Investigation of the mechanical, electronic, and thermodynamic properties of recently synthesized (Ta_1−xHf_x)₄AlC₃ and (Ta_1−xHf_x)₄Al_0.5Sn_0.5C₃ (0 ≤ x ≤ 0.25) solid solutions is conducted using density functional theory for the first time. The computed lattice constants are in good agreement with prior results. The calculated stiffness constants are used to check the mechanical stability of the studied compositions. The bulk modulus (B), shear modulus (G), and Young's modulus (Y) are found to be influenced by Hf and Sn substitution. The titled solid solutions are brittle in nature. The 3D presentations of elastic moduli and elastic anisotropy factors are used to disclose the anisotropic mechanical features of the considered compositions. The electronic band structure, density of states, and charge density mapping (CDM) show the metallic nature, the contribution from different states to electronic conductivity, and atomic bonding characteristics. The electronic band structure and CDM are also used together to investigate the change in bonding strength due to Hf and Sn substitutions. The Debye temperature (Θ_D), minimum thermal conductivity (K_min), Grüneisen parameter (γ), and melting temperature (T_m) of the studied solid solutions are estimated and analyzed. A good correlation is found between the mechanical and thermodynamic properties.

中文翻译：

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新合成的基于Ta的MAX相（Ta1-xHfx）4AlC3和（Ta1-xHfx）4Al0.5Sn0.5C3（0≤x≤0.25）固溶体：揭示机械，电子和热力学性质

最近合成的机械，电子，和热力学性质研究（TA _{1- X}铪_X）₄ ALC ₃和（TA _{1- X}铪_X）₄的Al _0.5的Sn _0.5 Ç ₃（0≤  X  ≤0.25）固体溶液是首次使用密度泛函理论进行。计算出的晶格常数与先前的结果非常吻合。计算出的刚度常数用于检查所研究组合物的机械稳定性。体积模量（B），剪切模量（G）和杨氏模量（B）发现Y）受Hf和Sn取代的影响。标题为固体的溶液本质上是脆性的。弹性模量和弹性各向异性因子的3D表示用于揭示所考虑组合物的各向异性力学特征。电子能带结构，状态密度和电荷密度映射（CDM）显示出金属性质，不同状态对电子导电性的贡献以及原子键合特性。电子带结构和CDM也一起用于研究由于Hf和Sn取代引起的键合强度变化。德拜温度（Θ _d），最小的热导率（ķ_分钟），Grüneisen参数（γ）和熔融温度（对所研究的固溶体的T _m）进行估计和分析。在机械性质和热力学性质之间发现良好的相关性。