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

Abstract

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 directmethods procedures more robust and for improving the accuracy of the least-squares techniques. The performances of EXTRA [Altomare, Burla, Cascarano, Giacovazzo, Guagliardi, Molitemi & 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 Pawleymethod-based decomposition programs.

Automatic structure determination from powder data withEXPO2004

“…The full-pattern decomposition is performed via the Le Bail et al (1988) algorithm, which has the great advantage that the intensity values can be optimized if additional prior information is available (Altomare, Carrozzini et al, 1996;Altomare, Foadi et al, 1996;Altomare et al, 1998;Carrozzini et al, 1997;Rodriguez-Carvajal, 1990;Estermann et al, 1992). Its main limit is the tendency to equipartition the intensity of strongly overlapped reflections.…”

“…(a) The traditional two-stage method (Altomare, Carrozzini et al, 1996;Lasocha & Schenk, 1997) based on the extraction of the structure-factor amplitudes from the experimental pattern and the application of direct or Patterson methods. (a) The traditional two-stage method (Altomare, Carrozzini et al, 1996;Lasocha & Schenk, 1997) based on the extraction of the structure-factor amplitudes from the experimental pattern and the application of direct or Patterson methods.…”

Solving a Structure in the Reciprocal Space, Real Space and Both by Using the EXPO Software

“…Because of diffraction peak overlap, the accuracy of the extracted moduli is usually poor even if it can be improved by the use of prior information in the Le Bail algorithm [8] in EXPO. Peak overlap can be reduced, but not completely eliminated.…”

“…After that a feasible solution has been attained in the real space, we can go back to the reciprocal space for confirming the SA solution also in the reciprocal space: such an occurrence strengthens the reliability of the SA model, which can be then moved to the final structure refinement step. In EXPO, the information derived in the real space can be suitably exploited in the reciprocal space, by the Le Bail method [8], which is used for extracting the structure factor moduli from the experimental diffraction profile. In absence of additional information, that is in a standard way, the Le Bail formula iterates starting arbitrary integrated intensity values and finally estimates the experimental structure factor moduli, whose goodness mainly depends on the peak overlap level in the pattern.…”

Solving Crystal Structures from Powder Data. IV. The Use of the Patterson Information for Estimating the |F|'s

“…The papers by Altomare, Carrozzini et al (1996), Altomare, Foadi et al (1996) and Carrozzini et al (1997) are referred to as papers I, II and III, respectively.…”