Abstract The (100), (110) and (111) surface energies of random Al x Ti 1 - x N alloys with homogeneous concentration profile are determined in first-principles calculations. The (100) surface has the lowest energy of 1.25 J/m2 in the case of TiN and 1.32 J/m2 for cubic AlN and exhibit very little concentration dependence. The (110) and (111) surfaces have much higher energy for all the compositions. The segregation energies of Ti and Al were obtained for the (100) surface of pure TiN and cubic AlN as well as Al 0.5 Ti 0.5 N and Al 0.9 Ti 0.1 N random alloys. In the latter case, we have used two different methods: direct averaging of the substitution energies with respect to the local environment of the substitution site and the cluster expansion technique (CLE). We find that the segregation of Ti is favorable in the whole concentration range of random Al x Ti 1 - x N alloys. However, it is weak in almost the whole concentration range except in the Al-rich alloys: Al 0.9 Ti 0.1 N and cubic AlN. The strengthening of the surface segregation of Ti in the latter case is related to the sharp increase in phase separation tendency in Al x Ti 1 - x N alloys at compositions close to pure AlN. The increased tendency for Ti segregation close to pure AlN helps explain the formation of a lamella structure in industrially important Al x Ti 1 - x N coatings. As for nitrogen vacancies, their segregation energies are relatively small in the whole concentration range, but for pure AlN where they exhibit strong preference for the surface. The latter is obviously connected with the fact that cubic AlN has a high degree of ionic bonding and a vacancy creation on the nitrogen sublattice is highly energetically unfavorable, especially in the bulk due to a larger number of Al-N ionic bonds.

中文翻译：

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AlxTi1-xN 合金的表面能学

摘要 利用第一性原理计算确定了具有均匀浓度分布的随机Al x Ti 1 - x N合金的(100)、(110)和(111)表面能。(100) 表面在 TiN 的情况下具有 1.25 J/m2 的最低能量，在立方 AlN 的情况下为 1.32 J/m2，并且表现出非常小的浓度依赖性。(110) 和 (111) 表面对于所有组合物都具有高得多的能量。Ti和Al的偏析能是针对纯TiN和立方AlN以及Al 0.5 Ti 0.5 N和Al 0.9 Ti 0.1 N无规合金的(100)表面获得的。在后一种情况下，我们使用了两种不同的方法：相对于替代位点局部环境的替代能量的直接平均和簇扩展技术（CLE）。我们发现，在随机 Al x Ti 1 - x N 合金的整个浓度范围内，Ti 的偏析是有利的。然而，除了富铝合金：Al 0.9 Ti 0.1 N 和立方 AlN 外，它几乎在整个浓度范围内都很弱。在后一种情况下，Ti 表面偏析的增强与 Al x Ti 1 - x N 合金在接近纯 AlN 的成分下相分离趋势的急剧增加有关。接近纯 AlN 的 Ti 偏析趋势增加有助于解释在工业上重要的 Al x Ti 1 - x N 涂层中形成薄片结构。对于氮空位，它们在整个浓度范围内的偏析能相对较小，但对于纯 AlN，它们表现出对表面的强烈偏好。