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The Rietveld method is the most widely used approach for refining crystal structures from powder diffraction patterns. It requires sufficiently accurate structure models and user skill. A method is described which is often able to complete and refine a structure model by using an automatic least-squares procedure applicable to reflection integrated intensities. A weighting scheme has been devised that is capable of taking into account the lower accuracy of the estimates of the overlapping reflections.

New procedures have been introduced in EXPO2004 (Altomare, A., Caliandro, R., Camalli, M., Cuocci, C., da Silva, I., Giacovazzo, C., Moliterni, A. G. G. & Rizzi, R. , J. Appl. Cryst. Submitted) aiming at making the solution process more straightforward, particularly for cases very resistant to the ab-initio approach.

The ab-initio crystal structure solution by powder diffraction data requires great efforts because of the collapse of the experimental information onto the one dimensional 2θ axis of the pattern. Different strategies will be described aiming at improving the process of extraction of the integrated intensities from the experimental pattern in order to make more straightforward the structure solution process by direct methods. Particular attention will be devoted to the EXPO program. Some of its performance will be analysed and results will be shown.

Ab initiocrystal structure solution from powder diffraction data can be attained by means of the two-stage method: first the integrated intensities of individual reflections are extracted from the experimental profile; then the extracted intensities are processed by direct methods to recover their phase. The efficiency of the direct-methods process is strongly affected by the accuracy of the extracted intensities and this is a serious drawback for the solution of organic compounds, where the presence of light atoms leads to a rapid decrease of the scattering at high angles. In order to overcome this problem, a procedure is proposed which generates a set of different intensity partitions for groups of reflections in strong overlap: the resulting decomposition trials are supplied to direct methods. The procedure is able to reduce the phase error at the end of the phasing process by up to 50° and enables the solution of organic structures with data resolution not worse than 1.5 Å in a reasonable computing time. The procedure has been implemented in theEXPOprogram, which makes use of the Le Bail extraction algorithm.

C17H28N2O3 ,t riclinic, P1 (no. 2), a =6 .098 A, b =1 1.703 A, c =1 2.721 A, 2 =8 1.95°, 0 =8 0.11°, / =7 7.35°, V =8 67.7 A 3 , Z =2 , Rgt(F) =0 .059, wRref(F 2 ) =0 .139, T =2 93 K. Source of material The title compound was synthesized according to [1] by treatment of 2-lithiated 2-alkyl-2-oxazoline with N-cumyl-2-p-metoxyphenylnitrone and subsequent reduction. To ap re-cooled ($78 °C) solution of alkyloxazoline (1.2 mmol) in 10 ml of THF under N2 was added s-BuLi (solution in cyclohexane, 1.4 M, 1.3 mmol). The resulting orange mixture was stirred for 15 min at this temperature before adding dropwise as olution of nitrone (THF, 5.0 ml, 1.0 mmol). Then, the reaction mixture was warmed up to room temperature, quenched with sat. aq. NH4Cl, poured into 20 ml of saturated brine, extracted with Et2 O( 30 ml), dried Na2SO4 and the solvent evaporated under reduced pressure. The crude mixture was filtered on silica gel (petroleum ether :A cOEt =8:2 ) to obtain am ixture [2] of equilibrating N-cumyl-3,3-dimethyl-8p-metoxyphenyl-9-methyl-9-ethyl-1,6-dioxa-4,7-diazaspiro[4,4]nonane and N-cumyl-2-methyl-1-p-metoxy-phenyl-2-(oxazolin-2-yl)hydroxylamine. To as olution of the mixture (0.5 mmol) in MeOH (5 ml) Pd on charcoal (10 %, w/w )w as added and the resulting mixture hydrogenated in "Buchi Mini Clave" apparatus at 10 bar overnight. Then the solution was filtered on celite pad and the solvent evaporated in vacuo affording the title compound as colorless crystals of inseparable mixture of diastereo-isomers with ratio 89/11 (after crystallization from hexane/Et2O, dr =9 5/5). The structure was confirmed by 1 H NMR, 13 CN MR, MS and IR, the data are available in the CIF. Experimental details Hydrogen atoms at nitrogen N1 were located by ad ifference Fourier and fixed during the refinement. Others Ha toms were geometrically positioned and included in the final refinement using the riding model approximation, with methyl d(C—H) =0 .96 A , methine d(C—H) =0 .98 A,m ethylene d(C—H) =0 .97 A,a romatic d(C—H) =0 .93 A, d(O—H) =0 .82 A, d(N—H) =0 .86 A and Uiso(H) =1 .5 Ueq for methylic groups, Uiso(H) =1 .2 Ueq for others groups. The large Rv alues are due to the poor quality of crystal. Solvent molecules were not found in the structure.

The joint probability distribution function method has been developed in P1¯ for reflections with rational indices. The positional atomic parameters are considered to be the primitive random variables, uniformly distributed in the interval (0, 1), while the reflection indices are kept fixed. Owing to the rationality of the indices, distributions like P(F p 1 , F p 2 ) are found to be useful for phasing purposes, where p 1 and p 2 are any pair of vectorial indices. A variety of conditional distributions like P(|F p 1 | | |F p 2 |), P(|F p 1 | |F p 2 ), P(\varphi_{{\bf p}_1}|\,|F_{{\bf p}_1}|, F_{{\bf p}_2}) are derived, which are able to estimate the modulus and phase of F p 1 given the modulus and/or phase of F p 2 . The method has been generalized to handle the joint probability distribution of any set of structure factors, i.e. the distributions P(F 1, F 2,…, F n+1), P(|F 1| |F 2,…, F n+1) and P(\varphi1| |F|1, F 2,…, F_{n+1}) have been obtained. Some practical tests prove the efficiency of the method.

Various authors have tried to exploit Harker sections to estimate the moduli and the phases of the one-phase structure seminvariants (s.s.) of the first rank from single crystal data. The estimates are sufficiently accurate if false Harker peaks are absent; therefore, if some heavy atoms are present in the structure, and this last is not too complex, the results are quite satisfactory. Such a technique has never been applied, until now, to powder data. In this case there is the basic advantage that the average crystal structure size is relatively small; on the contrary the unavoidable distortion of the Patterson map, due to the fact that this is calculated by using distorted structure factor magnitudes, is often severe.

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.

EXPOis the integration of two programs,EXTRAandSIRPOW.92, the first devoted to full powder pattern decomposition and the second to the solution and refinement of crystal structures. The program is able to exploit the prior information obtained during the crystal structure solution process for improving the classical decomposition.EXPOalso allows preliminary cycles of Rietveld refinement.

Recently devised techniques for powder pattern decomposition will be discussed: they exploit the supplementary information available during the phasing process, so improving by far the pattern decomposition and the crystal structure solution process. A new package, EXPO, integrates EXTRA [1], a Le Bail-based [2] full pattern decomposition program, with a new version of SIRPOW.92 [3], a direct methods package optimized for powder data. Different ways of combining various kinds of structural information will be discussed and some applications to test structures will be presented.

Decomposition programs of powder patterns play a basic role for crystal structure solution from powder data. Indeed, they provide the structure-factor ampli- tudes to which direct or Patterson methods can be applied. The decomposition process is not always satisfactory: large errors in the estimates frequently frustrate any attempt to solve crystal structures. This paper describes a probabilistic method that, integrated with the Le Bail algorithm, is able to improve amplitude estimates. The method uses triplet-invariant distribution functions, from which marginal distributions estimating structure-factor moduli were derived.

In direct procedures for crystal structure solution from powder data, information on the location and orientation of a molecular fragment may readily become available. Such information may be used retrospectively to improve the powder-pattern decomposition, with favourable effects on the phasing process. A method is described by which accurate estimation of a large number of structure-factor moduli is possible by exploiting the prior partial structural information.