First-principles study of porosity in amorphous silica and alpha quartz

We have investigated the SiO₂ systems, amorphous silica and alpha quartz, to understand the energy dependence on increasing porosity from closed cell to open cell foam from first-principles. A series of first-principles, density functional theory (DFT), calculations on these systems were examined with increasing porosity from 0 to nearly 50%. The formation energy per surface area of the void was calculated as a function of radius. The results from this study can be potentially useful to inform larger scale, continuum hydrocode models and provide initial internal energy and pressure for the first-principles Hugoniot as a porous SiO₂ foam is compressed. The Pade model for a liquid-drop, which spans the limits from drop to planar surface as a function of radius, was used to fit our DFT results. The extrapolation of the model suggests a gradual approach to the planar surface limit, beyond the radius of 300 Å for both ordered and disordered systems, indicating a universal behavior in the SiO₂ systems.