This tutorial describes the basic steps required to perform a simple quantitative analysis by manually configuring the refinable model parameters. The diffraction data comes from the IUCR CPD Round Robin on Quantitative Phase Analysis (sample 1-e).
First of all, make sure to download the ReX package and follow the installation instructions to get started. Start the program by double clicking on the ReX executable. Starting from version 0.9.3, a welcome panel appears instead on program startup:
In our case, we want to choose the “Open Project” button, which will allow us to load the instrument calibration. To do so, locate the cpd-qa folder in the ReX examples archive and open the “cpd-calibration.rxp” project file. The instrument calibration will be loaded as well as a basic analysis setup, consisting of the calibrated Instrument model, an empty sample model, an empty dataset as well as a default powder diffraction analysis:
In older program versions (< 0.9.3), no welcome screen appears on startup and the program preloads a default analysis setup; in this case, you may load “cpd-calibration.rxp” file by just clicking on the Load Project button on the main toolbar, obtaining a a totally equivalent project configuration.
Next, import the diffraction pattern cpd-1e.xy located in the cpd-qa folder by selecting the “File->Load Data” menu item from the application menu; a confirmation dialog will appear, asking if you want to add the pattern to the active dataset or create a new one; simply click “OK” to accept the default:
Please note that you may also import the data by directly selecting the Dataset node in the project tree view and clicking the “Load Experimental Data” command from the context menu, or even dropping supported powder diffraction data files on the dataset plot view. In either case, the imported powder pattern will be displayed in the plot view.
To better visualize the details in the high angle region of the pattern, it might be convenient to change the scale of the y plot axis to display the squared roots of the intensity counts, if not already configured so. To do so, select the “Y axis scale” menu located on the top of the dataset plot view and choose the “square root” option; the plot view is updated accordingly.
Next, we are going to slightly reduce the active computation range of the pattern. Make sure the Properties view is visible, by expanding the parent dataset object in the project tree and selecting the cpd-1e pattern:
The active pattern data interval is displayed in the properties view.
In the “Used” data subpanel, type 20 and 120 for the X min and X max values, respectively. The dataset plot gets updated accordingly (you may need to click on the pattern or the dataset items in the project tree for the plot to fully update).
At this point, we are going to complete the definition of the diffraction model by loading the three crystal phases contained in the sample (which are known from the Round Robin sample description), namely Al2O3, CaF2 and ZnO. To do so, right click on the “Sample” object in the project tree; select the “Load Phase” item from the popup menu which shows up.
From the cpd-qa tutorial directory select the three cif files corresponding to the three crystallographic phases (Al2O3.cif, CaF2.cif and ZnO). In alternative, you may just drag and drop the files on the Sample node or in the sample composition panel visible in the Properties view. When more than one structure file is selected, a dialog box will appear with the list of the imported crystal structures; in this case, simply select all the structures and click OK. Expand the Sample object in the project tree to make sure the three phases have been correctly loaded in the sample model.
Before proceeding into the actual analysis, let’s check that the same is correctly configured by clicking on the “Analysis (Powder Diffraction)” node located at the end of the project tree; in particular, make sure that the “Data” combo box at the end of the Setup options group has the CPD-1E pattern selected.
Now click on the “Update model” button located on the main program toolbar. If the button is grayed out, check that the analysis is configured correctly as described in the previous paragraph (you may need to click the analysis node once more). The plot window is updated with the predicted diffraction pattern (in black), the error bar (violet) and the reflection marks at the bottom.
In the first step of the quantitative analysis we are going to refine the background contribution and the phase intensity scale factors. To do so, activate the Parameters view by clicking on top of the “Parameters” tab near the properties view:
The parameters view is context sensitive; this means that its content depends on the active selection in the project tree view. Now, select the Instrument object to display only the instrument-related parameters; scroll down the parameter tree and locate the Background group; enable the refinement of all the coefficients, by clicking on each one or simply checking the parent “Background (polynomial)” object.
We are now going to refine the phase volume fractions. Go to the Parameters view and then select the Sample object on the project tree; the sample-specific parameters are now displayed. For all the three crystal phases, enable the “Volume fraction” parameter refinement; to make things faster, you may filter the parameters view by typing the first letters of the parameter label (“vol..” in our case) in the text box located on the top, and then select the “Check all” command in the edit menu on the right.
Now we can start the refinement by clicking on the “Start optimization” button located on the main toolbar.The refinement should converge after a few iterations, as the Rietveld step configuration panel reporting the figures of merit:
A report window will appear after the refinement displaying all the refined parameter values, which can be exported as a text file. Sample composition can be directly checked by clicking on the Sample item in the Project tree (make sure the Properties view is active):
Also, the plot window refreshed with the updated fit:
The fit has obviously improved with respect to the starting model in terms of background and reflection intensities, however there is still some discrepancy in terms of peak positions, as also hinted by the error plot. Different parameters can be refined with the goal to adapt calculated reflection positions to experimental ones, in particular phases lattice parameters and instrumental errors. In this case, there are strong hints that a sample displacement error is the likely source of the reflection mismatch; this can be taken into account b refining the z position of the sample, located near the middle of the Instrument parameter tree:
Once the Sample position@z parameter has been checked, click again on the Start Optimization button; the refinement should converge in a few iterations, and a considerably better fit should be achieved, both in terms of figures of merit and of visual correspondence between experimental and calculated data.
Also, the sample composition will slightly change according to the updated fitting; in such respect, you may want to experiment a bit with other sample parameters (e.g. crystallite sizes, cell constants) and see how the sample composition is affected.