A new program has been developed for ab initio crystal structure determination from powder diffraction data (X-ray and neutron). It uses global-optimization algorithms to solve the structure by performing trials in direct space. It is a modular program, capable of using several criteria for evaluating each trial configuration (e.g. multi-pattern). It is also modular in the description of the crystal content, with the possibility of describing building blocks in the sample, such as polyhedra or molecules, and with automatic adaptive handling of special positions and sharing of identical atoms between neighbouring building blocks. It can therefore find the correct structure without any assumption about the connectivity of the building blocks and is suitable for any kind of material. Several optimization algorithms (simulated annealing, parallel tempering) are available, with the possibility of choosing the convergence criterion as a combination of available cost functions. This program is freely available for Linux and Windows platforms; it is also fully `open source', which, combined with an object-oriented design and a complete developer documentation, ensures its future evolution.

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FOX, `free objects for crystallography': a modular approach to ab initio structure determination from powder diffraction

Techniques and methods to facilitate the solution of structures by simulated annealing have been developed from the starting point of a space group and lattice parameters. The simulated-annealing control parameters have been systematically investigated and optimum values characterized and determined. Most significant is the inclusion of electrostatic-potential penalty functions in a non-linear least-squares Rietveld refinement procedure. The long-range electrostatic potentials are calculated using a general real-space summation which can be used for all space groups. In addition, a general weighting scheme for penalty functions negates the need to determine weighting schemes experimentally. Also investigated and improved is the non-linear least-squares minimization procedure used in the refinement of structural parameters. The behaviour and success of the techniques have been tested on X-ray diffraction powder data against the known structures of AlVO4 in P1 with 18 atoms in the asymmetric unit, K2HCr2AsO10 in P31 with 15 atoms in the asymmetric unit excluding hydrogen, and [Co(NH3)5CO3]NO3.H2O in P121 with 15 atoms in the asymmetric unit excluding hydrogen.

Whole-profile structure solution from powder diffraction data using simulated annealing

Advances made over the past decade in structure determination from powder diffraction data are reviewed with particular emphasis on algorithmic developments and the successes and limitations of the technique. While global optimization methods have been successful in the solution of molecular crystal structures, new methods are required to make the solution of inorganic crystal structures more routine. The use of complementary techniques such as NMR to assist structure solution is discussed and the potential for the combined use of X-ray and neutron diffraction data for structure verification is explored. Structures that have proved difficult to solve from powder diffraction data are reviewed and the limitations of structure determination from powder diffraction data are discussed. Furthermore, the prospects of solving small protein crystal structures over the next decade are assessed.

Structure determination from powder diffraction data

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Structure determination from powder diffraction data.

X-Cell is a novel indexing algorithm that makes explicit use of systematic absences to search for possible indexing solutions from cells with low numbers of calculated reflections to cells with high numbers of reflections. Space groups with the same pattern of systematic absences are grouped together in powder extinction classes, and for a given peak number range an independent search is carried out in each powder extinction class. The method has the advantage that the correct cell is likely to be found before the rapid increase of possible solutions slows down the search significantly. A successive dichotomy approach is used to establish a complete list of all possible indexing solutions. The dichotomy procedure is combined with a search for the zero-point shift of the diffraction pattern, and impurity peaks can be dealt with by allowing for a user-defined portion of unindexed reflections. To rank indexing solutions with varying numbers of unindexed reflections, a new figure of merit is introduced that takes into account the highest level of agreement typically obtained for completely incorrect unit cells. The indexing of long and flat unit cells is facilitated by the possibility to search for rows or zones in reciprocal space first and then to use the lattice parameters of the dominant row or zone in the unit-cell search. The main advantages of X-Cell are robustness and completeness, as demonstrated by a validation study on a variety of compounds. The dominant phase of phase mixtures can be indexed in the presence of up to 50% of impurity peaks if high-quality synchrotron data are available.

X-Cell: a novel indexing algorithm for routine tasks and difficult cases

A new direct-space method for ab initio solution of crystal structures from powder diffraction diagrams is presented. The approach consists of a combined global optimization (`Pareto optimization') of the difference between the calculated and the measured diffraction pattern and of the potential energy of the system. This concept has been tested successfully on a large variety of ionic and intermetallic compounds.

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Combined method for ab initio structure solution from powder diffraction data

A new method is presented for the study of the structure of the energy hypersurface of continuous systems. This so-called threshold algorithm is an adaptation of the `lid method' introduced by Sibani and co-workers in 1993 (Sibani P et al 1993 Europhys. Lett. 22 479 - 85) for the investigation of discrete energy landscapes. The algorithm produces an estimate of the local densities of states near deep-lying local minima of the potential energy of the system together with the barrier heights around these minima. This allows the computation of, for example, specific heats, the estimation of the kinetic stability of configurations that represent metastable minima of the potential energy, and the description of the relaxation behaviour of the system. As an example, a two-dimensional neon crystal is studied, where for example the calculated specific heat is found to agree with the experimental values of the three-dimensional case scaled to two dimensions.

Studying the energy hypersurface of continuous systems - the threshold algorithm

The structures of four different Ba-silicate glasses were analysed applying a broad spectrum of diffraction and spectroscopic methods, atomic force microscopy and computer simulations. This collaborative study offers new insights into the influence of the network modifier BaO. 3 at.% carbon were incorporated into two of the glasses with the intention to obtain additional information about the effect of partial substitution of carbon for oxygen on the considered structures. A structure model for Ba-silicate glasses with compositions close to BaSi 2 O 5 is discussed that differs with respect to other models proposed in previous studies. We propose that [SiO 4 ] tetrahedra do not exclusively form six-membered rings, but also considerable numbers of smaller rings arranged in (slightly) folded layers which alternate with barium layers and/or barium chains. Additionally, the occurrence of tetrahedral chains, possibly isolated rings and of regions in which the [SiO 4 ] tetrahedra form a silica-like network is assumed.

Structure analyses of Ba-silicate glasses

Using global optimization methods (Simulated Annealing, Quench, Gradient Descent) possible structures of crystals consisting of binary combinations of the four considered noble gases Ne, Ar, Kr and Xe have been investigated. The computer simulations showed that in all instances they should crystallize either in separate phases of the pure noble gases or in a shared close-packed structure. No other structure types occurred among the optimal configurations. Phase separation was observed in all systems containing Ne and in the system Ar/Xc. Mixing Ar and Kr led to a random distribution of the two species on the sites of a close-packed structure, i.e. to a solid solution. This corresponds to experimental observations.

H. Putz

Papers

Combined method for ab initio structure solution from powder diffraction data

Studying the energy hypersurface of continuous systems - the threshold algorithm

Structure analyses of Ba-silicate glasses

Strukturvorhersage von Kristallen aus binären Edelgasgemischen mit globalen und lokalen Optimierungsmethoden