Crystal melting influenced by particle cooperativity of the liquid

Recently, a universal relation between the thermal expansion coefficient of glasses ${\ensuremath{\alpha}}_{\mathrm{g}}$, their glass-transition temperature ${T}_{\mathrm{g}}$, 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 ${\ensuremath{\alpha}}_{\mathrm{g}}/m\ensuremath{\propto}1/{T}_{\mathrm{g}}$ [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 ${T}_{\mathrm{g}}$ and the melting temperature ${T}_{\mathrm{m}}$ is about 2/3 for almost all materials, for crystals a similar relation, ${\ensuremath{\alpha}}_{\mathrm{c}}/m\ensuremath{\propto}1/{T}_{\mathrm{m}}$, should apply. Indeed, we find that the available experimental data are quite consistent with such a relation. This implies that the melting of a crystal into an ordinary (nonsupercooled) 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'' (noncooperative) melting temperature arising from the cooperativity of the particle motion in the liquid state above ${T}_{\mathrm{m}}$. 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.