Extension of the Ising model for calculations on order-disorder phenomena in alloys by allowing for atomic vibrations

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Abstract
As an extension of the Ising model for calculations on order-disorder phenomena in alloys, normal modes giving rise to a vibrational entropy contribution, were allowed. Calculations were performed on a (hypothetical) AB alloy crystallising in the simple cubic (NaCl) structure, where an exact analytical expression for the vibrational entropy exists. As a first step the problem was handled using the Bragg-Williams approximation. Arguments are given for why the introduction of the vibrational entropy should have a drastic influence on quantities of interest, such as the degree of order at a certain temperature, the order-disorder temperature and the specific heat. It is argued that for 'exact' solutions and realistic structures, computer simulation studies are necessary.