Abstract The elastic constants play a central role in the regulation of the thermo-mechanical and anisotropic response of materials. Nevertheless, there is still a lack of theoretical and experimental data on these constants which limits the possibility of developing new materials with targeted mechanical responses. The elastic constants of diamond and silicon as second and third-order are obtained using density functional theory (LDA, GGA, and HSE) and for the first time with the adiabatic-connection fluctuation–dissipation theorem in the random phase approximation. Our SOECs calculations show an excellent agreement with experimental data. In this framework, we study the mechanical properties such as Young’s modulus, Poisson’s ratio, bulk modulus, and shear modulus of diamond and silicon structures. Also, we visualize the 3D plot, as well as 2D for Young’s modulus, Poisson’s ratio, and others. For the TOECs, we show that can be taken our RPA results as a reference, since there is still a lack of reliable previous theoretical and experimental data of these materials.

中文翻译：

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使用密度泛函理论和随机相位近似的立方金刚石和硅的弹性和机械性能

摘要 弹性常数在调节材料的热机械和各向异性响应中起着核心作用。尽管如此，仍然缺乏关于这些常数的理论和实验数据，这限制了开发具有针对性机械响应的新材料的可能性。金刚石和硅的二阶和三阶弹性常数是使用密度泛函理论（LDA、GGA 和 HSE）获得的，并且首次使用随机相位近似中的绝热连接涨落-耗散定理获得。我们的 SOEC 计算结果与实验数据非常吻合。在此框架中，我们研究了机械性能，例如金刚石和硅结构的杨氏模量、泊松比、体积模量和剪切模量。此外，我们将 3D 绘图可视化，以及杨氏模量、泊松比等的二维。对于 TOEC，我们表明可以将我们的 RPA 结果作为参考，因为这些材料仍然缺乏可靠的先前理论和实验数据。