Coordination, in crystals

There has been much discussion of the probable limits of error of atomic coordinates in crystal structures, the upshot of which is the conclusion that earlier estimates of accuracy were too optimistic. Cruickshank (1949) showed that the relation between the standard deviation a x) of a coordinate of an atom and the differences between... 

Figure 9 Coordination of selenium in crystalline Sep4 as compared to the Te coordination in crystals of polymeric Tep4...

Addition of halide ions to aqueous copper(II) solutions can give a variety of halo-complexes for example [CuCl4] (yellow square-planar, but in crystals with large cations becomes a flattened tetrahedron) [CuClj] (red, units linked together in crystals to give tetrahedral or distorted octahedral coordination around each copper). 

Here Tq are coordinates in a reference volume Vq and r = potential energy of Ar crystals has been computed [288] as well as lattice constants, thermal expansion coefficients, and isotope effects in other Lennard-Jones solids. In Fig. 4 we show the kinetic and potential energy of an Ar crystal in the canonical ensemble versus temperature for different values of P we note that in the classical hmit (P = 1) the low temperature specific heat does not decrease to zero however, with increasing P values the quantum limit is approached. In Fig. 5 the isotope effect on the lattice constant (at / = 0) in a Lennard-Jones system with parameters suitable for Ne atoms is presented, and a comparison with experimental data is made. Please note that in a classical system no isotope effect can be observed, x "" and the deviations between simulations and experiments are mainly caused by non-optimized potential parameters. 

Molecules in a gas are not distinguishable. Molecules in a solid, where we can give them coordinates in a crystal lattice, are distinguishable. We will return to this condition later when we use our statistical methods to describe vibrations in a solid. 

The diazonio group of one zwitterion is stabilized by intermolecular interactions with the carboxylato oxygens of two neighbouring zwitterions. The same type of coordination is observed in crystals of benzene diazonium chloride, tribromide, and tetrafluoroborate (Andresen and Romming, 1962 Romming, 1963 Cygler et al., 1982). 

In contrast to single-crystal work, a fiber-diffraction pattern contains much fewer reflections going up to about 3 A resolution. This is a major drawback and it arises either as a result of accidental overlap of reflections that have the same / value and the same Bragg angle 0, or because of systematic superposition of hkl and its counterparts (-h-kl, h-kl, and -hkl, as in an orthorhombic system, for example). Sometimes, two or more adjacent reflections might be too close to separate analytically. Under such circumstances, these reflections have to be considered individually in structure-factor calculation and compounded properly for comparison with the observed composite reflection. Unobserved reflections that are too weak to see are assigned threshold values, based on the lowest measured intensities. Nevertheless, the number of available X-ray data is far fewer than the number of atomic coordinates in a repeat of the helix. Thus, X-ray data alone is inadequate to solve a fiber structure. 

Summarizing, in the crystal there are 36 Raman active internal modes (symmetry species Ug, hig, 2g> and 26 infrared active internal modes (biw b2w hsu) as well as 12 Raman active and 7 infrared active external vibrations (librations and translations). Vibrations of the type are inactive because there appears no dipole moment along the normal coordinates in these vibrations of the crystal. 

---