Density, crystallographic

Key words Macromolecular Complementarity, Docking, Electron Density, Crystallographic Medium Resolution, Critical Points, Genetic Algorithms... 

Figure 7. 5. Time evolution of crystallographic texture [(0002) pole figures] along the axis of an explosively driven, hemispherical, titanium liner [66]. A high density of contours near the center of the circle indicate the c-axes of individual crystals are all normal to liner surface.

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

It is well known that the 0 of a metal depends on the surface crystallographic orientation.6,65,66 In particular, it is well established that 0 increases with the surface atomic density as a consequence of an increase in the surface potential M. More specifically, for metals crystallizing in the face-centered cubic (fee) system, 0 increases in the sequence (110) <(100) <(111) for those crystallizing in the body-centered cubic (bcc) system, in the sequence (111) < (100) <(110) and for the hexagonal close-packed (hep) system, (1120) < (1010) < (0001). 

Eas,o is found to depend on the crystallographic orientation of Ag faces, increasing with the atomic density of the faces. The dependence of Eas0 on the density of broken bonds on the surface of fee metals has been discussed by De Levie426 and Trasatti and Doubova.32 They found that... 

Figure 12(a) shows graphically the dependence of the pzc on the crystallographic orientation of the surface for Ag, Au, and (tentatively) Cu, all three crystallizing in the same fee system. The plots exhibit a typical pattern, with minima and maxima that fall at the same angle for all three metals, and that are correlated with the density of atoms on the given surface. In particular, the pzc is more positive for dense surfaces and more negative for open surfaces. 

Figure 12. (a) Dependence of the potential of zero charge, Eaw0, on the crystallographic orientation for the metals Cu, Ag, and Au, which crystallize in the fee system. From Ref. 32, updated, (b) (pg. 155) Correlation between Eam0 of single-crystal faces of Cu, Ag, and Au, and the density of broken bonds on the surface of fee metals. From Ref. 32, updated. 

Oldfield TJ. Pattern-recognition methods to identify secondary structure within X-ray crystallographic electron-density maps. Acta Cryst. 2002 058 487-93. 

Final structure Fit electron density Solve structure Collect diffraction data Figure 12.1 The crystallographic pipeline. 

The structure was refined by block-diagonal least squares in which carbon and oxygen atoms were modeled with isotropic and then anisotropic thermal parameters. Although many of the hydrogen atom positions were available from difference electron density maps, they were all placed in ideal locations. Final refinement with all hydrogen atoms fixed converged at crystallographic residuals of R=0.061 and R =0.075. 

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