Universal scaling laws in melting thermodynamics of gold nanoparticles: Insights from machine learning molecular dynamics

Understanding the melting behavior at the nanoscale regime serves a fundamental role in both the scientific community and industrial applications. In particular, the melting of nanoparticles (NPs) exhibits behaviors that differ qualitatively from bulk materials due to pronounced size-dependent properties and surface/volume ratio effects, but a unified theoretical understanding remains elusive. Here, by developing a machine-learning interatomic potential applicable across diverse local atomic environments and wide temperature ranges, we systematically investigate the melting thermodynamics of Au NPs spanning from small clusters (102 atoms) to large NPs (105 atoms) through a series of nanosecond-long molecular dynamics simulations. A complete solid-liquid phase diagram of NPs across 1-14 nm diameters is presented, clearly distinguishing the unique surface premelting behavior and complete melting. The size-dependent melting curve follows the Gibbs-Thomson relationship. More importantly, we demonstrate that the melting entropy changes in nanoparticle systems substantially deviate from the empirical Richard's rule and its generalized form valid for bulk elemental systems. Moreover, we found that all the components of melting entropy follow the same scaling law, based on which we derived a thermodynamic correlation between the NP system and its bulk values. These results bridge the thermodynamic description from the single-atom limit to bulk materials, providing a unique insight for understanding and predicting nanoscale melting thermodynamics.