Effective cluster interaction

Often the most important effective cluster interaction of the concentration fluctuation expansion of the configurational free energy is the EPI which is defined as... 

Ab-initio studies of surface segregation in alloys are based on the Ising-type Hamiltonian, whose parameters are the effective cluster interactions (ECI). The ECIs for alloy surfaces can be determined by various methods, e.g., by the Connolly-Williams inversion scheme , or by the generalized perturbation method (GPM) . The GPM relies on the force theorem , according to which only the band term is mapped onto the Ising Hamiltonian in the bulk case. The case of macroscopically inhomogeneous systems, like disordered surfaces is more complex. The ECIs can be determined on two levels of sophistication ... 

We have developed a theory that allows to determine the effective cluster interactions for surfaces of disordered alloys. It is based on the selfconsistent electronic structure of surfaces and includes the charge redistribution at the metal/vacuum interface. It can yield effective cluster interactions for any concentration profile and permits to determine the surface concentration profile from first principles in a selfconsistent manner, by... 

Effective cluster interactions. The second important parameter in all cluster models is a series of interaction coefficients that define the bond strengths. An... 

Figure 7.13. Estimated fractional change in the ordering temperature resulting fiem incorporating the effect of ordering on the vibrational spectrum by an additional effective cluster interaction (ElCIvib) (Gaibulsky and Ceder 1996).

In general, once both the effective cluster interactions and the statistical treatment resulting from the cluster variation method are in hand, the alloy free energy can be written as... 

The effective pair interactions V are deduced from the general effective cluster interactions (Sanchez et al. 1984) using the cluster variation method (CVM) approximation. Thus for the basal plane of 123-0 (Cul-0, mirror plane of the structure) the effective 0-0 pair interactions are given by the linear combination of the total energies ... 

Figure 15.8 The duster expansion formalism (a) basic lattice, (b) configuration a, and (c) effective cluster interactions...

Garbulksy, G.D. and Ceder, G. (1995) Linear-programming method for obtaining effective cluster interactions in alloys from total-energy calculations application to the fee Pd-V system. Phys. Rev. B, 51 (1), 67-72. 

ECI effective cluster interaction HRTEM high-resolution transmission electron... 

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