The use of error-correcting codes for the decomposition of a powder diffraction pattern

The decomposition of a powder diffraction pattern consists of the extraction of the intensities of the individual reflections from the experimental profile. The process is crucial for structure determination from powder diffraction data, but its accuracy is limited by the intrinsic peak overlap. A substantial improvement is achieved by considering clusters of reflections in strong overlap and partitioning in a systematic way the total intensity of each cluster among the constituent reflections. In this paper, error-correcting codes are used to explore the set of decomposition trials obtained by combining the partitions of various clusters of overlapping reflections. Linear ternary codes resulting from modifications of the Hamming codes [13, 10] and [40, 36] have been considered as the most suited for the present problem. They have been included in the EXPO program via their generator matrices. Tests on a set of experimental powder patterns show that an efficient decomposition procedure consists of performing only 27 decomposition trials, determined as the codewords of an [ndoub, 3] code, where ndoub is the number of doublets of strong overlapping reflections found in the experimental profile. This allows a reduction in the number of trials, thus processing about 2% of the number used in a previous design of the same procedure, leading to a reduction of the total execution time by nearly the same amount.