Niobium-based compounds with the A15 structure have been widely applied in fusion engineering test reactor and superconducting materials. Hence, for a better understanding of the physical properties of A15-type Nb₃X (X = Si, Ge, Sn and Pb) compounds, their structural, electronic, elastic and thermodynamic properties were investigated using the first-principles calculations. The calculated formation enthalpies indicated that these Nb₃X compounds are energetically favorable and the sequence of thermodynamic stability is Nb₃Si > Nb₃Ge > Nb₃Sn > Nb₃Pb. Meanwhile, the phonon dispersions verified that these Nb₃X compounds are dynamically stable. The electronic properties, such as the density of state, band structure, electron density difference and Mulliken population, suggested that these compounds are metallic, and Nb-Nb and Nb-X chemical bonds are ionic-covalent mixed bonds. The single-crystal and polycrystalline elastic properties were calculated. Moreover, the elastic anisotropy was discussed by elastic anisotropic indexes, three-dimensional surface construction and planar projections of elastic modulus, and the sequence of elastic anisotropy is Nb₃Si > Nb₃Ge > Nb₃Sn > Nb₃Pb. Finally, thermal properties such as Debye temperatures and sound velocities were analyzed based on elastic moduli.

具有A15结构的铌基化合物已广泛应用于聚变工程测试反应堆和超导材料中。因此，为了更好地理解A15型Nb ₃ X（X = Si，Ge，Sn和Pb）化合物的物理性质，使用第一性原理研究了它们的结构，电子，弹性和热力学性质。计算出的形成焓表明这些Nb ₃ X化合物在能量上是有利的，并且热力学稳定性的顺序为Nb ₃ Si> Nb ₃ Ge> Nb ₃ Sn> Nb ₃ Pb。同时，声子色散证实了这些Nb ₃X化合物是动态稳定的。电子性质，例如态密度，能带结构，电子密度差和Mulliken种群，表明这些化合物是金属的，Nb-Nb和Nb-X化学键是离子-共价混合键。计算了单晶和多晶的弹性。此外，通过弹性各向异性指数，三维表面构造和弹性模量的平面投影来讨论弹性各向异性，并且弹性各向异性的顺序为Nb ₃ Si> Nb ₃ Ge> Nb ₃ Sn> Nb ₃ Pb。最后，基于弹性模量分析了热性能，例如德拜温度和声速。