Unlocking Charge-Mediated Phase Transformation in Titanium: A Machine Learning Force Field and Phonon Free Energy Study

The phase stability of metals is fundamentally governed by thermodynamic variables, but recent findings highlight electronic charge as a critical, emerging factor influencing phase behavior. Titanium (Ti) serves as a key system, undergoing a solid-state phase transformation from the low-temperature α-phase (hcp) to the high-temperature β-phase (bcc). While this α→β transition is theoretically linked to specific phonon softening, a quantitative understanding via first-principles methods, particularly the influence of excess electronic charge, remains a significant challenge.In this work, we employ large-scale molecular dynamics (MD) simulations driven by a machine learning force field (MLFF), accurately trained on ab initio MD (AIMD) data. This MLFF framework provides the necessary efficiency and accuracy to handle complex thermal and electronic effects. We rigorously apply the Temperature-Dependent Effective Potential (TDEP) method to calculate the phonon free energies of both α and β phases across a broad temperature range.Our results quantitatively validate the long-standing theoretical model: the β phase is confirmed to be thermodynamically more stable at high temperatures, establishing the phonon-driven transition mechanism at the Density Functional Theory (DFT) level. Furthermore, by extending the TDEP framework to explicitly model charged systems, we demonstrate that an increased electron density significantly lowers the α→β transition temperature by preferentially stabilizing the β phase. The MLFF-based approach allows for a highly efficient and detailed analysis of transition dynamics, far surpassing the limitations of conventional AIMD. These findings not only advance the understanding of solid-state phase transitions under external stimuli but also provide a predictive, high-throughput computational framework for phase engineering via charge doping and temperature control.