t75" alt="GSAS-II project: NiTi-A.gpx" style='width:5in;height:199.5pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1055" type="#_x0000_t75" alt="GSAS-II plots: NiTi-A.gpx" style='width:5in;height:339pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1054" type="#_x0000_t75" alt="GSAS-II project: NiTi-A.gpx" style='width:5in;height:142.5pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1053" type="#_x0000_t75" alt="GSAS-II plots: NiTi-A.gpx" style='width:358.5pt;height:337.5pt;visibility:visible;mso-wrap-style:square'>

This completes the tutorial on Method A for doing texture analysis. It is useful for a case like this one where there are very few data sets required for the texture analysis. However, for the case of lower sample symmetry one must several dozen or even a few hundred histograms and then the suite of parameters can easily be > 1000 of which only a few dozen describe the texture. This leads to the next Methods for texture analysis in GSAS-II.

the tutorial on Method A for doing texture analysis. It is useful for a case like this one where there are very few data sets required for the texture analysis. However, for the case of lower sample symmetry one must several dozen or even a few hundred histograms and then the suite of parameters can easily be > 1000 of which only a few dozen describe the texture. This leads to the next Methods for texture analysis in GSAS-II.

This begins the texture analysis in much the same way as Method A except that all the initial refinements are done sequentially, that is refinements are done for the parameters associated with each powder pattern to convergence in a serial the texture analysis in much the same way as Method A except that all the initial refinements are done sequentially, that is refinements are done for the parameters associated with each powder pattern to convergence in a serial fashion. In this case where there are 10 PWDR data sets, there will be 10 refinements done in sequence. Parameters that span all the data (e.g. lattice o:spid="_x0000_i1052" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx" style='width:360.75pt;height:183pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1051" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:360.75pt;height:183pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1050" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:357.75pt;height:108.75pt;visibility:visible;mso-wrap-style:square'>

There is a row for each data set and columns for all refined parameters and some derived ones along with residual and convergence indicators. The residuals are not very good (we havent really refined much) but the Δχ2 column shows that convergence was achieved (NB: poor convergence will be highlighted in yellow or red depending on how bad it is).

for each data set and columns for all refined parameters and some derived ones along with residual and convergence indicators. The residuals are not very good (we havent really refined much) but the Δχ2 column shows that convergence was achieved (NB: poor convergence will be highlighted in yellow or red depending on how bad it is).

If you examine one of the PWDR entries, youll see that just in this point in Method A much of the misfit is texture and perhaps peak position.

one of the PWDR entries, youll see that as at the same point in Method A much of the misfit is texture and perhaps peak position.

o:spid="_x0000_i1048" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:357.75pt;height:300pt;visibility:visible;mso-wrap-style:square'>

minor-latin'>Harmonic order to 6 and check the 6 and check the Refine box for it (Preferred orientation). Then in two steps, first do Refine box for it (Preferred orientation). Then in two steps, do Edit Phase/Copy flags and Set All for the file selection. Then do Edit Phase/Copy selected data; that will bring up a new popup

minor-latin;mso-bidi-theme-font:minor-latin'>Edit Phase/Copy flags and Set All for the file selection. Then do Edit Phase/Copy selected data; that will bring up a new popup

style='mso-bidi-font-weight:normal'>Pref. Ori. And press Pref. Ori. and press OK; o:spid="_x0000_i1046" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:357.75pt;height:321pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1045" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:357.75pt;height:87.75pt;visibility:visible;mso-wrap-style:square'>

It is probably best to do another round of sequential refinement (I had to do two) to get convergence. A plot of one PWDR entry gives

best to do another round of sequential refinement (I had to do two) to get convergence. A plot of one PWDR entry gives

As our experience in Method A, the calculated peaks are too sharp. We need to vary the mustrain parameters for both phases. Go to the Data tab for each phase, check the Data tab for each phase, check the microstrain o:spid="_x0000_i1043" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:5in;height:88.5pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1042" type="#_x0000_t75" alt="GSAS-II plots: NiTi-B.gpx" style='width:358.5pt;height:337.5pt;visibility:visible;mso-wrap-style:square'>

Showing that perhaps the B19 phase needs high order spherical harmonics. Select the Data perhaps the B19 phase needs high order spherical harmonics. Select the Data tab for the B19 phase and change the

parameters (Dij) for peak position shifts and microstrain for peak shape. We modeled the intensity variation with a spherical harmonics preferred orientation correction. If you select any PWDR entry from the GSAS-II data tree and pick the Reflection List subentry (at the bottom) you can see the magnitude of this variation with a spherical harmonics preferred orientation correction. If you select any PWDR entry from the GSAS-II data tree and pick the Reflection List subentry (at the bottom) you can see the magnitude of this correction for each reflection in each phase.

o:spid="_x0000_i1040" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:357.75pt;height:96pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1039" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:468pt;height:160.5pt;visibility:visible;mso-wrap-style:square'>

The preferred orientation correction is Prfo; notice a few entries in red. These are nonphysical correction values (the correction cant be negative) but by in large these are small. This next step uses these corrections as input data for a texture refinement. To start select the Texture tab for the B2 phase; youll see

The preferred orientation correction is Prfo; notice a few entries in red. These are nonphysical correction values (physically, the correction cant be negative) but by in large these are small. This next step uses these corrections as input data for a texture refinement. To start select the Texture tab for the B2 phase; youll see

o:spid="_x0000_i1037" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:358.5pt;height:151.5pt;visibility:visible;mso-wrap-style:square'>

mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font: minor-latin'>Texture/Refine texture
from the menu; the window will be repainted and a bullseye pole figure will appear. Change the Texture plot type to Inverse pole figure to get a more useful plot

minor-latin'>Texture plot type to Inverse pole figure to get a more useful plot

Now select the Texture tab for the B19 phase and do the same; use Texture tab for the B19 phase and do the same; use Harmonic o:spid="_x0000_i1035" type="#_x0000_t75" alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" style='width:5in;height:192.75pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1034" type="#_x0000_t75" alt="GSAS-II plots: NiTi-B.gpx" style='width:358.5pt;height:337.5pt;visibility:visible;mso-wrap-style:square'>

This uses the same approach as Method B except that after the sequential refinements are finished we then fix almost all the parameters and then do a final texture refinement with all the data. Thus, this is a replacement for Step 2 in Method B. To begin do File/Open project for the NiTi-B.gpx file created in Method B and then do a File/Save project as to save it as File/Open project for the NiTi-B.gpx file created in Method B and then do a File/Save project as to save it as NiTiNiTi-C. This renames the project and it should have one IMG, 10 PWDR entries and two phases of NiTi (B2 and B19).

minor-latin;mso-hansi-theme-font:minor-latin'>-C
. This renames the project and it should have one IMG, 10 PWDR entries and two phases of NiTi (B2 and B19).

Background: as the background was fit during the sequential refinement we should fix it here. Select any PWDR entry and choose the Background subentry for it. Clear the PWDR entry and choose the Background subentry for it. Clear the Refine flags and the do

id="Picture_x0020_114" o:spid="_x0000_i1032" type="#_x0000_t75" alt="GSAS-II project: NiTi-C.gpx (sequential refinement)" style='width:345.75pt;height:143.25pt;visibility:visible;mso-wrap-style:square'>

To clear the sequential refinement set up, select Controls from the main data tree.

sequential refinement set up, select Controls from the main data tree.

Then do Reselect datasets, a popup window will appear

Then do Reselect datasets, a popup window will appear

Do Toggle All to clear the check marks and press OK. The Controls will no longer show how many data sets are used in a sequential refinement.

Do Toggle All to clear the check marks and press OK. The Controls will no longer show how many data sets are used in a sequential refinement.

from the main menu; it will be a combined refinement on texture parameters.

In this case you do want to do a nonsequential full refinement, so press the OK button. A quick look at the console will show that there are 61 variables in this refinement. If yours shows more then you didnt clear all the flags in Step 1. The Sequential results entry is deleted from the GSAS-II data tree. A progress bar will show giving the residuals during the refinement. When finished, select the B2 phase and its Texture tab; if the Texture plot type is still Inverse pole figure (from Method B) you should see

A quick look at the console will show that there are 61 variables in this refinement. If yours shows more then you didnt clear all the flags in Step 1. The Sequential results entry is deleted from the GSAS-II data tree. A progress bar will show giving the residuals during the refinement. When finished, select the B2 phase and its Texture tab; if the Texture plot type is still Inverse pole figure (from Method B) you should see

o:spid="_x0000_i1027" type="#_x0000_t75" alt="GSAS-II project: NiTi-C.gpx" style='width:357pt;height:153.75pt;visibility:visible;mso-wrap-style:square'>

o:spid="_x0000_i1026" type="#_x0000_t75" alt="GSAS-II plots: NiTi-C.gpx" style='width:5in;height:339pt;visibility:visible;mso-wrap-style:square'>

and also almost identical to what was obtained in Method A; the coefficients are seen in

and also, almost identical to what was obtained in Method A; the coefficients are seen in

• ## Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II_files/filelist.xml

 r4949
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