Determining Profile Parameters from a Standard

The goal of this exercise is to determine approximate instrument profile parameters by a quick peak fit to a sample with a lab diffractometer. Ideally, one should use a material or mixture of materials that has peaks over the entire range where you collect data and use a material(s) that have negligible sample broadening (from crystallite size or microstrain). The NIST LaB₆ standards (SRM 660, 660a and 660b) are good choices for this, as it has very little sample broadening and a relatively small number of peaks over a wide angular range, although it would be good to have peaks starting somewhat lower in 2theta.

Note that it is highly recommended to collect reference data to a much higher 2theta angle than here. What is done here serves as an example, and is sufficient only if one will never collect and use data above 70 degrees (unlikely!).

To get started, create a new project in GSAS-II, either by starting the program fresh or using File/New Project.

Step 1: Read in the Diffraction Data

Use Import/Powder Data/from Brucker RAW file to read file LaB6_Jan2018.raw from the Tutorials CWInstDemo/data directory (download from https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/CWInstDemo/data/). After selecting this file, answer yes to “Is this the file you want?”

Step 2: Select Default Instrument Parameters

The next dialog to appear is titled, “Choose inst. Param file for LaB6_Jan2018.raw Scan 1 (or Cancel for default)” since we do not have a set of parameters to read, we must use a default set. Press Cancel.

This raises the default inst parms dialog, as below

Here, choose the first option for CuKa lab data (which is for a standard instrument with Kalpha1 and Kalpha2 radiation) and press OK. A plot of the data will appear as below.

Step 3: Change Data Range.

Note that the data begins at 10 degrees, but the first peak is above 21 degrees, we can simplify the background fitting by changing the data limits. Click on the Limits data tree item, and either change the Tmin value from 10 to 20 or in the plot “drag” the green line to the right to approximately 20 degrees.

Step 4: Add Peaks to Fit

To define peaks, click on the “Peak List” data tree item. Note that as below, the peak list is initially empty.

Move the mouse to any of the data points close to the top of the first peak and click the left mouse button. A line will be drawn through the peak and the position will be added to the peak table and a line marking this is added to the plot, as below.

Repeat this for all 8 peaks in the pattern. Note that if a peak is entered in the wrong place it can be moved by “dragging” it with the mouse, or use a right-click to delete it. Be careful to make sure two peaks are not entered in the same place by accident,.

The peak table appears as:

Step 5: Refine Peak Areas

By default, the peak intensities are flagged as to be varied, but not any of the other parameters. It is wise to refine them all, but we want to make sure the parameters have a chance to converge one step at a time and we should start with only the intensities. Use the Peak Fitting/Peakfit menu item to perform a peak refinement. You will be asked for a name to save the project (enter a name such as peakfit.gpx and press Save). The peaks are then fit, here optimizing only the intensity values. The console window shows the details of the refinement:

The warning at the end is because the default peak parameters describe a peak shape that is significantly sharper than what is actually present for these data; the step size is actually fine. This warning will later go away, but if it did not this would indicate that it would be better to recollect the data with a step size decreased by a factor of 3-4.

Step 6: Refine peak areas and heights

In the peak list window, double click in the refine heading for the peak position flags, this will bring up a dialog that allows all peak positions to be varied.

Select “vary all” and press OK. Now all peak positions and areas will be refined.

Use the Peak Fitting/Peakfit menu item to start peak refinement.

The fit improves significantly, as below, but further improvements are needed.

Step 7: Refine peak areas, heights and widths (optional)

Double-Click on the refine headings for the sigma (Gaussian width) and gamma (Lorentzian width) parameters so that all parameters can be refined. Use the Peak Fitting/Peakfit menu item to start peak refinement. The results in the console window are as below. This is being done here just to see how the individual peaks vary before we fit them with a parametric equation. This step is not necessary, but provides a useful graphical reference to look for any anomalous peaks that one might not want to use.

Step 8: Add more Background terms

Use the zoom feature (magnifying glass) to draw a box around the low intensity data

Looking at the plot (see below), makes it clear that the background is not well fit. Adding more background terms will fix this.

Select the Background tree item and change the number of coefficients to 6, as shown below.

Then return to the Peak List data tree item and use the Peak Fitting/Peakfit menu item to perform a peak refinement. At this point it is instructive to click on the Instrument Parameters data tree item to see a plot of peak widths:

Note that the solid curves here are plots of the profile coefficients from the default instrument parameters (which are unimportant here), but the fits for the individual peaks are shown (in units of Q/delta-Q vs Q), with Lorentzian widths (gamma) in green, Gaussian widths (sigma) in red and their convolution (total broadening) in blue.

Step 9: Refine Profile Parameters

Now, select the profile terms to be refined. Use Gaussian U, V, & W and Lorentzian X & Y (note that Z, which provides constant broadening, independent of Q, is provided as an option, but is rarely if ever needed.)

Note that these U, V & W values will be used to set the Gaussian peak widths for those peaks where sigma is not being refined and likewise X, Y & Z will be used to determine the Lorentzian widths where gamma is not refined for that peak. If we had any peaks that were not consistent with the width of the others, we might choose to continue to refine their sigma & gamma values so they would not affect U, V,…, but here we will refine U, V, W, X & Y against all peaks. Select the Peak List data tree item and remove refinement of sigma & gamma for all peaks by double-clicking on the refine column headers for each and select “N – vary none” so that the table appears as below:

Use the Peak Fitting/Peakfit menu item to perform a peak refinement optimizing U, V, W, X & Y:

Note that the sigma and gamma values are now computed from U, V, & W and X & Y, respectively. The difference curve shows very small deviations.

Note that the background is also quite well fit now.

Step 10: Save the Profile Parameters

So that we can use these profile terms as the starting point for a future refinement, save the profile terms to a file by clicking on the Instrumental Parameters data tree item and use the Operations/Save Profile menu command. Give the file a name that will be helpful for future use (<MyInstrument>20-70deg.instparm might be good) and put this file in the directory(s) where you will keep your data files.

Clicking on the Instrument Parameters data tree item will show the peak widths from U, V, W, X & Y, and also the individual peak widths generated from those values (not very useful). For a more useful plot we refining the individual peak widths independently again, as shown in the next section.

Step 11: Plot Profile Parameters with Individual Peak Widths (optional)

First we stop refining U, V, W, X & Y by clicking on Instrumental Parameters data tree item and turning the refinement flags off.

In the Peak List data tree item, turn on refinement of all individual peak widths (as we did in Step 7)

and use the Peak Fitting/Peakfit menu item to perform a peak refinement optimizing individual peak widths, as before. Returning to the Instrumental Parameters data tree item provides this plot:

The displayed lines and points are as follows, where Lorentzian widths are shown in green, Gaussian widths are in red and their convolution (total broadening) is shown in blue:

· Solid curves: profile terms from original instrument parameter file (here the CuKa lab data defaults). Note since X, Y & Z are zero, there is only Gaussian broadening and the total broadening is exactly the same as the Gaussian so the blue curve hides the red one.

· Dashed curves: these values are generated by U, V & W and X, Y & Z. Note that the broadening from this instrument is significantly greater than the default values.

· Plus signs (points): these are the widths for the individual reflections unconstrained. Note that they agree well with the fitted curves (dashed lines).