Elastic Constants of Disordered Solids. II: Temperature Dependence

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Abstract
We consider the extension of the preceding theory to finite temperatures, while retaining the previous assumptions of affine deformation, of a linear elastic range, and of central interparticle forces. At sufficiently low temperatures, a quasi‐harmonic approximation with volume and strain dependent frequencies ensues. It accounts for an initial linear increase of the Poisson constant μ and a similar decrease of Young's modulusY with increasing temperature. Numerical evaluation of the complete cell potential and of the free‐volume integral shows that this is followed by plateau regions for both functions, whereas the bulk modulus is but weakly dependent on temperature over the same range of temperatures. This includes a third region of more rapidly decreasing Y and increasing μ. However, these latter results require further examination. For upon a further increase in temperature, the validity of the model breaks down, when it would predict a reversal in the sign of the temperature coefficient of Y and impermissible values for μ. This is qualitatively similar to the performance of the cell theory in predicting the thermal expansivity of glasses at low temperatures. Examination of experimental results for some inorganic and organic glasses indicates the existence of the three regions referred to above, or at least the last two.

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