Effective pair interaction

One of the major ingredient for the understanding of alloy phase stability is the configurational energy. Models have been proposed to represent the configurational energies in terms of effective multisite interactions, in particular effective pair interactions (EPls). 

EXPERIMENTAL STUDY OF THE SHORT RANGE ORDER IN THE PT-V SYSTEM EFFECTIVE PAIR INTERACTIONS AS A FUNCTION OF THE CONCENTRATION... 

We define a fee lattice and affect at each site n, a spin or an occupation variable <7 which takes the value +1 or —1 depending on whether site n is occupied by a A or B atom. Within the generalized perturbation method , it has been shown that substitutional binary alloys AcBi-c may be described within a Ising model with effective pair interactions with concentration dependence. Thus, the energy of a configuration c = (<7i,<72,- ) among the 2 accessible configurations for one system can be written... 

Those Warren-Cowley parameters have been determined in situ above the order-disorder transition temperature by diffuse neutron scattering. From these experimentally determined static correlations, the first nine effective pair interactions have been deduced using inverse Monte Carlo simulations. 

Figure 3. Compared effective pair interaction for the two sets Pt V and PtgU in ineV.

Fig. 1. The mixing energies agree rather well with the results of Pasturel et al. and those of Abrikosov et al. . The pair interaction i> (c) is In a very good agreement with the locally relaxed quantity given by Carlsson, and also it is rather similar to the effective pair interaction found by Pasturel et al., although it is smaller approximately by a factor 0.7. The pair interaction u (c) differs from the corresponding quantity reported by Abrikosov et al. , which can be probably attributed to different computational schemes, as we assume neutral spheres, while Abrikosov et al. suppose equal sphere radii. The pair interaction (c) closely follows u (c) for Ni-rich alloys and v (c) for Al-rich alloys, at intermediate concentrations all three quantities...

Figure 1. The effective pair interactions as functions of alloy composition for the alloy system Al-Ni. The results of the CWIS based on the FP-LAPW calculations for 5 ordered structures (full line) and on the TB-LMTO-CPA for 5 disordered alloys (dash line) are compared with the the results of the GPM (dotted line).

EFFECTIVE PAIR INTERACTIONS IN RANDOM ALLOYS BY DIRECT CONFIGURATIONAL AVERAGING... 

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... 

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.

Effective pair interaction parameters. In the CVM formalism, effective pair interaction coefficients, defined by the symbol are given in Eq. (7.20)... 

Next, we present some observations concerning the connection between the reconstruction process and the iterative solution of either CSE(p) or ICSE(p). The perturbative reconstruction functionals mentioned earlier each constitute a finite-order ladder-type approximation to the 3- and 4-RDMCs [46, 69] examples of the lowest-order corrections of this type are shown in Fig. 3. The hatched squares in these diagrams can be thought of as arising from the 2-RDM, which serves as an effective pair interaction for a form of many-body perturbation theory. Ordinarily, ladder-type perturbation expansions neglect three-electron (and higher) correlations, even when extended to infinite order in the effective pair interaction [46, 69], but iterative solution of the CSEs (or ICSEs) helps to... 

Here erf, and erf are the Pauli matrices, that act on the proton (deuteron) wavefunctions potential wells of the proton (deuteron) potential energy profile of the th H-bond (in accordance with the available diffraction data the short H-bonds O-H- O with two off-center sites of a proton are considered). The parameters of Hamiltonian (1), i.e., the tunneling parameter Cl and the Ising parameters J,p describe the motion of a proton (deuteron) along H-bond and the effective pair interactions of these particles, respectively. When Cl is substantially smaller than Jy the static approximation (Cl = 0) becomes valid. Instead of equation (1) one has in this case... 

Thus, perturbation potential of the solution and the distinguished solute in conformation i ". If is not decomposable according to solute-solvent pairs conditional on the solute conformation i ", then this relation introduces an effective pair interaction as the perturbation. 

Traditionally, common starting point towards understanding the properties of fluids has been an analysis of the effective pair interaction or, more accu-... 

Figure 3. (a) The effective pair interaction between two isolated macroions. The thick solid... 

In the following, we employed the effective pair interaction W(r) between two macroions in a Metropolis scheme of MC simulations to study the macroion structuring under plane-parallel and wedge-shaped confinements. 

A quantitative analysis of relationship between the local structure and local energetics of PWCs is based on a special decomposition of stabilization energy within the framework of additive models of interaction. In this approximation, the stabilization energy of PWCs is equal to the sum of all pair interactions. We define the effective pair interaction in PWCs (effective energy of H-bond) as the following ... 

Recently we have proposed a decomposition scheme of inter-molecular interaction energy in polyhedral water clusters. Central to the scheme is the concept of effective pair interaction energy (effective H-bond energy). In additive approximation, the interaction energy of any molecular system is equal to the sum of all pair interactions. The effective energy of pair interaction (effective energy of H-bond) is... 

Using the concept of effective pair interactions we have developed a new discrete model of inter-molecular interactions in gas hydrate frameworks. Contrary to H-bond types on a surface of polyhedral clusters, in this case it is beyond reason to divide additionally the trans- and c/ -configurations of distinct H-bonded dimer. It is necessary to take into consideration an interactions of all surrounding molecules. We have found that there are 1098 symmetry-distinct types of H-bond surroundings (extended H-bonds). Among them 369 types (33.6%) correspond to strong H-bonds. The rest of them contain weak H-bonded dimer. Taking into account antisymmetry, the number of different extended H-bonds is 567. 

In concentrated suspensions many body interactions between the colloidal particles determine the effective colloid-colloid interaction. Beresford-Smith and Chan (1983) [37] showed that in that case the effective colloid-colloid interaction can nevertheless be described by an effective pair interaction energy to characterise the electrical double layer interaction. This pair interaction energy also has a screened Coulomb form just as in the classical DLVO theory but the Debye screening parameter k now depends on the intrinsic coxmterion concentration and the concentration of added electrolyte in the system. This makes the effective pair energy dependent on the volume fraction of the particles (see general discussion of the paper of Beresford-Smith and Chan [38]. 

Inverse Monte Carlo approaches have also been used to extract information from single-crystal diffuse scattering data. For example, effective pair interactions were extracted from vanadium hydride, an important potential hydrogen... 

Effective Pair Interactions from Pair Functionals The pair functional formalism may be recast in the language of pair potentials by computing an effective pair potential which is valid for environments close... 

Fig. 6.16. Effective pair interactions for Mg at different electron densities (adapted from Moriarty and Althoff (1995)).

To obtain appropriate expressions relating the dielectric constant to the mean square moment, De Leeuw et al. consider the periodic sphere formed by replicating the central cell to be embedded in an infinite continuum of dielectric constant e. This is reminiscent of techniques first applied by Kirkwood, and the inJ inite limits must be taken properly. One then finds that the effective pair interaction for this system, (e 12), can be written as... 

In this case, u(r) is not the correct pair interaction but some effective pair interaction which simulates the multibody terms. 

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