Bounds on the Poisson’s Ratios of Diamond-Like Structures

Abstract

Poisson’s ratios of diamond-like structures, such as cubic C, Si, and Ge, have been widely explored because of their potential applications in solid-state devices. However, the theoretical bounds on the Poisson’s ratios of diamond-like structures remain unknown. By correlating macroscopic elastic constants with microscopic force constants of diamond-like structures, we here derived analytical expressions for the minimum Poisson’s ratio, the maximum Poisson’s ratio, and the Poisson’s ratios averaged by three schemes (i.e., Voigt averaging scheme, Reuss averaging scheme, and Hill averaging scheme) as solely a function of a dimensionless quantity (λ) that characterizes the ratio of mechanical resistances to the angle bending and bond stretching. Based on these expressions, we further determined the bounds on the Poisson’s ratios, the minimum Poisson’s ratio, the maximum Poisson’s ratio, and the Poisson’s ratios averaged by three schemes (i.e., Voigt averaging scheme, Reuss averaging scheme, and Hill averaging scheme), which are (−1, 4/5), (−1, 1/5), (0, 4/5), (−1, 1/2), (−1/3, 1/2), and (−2/3, 1/2), respectively. These results were well supported by atomistic simulations. Mechanism analyses demonstrated that the diverse Poisson’s behaviors of diamond-like structures result from the interplay between two deformation modes (i.e., bond stretching and angle bending). This work provides the roadmap for finding interesting Poisson’s behaviors of diamond-like structures.