Despite their great interest showing that LuAuSn half-Heusler is a topologically trivial semimetal, most of information about its physical behaviors seem rather remote from completion for the fact that several of its physical properties remain still unknown. Therefore, we try to outline, going into much specific details, a study on elastic anisotropy, mechanical and dynamical stability, electronic properties as well as the analysis of bonding and weak interactions. The lattice parameter value obtained by GGA-WC is very close to the experimental one, therefore, this functional has been chosen to carry out the rest of this work. The detailed study of the elastic behavior has revealed the mechanical stability of this compound, it results that its structure resists to slight strains. The obtained results also indicate a large elastic anisotropy of LuAuSn. Electronic results obtained by TB-mBJ(SOC) have confirmed its semimetallic behavior as well as being topologically trivial. This last property has been confirmed not only by the absence of band overlap but also by the absence of band inversion by the analysis of fat bands with and without SOC effect. The analysis of bonding and weak interactions has shown that the covalent character is predominant with the presence of weak repulsive interactions in cage regions and strong repulsive interactions between Lu and Sn. The vibrational study has revealed the dynamical stability of LuAuSn in the ground state, which indicates that this compound keeps its half-Heusler structure even at very low temperatures. Also, its zone center phonon modes have been determined and analyzed in detail by showing their frequencies and polarizations.

尽管他们非常感兴趣地表明 LuAuSn half-Heusler 是一种拓扑微不足道的半金属，但关于其物理行为的大部分信息似乎离完成还很遥远，因为它的一些物理特性仍然未知。因此，我们试图概述弹性各向异性、机械和动力学稳定性、电子特性以及键合和弱相互作用分析的研究，并进入更多具体细节。GGA-WC 获得的晶格参数值与实验值非常接近，因此，选择此泛函来执行其余的工作。对弹性行为的详细研究揭示了该化合物的机械稳定性，它的结构可以抵抗轻微的应变。所得结果还表明 LuAuSn 具有较大的弹性各向异性。TB-mBJ(SOC) 获得的电子结果证实了其半金属行为以及拓扑微不足道。通过对有和没有 SOC 效应的胖条带的分析，不仅没有带重叠，而且没有带反转，这最后一个特性已经得到证实。键合和弱相互作用的分析表明，共价特征占主导地位，笼区存在弱排斥相互作用，Lu和Sn之间存在强排斥相互作用。振动研究揭示了 LuAuSn 在基态下的动态稳定性，这表明该化合物即使在极低的温度下也能保持其半赫斯勒结构。还，