Using highly accurate ab initio molecular dynamic simulations we calculate elastic constants of Ti${}_{0.5}$Al${}_{0.5}$N as a function of temperature up to 1500 K and compare the results with those obtained for TiN. We analyze the variation of the material’s elastic anisotropy with temperature by calculating directional Young’s moduli and Poisson ratios on the (100), (110) and (111) crystallographic planes. We show that though the elastic moduli of Ti${}_{0.5}$Al${}_{0.5}$N strongly decrease upon heating, the elastic anisotropy increases with temperature unlike in TiN. Since several approximate approaches have recently been utilized to predict elastic constants of Ti${}_{0.5}$Al${}_{0.5}$N at elevated temperature we compare our results with published data and benchmark the different approximate schemes. Giving the fact that Ti${}_{1-x}$Al${}_x$N is a prototypical system for hard coating applications, we conclude that the recently developed symmetry imposed force constants approach combined with the temperature dependent effective potential method is accurate and computationally cost-effective for this material class.

使用高度准确的从头算分子动力学模拟，我们计算了 Ti 的弹性常数${}_{0.5}$铝${}_{0.5}$N 作为温度的函数，最高可达 1500 K，并将结果与​​ TiN 获得的结果进行比较。我们通过计算 (100)、(110) 和 (111) 晶面上的方向杨氏模量和泊松比来分析材料弹性各向异性随温度的变化。我们表明，虽然 Ti 的弹性模量${}_{0.5}$铝${}_{0.5}$加热时 N 急剧下降，弹性各向异性随温度增加，与 TiN 不同。由于最近使用了几种近似方法来预测 Ti 的弹性常数${}_{0.5}$铝${}_{0.5}$N 在升高的温度下，我们将我们的结果与已发布的数据进行比较，并对不同的近似方案进行基准测试。考虑到 Ti${}_{1-X}$铝${}_X$N 是用于硬涂层应用的原型系统，我们得出结论，最近开发的对称施加力常数方法与温度相关的有效电位方法相结合，对于此类材料而言是准确且具有计算成本效益的。