The $\alpha$ and $\beta$ modifications of quartz and cristobalite silica have been successfully simulated using molecular dynamics simulations based on a single parametrization of a charge transfer three-body potential. The simulated $\alpha$ forms exhibit positive thermal expansion; it is almost zero for $\beta$ cristobalite up to 1500 K and slightly negative at higher temperatures, while a negative thermal expansion of $\beta$ quartz is observed immediately above the $\alpha$-to-$\beta$ transition. A detailed analysis of atomic trajectories reveals that the origin of negative thermal expansion in the high-temperature $\beta$ forms of silica is a gradual reactivation of the same displacement mode that underlies the transformation between the $\alpha$ and $\beta$ modifications.

• Received 14 December 2004

DOI:https://doi.org/10.1103/PhysRevLett.95.215901