Computer Programs for Indexing X-ray Powder Patterns

Abstract

Fortran Programs were prepared for indexing X-ray powder patterns. These programs can also give lattice constants and possible space groups. The algorithm is as follows. Assuming a diffraction group, possible reflection indices were selected by the extinction rule, and were compared with the peaks of the powder pattern. If more than a definit number of peaks have been assigned to their reflection indices, the indexing is considered to be successful for the diffraction group. Similar procedures were repeated for other diffraction groups. Because it is not necessary for every peak to be corresponded to the indices, these programs can be used in case some of the peaks were missed and/or extraneous peaks, such as those from impurities, were included. In Fig. 1 and Fig. 2 were shown the flow charts of these programs.
There were four programs, viz. programs for the cubic system, for the hexagonal and the trigonal systems, for the tetragonal system, and for the orthorhombic system. The numbers of the Fortran statements were 494 for the cubic system, 774 for the hexagonal and the trigonal systems, 814 for the tetragonal system, and 821 for the orthorhombic system. The total memory sizes were about 43 kilo-bytes, 66 kilo-bytes, 78 kilo-bytes, and 168 kilo-bytes respectively, on the FACOM M200 computer in Data Processing Center, Kyoto University.
The diffraction patterns of the powder of sodium chloride (space group Fm 3 m, diffraction group F*3*-1), α-alumina(R3c, R*C-1), rutile (P4₂/mnm, P4/*N-*1), barium carbonate (Pmcn, PNA*-1), and forsterite (Pbnm, PNA*-1) were processed. In Table 3 and Table 5 are given examples of the input data and the results with the running time on the FACOM M200 computer. In Table 4, the output of the Case 1 in Table 3 is presented, where it is indicated that the peaks of 1.1.3., 3.3.3./1.1.5., and 1.3.5. were missed and the peak of 2θ =95.00 was extraneous. The results show that these programs were practical.