Simulating Powder Diffraction with GSAS-II

While GSAS-II provides an environment for fitting of diffraction data, it can also be used to simulate diffraction experiments, where results are quantitative models for what can be expected, provided that an accurate instrument description is used. Here we demonstrate how a simulation is done for a two-phase mixture with multiple instrument types.

Step 1: Read in Phases

First we will read in two phases, CuCr₂O₄ and CuO from files CuCr2O4.cif and CuO.cif, which can be downloaded from directory https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/.

Create a new project by starting GSAS-II or by using the File/New Project menu item. Then use the Import/Phase/“from CIF file” and select the CuCr2O4.cif for the “Choose Phase input file” dialog window. Click “Ok” and “Yes” in the “Is this the file you want?” confirmation window.  The default Phase name, CuCr2O4 is fine.

Repeat this to read in the second phase: use the Import/Phase/“from CIF file” and select the CuO.cif for the “Choose Phase input file” dialog window. Click “Ok” and “Yes” in the “Is this the file you want?” confirmation window.  The default Phase name, CuO is also fine.

Step 2: Create Simulation Histograms

Part A: Use the Import/Powder Data/“Simulate a dataset” menu item (at bottom of menu list) to create a simulation (dummy) histogram. The program then requests an instrument parameter file name. Click Cancel and a list of default instrument parameters are then displayed, as shown to the right. Select the APS 11-BM instrument listing and press OK.

A dialog window is then displayed that with the name for the histogram, the range of data and the step size. Below, note that the name and start angle have been changed from the defaults. Then press OK and the “Add to phase(s)” dialog is displayed.

Finally, in this dialog, we need to indicate which phases are linked with this histogram. We want to include both in the simulation, so use the “Set All” button (or select each phase) and press OK.

Note that a new histogram is now added to the data tree, as below. (Note the "Edit range" button which can be used to change the values entered on the previous dialog).

Part B: Again use the Import/Powder Data/“Simulate a dataset” menu item (at bottom of menu list) to create a simulation (dummy) histogram. This time when the program then requests an instrument parameter file name, supply file BT1.prm, which can also be downloaded from directory https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/.

Click Open and a dialog opens for the dataset name and range for this histogram. Change the range to 1 to 120 degrees with 0.025 degree steps and optionally change the name, as below.

Press OK and then the “Add to phase(s)” dialog is displayed. As before, add link both phases to this histogram.  At this point a second histogram is shown in the data tree:

It is important to understand how the scale factor (found each histogram's Sample Parameters tree entry) and phase fractions (found in each phase's data tab) are used in GSAS-II. The scattering contribution for each phase is set from the product of the histogram scale factor multiplied by the phase fraction for each phase in that histogram which multiplies the scattering power of each atom in the unit cell. This means that the phase fraction effectively represents the relative number of unit cells present for each phase. Note that after reading in the two phases in the previous step, their phase fractions default to 1 for each. The contents of each phase are shown on the General tab. Note that the unit cell contents for each phase are Cu₈Cr₁₆O₃₂ (1852.3 g/mol) and Cu₄O₄ (318.2 g/mol), with equal numbers of unit cells, the mass (or equivalently weight) fractions will be 1852.3/(318.2+1852.3)=85.3% and 318.2/(318.2+1852.3)=14.7%. This can be confirmed on the Data for each phase, as below.

For this tutorial, we will choose to set the mass fractions to give 90% CuCr₂O₄ and 10% CuO, so 90/1852.3=0.04859 and 10/318.2=0.03143. Equivalently, we can normalize the phase fractions sum to 1 or so that either phase fraction is 1. We will use 1 for CuCr₂O₄, and 10*1852.3/(318.2*90)=0.6468 for CuO. Enter 0.6468 for the CuO Phase fraction.  When the mouse is moved out of the box, the mass fraction to be recomputed and appears as 10%, as expected:

This must be set for both histograms. Clicking on the second histogram allows that phase fraction to be edited. Even easier is to use the “Edit Phase”/“Copy data” menu item to copy all CuO data settings from histogram 1 to histogram 2. Note that if the CuCr₂O₄ Data tab is selected for either phase, the mass fraction is now shown as 90%.

Step 4: Turn off Optimization

A refinement computation is needed to cause the pattern to be simulated. When a pattern is first simulated, the observed pattern is set to the computed pattern (this can be reset by using the "Edit range" button when the histogram data tree item is selected. This means that it is actually possible to optimize any parameters that are selected to be refined, which can be used to test the sensitivity of different models refined against a simulated dataset. In this case we only need to compute the simulated pattern, so we will turn off optimization by setting the number of cycles to zero. Do this by clicking on the Controls data tree entry and set the Max cycles value to 0 using the pull-down menu:

As discussed earlier, the range of intensities is determined by the histogram scale factor. For x-rays, a histogram scale factor with the default value of 1 produces a reasonable intensity range, but with CW neutrons, a much larger scale factor value is needed to produce a pattern with non-negligible intensity values. Note that GSAS-II adds simulated noise to patterns, so if the scale factor is too small, only random counts are seen. Select the Sample Parameters tree item for the second histogram and change the scale factor to 1000, as below.

Step 6: Simulate the Pattern

Use the Calculate/Refine menu item to compute the simulated pattern. Clicking on the histogram entry in the data tree causes the pattern to be displayed as below. This has the reflection tickmarks and the difference curve located at zero. While both can be dragged to new positions, this is hard to do when they are obscured by the “observed” and computed patterns. (The observed pattern has been set to the computed pattern with the addition of simulated noise, which is why the difference curve is non-zero.)

A nice trick for resetting the tickmarks to their usual default positions is to press “s” to scale to sqrt(I) and press it again to return to normal scaling, as shown below. These changes in scaling can also be done via the “K” (keyboard) button on the bottom toolbar.

Note that the Commands menu offers menu items for moving the difference curve and tickmarks, as well as using drag and drop. Use of this, as well as using the rescaling graphics toolbar item (the home button indicated by small house on the lower left) allows more fine arrangement of locations. Exporting the plot (using the “floppy disk” button allows the plots below to be created. Note the very big differences in intensities, data range and resolution between the two simulations.