Anisotropic thermal expansion and themomechanic properties of α-phase group-VA monolayers

The theoretical investigations of anisotropic thermal expansion are quite few as the huge computational cost. In this work, a scheme of Taylor expansion for phonon free energy is introduced to investigate anisotropic thermal expansion, which can save lots of computational cost. The anisotropic thermal expansion and thermomechanic properties of α-phase group-VA monolayers (α-P, α-As, α-Sb and α-Bi) are investigated systematically by using first-principles calculations. It is found all the four monolayers show remarkably anisotropic thermal expansion, and very different from each other. In α-As and α-Bi monolayers, remarkable negative thermal expansion appears along armchair direction. From α-P to α-Bi monolayer, the absolute value of linear thermal expansion coefficient becomes larger. In particular the linear thermal expansion coefficient of α-Bi is in terms of order of magnitude close to 10−4 K−1 at 300 K. The macroscopic Grüneisen parameters and elastic constants are also investigated to unveil the underlying physical mechanisms.