Direct-space techniques

For stmcture solution by the direct-space approach, the complexity of the stmcture solution problem is dictated largely by the dimensionality of the hypersurface to be explored (i.e. the total number of stmctural variables in the set F) rather than the number of atoms in the asymmetric unit. Thus, the greatest challenges in the application of direct-space techniques arise when the number of stmctural variables is large this situation occurs when there is considerable molecular flexibility (i.e. when the molecular geometry is defined by a large number of variable torsion angles) and/or when there are several independent molecules in the asymmetric unit. 

Macroscopic experiments, both reciprocal-space techniques and direct-space techniques, conclude that the (110) surfaces of Pt, Ir and Au reconstruct to a (1 x 2) structure.30 Several atomic models have been proposed,31 of which the simple missing row model agrees better with various experimental data. In this model every other [110] atomic row is missing from the reconstructed (1 X 1) surface. To transform a (1 x 1)... 

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... 

Direct Methods Direct-Space Techniques Patterson Methods Monte Carlo Simulated Annealing Genetic Algorithm Degree of Freedom Cost Function... 

CO2 hydrate is perhaps one of the best understood clathrate hydrate regarding structural, thermodynamic, as well as other physical properties. Figure 7(a) and (b) show the CO2 molecules with full symmetry in small and large cages in cubic structure I analyzed by the Rietveld refinement with the direct-space technique. In the large cage, the best... 

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