Pattern decomposition using Le Bail method


Pattern decomposition aims at obtaining reflection intensities I(hkl) from powder diffraction data. The method is pretty similar to Rietveld refinement, in the sense that it tries to mimic an experimental powder diffraction profile by refining certain parameters of a model (function). However, in contrast to Rietveld refinement, pattern decomposition does not require the availability of full crystal structure data. Instead, it just needs unit cell parameters and maybe the space group (if available) for all phases that are present in the sample. Hence, you can also apply it in cases where no atomic coordinates are available.

This is possible because in pattern decomposition using the Le Bail method the reflection (or peak) intensities I(hkl) are not calculated from the given crystal structure data, but are obtained directly from an iterative partitioning of the experimental intensities according to the intensities calculated from the model.

There are basically three purposes for pattern decomposition:

  1. Obtain reflection intensities I(hkl), e.g. for crystal structure solution
  2. Determine the lowest possible R-factor (or chi2 value) that can be expected from a corresponding Rietveld refinement.
    The background is that in pattern decomposition the I(hkl) values are not constrained by the atomic coordinates. Instead, they can be freely adapted to the experimental peak intensities, in order to mimic them as closely as possible, thus leading to the best possible agreement between calculated and experimental diffraction pattern (lowest possible R-factor).
  3. Verify the space group selection, by comparing the results of two (or even more) calculations in different space groups

Pattern decomposition in Match! using FullProf

For pattern decomposition, Match! uses the well-known Le Bail method, as it is implemented in the Rietveld program FullProf (J. Rodriguez-Carvajal, Physica B 192, 55 (1993)) in its so-called "Profile matching" mode. 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.


Before you start your actual pattern decomposition calculations in Match!, please check the following requirements:

Setting up and running pattern decomposition calculations

Once you have checked the prerequisites mentioned above, you are ready to setup and run pattern decomposition calculations. This is achieved by running the menu command "Tools / Pattern decomposition (Le Bail fit) using FullProf…" or by pressing the corresponding button in the toolbar. This will open the so-called "Parameter Turn-On" dialog (please follow this link for more instructions).

We recommend to refine the following parameters in subsequent refinement calculations (although you can use your own scheme, of course!):

  1. refinement
  2. refinement
  3. refinement
  4. refinement
  5. refinement
  6. refinement
  7. refinement
Just like in Rietveld refinement, try to reduce the R-factor (chi2 value) as much as possible, while selecting only reasonable parameters for refinement.

Results viewing and exporting

When the FullProf refinement 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:

If the peak data of a match list entry result from a pattern decomposition calculation, this is indicated by a "[PD]" in the legend of the pattern graphics.

In order to export the resulting I(hkl) data, please run the menu command "File / Export / Reflection data I(hkl) or |F(hkl)|".

Quantitative analysis

Once a pure 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).

However, if a mixed (Rietveld and pattern decomposition) or a pure pattern decomposition refinement has been performed, the entries where pattern decomposition has been applied are not included in the quantitative analysis (their amounts will be displayed as zero (0.0)). In these cases it is possible to perform a full quantitative analysis if the amounts of these phases are known from other sources: You can enter the known amount(s) manually in the match list, by double-clicking the corresponding "missing" amount value "0.0" in the match list, entering the "true" amount, and finally pressing <Return>. Match! will re-scale the amounts of the remaining phases accordingly.


More information about pattern decomposition and its history can be found e.g. here: