Nearest neighbour bond model

Formula for the chemical potentials have been derived in terms of the formation energy of the four point defects. In the process the conceptual basis for calculating point defect energies in ordered alloys and the dependence of point defect concentrations on them has been clarified. The statistical physics of point defects in ordered alloys has been well described before [13], but the present work represents a generalisation in the sense that it is not dependent on any particular model, such as the Bragg-Williams approach with nearest neighbour bond energies. It is hoped that the results will be of use to theoreticians as well as... 

The ratio of the bond integrals for sp-valent elements was found by Harrison (1980) by fitting a nearest-neighbour model to the first principles band... 

These macroscopic quantities can be related to the bond energies eaa and bb in the bulk phases and eAB at the interface by a simple nearest neighbour interaction model. Assuming that ... 

Our third and final example is the use of SAW to model the micromanipulation of polymer molecules, particularly DNA, attached to a surface. In this situation, optical tweezers [77,78] are used to pull the adsorbed biological molecule from the surface. This force is applied perpendicular to the adsorbing surface and will favour desorption. It is reasonable to expect some sort of a phase transition. At low levels of the force, the polymer remains adsorbed, but at higher levels it will be desorbed. There will be a temperature dependent force /c(T) between these two states. The shape of the force-temperature curve is of considerable interest, and can be considered a phase boundary in the T — f plane. This can be modelled by a SAW, tethered to a wall, with a fugacity associated with nearest-neighbour bonds, subject to a force perpendicular to the wall, as shown in the figure below. 

The photoelectron wave-vector k is evaluated using = 2m(E — E ) where E is the energy of the X-ray photon, , a reference energy and m, the mass of the electron. x(k) is multiplied by k"(n = 2 or 3 usually) to magnify the faint EXAFS at large k (Lytle et al, 1975) /c"x(k) is Fourier transformed to yield the RSF, < (R). In the model compound, the first peak at a distance Rj represents the distance to the nearest-neighbour shell and may be compared to R[, the known distance. We can then define a as (R — Rj), which represents the experimentally determined phase correction. In principle, 2a should be equal to the theoretically estimated k-dependent part of /k), viz. if the identity of the scatterer environment has been correctly assumed. It must be emphasized that wherever scatterer identities are obscure (e.g. in several covalently bonded and disordered systems) use of a (and not j) is advisable. Further, the k-dependence of < /k) introduces an intrinsic limitation to its quantitative accuracy. 

This totally unexpected result can be proved as follows. Within a first nearest-neighbour model, the bond order of these lattices may be written from eqs (7.101) and (7.103) as... 

Fig. 9. Schematic diagrams of the three types of polarisable potentials. The left-hand diagram shows a point polarisability model (e.g. SK [35] and DC potentials [36]). The centre diagram shows die polarisation on the two 0-H bonds (e.g. NCC potential [37]). The right-hand diagram shows the all-atomic (or three-) polarisation models (e.g. Bernardo et al [44] and Burnham [26]). The lower diagram schematically illustrates the relative orientations of molecular dipole moments of the four nearest neighbour molecules would in possible to cancel out due to the ice rule and give rise a strong local field.

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