Melting as an Instability of Crystal Structure with respect to Transverse Acoustic Wave, Quasi-Harmonic Approach

It is suggested that the precursor of melting in some crystals can be a macroscopic shear deformation such as the transverse sound wave. This hypothesis is examined basing on the quasi-harmonic approach to lattice dynamics within the two-body ion-ion concept of interaction in metals. One finds that due to the temperature induced modification of effective ion-ion interaction appearing in the quasi-harmonic approximation the crystal ceases to support propagation of transverse sound waves when its temperature approaches a certain critical temperature $T_{cr}$, understood here to be the melting temperature T_{m}.