AI 中文总结
研究锡中α→β相变温度预测难题，构建ACE势，通过全热力学积分考虑振动非谐性，得出捕捉全晶格非谐性对预测锡相稳定性至关重要，绝对转变温度受0K能量学精度限制的结论。
AI 中文摘要
预测锡中α→β（灰到白）的转变温度对原子模拟来说一直是个挑战，现有理论方法与实验边界（286K）相差高达数百开尔文。本文构建基于密度泛函理论数据训练的原子团簇展开（ACE）势来评估两相的有限温度自由能。在同一势能面上，准谐近似预测转变温度为377K，而考虑显式振动非谐性的全热力学积分得到288K。该变化直接量化了显式非谐自由能，对金属β-Sn很重要，对半导体α-Sn可忽略。β-Sn的各向异性非谐性通过其过剩热容、振动谱的温度驱动重整化以及原子力和位移与谐性参考的偏差得到证实。结果表明，捕捉全晶格非谐性对预测锡的相稳定性至关重要，而绝对转变温度仍受基础0K能量学精度限制。
英文摘要
Predicting the $α\to β$ (grey-to-white) transition temperature in tin presents a longstanding challenge for atomistic simulations, with existing theoretical approaches over- or underestimating the experimental boundary (286 K) by up to several hundred Kelvin. In this work, we construct an Atomic Cluster Expansion (ACE) potential trained on density functional theory data to evaluate the finite-temperature free energies of both phases. Evaluated on the same potential energy surface, the quasi-harmonic approximation predicts a transformation temperature of 377 K, whereas full thermodynamic integration, which accounts for explicit vibrational anharmonicity, yields 288 K. This shift directly quantifies the explicit anharmonic free energy, which is substantial for metallic $β$-Sn but negligible for semiconducting $α$-Sn. The anisotropic anharmonicity in $β$-Sn is corroborated by its excess heat capacity, temperature-driven renormalization of its vibrational spectrum, and deviations of its atomic forces and displacements from the harmonic reference. Our results demonstrate that capturing full lattice anharmonicity is essential for predicting the phase stability of tin, while the absolute transition temperature remains limited by the accuracy of the underlying 0 K energetics.
Comments14 pages, 7 figures
