# Changeset 4937

Ignore:
Timestamp:
Jun 8, 2021 3:12:38 PM (2 years ago)
Message:

Location:
Tutorials/2DTexture
Files:
2 edited

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

 r4936 Von DreeleVon Dreele, Robert B.22288323102021-06-08T17:35:00Z2021-06-08T17:35:00Z2021-06-08T20:11:00Z47440725121440025081Argonne National Laboratory20958294702942316.00 Print Clean Clean false font-family:"Times New Roman",serif; mso-fareast-font-family:"Times New Roman";} span.SpellE {mso-style-name:""; mso-spl-e:yes;} span.GramE {mso-style-name:""; mso-gram-e:yes;} .MsoChpDefault {mso-style-type:export-only;

·· Exercise files are found here

Exercise files are found here

analysis using GSAS-II employs spherical harmonics modeling, as described by Bunge, "Texture Analysis in Materials Science" (1982), and implemented by Von Dreele, J. Appl. Cryst., 30, 517-525 (1997) in GSAS. The even part of the orientation distribution function (ODF) via the general axis equation

implemented by Von Dreele, J. Appl. Cryst., 30, 517-525 (1997) in GSAS. The even part of the orientation distribution function (ODF) via the general axis equation

, 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, Cs, 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.

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 with the cylinder axis parallel to K 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, (W, C, F) are specified in the Sample Parameters table in the GSAS-II data tree structure and are applied for either description.

In this tutorial we will use both of these descriptions to determine the texture of the two phases in a NiTi shape memory alloy sample with cylindrical symmetry (wire texture) as collected at APS on beam line 1ID-C (data kindly provided by Paul Paradise & Aaron Stebner of Colo. School of Mines). Thus, there are three ways within GSAS-II that can be used for this texture analysis all beginning with the same 2D area detector image. Each will be described in turn after the initial setup of the GSAS-II project, image input & integration.

descriptions to determine the texture of the two phases in a NiTi shape memory alloy sample with cylindrical symmetry (wire texture) as collected at APS on beam line 1ID-C (data kindly provided by Paul Paradise & Aaron Stebner of Colo. School of Mines). Thus, there are three ways within GSAS-II that can be used for this texture analysis all beginning with the same 2D area detector image. Each will be described in turn after the initial setup of the GSAS-II project, image input & integration.

The detector was previously calibrated and the coefficients are stored in a file found by doing Parms/Load was previously calibrated and the coefficients are stored in a file found by doing Parms/Load Controls from the Flat Bkg (I chose Flat Bkg (I chose 1700 for this). The image will now show the rings much more clearly.

o:title=""/>

"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: minor-latin'>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 Show integration limits? box and uncheck the Do full integration? box, enter 10 minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth bins, enter -5 in the No. azimuth bins, enter -5 in the Start azimuth box (it will change to 355) and enter 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'>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

o:title=""/>

o:title=""/>

threshold 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

mso-hansi-theme-font:minor-latin'>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

o:title=""/>

Step 2. Enter NiTi phases

This NiTi alloy consists of two phases, cubic B2 and monoclinic B19. Their parameters are:
0in;line-height:115%'>Step 2. Enter NiTi phases

This NiTi alloy consists of two phases, cubic B2 and monoclinic B19. Their parameters are:
B2: P m 3 m, Ni 0,0,0, Ti œ,œ,œ, Uiso=0.005 for both.
Ti œ,œ,œ, Uiso=0.005 for both.
B19:  96.821, Ti 0.5787,0.2841,Œ, Ni 0.5787,0.2841,Œ, Ni 0.9700,0.8209,Œ, Uiso=0.005 for both.
Uiso=0.005 for both.

o:title=""/>

o:title=""/>

o:title=""/>

You should now save the project file (I used NiTi for a name); we will use this as a starting point for three different texture determinations. Do a File/Save project as and give it a new name (I used NiTi-A); this will become the new project name for the next part of this tutorial.

minor-latin;mso-hansi-theme-font:minor-latin'>NiTi
for a name); we will use this as a starting point for three different texture determinations. Do a File/Save project as and give it a new name (I used NiTi-A); this will become the new project name for the next part of this tutorial.

PWDR NDC5_01588_1.ge2 Azm= 40.00). Uncheck the PWDR NDC5_01588_1.ge2 Azm= 40.00). Uncheck the Histogram scale factor box and then do Histogram scale factor box and then do Command/Copy flags; select Set All and then press Command/Copy flags; select Set All and then press OK. That will clear the scale factor refinement flag for all histograms; we will be o:title=""/>

o:title=""/>

o:title=""/>

minor-latin'>Refine texture and Show coeff. The window should look like

mso-hansi-theme-font:minor-latin'>Show coeff. The window should look like

o:title=""/>

o:title=""/>

tab for the B19 phase and check all 4 of the Dij boxes and do Edit Phase/Copy flags as before. The tab will look like

minor-latin'>B19 phase and check all 4 of the Dij boxes and do Edit Phase/Copy flags as before. The tab will look like

style='mso-bidi-font-weight:normal'>Calculate/Refine from the main menu. The refinement will finish with Rw ~27%; the 1st PWDR pattern looks like

from the main menu. The refinement will finish with Rw ~27%; the 1st PWDR pattern looks like

The calculated peaks for both phases are too sharp. It is likely that this is a microstrain effect. Select Data for the B2 phase and select the microstrain box. Then do Edit Phase/Copy flags to set it for the other PWDR data sets. Do the same for the B19 phase. Then do Data for the B2 phase and select the microstrain box. Then do Edit Phase/Copy flags to set it for the other PWDR data sets. Do the same for the B19 phase. Then do Calculate/Refine from the main menu. The fit will be substantially improved with Rw ~10%.

minor-latin'>Calculate/Refine from the main menu. The fit will be substantially improved with Rw ~10%.

Looking at the individual PWDR data sets (e.g. the one for Azm=20.00)

individual PWDR data sets (e.g. the one for Azm=20.00)

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 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

And a drawing of the 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

of the 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

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.

This phase is very strongly textured (the cursor shows 12-13 MRD at the peaks) along the -140 direction. Again we want to increment the Harmonic order to the next higher level (8). Again do Calculate/Refine from the main menu; the Rwp has dropped to ~8.9%. One can add the atom Uiso for the Ni and Ti atoms in the B2 phase and the coordinates and Uiso for the B19 phase. The Rw drops a bit further to ~8.4%. Finally, we can increase the harmonic order again for the B19 phase (it is very strongly textured!) to 10 and the B2 phase to 12; the final refinement converged to Rw ~7.8% and the B19 inverse pole figure has peaks at ~18 MRD (Multiple of Random Distribution) and the B2 phase peaks are ~7MRD.

direction. Again we want to increment the Harmonic order to the next higher level (8). Again do Calculate/Refine from the main menu; the Rwp has dropped to ~8.9%. One can add the atom Uiso for the Ni and Ti atoms in the B2 phase and the coordinates and Uiso for the B19 phase. The Rw drops a bit further to ~8.4%. Finally, we can increase the harmonic order again for the B19 phase (it is very strongly textured!) to 10 and the B2 phase to 12; the final refinement converged to Rw ~7.8% and the B19 inverse pole figure has peaks at ~18 MRD (Multiple of Random Distribution) and the B2 phase peaks are ~7MRD.

The B19 o:title=""/>

o:title=""/>

o:title=""/>

o:title=""/>

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 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; mso-hansi-theme-font:minor-latin'>File/Open project for the NiTi.gpx file created in the first step and then do a NiTi.gpx file created in the first step and then do a File/Save project as to save it as File/Save project as to save it as NiTi-B. 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'>NiTi
-B. This renames the project and it should have one IMG, 10 PWDR entries and two phases of NiTi (B2 and B19).

This begins the same way as Method A so Ill be brief. Do the following steps:

the same way as Method A so Ill be brief. Do the following steps:

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 o:title=""/>

Next do the same thing for the B19 phase; here there are 4 Dij parameters to check (do all of them) and use spherical harmonics order 4. When done that Data window will look like

minor-latin'>Dij parameters to check (do all of them) and use spherical harmonics order 4. When done that Data window will look like

refine. Be careful not (by habit say) pick Refine; a warning popup will appear. After it completes the Sequential refinement results shows that the fit is better but convergence wasnt quite complete.

the fit is better but convergence wasnt quite complete.

o:title=""/>

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 microstrain box and do Edit Phase/Copy flags for all the data sets. Then do another Calculate/Sequential refine. My Sequential refinement results showed great improvement but incomplete refinement

the microstrain box and do Edit Phase/Copy flags for all the data sets. Then do another Calculate/Sequential refine. My Sequential refinement results showed great improvement but incomplete refinement

o:title=""/>

Examination of the PWDR data sets showed a fairly good fit but some discrepancies (especially for Azm=20.00)

for Azm=20.00)

Then do Edit Phase/Copy selected data for Pref.Ori. minor-latin'>Edit Phase/Copy selected data for Pref.Ori. to the other data sets. This (after few repeats) gives a further improvement in the fit

o:title=""/>

During the sequential refinements done in Step 1, we fitted the profiles allowing strain parameters (Dij) for peak position shifts and microstrain for peak shape. We modeled the intensity variation with a spherical harmonics preferred 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 o:title=""/>

o:title=""/>

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

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

Show coeff boxes. The data window will be redrawn (and an orange blank plot will appear).

minor-latin'>Show coeff boxes. The data window will be redrawn (and an orange blank plot will appear).

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.

be repainted and a bullseye pole figure will appear.

o:title=""/>

o:title=""/>

o:title=""/>

Again this is very similar to what we found in Method A but again not quite as strong (max MRD ~10 instead of ~18) and a bit choppier.

Again this is very similar to what we found in Method A but again not quite as strong (max MRD ~10 instead of ~18) and a bit choppier.

Now do a 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 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 NiTi-B.gpx file created in Method B and then do a File/Save project as to save it as NiTi-C. minor-latin;mso-hansi-theme-font:minor-latin'>NiTi-C. This renames the project and it should have one IMG, 10 PWDR entries and two phases of NiTi (B2 and B19).

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 refinement we should fix it here. Select any PWDR entry and choose the Background subentry for it. Clear the Refine flags and the do B2 phase: we do not want to refine either the microstrain, D11, or preferred orientation coefficients. Select the B2 phase and its Data tab. Clear the B2 phase and its microstrain, D11 and Data tab. Clear the microstrain, D11 and Preferred orientation boxes. Also set the Edit Phase/Copy selected data for Pref.Ori to copy the zeroed out harmonic coefficients.

Phase/Copy selected data
for Pref.Ori to copy the zeroed out harmonic coefficients.

B19: we do not want to refine either the microstrain, Dij, or preferred orientation coefficients. Select the B19 phase and its Data tab. Clear the B19 phase and its microstrain, four Dij and Preferred orientation boxes. Also set the Data tab. Clear the microstrain, four Dij and Preferred orientation boxes. Also set the Harmonic order to zero (this will Phase/Copy flags selecting all data to clear all the flags and an Edit Phase/Copy selected data for Pref.Ori to copy the zeroed out harmonic coefficients.

mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit Phase/Copy selected data for Pref.Ori to copy the zeroed out harmonic coefficients.

which is almost identical to that from Method A. The coefficients are seen in

which is almost identical to that from Method A. The coefficients are seen in

o:title=""/>

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

 r4936
Note: See TracChangeset for help on using the changeset viewer.