Unifying two criteria of Born: Elastic instability and melting of homogeneous crystals

The criteria formulated by M. Born for the onset of melting (1939) and lattice stability (1940) are re-examined on the basis of more general considerations of elastic instabilities. With the aid of molecular dynamics simulations, we show that (1) Bornʹs stability criteria are valid only in the case of zero external stress, and (2) his thermoelastic melting criterion, with some modification, is valid for the homogeneous process (mechanical melting or upper limit of superheating) which can occur when the free-energy-based heterogeneous process (melting by nucleation and growth) is kinetically suppressed. These and other related recent results on crack nucleation, pressure-induced polymorphic transition and amorphization emphasize the fundamental role of elastic instabilities in triggering unstable structural responses of homogeneous crystals.