Quantitative analysis

This tutorial describes the basic steps required to perform a simple quantitative analysis. 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. The main application window will appear with the default layout, showing the project view, the properties view and the main data plot.

Next, download the archive containing the tutorial data and decompress it in a folder of your choice. Load the “cpd-calibration.rxp” project file, containing the instrumental calibration, by clicking on the Load Project button on the main toolbar. Next, import the diffraction pattern cpd-1e.xy by right clicking on the “Dataset” object in the project tree view and selecting the “Load Data” command   from the popup menu.


After a confirmation dialog, the imported powder pattern is 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. 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; after expanding the parent dataset object, select 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 tutorial directory load the three cif files corresponding to the three crystallographic phases (Al2O3.cif, CaF2.cif and ZnO). If more than one structure file is selected, a dialog box will open with the list of the loaded crystal structures; in this case, simply click on the “Load all” button. Expand the Sample object in the project tree to make sure the three phases have been correctly loaded in the sample model.

Now click on the “Update model” button  located on the main program toolbar; 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 just a few basic parameters, namely the intensity scale factor, the instrument 2-theta offset and the background contribution. 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; locate the “Scale factor” and “2-theta offset” parameters and enable their refinement by clicking on the corresponding checkboxes:

Then, 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.

Now we can start the refinement by clicking on the “Start optimization” button located on the main toolbar. The analysis panel is automatically displayed; the refinement should converge after a few iterations, and the plot window refreshed with the updated fit.


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.

Once done, click again on the Start Optimization  button; the refinement should converge in about a dozen iterations, and a considerably better fit should be achieved.

Make sure the Properties view is active, then click on the Sample item in the Project tree; the sample composition (both in terms of volume fractions and weight fractions) is displayed.

At this point, the basic analysis procedure is complete. 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.