The development of transition-metal-alloyed (Ti,Al)N thin films has become a common strategy to achieve optimized mechanical and thermal properties. Selection of a suitable alloying element, however, should consider the effect on Al solubility, directly influencing phase stability during the deposition. Here we use high-throughput formation enthalpy calculations to assess stability of the cubic (c) vs. hexagonal wurtzite-type (w-) phase of TM-alloyed (Ti,Al,TM)N. This compositionally-limited dataset serves to fit several machine-learning (ML) models enabling phase stability predictions over the entire compositional range. Of all the models, the linear regression using feature descriptor pre-processed by a genetic algorithm has the highest accuracy. For Ta, Nb, Mo, and W addition below ∼10 at.%, our ML model predicts enhanced stability of c-(Ti,Al,TM)N due to increased solubility of Al. Other alloying elements, especially Sc and Y from IIIB group and Hf and Zr from IVB group, decrease the cubic metastable solubility limit. In agreement with available experimental data, all transition metals except for Cr and V increase the volume of c-(Ti,Al,TM)N and w-(Ti,Al,TM)N.

中文翻译：

---

通过高通量从头计算和机器学习预测 (Ti,Al,TM)N（TM = III-VIB 族过渡金属）的形成焓和相稳定性


过渡金属合金（Ti，Al）N薄膜的开发已成为实现优化机械和热性能的常见策略。然而，选择合适的合金元素应考虑对铝溶解度的影响，直接影响沉积过程中的相稳定性。在这里，我们使用高通量形成焓计算来评估 TM 合金 (Ti,Al,TM)N 的立方 (c) 与六方纤锌矿型 (w-) 相的稳定性。这个成分有限的数据集适合多种机器学习 (ML) 模型，从而能够在整个成分范围内进行相稳定性预测。在所有模型中，使用遗传算法预处理的特征描述符的线性回归具有最高的精度。对于 Ta、Nb、Mo 和 W 添加量低于 ∼10 at.% 的情况，我们的 ML 模型预测由于 Al 的溶解度增加，c-(Ti,Al,TM)N 的稳定性增强。其他合金元素，特别是来自 IIIB 族的 Sc 和 Y 以及来自 IVB 族的 Hf 和 Zr，会降低立方亚稳态溶解度极限。与现有实验数据一致，除 Cr 和 V 之外的所有过渡金属都会增加 c-(Ti,Al,TM)N 和 w-(Ti,Al,TM)N 的体积。