Abstract The elastic anisotropy and thermodynamic properties of MB12 (M = Zr, Hf, Y and Sc) compounds with UB12-type structure have been investigated by combining the first principles with the quasi-harmonic Debye model. The results show that these structures exhibit strong resistance to the uniaxial stress. The Young’s modulus E is 50% higher than bulk modulus B and shear modulus G and the latter two are very close to each other. All MB12 compounds are brittle at 0 GPa. The Vickers hardness values are all lower than that of the traditional threshold for super hard material (40 GPa). Comparative studies reveal that ZrB12 and HfB12 show similar fracture toughness, while ScB12 shows the lowest one. Elastic anisotropy is evaluated by the universal anisotropy index AU, Emax/Emin, anisotropy shear Ashear, shear factor A1 and the 3D surface constructions of Young’s modulus. The 3D contours of the Young's modulus of four materials are very similar at both 0 GPa and 100 GPa. Also, pressure can increase the anisotropy for MB12. The pressure and temperature dependence of the heat capacity, thermal expansion coefficient and Debye temperature of MB12 are also comprehensively discussed. These results will be able to meet the multifunctional requirements of these multifunctional materials in production.

中文翻译：

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高压下金属十二硼化物的弹性各向异性和热力学性质

摘要 结合第一性原理和准谐德拜模型，研究了具有UB12型结构的MB12（M = Zr、Hf、Y和Sc）化合物的弹性各向异性和热力学性质。结果表明，这些结构对单轴应力表现出很强的抵抗力。杨氏模量 E 比体积模量 B 和剪切模量 G 高 50%，后两者非常接近。所有 MB12 化合物在 0 GPa 时都很脆。维氏硬度值均低于超硬材料的传统阈值（40 GPa）。比较研究表明，ZrB12 和 HfB12 显示出相似的断裂韧性，而 ScB12 显示出最低的断裂韧性。弹性各向异性通过通用各向异性指数AU、Emax/Emin、各向异性剪切Ashear、剪切因子 A1 和杨氏模量的 3D 表面结构。四种材料的杨氏模量的 3D 轮廓在 0 GPa 和 100 GPa 下都非常相似。此外，压力可以增加 MB12 的各向异性。还全面讨论了MB12的热容量、热膨胀系数和德拜温度的压力和温度依赖性。这些结果将能够满足这些多功能材料在生产中的多功能要求。