Structure solution direct-space

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. 

In addition to reciprocal and direct space techniques considered in the previous sections, a large variety of approaches may be employed to create a model of the crystal structure in direct space. One of these, i.e. the geometrical method, has been implicitly employed in section 6.9, where the location of a single La atom in the unit cell was established from a simple analysis of the unit cell dimensions and from the availability of low multiplicity sites in the space group symmetry P6/mmm. Here we consider a more complex example, i.e. the solution of several crystal structures occurring in the series of Gd5(SixGei x)4 alloys. These examples illustrate the power of the powder diffraction method in detecting subtle details of the... 

Chowdhury K., Bhattacharya, S. and Mukherjee, M. (2005). Ab initio structure solution of nucleic acids and proteins by direct methods reciprocal-space and real-space approach. /. Appl. Cryst. 38,217-222. 

Keywords Powder diffraction Molecular solids Organic crystals Crystal structure Direct space Structure solution Structure determination... 

Validation Before Direct-Space Structure Solution. 147... 

Techniques for structure solution from powder XRD data can be subdivided into two categories the traditional and direct-space approaches. 

Aspects of validation prior to direct-space structure solution are focused on (1) establishing the correct representation of molecular geometry to be used in the direct-space structure solution calculation and (2) establishing independent evidence for the correct number of molecules in the asymmetric unit. 

A number of oligopeptide structures have been determined from powder XRD data using the direct-space strategy for structure solution. The first example concerns Phe-Gly-Gly-Phe [100], for which the stmcture solution calculation (employing... 

Fig. 12 (a) The molecular fragment (thick lines), comprising half the TDMM molecule, used in the direct-space genetic algorithm stmcture solution calculation from powder XRD data. The arrows indicate the variable torsion angles. The central carbon atom is located on a twofold rotation axis (as indicated), and the other half of the molecule (faint lines) is generated by this symmetry operation, (b) The final refined crystal structure of TDMM, with hydrogen atoms omitted for clarity... 

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. ... 

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