Structure solution from powder diffraction data

Model building remains a useful technique for situations where the data are not amenable to solution in any other way, and for which existing related crystal structures can be used as a starting point. This usually happens because of a combination of structural complexity and poor data quality. For recent examples of this in the structure solution of polymethylene chains see Dorset [21] and [22]. It is interesting to note that model building methods for which there is no prior information are usually unsuccessful because the data are too insensitive to the atomic coordinates. This means that the recent advances in structure solution from powder diffraction data (David et al. [23]) in which a model is translated and rotated in a unit cell and in which the torsional degrees of freedom are also sampled by rotating around bonds which are torsionally free will be difficult to apply to structure solution with electron data. 

In general, structure solution from powder XRD data has a good chance of success only if the experimental powder XRD pattern contains reliable information on the intrinsic relative intensities of the diffraction maxima, which requires that there is no preferred orientation in the powder sample. Preferred orientation arises when the crystallites in the powder sample have a nonrandom distribution of orientations, and this effect can be particularly severe when the crystal morphology is strongly anisotropic (e.g. long needles or flat plates). When a powder sample exhibits preferred orientation, the measured relative peak intensities differ from the intrinsic relative diffraction intensities, limiting the prospects for determining reliable structural information from the powder XRD pattern. In order to circumvent this... 

Crystal Structure Solution from Powder Diffraction Data Using ... 

In this article we focus on fundamental aspects of our implementation of the GA method for structure solution from powder diffraction data (Sect. 3.2), highlighting some examples of the application of this method (Sect. 3.3). 

In view of the advantages just described, the Lamarckian GA method incorporating local minimization of R is now our standard approach for tackling structure solution from powder diffraction data. 

We note that a figure-of-merit with fixed weighting parameter has been employed previously [85] in structure solution from powder diffraction data, although the figure-of-merit used in that paper differs in several respects from G(T) defined here. The figure-of-merit used in Ref. [85] did not consider normalized energy and normalized R-factor functions, and the R-factor was based on the use of integrated peak intensities rather than a whole-profile fit to the powder diffraction pattern. 

As already described, the GA approach has proven very successful as a tool for direct-space crystal structure solution from powder diffraction data. However, there remain many opportunities for optimizing GA methodologies. In this section, we discuss one approach for increasing the power and scope of GA methodologies which takes advantage of modern computational techniques. 

In theory single crystal methods can be effectively used for structure solution from powder diffraction X-ray data. However, in powder diffraction the number of peaks involved are limited, and hence the data-to-parameter ratio is very small, due to the transfer of the three-dimensional data to one dimension, namely, 29. In spite of the inherent shortcomings, conventional crystallographic methods such as Direct, Patterson and maximum entropy methods have been successfully applied to powder diffraction data. The most popular program, which uses reciprocal space methods for stmcture solution is EXPO. ... 

Patterson methods have also been successfiilly used for structure solution from powder diffraction data. By taking advantage of the Patterson function Fi, usefiil information about the crystal structure can be deduced. Compared to Direct methods, Patterson techniques are more suitable for powder diffraction data with lower resolution, and peak overlap causing significant difficulties. The Patterson function can be calculated by using the equation... 

MacLean et al. (2000) have recently smdied the dimorphic behaviour of the pigment precursor ( latent pigment) derivative of 8-VI (R = COOr-but, R = H) (abbreviated DPP-Boc). The latency is due to the thermal decomposition reaction of both polymorphs resulting in the commercially important pigment DPP. The a form of DPP-Boc contains three half molecules in the asymmetric unit (see also Ellern et al. 1994) while the form contains one half molecule per asymmetric unit. Hence, they are easily distinguishable by solid state NMR as well as by X-ray powder diffraction. The crystal structure solution from powder data and Rietveld refinement of both polymorphs is an exemplary smdy demonstrating the potential of these methods in determining the detailed crystal structure of these compounds which are often difficult to crystallize. 

Andreev, Y. G, Lightfoot, P. and Bruce, P. G. (1997). A general Monte Carlo approach to structure solution from powder-diffraction data application to poly(ethylene oxide)3 LiN(S02CF3)2. J. Appl. Cryst., 30, 294-305. [Ill]... 

Putz, H., Schon, J. C. and Jansen, M. (1999). Combined method for ab initio structure solution from powder diffraction data. J. Appl. Crystallogr, 32, 864-70. [Ill] Ramamurthy, V. and Venkatesan, K. (1987). Photochemical reactions of organic crystals. Chem. Rev., 87,433-81. [236]... 

Structure solution from powder diffraction data... 

In the context of this book, structure solution from first principles (also referred to as the ab initio structure determination) means that all crystallographic data, including lattice parameters and symmetry, and the distribution of atoms in the unit cell, are inferred from the analysis of the scattered intensity as a function of Bragg angle, collected during a powder diffraction experiment. Additional information, such as the gravimetric density of a material, its chemical composition, basic physical and chemical properties, may be used as well, when available. 

Below we will examine some practical applications of the theory of kinematical diffraction to solving crystal structures from powder diffraction data. When considering several rational examples in reciprocal space, we shall implicitly assume that the crystal structure of each sample is unknown and that it must be solved based solely on the information that can be obtained directly from a powder diffraction experiment and from a few other, quite basic properties of a polycrystalline material. The solution of a number of crystal structures in direct space will be based on the previously known structural data and supported by the results of powder diffraction analysis, such as unit cell dimensions and symmetry. 

K.D.M. Harris, R.L. Johnston and B.M. Kariuki, The genetie algorithm Foundations and applications in structure solution from powder diffraction data, Acta Cryst. A54, 632 (1998) K. Shankland, B. David, and T. Csoka, Crystal structure determination from powder difffaetion data by the applieation of a genetie algorithm, Z. Kristallogr. 212, 550 (1997). 

A.A. Coelho, Whole-profile structure solution from powder diffraction data using simulated annealing, J. Appl. Cryst. 33, 899 (2000). 

By solving crystal structures of different classes of materials," we will illustrate only a few of the possible approaches to the ab initio structure solution from powder diffraction data. Whenever possible the structure factors obtained from full pattern decompositions should be used until the coordinates of all atoms are established. In some cases it may be necessary to re-determine individual structure factors based on the nearly completed structural model, especially when locations of lightly scattering atoms are of concern after all strongly scattering species have been correctly positioned in the unit cell. This re-determination may be routinely performed during Rietveld refinement and will be briefly discussed in Chapter 7. 

Putz H, Schon JC, Jansen M (1999) Combined method for ab initio structure solution from powder diffraction data. J Appl Crystallogr 32 864-870... 

The application of DM to powder data requires the previous application of a full pattern decomposition procedure (see Chapter 5) in the following we will suppose that single diffraction intensities are available for each reflection in the measured 26 range. Owing to the peak overlap the estimates of the diffraction moduli will be affected by unavoidable errors this weakens the efficiency of DM (naively, wrong moduli will produce wrong phases), and still today makes crystal structure solution from powder data a challenge. 

Two research groups have independently introduced the GA technique for structural solution from powder diffraction data Kariuki et al and Shankland et al They both use the following strategy ... 

Endeavour Combined Method for Ab initio Structure Solution from Powder Diffraction Data, H. Putz, J. C. Schoen, M. Jansen, J. Appl. Crystallogr., 1999, 32, 864 870 Direct space and energy minimization... 

Pretsch, 1994 Xiao and Williams, 1994) uses genetic algorithms. These methodologies maintain a set of configurational states which are combined and retained or discarded on the basis of a variety of selection criteria. Genetic algorithm based optimization combined with an appropriate energy function has recently been shown to provide reasonable structural models and, indeed, permitted the structure solution from X-ray powder diffraction data of a novel lithium ruthenate compound (Bush et al., 1995), as described in Chapter 1. 

The primary problem in structure solution from the powder x-ray diffraction pattern is the overlap of peaks in the pattern, which leads to severe ambiguities in determining the intensity of individual peaks and consequently the position of the atoms in the structure. High resolution x-ray diffraction patterns, which can be obtained using synchrotron x-radiation, are necessary for accurate structure determinations [92]. In addition to the x-ray diffraction patterns, neuron diffraction data have also been used for structure determination [99]. 

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