Solving Crystal Structures from Powder Data. I. The Role of the Prior Information in the Two-Stage Method

The principal limitation of the diffraction methods for crystal structure analysis from powder data is originated by the collapse of the three-dimensional reciprocal space into the one dimension of the powder diffraction pattern. The degradation of the information can make difficult even the solution of small crystal structures and can generate inefficiencies in the least-squares methods devoted to crystal structure refinement. In this paper, the current two-stage procedures, the first stage dedicated to powder-pattern decomposition and the second to direct phasing of powder data, are analysed. It is shown that in the first stage such procedures disregard a large amount of information that can become available during the process of crystal structure solution and analysis. The use of such information is essential for making direct-methods procedures more robust and for improving the accuracy of the least-squares techniques. The performances of EXTRA [Altomare, Burla, Cascarano, Giacovazzo, Guagliardi, Moliterni & Polidori (1995). J. Appl. Cryst. 28, 842-846], a program for full-pattern decomposition based on the Le Bail algorithm, and of SIRPOW.92 [Altomare, Burla, Cascarano, Giacovazzo, Guagliardi, Polidori & Camalli (1994). J. Appl. Cryst. 27, 435-436], a direct-methods program optimized for powder data, are discussed in order to offer to the reader a logical pathway for the analysis of the traditional techniques and for the proposition of a new approach. It is shown that pattern-decomposition programs based on the Le Bail algorithm are able to exploit the prior information in a more effective way than Pawley-method-based decomposition programs.