## Rietveld Refinement

### Basics

Before we start: An excellent, quick introduction to Rietveld refinement suitable even for absolute beginners is the very clearly structured document Lesson 5: Rietveld Refinement of Nicola Döbelin's Lecture Handouts.

Rietveld refinement is a tool that tries to model a full powder diffraction profile based on crystal structure data, specimen and instrument effects. This is achieved by introducing certain functions that describe typical phenomena in powder diffraction experiments, like 2theta errors or peak broadening, and by fitting the corresponding parameters afterwards. The parameters are varied using a least-squares procedure, in order to minimize the difference between the calculated and the experimental powder diffraction pattern.

The Rietveld method was first introduced by Hugo Rietveld in 1967 and 1969. Details of the method are available in the literature:

• H.M. Rietveld, Acta Cryst. 22, 151-2 (1967).
• H.M. Rietveld, J. Appl. Cryst. 2, 65-71 (1969).
• R.A. Young (ed.), "The Rietveld Method", International Union of Crystallography, Oxford University Press, New York 1993.

One of the key issues of Rietveld refinement is that the method is rather sensitive to problems and errors in the model, resulting in non-convergence and other issues. Hence, it has become a common agreement for many scientists that a successful phase analysis should be proven by a successful Rietveld refinement converging at low R- and chi2-factors.

In addition, running Rietveld refinements on your diffraction pattern will give you an opportunity to think and learn more about your sample, your experiment and your model. Please take a look at the chapter Some Hints, Tips and Tricks for Rietveld Refinement. Here we give you some advice which important facts you should always keep in mind when running Rietveld refinement calculations, as well as some tips what you can do in case of problems.

### Rietveld refinement in Match! using FullProf

Today a variety of excellent programs for Rietveld refinement are available, so there is little need to invent the wheel again and again. Match! uses the well-known Rietveld program FullProf (J. Rodriguez-Carvajal, Physica B 192, 55 (1993)) to actually perform the calculations. You do not have to interact with FullProf directly though; instead, you can use the Match! user interface to define ("turn-on") the parameters, setup the calculations and evaluate the results.

### Defining the Match!/FullProf connection/path

When you run Match! for the first time, the program tries to automatically determine the path to the FullProf software. If this is not possible, you will be asked if you would like to manually select this path. Finally, if this is not successful (e.g. if you pressed the "Cancel" button), you will be asked if you would like to download and install FullProf from the Crystal Impact web site.

This “checking for FullProf” procedure is carried out only once. If there is no valid path to FullProf available at its end (e.g. because you have pressed the “Cancel” buttons), you won’t be asked again until you try to run a Rietveld refinement calculation. However, you can download and install FullProf manually later on by selecting the “FullProf download” command from the “Tools” menu. As an alternative, you can define or modify the path to FullProf any time on the Refine tab of the “Options” dialog (which can be opened e.g. from the “Options” menu).

### Setting up and running Rietveld refinement calculations

Once you have defined the path to FullProf, you are ready to setup and run Rietveld refinement calculations from within Match!. This is achieved by opening the so-called "Parameter Turn-On" dialog.

### Results viewing

When the FullProf calculation has finished there are several facilities to view and evaluate the results of a refinement calculation:

First of all, the convergence, the weighted average Bragg R-factor, the final reduced chi2 and the FullProf comment are displayed at the top of the Refine tab on the upper right-hand side of the screen. Below, there are several buttons using which more detailed information is available:

• The View results button displays a table in which you can compare the parameter values before and after the refinement calculation.
• If FullProf has detected correlated parameters during the calculation, you can display them by pressing the “Display correlated parameters” button below.
• To the right, you can display the original FullProf files resulting from the calculation, simply by selecting the file you would like to view in the Display result file combobox. A window will open where you can view and maybe copy the contents of the selected file.
This facility is especially useful if the result of a calculation is not to your satisfaction and you would like to view more details of the calculation.
• Finally, you can copy the original FullProf result files to a user-defined directory by pressing the Save resulting files button. Note that if you do not save the FullProf files using this button, they will be deleted when you open or create a new Match! document!

### Quantitative analysis

Once a Rietveld refinement calculation using FullProf has converged, the amounts of the individual phases resulting from the calculation are copied back into the Match list, so that the results of the quantitative analysis are available there. Hence, the values in the "Quant. (%)" column in the Match list may change when a Rietveld/FullProf calculation has been run successfully (i.e. convergence was reached).