Phase Transformation in Silicon: Anomalies Revealed by Computational Free Energy Analysis

Abstract

Silicon holds critical importance as both a technological and structural material. In this study, the melting mechanism of silicon is systematically investigated using molecular dynamics (MD) simulations with the Stillinger–Weber1 (SW) potential, emphasizing free energy analysis. A first-order solid–liquid phase transition is proposed to elucidate silicon’s anomalous behavior. Unlike conventional substances, silicon exhibits a density anomaly: a sharp density drop during quenching and an abrupt increase upon heating2. The liquid– liquid transition (TLL) is identified at ~1375 K, characterized by a change in the first-shell coordination number from ~8 to ~5 with decreasing temperature (Fig. 1). During quenching, the tetrahedral order parameter rises markedly from 0.57 to 0.92 near 1050 K, signifying the nucleation of the diamond crystalline structure. Free energy differences between phases are quantified using a three-stage reversible thermodynamic cycle, with multiple histogram reweighting3 (MHR) applied to extract the equation of state. The free energy difference near the melting point is −0.3520 ± 0.0135 kJ/mol. The solid–liquid coexistence temperature is estimated as 1673 ± 5 K. Furthermore, the melting line obtained from Gibbs–Duhem integration reveals a negative slope, with a coexistence line gradient of approximately −61.7 K/GPa, indicating a pressure-induced reduction in melting temperature.