Real-space rigid-unit-mode analysis of dynamic disorder in quartz, cristobalite and amorphous silica

We use a recently developed tool based on geometric algebra to analyse the phase transition in quartz, the nature of the disordered high-temperature phase of cristobalite and the dynamics of silica glass. The approach is to analyse configurations generated by the reverse Monte Carlo or molecular dynamics simulations in terms of rigid-unit-mode (RUM) motions, but concentrating on quantifying the real-space distortions rather than performing a reciprocal-space analysis in terms of RUM phonons. One of the important results is a measure of the extent to which the amplitudes of motion are directly attributable to RUMs, and how the RUM fraction changes as a result of a phase transition.