Elastic Constants of Disordered Solids. II: Temperature Dependence

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 modulus Y 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 imp...