  Atomistic non-equilibrium molecular dynamics (NEMD) simulations of shock wave
compression of quartz have been performed using the so-called BKS
semi-empirical potential of van Beest, Kramer and van Santen to construct the
Hugoniot of quartz. Our scheme mimics the real world experimental set up by
using a flyer-plate impactor to initiate the shock wave and is the first shock
wave simulation that uses a geom- etry optimised system of a polar slab in a
3-dimensional system employing periodic boundary conditions. Our scheme also
includes the relaxation of the surface dipole in the polar quartz slab which is
an essential pre-requisite to a stable simulation. The original BKS potential
is unsuited to shock wave calculations and so we propose a simple modification.
With this modification, we find that our calculated Hugoniot is in good
agreement with experimental shock wave data up to 25 GPa, but significantly
diverges beyond this point. We conclude that our modified BKS potential is
suitable for quartz under representative pressure conditions of the Earth core,
but unsuitable for high-pressure shock wave simulations. We also find that the
BKS potential incorrectly prefers the {\beta}-quartz phase over the
{\alpha}-quartz phase at zero-temperature, and that there is a {\beta}
\rightarrow {\alpha} phase-transition at 6 GPa.
