Molecular dynamics interpretation of structural changes in quartz

Constant temperature and constant pressure molecular dynamics (MD) simulations were applied to quartz to calculate the structural details which are indeterminable in usual X-ray structure studies. The dynamics of the structural changes was analyzed by means of time-dependent atomic displacement parameters. The Si-O bonds expand with increasing temperatures through the alpha- and beta -phases, and atoms vibrate around the alpha (1)- (or alpha (2)-) sites at lower temperatures in the alpha -phase, and over the energy barriers between the alpha (1)- and the alpha (2)-sites at higher temperatures in the alpha- and the beta -phases. The ratios of time lengths spent by atoms in the alpha (1)- and alpha (2)-Sites determine the apparent atomic positions as obtained in usual structure studies of alpha -quartz. More frequent transfer of atoms over the alpha (1)- and the alpha (2)-sites contributes positively to the thermal expansions, whereas larger amplitudes of vibrations, which carry atoms more distantly and more frequently from the beta -sites, contribute negatively. The well-known steep thermal expansion in the alpha -phase is attributed to the additive contribution from the expansions of the Si-O bond lengths, the widening of Si-O-Si angles, and the increase of the atomic transfer-frequency between the alpha (1)- and the alpha (2)-sites. The nearly zero or negative expansion in the beta -phase is caused by balancing the negative to the positive effects. The MD crystal transforms to the beta -phase via a transitional state, where the alpha- and beta -structures appear alternately with time, or coexist. The slight and continuous expansions observed right after the steep rise(s) of the volume or cell dimensions up to the nearly horizontal curve(s) are attributed to the continuous changes within the transitional state.