Molecular dynamics interpretation of structural changes in quartz

Abstract

 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 α- and β-phases, and atoms vibrate around the α₁- (or α₂-) sites at lower temperatures in the α-phase, and over the energy barriers between the α₁- and the α₂-sites at higher temperatures in the α- and the β-phases. The ratios of time lengths spent by atoms in the α₁- and α₂-sites determine the apparent atomic positions as obtained in usual structure studies of α-quartz. More frequent transfer of atoms over the α₁- and the α₂-sites contributes positively to the thermal expansions, whereas larger amplitudes of vibrations, which carry atoms more distantly and more frequently from the β-sites, contribute negatively. The well-known steep thermal expansion in the α-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 α₁- and the α₂-sites. The nearly zero or negative expansion in the β-phase is caused by balancing the negative to the positive effects. The MD crystal transforms to the β-phase via a transitional state, where the α- and β-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.