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The cluster/site approximation for multicomponent solutions -- a practical alternative to the cluster variation method

Journal Article · · Scripta Materialia
;  [1]
  1. Forschungszentrum Juelich GmbH (Germany). Inst. fuer Festkoerperforschung

In the calculation of phase diagrams the thermodynamic models used for the phases involved are usually based on the Ising or bond energy model. A good discussion of the mapping of the energy of real alloys onto effective pair interactions for use in this model has been given by Ceder. In using the bond energy model it is often desirable to go beyond the point approximation in the calculation of the free energy and it has been recognized that Kikuchi`s Cluster Variation Method (CVM) is highly satisfactory for this purpose. Good agreement is found when the results from CVM calculations are compared with the (exact) results from Monte Carlo simulations of the same system. The calculation of phase diagrams via first principle calculations of the energy of various ordered phases, the use of these energies in a cluster expansion for obtaining the effective cluster interactions and their subsequent use in a CVM calculation of the phase diagram has been a particularly exciting development over the last decade. Notwithstanding these successes, a major disadvantage of the CVM has been recognized--the large number of non-linear simultaneous equations which must be solved in order to obtain the free energy and the equilibrium species distribution. In the present note, the authors should like to suggest the use of an alternative cluster approach which results in a considerable reduction in the number of equations to be solved as compared with the CVM. Although the approximation is not new, its relevance to calculations on multicomponent solutions appears to have been overlooked in the excitement generated by the success of the CVM.

OSTI ID:
367264
Journal Information:
Scripta Materialia, Journal Name: Scripta Materialia Journal Issue: 5 Vol. 35; ISSN 1359-6462; ISSN XZ503X
Country of Publication:
United States
Language:
English

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