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. In this paper, we have derived analytical expressions for the minimum and maximum Poisson's ratios, as well as the Poisson's ratios averaged by three different schemes (i.e., Voigt, Reuss, and Hill averaging schemes). These expressions are based on the correlation between macroscopic elastic constants and microscopic force constants of diamond-like structures, and are solely a function of a dimensionless quantity (λ) that characterizes the ratio of mechanical resistances between angle bending and bond stretching. Based on these expressions, we have determined the bounds on the Poisson's ratios, as well as the minimum and maximum Poisson's ratios, and the Poisson's ratios averaged by the three schemes mentioned above. Specifically, these bounds 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.