A Pair-Wise Interaction Model for Multi-Sublattice Phases

ABSTRACTThe use of simple nearest neighbour pair-wise interaction models for the description of the thermodynamic properties of ordered alloys is reviewed and extended to the treatment of phases containing several sublattices. Employing individual sublattice occupation parameters to define atomic distributions, enthalpies corresponding to these are described by the summation of pair-wise interaction energies over all the resulting first co-ordination shell neighbours. Invariant like and unlike bond energies are assumed, their respective values being estimated using heats of vaporisation of the elements and a heat of formation of the phase at a single composition. Combination of the enthalpies with corresponding configurational entropies yields an expression for the free energy of the phase which may be minimised with respect to variation of the sublattice occupation parameters. This leads to the prediction of the stable atomic distributions and the variation of these and the thermodynamic properties with composition. The application of the model to sigma phases and other multi-sublattice structures is discussed