A detailed study of the ground state structure, non-zero elastic constants, high pressure lattice dynamics as well as theoretical tensile and shear strengths of the cubic intermetallic compounds LaIn₃ and LaTl₃ with AuCu₃ (L12)-type has been made through first-principles. The optimized equilibrium crystal constants, cell volumes, bulk modulus and its pressure derivative, and single-crystalline elastic constants are in fair agreement with available experimental data and other calculations. More importantly, high pressure phonon spectrum, total and partial phonon densities of states in LaIn₃ and LaTl₃ up to 10 GPa are reported by employing Density Functional Perturbation Theory (DFPT), and the present results have demonstrated that both systems are dynamically stability up to 10 GPa. The differences between the dynamical properties of LaIn₃ and LaTl₃ have also been discussed systematically. Additionally, the tensile and shear stress-strain responses and the theoretical strengths of LaIn₃ and LaTl₃ are further calculated, we have found that LaIn₃ exhibits larger tensile and shear strengths than LaTl₃. These investigations are expected to provide beneficial references for further exploring the physical properties of rare earth compounds.

基态结构的详细研究，非零的弹性常数，高压晶格动力学以及理论拉伸和立方金属间化合物的剪切强度LAIN ₃和LaTl ₃与AuCu的₃（L12）型已经通过先制成-原则。优化的平衡晶体常数，晶胞体积，体积模量及其压力导数和单晶弹性常数与可用的实验数据和其他计算结果完全吻合。更重要的是，LaIn ₃和LaTl _3中的高压声子谱，状态的全部和部分声子密度通过使用密度泛函扰动理论（DFPT）报道了高达10 GPa的动态，目前的结果表明这两个系统在高达10 GPa的情况下都是动态稳定的。还已经系统地讨论了LaIn ₃和LaTl ₃动力学性质之间的差异。此外，进一步计算了LaIn ₃和LaTl ₃的拉伸和剪切应力-应变响应以及理论强度，我们发现LaIn ₃比LaTl ₃表现出更大的拉伸和剪切强度。这些研究有望为进一步探索稀土化合物的物理性质提供有益的参考。