The 2/3 Rule of Glass Physics Implies Universalities in Crystal Melting
Since more than 100 years, melting is thought to be governed by the Lindemann criterion. It assumes that a crystal melts when, upon heating, the growing atomic vibration amplitudes become sufficiently large to destabilize its crystalline lattice. However, it is unclear why the viscosities eta or the related relaxation times tau of the resulting liquids, measured directly at the melting point Tm, differ by up to nine decades, depending on the material. Based on the empirical rule that the ratio of the glass-transition temperature and Tm is about 2/3, here we show that this strong variation is due to differences in the liquid's fragilities, a property associated with pronounced non-Arrhenius behavior and often ascribed to cooperative motions. We propose that, without cooperativity, all crystals would melt into liquids with a universal viscosity value and relaxation time. Hence, the real melting point is only partly determined by the Lindemann criterion and strongly enhanced by the cooperativity of the resulting liquid. Our findings are corroborated by the determination of the idealized, fragility-free melting temperatures, and of the corresponding eta and tau values for various example materials.