First-principle study of the nonlinear elastic properties of amorphous silicon and silica

First-principle calculations and homogeneous finite deformation method are used to calculate second- and third-order elastic coefficients of amorphous silicon and amorphous silica, for model structures generated via melt-quench approach based on force-field molecular dynamics simulations. Second-order elastic coefficients are used to deduce macroscopic elastic moduli, such as bulk, Young, and shear moduli, and their pressure derivatives. The third-order elastic coefficients are used to calculate acoustic Gr\"{u}neisen parameter. Our data show that elastic properties, both linear and nonlinear, of amorphous silicon reach isotropy within the nanometer length scale, displaying similar features comparable to those of crystalline silicon. In the same scale of length the nonlinear elastic properties of silica show anisotropy, featuring pressure-induced softening of elastic coefficients. This elastic anomaly of silica is found to be correlated with the large negative values of the Gr\"{u}neisen parameter in the long-wavelength limit.