Abstract
A simple modified first nearest-neighbours Ising Hamiltonian accounting for elastic displacements, both static and thermal, in binary alloys is detailed here. The vibrational partition function is obtained by a classic harmonic approximation. Using the Landau theory (mean field approximation), it is shown that the critical temperature is raised or lowered by vibrational effects when the elastic coupling constants of heterogeneous pairs are different from those of homogeneous ones. In any case, the symmetry of the miscibility gap is conserved only if the bond rigidities differ and no size effects are present. Mean field predictions are verified by Monte-Carlo calculations.
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