For this demo, data were collected with a MAR2300 area detector at APS 1-ID-C with a wavelength 0.12398 Å (100mm diameter beam) from a 1.5mm square hot rolled steel test specimen; the front surface has been dusted with some CeO2 to aid in calibration. Two images are used here; one is with no load on the sample and the other is with the sample under tension along the y-axis (vertical). The loading will distort the steel (ferrite & austenite) diffraction rings and our purpose here is to characterize this distortion via a strain model by B. B. He & K. L. Smith (Adv. in X-ray Anal. 41, 501, 1997). Note that menu entries are listed in bold face below as Help/About GSAS-II, which lists first the name of the menu (here Help) and second the name of the entry in the menu (here About GSAS-II).
Use the Data/Read image data menu item to
read the data file into a new GSAS-II project. A file selection dialog will be
shown; its appearance will depend on your OS. Change the search directory to /Exercises/strain-texture/nx09_strain_data
and then select the files nx09_strain_001.mar2300 and nx09_strain_012.mar2300
and press Open. Select the 1st image (001) from the
GSAS-II data tree and select Image Controls; adjust the Max intensity so that
the CeO2 rings are visible (~1500 will suffice). You should see:
For the image and
for the controls.
This image is a superposition of three diffraction patterns; CeO2 calibrant, ferrite (BCC iron) and austenite (FCC iron). Consequently the calibration needs to be done with some care; the steps are as follows:
Set the wavelength to 0.12398
Set the calibrant to CeO2 SRM674b
Set Min calib d-spacing to 1.09; this avoids picking a CeO2 ring that overlaps one of the steel ones.
Pick Show ring picks? check box
Use Operations/Calibrate, select 5 points on the inner CeO2 ring with left mouse button and start calibration with right mouse button. The result should be something like
I’ve zoomed in to show that the CeO2 rings are well fitted and don’t overlap any of the more intense steel ones. The calibration results show on the data window
and the console
You should now copy these results to the other image. Use Operations/Copy controls; a popup dialog will appear; select All IMG and OK.
In this step you will select the diffraction rings to be analyzed for strain; it is best to pick a few CeO2 ones as well to confirm that the sample position does not shift during loading. Select the first image (001) and the Stress/Strain tree item. An empty plot (“Strain”) will appear and the initial Stress/Strain data window
Change Sample delta-z to -0.75 since center of the steel sample is that much closer to the detector than the CeO2 calibrant. Then select 2D Powder Image and follow the instruction to add a ring; press a and use the mouse left button to select a ring. Do as many as you like but be sure to select some CeO2 rings as well; it is useful to zoom in to help with the selection. You can control the image display with the Image Controls. Each time you pick a ring, GSAS-II will display (briefly) the Strain plot with the points it found and then show the 2D Powder Image zoomed in where you were looking before your selection. I chose 12 rings. My Strain plot showed
Notice that each ring is plotted in different colors (they are somewhat mixed for the two lines ~2Å! We will fix this next.)
The 2D Powder Image shows the picks as well
And the rings are listed on the Stress/Strain data window; a scroll bar allows easy access to all the entries.
We can now fix the mixing of the two 2Å lines; change the Pixel search range to 5 for both. Each change will cause a refresh of the ring selections; after you are done the Strain plot should look like
We are now ready for the first strain fit; do Operations/Fit stress/strain. Each ring will be fitted to the three strain tensor elements (ε11, ε12 & ε22) that can be determined from a single 2D diffraction ring. The resulting Strain plot now shows curves calculated from the fitted tensor elements; these are very nearly straight lines as expected from an unloaded sample. In particular the austenite 111 line (~2.08Å) is much flatter than the ferrite 200 line (~2.03Å); this reflects the sample history (hot rolled steel). The tensor elements with esds are shown on the console and in the data window
The d-zero ave is the average d-spacing around each ring; this can be used as the reference d-spacing. Each d-zero value for this no load sample can be set to this value; this will suppress any residual stress offset. To update all the d-zero values to the calculated ones do Operations/Update d-zero then repeat Operations/Fit stress/strain. Repeat as needed to make d-zero match d-zero ave for all lines. I got for the no load sample
Finally you want this set of d-zero values to be applied to the image from the loaded sample; do Operations/Copy stress/strain to apply them to the other image.
In this step you are going to fit the strain tensor elements to the steel test sample under an applied load. Do Operations/Fit stress/strain; the data window shows
The console window gives values and esds
I only show the bottom of the listing. The strain plot gives (I zoomed in on just one line; ferrite 211).
When you look at the other lines, you should notice that the ones at ca. 3.13Å, 1.91Å, and 1.63Å remain straight lines; these are from CeO2 and should be unchanged under load.
Again you could save the project with File/Save project on the main GSAS-II data tree menu although it is not needed for any further tutorials. The strain results from each image can be exported as a comma delimited set of values which can easily be read by Microsoft Excel and other spread sheet programs; see Export/Image data as/Strain CSV file.