Bayesian approach to powder phase identification

Abstract

Identification of unknown materials using X-ray powder diffraction patterns is a commonly used and well established technique with a number of proved implementations. Generally, qualitative phase analysis of X-ray diffraction data includes ranking of candidate phases on the basis of similarity of their diffraction patterns to the measured one. A standard strategy of such a ranking by algorithmization of manual search criteria may become inconvenient for modification and adaptation for problems that are not supported by our intuition. Here, the problem of providing physically grounded expressions for candidate phase ranking is addressed. The approach is based on calculation of Bayesian posterior probabilities of the phases' presence in the sample. The choice of the expressions for the prior probabilities for deviations of phases' diffraction patterns from database entries determines the degree of physical detailing and may be made according to the specifics of the problem being solved. It is shown that even for simple exponential expressions for prior probabilities the approach identifies the phases for IUCr round robin cases correctly, as well as ensuring sufficient robustness of the results with respect to diffraction peak shifts and intensity variations.