Next nearest neighbour effects

Summary of F shift trends and other NMR properties. Fluorine shifts in inorganic solids are affected by both nearest and next-nearest neighbour effects. It is often difficult to make unequivocal assignments of F NMR resonances of samples which are either genuinely disordered or consist of low-coverage surface phases... 

Wheland and Pauling (1959) tried to explain the inductive effect in terms of ar-electron theory by varying the ax and ySxY parameters for nearest-neighbour atoms, then for next-nearest-neighbour atoms and so on. But, as many authors have also pointed out, it is always easy to introduce yet more parameters into a simple model, obtain agreement with an experimental finding and then claim that the model represents some kind of absolute truth. 

However, with the improved resolution of modem XPS instruments, BE shifts as small as 0.1 eV can be detected and may be significant. These shifts can be interpreted, to a first approximation, by changes in the atomic charge (an intraatomic effect), but to account for more subtle differences, as seen in the mixed-metal phosphides M aM P and mixed arsenide phosphides MAsi -VP>, the role of next-nearest neighbours cannot be neglected. These interatomic effects, as incorporated into the charge potential model, help explain the unusual trends in BE observed in these series. 

The reciprocal lattice model as derived above is the basis for many different variants. For simplicity we have assumed the interactions between the next nearest neighbours A+ -B+ andC- I) to be independent of composition, even though experiments have shown that this is often not the case. It is relatively simple to introduce parameters which allow the interaction energy, for example between A+ and B+, to depend on the concentration of C and D [14], One may also include other terms that take into account excess enthalpies that are asymmetric with regard to composition and the effects of temperature and pressure. 

In between these extremes lie a large number of CVM treatments which use combinations of different cluster sizes. The early treatment of Bethe (1935) used a pair approximation (i.e., a two-atom cluster), but this cluster size is insufficient to deal with fhistration effects or when next-nearest neighbours play a significant role (Inden and Pitsch 1991). A four-atom (tetrahedral) cluster is theoretically the minimum requirement for an f.c.c. lattice, but clusters of 13-14 atoms have been used by de Fontaine (1979, 1994) (Fig. 7.2b). However, since a comprehensive treatment for an [n]-member cluster should include the effect of all the component smaller (n — 1, n — 2...) units, there is a marked increase in computing time with cluster size. Several approximations have been made in order to circumvent this problem. 

Bohanon et al. [86] studied heneicosanoic acid (which contains 21 carbon atoms) and Lin et al. [87] studied this material with particular reference to the effect of pH and the presence of divalent cations in the subphase. The former authors made use of in-plane diffraction (method 2 above) and obtained first order and second order diffraction peaks. They were able to show that, at high pressures ( r=35 mN m-1), at low pH (pH = 2) and at temperatures in the region of 0-5 °C, the material packs into a distorted hexagonal structure with the tilt towards the nearest neighbours. However, in the region 5-10°C the tilt is towards the next nearest neighbours. In the latter study [87] in-plane diffraction was studied as a function of pH and the presence of Ca2+ or Cu2+ in... 

In this equation, the interaction between active local distortions up to three next nearest neighbour octahedra along the chain was taken into account, while the force constants Km include the effects of interchain interactions. If the interchain contribution is confined by nearest neighbours then only the elastic constant corresponding to the interaction between nearest neighbour octahedra within the chain is renormalized ... 

At the simplest level, calculations of the elastic-strain energy in the matrix between a pair of CS planes, (1/5)2, allows the strain energy in an ordered array of CS planes to be estimated. The earliest way to do this is to add the strain energy in the matrix between each pair of CS planes in the array. This assumes, of course, that there is no interaction from next-nearest neighbour CS planes, and that each CS plane is an effective screen to the forces causing strain in the matrix. The values calculated in this way for the elastic-strain energy between a pair of CS planes is shown in Figure 41. 

The situation in aluminosilicate glasses is complicated by the additional effects of next-nearest-neighbour Al on the Si shifts. Although some Q" sites can be unambiguously assigned, others such as Q (OAl) and Q (3A1) occur in the same chemical shift range and cannot be differentiated on this basis. Systematic variations in the Si peak positions and widths of sodium aluminosilicate and calcium aluminosilicate glasses can... 

---