Pair interaction energy

Figure 1 Disorder-Llo-Ll2 phase diagram [9]. The broken line indicates the (100) Spin-odal ordering locus and dotted lines e metastable phase boundaries. The temperature axis is normalized with respect to the neaiest neighbor pair interaction energy. The ordering transition temperatures of L q and LI2 phases are 1.89 and 1.92, respectively.

The aim of the present paper is to apply the impurity KKR Green s function method to the study of nearest-neighbor effective-pair interaction energies (NN-EPIE s) in low-concentrated fee di.sordered alloys (H = host, X = impurity c < 0.1). It is... 

Table 1. Pair interaction energies ( in eV) of l-4th neighbors in Alloys. The values of dilute limit are shown.

Fig.4 Effective pair interaction energies of CuNi, PdV, NiAl as well as the experimental values. The KKR-CPA-GPM result for PdV and the CWM result for NiAl are also shown for comparison.

Let us now turn our attention to an interpretation of Ycr particularly to the question of what numerical values might be appropriate under certain conditions. Based on the discussion above, we would expect to find that values in excess of 10 kg/mol-ns would be appropriate for materials below Tg. What we seek is a method of checking this prediction by calculating an approximate value from molecular parameters. To do this we will consider the repulsive interaction as largely a steric one due to the van der Waals repulsions of a pair of chain elements. To the extent that this picture applies, we can calculate an approximate 7c by expanding the van der Waals pair interaction, energy,... 

For large systems, the computation of the energy can require 98% or more of the total computational effort, and within the energy computation, the pair interaction energy (van der Waals and electrostatic terms) can represent more than 90% of the total effort. For this reason, the aspects of the program that deal with the generation of the nonbond list and the computation of the nonbond energy are of critical importance. 

Where V(r) is the pair interaction energy and Vm is the well depth. Here 2a is the collision diameter , i.e. the distance at which the interatomic potential is zero. Also plotted in Figure 2.2 is the interatomic force and the elastic modulus of what we may consider as an interatomic spring. (Recall that the force is the rate of change of energy with distance,... 

The major difficulty in predicting the viscosity of these systems is due to the interplay between hydrodynamics, the colloid pair interaction energy and the particle microstructure. Whilst predictions for atomic fluids exist for the contribution of the microstructural properties of the system to the rheology, they obviously will not take account of the role of the solvent medium in colloidal systems. Many of these models depend upon the notion that the applied shear field distorts the local microstructure. The mathematical consequence of this is that they rely on the rate of change of the pair distribution function with distance over longer length scales than is the case for the shear modulus. Thus... 

Hence, by adopting the appropriate approximation, it is possible to obtain quantitative information about the pair interaction energy from scattering experiments, over a wide variety of systems and particle concentrations. 

The characteristic time of this diffusion was estimated by carrying out the molecular dynamic relaxation of the film surface within the limits of the above model at 500°C. In MD calculations, the pair interaction energy between atoms is approximated by the Buckingham pair potential (Zr O, O-O) (see Table 9.4). To describe covalent bonds more correctly, a three-body O-Zr-O term in the Stillinger-Weber form was introduced in addition to the Coulomb term. 

An interesting application of many-body perturbation theory using a discrete orbital basis has been reported by Robb.162 In calculations on BH, comparison was made between the results and those of Houlden et a/.152 using Cl. Most of the pair-pair interaction energy can be recovered by this method. 

Table 20-4. Base pairing/interaction energy of GC and AT base pairs in their neutral, anionic and cationic radical states...

A different type of reference state was chosen by Mitchell et al. The pair interaction energy is written as... 

At least in lattice statistics, pair interaction energies are usually accounted for by a parameter w, which is positive for repulsion and negative for attraction for m = 0 the situation reduces to the Langmuir case. 

The thermodynamics of non-ideal bulk mixtures has been considered in sec. 1.2.18. Non-idealities can be expressed in terms of activity coefficients, excess functions, pair interaction energies (as In Regular Solution theory) or through vlrlal expansions. For all these methods surface equivalents can be formulated. 

---