Temperature Dependence of the Elastic Constants

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Abstract
This analysis presents a new approach to the problem of temperature dependence of elastic constants, which leads to a simple expression. A phenomenological model is assumed to explain and estimate the temperature dependence of elastic constants. The model consists of the usual harmonic oscillator with the applied force term plus a third-order term representing the anharmonicity of the oscillator. The state function ψ is evaluated in terms of the Hermitian polynomials using perturbation methods. The average mean displacement of the mass points (atoms or molecules) is obtained by using the state function and Maxwell-Boltzmann distribution. Consequently, the expression for the elastic constant and also for the coefficient of the thermal expansion is obtained. The result is again averaged over the range of frequencies, using Debye spectrum. The final expression shows good agreement with experimental results and other theories.

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