Crystal structure bonding

The circumstances under which intermetallics form were elucidated by the British metallurgist William Hume-Rothery (1899-1968) for compounds between the noble metals and the elements to their right in the periodic table (Hume-Rothery, 1934 Reynolds and Hume-Rothery, 1937). These are now applied to all intermetaUic compounds, in general. The converse to an intermetaUic, a solid solution, is only stable for certain valence-electron count per atom ratios, and with minimal differences in the atomic radii, electronegativities, and crystal structures (bonding preferences) of the pure components. For example, it is a mle-of-thumb that elements with atomic radii differing by more than 15 percent generally have very little solid phase miscibility. 

When there are significant differences in the electronegativities, atomic radii, and/or crystal structures (bonding preferences), between the components, rather than randomly... 

For strongly ionic compounds such as the alkali halides the closed-shell or rare gas approximation to the electronic structure of the ions is extremely accurate. Goldschmidt and Pauling have shown that for such compounds there exist strong correlations between many physical properties (crystal structure, bond lengths, compressibilities, heats of fusion and sublimation, melting and boiling points, solubility) and the ratio p = R of cation univalent radius to anion... 

In certain crystals, e.g. in quartz, there is chirality in the crystal structure. Molecular chirality is possible in compounds which have no chiral carbon atoms and yet possess non-superimposable mirror image structures. Restricted rotation about the C=C = C bonds in an allene abC = C = Cba causes chirality and the existence of two optically active forms (i)... 

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

Try using obvious values for the parameters, such as bond lengths directly from crystal structures. This assumes that no interdependence exists between parameters, but it is a starting point. 

Table 4.14 Spatial Orientation of Common Hybrid Bonds Figure 4.1 Crystal Lattice Types Table 4.15 Crystal Structure...

Fig. 18. Crystal structures of recent clathrate design (a) coordinatoclathrate between host (39) (Fig. 17) and / -butanol (host—guest hydrogen bonding in the shaded area) (b) perspective view of the hehcal inclusion channel formed by diol host (43) (Fig. 17 all except one host molecule are represented...

The pyrimidine ring is virtually flat. Its corrected bond lengths, as determined by a least-squares analysis of the crystal structure data for a unit cell of four molecules, are shown in formula (2) (60AX80), and the bond angles derived from these data show good agreement with those (3) derived by other means (63JCS5893) for comparison, each bond... 

The structure of lumazine has been studied more precisely by X-ray analysis (72AX(B)659). The crystal structure is built up of almost coplanar, hydrogen-bonded dimers of lumazine with the oxygens of the pyrimidine moiety in the keto form and the observed bond distances indicating the pyrazine ring electrons to be delocalized. 

The crystals, or grains, in a polycrystal fit together exactly but their crystal orientations differ (Fig. 10.4). Where they meet, at grain boundaries, the crystal structure is disturbed, but the atomic bonds across the boundary are numerous and strong enough that the boundaries do not usually weaken the material. 

A3) Bond lengths and bond angles vary in protein crystal structures. 

A second example is that of an Ala-to-Cys mutation, which causes the fonnation of a rare SH S hydrogen bond between the cysteine and a redox site sulfur and a 50 mV decrease in redox potential (and vice versa) in the bacterial ferredoxins [73]. Here, the side chain contribution of the cysteine is significant however, a backbone shift can also contribute depending on whether the nearby residues allow it to happen. Site-specific mutants have confirmed the redox potential shift [76,77] and the side chain conformation of cysteine but not the backbone shift in the case with crystal structures of both the native and mutant species [78] the latter can be attributed to the specific sequence of the ferre-doxin studied [73]. 

X-ray structural studies have played a major role in transforming chemistry from a descriptive science at the beginning of the twentieth century to one in which the properties of novel compounds can be predicted on theoretical grounds. When W.L. Bragg solved the very first crystal structure, that of rock salt, NaCl, the results completely changed prevalent concepts of bonding forces in ionic compounds. 

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