Crystal Structure Solution from Powder X-ray Diffraction Data: The Development of Monte Carlo Methods To Solve the Crystal Structure of the γ-Phase of 3-Chloro-trans-cinnamic Acid

Abstract

Many important crystalline materials do not form single crystals of sufficient size and/or quality for single-crystal diffraction studies, and in such cases it is essential that the crystal structure can be solved from powder diffraction data; however, there are many difficulties associated with solving crystal structures, ab initio, from powder diffraction data. In this paper, we report the successful application of a Monte Carlo technique to solve the (previously unknown) crystal structure of the γ-phase of 3-chloro-trans-cinnamic acid from powder X-ray diffraction data. The “structural fragment” used in the Monte Carlo calculation comprised a rigid trans-cinnamic acid molecule (with the chlorine and hydrogen atoms omitted) with its oxygen atoms at a fixed distance from the crystallographic center of symmetry, and with the center of symmetry lying in the molecular plane. The structural fragment was rotated by a random angular displacement around a random axis constrained to pass through the center of symmetry. The “correct” position of this structural fragment was discriminated readily (on the basis of the agreement between experimental and calculated powder X-ray diffractograms) from “wrong” positions sampled during the Monte Carlo calculation, and the “correct” position was then used as the initial structural model in Rietveld refinement and difference Fourier calculations. The paper concludes with a discussion of general considerations relating to the application of the Monte Carlo method for crystal structure solution from powder diffraction data.