In this paper, we present the outcome of ab-initio band structure study carried out on cubic phase ternary B_xAl_1−xN (x = 0, 0.125, 0.25, 0.5, 0.75, 0.875, 1.0) alloys in order to analyze the elastic coefficients thereby the structural, thermoelectric, electronic, thermal, mechanical, and optical properties of these alloys. With the aim of enhancing the hardness of aluminium nitride (19 GPa), the present study on the proposed combinations reveal that B_0.75Al_0.25N (40.5 GPa) and B_0.875Al_0.125N (49.5 GPa) alloys turn out to be superhard materials as their hardness surpasses 40 GPa. Further, B_0.875Al_0.125N alloy has been identified to serve as a good thermoelectric as it has a high Seebeck coefficient value of 240 µV/K and of melting temperature of 4282 K. Except for the binary compounds AlN and BN, all the other ternary alloys are predicted to be direct band gap materials. The density of states, band structure, charge density plot, various elastic moduli, Debye’s temperature, elastic wave velocity, dielectric constant, Seebeck’s coefficient and other properties of interest are discussed in this paper. The results are compared and found to agree very well with the available literature.

中文翻译：

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硼对提高氮化锌铝的硬度及其机械，热和热电性能的影响的理论研究

在本文中，我们介绍了对立方相三元B _x Al _{1- x} N（x = 0，0.125，0.25，0.5，0.75，0.875，1.0）合金进行的从头算带结构研究的结果，以进行分析因此，这些合金的弹性系数具有结构，热电，电子，热，机械和光学特性。为了提高氮化铝（19 GPa）的硬度，目前对所提出的组合的研究表明B _0.75 Al _0.25 N（40.5 GPa）和B _0.875 Al _0.125 N（49.5 GPa）合金被证明是超硬材料因为它们的硬度超过40 GPa。另外，B _0.875 Al _0.125N合金已被确认为具有良好的热电性能，因为它的塞贝克系数值高达240 µV / K，熔化温度为4282K。除二元化合物AlN和BN之外，其他所有三元合金均预计为直接带隙材料。本文讨论了状态密度，能带结构，电荷密度图，各种弹性模量，德拜温度，弹性波速度，介电常数，塞贝克系数和其他感兴趣的性质。比较结果，发现与现有文献非常吻合。