Temperature variation of the isothermal bulk modulus in solids: Thermo-elastic instability and melting

A new expression for the temperature dependence of the isothermal bulk modulus B T of solids is represented in terms of the Lambert function. The derived equation predicts a non-linear decrease in the bulk modulus over the entire temperature range of the solid phase, from a value of B 0 at absolute zero to the nonzero value of B 0 e − 1 at the melting point. The quasi-harmonic Debye-Gruneisen model is used to show that upon heating, the solid loses its elasticity and melts, when the thermal pressure exceeds a critical value B 0 ( e δ T ) − 1, with δ T being the Anderson-Gruneisen parameter. The thermo-elastic instability criterion of melting and the Lindemann melting law are re-examined. The unspecified Lindemann scale factor is interpreted in terms of the Anderson and Anderson-Gruneisen parameters and the Poisson ratio.