Contribution of Lattice Vibrations to the Order-Disorder Transformation in Alloys

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Abstract
The lattice vibrational partition function for a binary crystal is constructed from the normal mode frequencies in the classical nearest‐neighbor harmonic approximation. The set of frequencies is computed as a function of the short‐range order parameter by the use of the Born‐von Karman analysis and second‐order perturbation theory. The resulting form of the lattice vibrational partition function closely resembles that of the static configurational partition function so that a reexamination of the statistical thermodynamics, including lattice vibrational effects, proves to be straightforward. The derived thermodynamic quantities are compared with experiment for the case of β‐brass. The theoretical heat capacity discontinuity as calculated by the method of Bethe and Kirkwood is increased from 1.7R to 6.1R by the inclusion of the lattice vibrational contribution. The agreement with the experimental value of about 5R is now satisfactory.

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