An indexing algorithm independent of peak position extraction for X-ray powder diffraction patterns

Lattice parameter determination from X-ray powder diffraction patterns, called indexing, invariably requires the extraction of peak positions which are then used by indexing algorithms that are peak position dependent. The success of these algorithms depends on the accuracy of the extracted peak positions. Peak positions that do not overlap significantly with nearby peaks can be readily determined with great accuracy. However, in heavily overlapped regions it is difficult to determine the number of peaks and even more difficult to determine the peak positions accurately. This paper describes a new indexing algorithm, Lp-Search, that is implemented in the computer program TOPAS Version 7 (Bruker AXS, Karlsruhe, Germany). Lp-Search does not require peak position extraction nor does it require knowledge of the number of peaks present. Lp-Search combines Monte Carlo searches of lattice parameter space with a Pawley refinement used at the end of each search. Critical to the success of the Monte Carlo search is a new figure of merit function which allows the parameter space to be searched efficiently. Lp-Search has proved to be effective for patterns with heavily overlapped peaks; monoclinic to cubic lattices are successfully indexed in a matter of seconds and triclinic lattices within a minute or two. Diffraction patterns spanning a limited range, such that 30–40 peaks of the highest d spacing peaks are omitted, can be successfully indexed; this demonstrates the robust nature of Lp-Search.