Empirical laws of melting

Although in general the melting and freezing transition is non-universal, there are some useful phenomenological criteria which are usually based on the properties of only one of the two coexisting phases. The advantages of these empirical rules is that they permit an estimation of the solid-liquid coexistence line, without carrying out any free energy calculation.

The empirical rule of bulk melting is the so called Lindeman criterion according to which a crystal melts when the amplitude of thermal vibrations (r.m.s.) exceeds a given thresholds of the order of the lattice space (83). For many materials this Lindemann ratio is about of $\simeq$ 0.15 of the lattice space.

Another interpretation of the Lindemann criterion is that an infinite solid will become mechanically unstable at a sufficiently high temperature. Although the ideal mechanical instability temperature of a solid is different, and of course somewhat higher than the true melting temperature $T_m$ (where the free energy crossing of solid and liquid phases takes place),nonetheless it can be heuristically taken as a qualitative indicator of the tendency of the solid to melt.