Atomistic origin of the entropy of melting from inelastic neutron scattering and machine learned molecular dynamics

The latent heat, L, is central to melting, but its atomic origin remains elusive. It is proportional to the entropy of fusion, ΔSfus = L/Tm (Tm is the melting temperature), which depends on changes of atom configurations, atom vibrations, and thermal electron excitations. Here, we combine inelastic neutron scattering and machine-learned molecular dynamics to separate ΔSfus into these components for Ge, Si, Bi, Sn, Pb, and Li. When the vibrational entropy of melting, ΔSvib, is zero, ΔSfus ≃ 1.2 kB per atom. This result provides a baseline for ΔSconfig and nearly coincides with “Richard’s Rule” of melting. The ΔSfus deviates from this value for most elements, however, and we show that this deviation originates with extra ΔSvib and extra ΔSconfig. These two components are correlated for positive and negative deviations from Richard’s rule – the extra ΔSconfig is consistently  ~ 80% of ΔSvib. Our results, interpreted with potential energy landscape theory, imply a correlation between the change in the number of basins and the change in the inverse of their curvature for the melting of pure elements. The atomistic components that drive entropy of fusion and ultimately characterize latent heat of melting are not well defined. Here, inelastic neutron scattering and machine-learned molecular dynamics are used to quantify these thermodynamic contributions to the entropy of fusion in pure elements.