Nonlinear Elasticity of Amorphous Silicon and Silica from Density Functional Theory

Density functional theory calculations and a finite deformation method are used to calculate second- and, most notably, third-order elastic constants of amorphous silicon and amorphous silicon dioxide, as represented by model structures generated via melt-quench force-field molecular dynamics simulations. Linear and nonlinear elastic constants are used to deduce macroscopic elastic moduli, such as the bulk and shear moduli, their pressure derivatives, and the elastic Grüneisen parameter. Our calculations show that the elastic properties of amorphous silicon reach the isotropic elastic limit within the nanometer length scale, attaining characteristics, both linear and nonlinear, comparable to those of crystalline silicon. In contrast, the nonlinear elastic properties of silica retain an anisotropic character over the nanometer length scales, yielding nonetheless the expected pressure-induced softening of the elastic moduli. This atypical elastic behavior is correlated to the occurrence of long-wavelength acoustic modes with negative Grüneisen parameters.