Crystal melting influenced by particle cooperativity of the liquid
Recently, a universal relation between the thermal expansion coefficient of glasses $\alpha_g$, their glass-transition temperature Tg, and the so-called fragility index m of the corresponding supercooled liquid state was found to be valid for more than 200 glass formers, namely $\alpha_g/m\propto 1/T_g$ [P. Lunkenheimer et al., Nat. Phys. 19, 694 (2023)]. Here we show that this could also have far-reaching consequences for our understanding of crystal melting. Namely, when considering the empirically founded 2/3-rule, stating that the ratio of Tg and the melting temperature Tm is about 2/3 for almost all materials, for crystals a similar relation, $\alpha_c/m\propto 1/T_m$, should apply. Indeed, we find that the available experimental data are well consistent with such a relation. This implies that the melting of a crystal into an ordinary (non-supercooled) liquid is influenced by the fragility, a property quantifying the non-Arrhenius dynamics in the supercooled-liquid state of the material. We argue that this can be explained by a significant enhancement of the "ideal" (non-cooperative) melting temperature arising from the cooperativity of the particle motion in the liquid state above Tm. Therefore, a reassessment of the currently widely accepted microscopic understanding of crystal melting, still founded on the general ideas that lead to the time-honored Lindemann melting criterion, may be necessary.