Figure-of-Merit Calculation

As described in the "Match! Basics" and in the "Search-Match Basics" chapters, the numeric value on which the complete search-match procedure is based is the so-called "figure-of-merit" (FoM), a numerical value describing the quality of the agreement between a certain reference database pattern and the pattern of the unknown sample.

The calculation of the figure-of-merit is to a large degree based on the peaks found in the unknown sample's diffraction pattern. In a first step, Match! tries to correlate the database pattern's peaks to the peaks in the unknown sample's pattern. Depending on the command used to run the search-match, Match! will either try to correlate all peaks (menu command "Search/Search-Match", shortcut <Ctrl+M>) or the marked peaks only (menu command "Search/Search-Match (marked peaks only)"; shortcut <Ctrl+Shift+M>). Afterwards, it calculates the FoM as a weighted sum of a variety of different pattern agreement criteria:

Depending on the kind of problem, some of these factors should be weighted to a larger or smaller degree. For instance, the "difference between the number of correlated peaks and the total number of peaks in the unknown pattern" favours entries which cover as much of the unknown pattern's peaks as possible, thus favouring single phases. The corresponding weighting factor should be reduced if the possibility that the unknown sample contains more than a single phase cannot be excluded. The search-match options chapter describes how this can be done.

Note: The weighting factors for the agreement criteria described above cannot be adjusted directly by the user; however, the individual weighting factors are calculated internally from the values of the search-match options and parameters adjusted by the user.