Crystal Structure Model-Assembly Program Using the Monte Carlo and the R-factor Method

Hiroyuki MIURA* and Takeshi KIKUCHI

(Received: February 16, 1999 ; Accepted for publication: August 29, 1999 ; Published on Web: October 20, 1999)

This paper describes a computer program which constructs crystal structure models using the Monte Carlo and the R-factor method from powder X-ray diffraction data. In order to study an unknown crystal structure by the Rietveld method, a correct structure model must be prepared in advance. This is usually very difficult when no information is available about the structure. A program which automatically constructs a crystal structure model of the object material would simplify the task of solving the structure of the powdered material by the Rietveld method. This program, which sets atomic positions by the Monte Carlo method, requires XRD data, cell constants, a space group, a chemical formula, and a Z-number (the number of the formula in a unit cell). Wyckoff positions and coordinates of independent atoms in a unit cell are selected by random numbers, and theoretical XRD data are calculated. The R-factor of the model is calculated from theoretical and observed XRD data. Hundreds of models of a low R value are selected and stored. As atoms of the stored model concentrate in a particular area, search areas are restricted to the vicinity of these atoms, a process which minimizes the total calculation time. Using this program and a personal computer (Pentium 166), the structure of brookite (TiO₂, Z=8) and forsterite (Mg₂SiO₄, Z=4) could be solved within one or two days, which demonstrates that this method is a powerful tool to solve the structure of powder materials.

Keywords: Crystal Structure Analysis, X-ray Powder Diffraction Data, Monte Carlo method, R-factor method, Crystal Structure Model

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