Paper 10.3

Analytical structure of the Cluster Expansion Method and some applications to Fe-based phases equilibria

Chen Y. ¹, Iwata S.¹ and Mohri T.²

¹Department of Quantum Engineering and System Science, School of Engineering, The University of Tokyo, Tokyo, Japan

² Division of Materials Science and Engineering, Graduate School of Engineering, Hokkaido University, Sapporo, Japan

In predicting thermodynamic properties of an alloy system, Cluster Expansion Method (CEM) is usually performed as an interface between electronic structure total energy calculations and some statistical thermodynamic approaches such as Cluster Variation Method (CVM) by extracting the effective cluster interaction energies. One of the main procedures of CEM in common practice is to calculate the inverse of the correlation function matrix which is constructed from the geometry of selected ordered phases.

The mathematical structure of the correlation function matrix and its inverse have been investigated. It is recognized that the effect of newly extracted cluster interaction energies on the basic set can be predicted based on the analytical structure of the correlation matrix, which provides hints for selecting ordered phases in CEM. Some applications to Fe-based binary alloy systems, Fe-X (X=Ni, Pd and Pt), are discussed.