Machine learning-assisted MD simulation of melting in superheated AlCu validates the Classical Nucleation Theory

Abstract

The validity of the Classical Nucleation Theory (CNT), the standard tool for describing and predicting nucleation kinetics in metastable systems, has been under scrutiny for almost a century. While the CNT is commonly employed to describe liquid → crystal and liquid ↔ vapor phase transitions, its application to the crystal → liquid case has been limited because of the experimental challenges in achieving superheating states and detecting homogeneous liquid nucleation. In this study, we performed comprehensive molecular dynamics (MD) simulations of spontaneous melting of a superheated AlCu crystal under atmospheric pressure at five temperatures, covering a superheating range of T/TL = 1.1–1.3, where TL is the liquidus temperature. Two realistic AlCu models were investigated: one described by the modified embedded atom method (MEAM) and the other by an interatomic potential generated by an artificial neural network machine learning (ML) approach, extensively trained on an ab initio dataset of liquid and crystal configurations. Fifty independent melting events were simulated at each temperature. By analyzing the distribution of melting times using the Poisson law, the homogeneous nucleation rate was determined through the mean lifetime method. Additionally, the Zeldovich factor, critical nucleus size, and work of formation were obtained using the mean first-passage time method, utilizing the disorder parameter based on atomic displacements (liquid-like atoms in the superheated crystal) as the reaction coordinate. Also, the effective atomic transport coefficient across the metastable crystal/critical liquid nucleus interface was determined by MD simulations as the interfacial attachment coefficient for nuclei growth rates. Using these simulation-generated data, the theoretical nucleation rates were calculated by the CNT with no fitting parameters. We found excellent agreement between the theoretically and MD-computed liquid nucleation rates for both MEAM and ML crystals. Notably, the effective solid-liquid interfacial free energy value obtained from the MD data aligns with its recent experimental measure. Moreover, the CNT qualitatively and quantitatively described the underlying details of liquid drop nucleation in our ML solid, unprecedentedly and accurately reproducing the kinetic prefactor and the size, formation energy, and growth rate of the critical nuclei. Thus, the melting of the AlCu model created through machine learning-processed quantum calculations, that is, not relying on hand-crafted interatomic potential functions, was successfully described by the CNT phenomenological formalism, without any adjustable parameters. This finding confirms the CNT as a very reliable descriptor of homogeneous nucleation in the superheated AlCu alloy and generalizes this theory as a powerful tool for analyzing and predicting the kinetics of crystal-liquid transitions.