Journal of Conference Abstracts

A One-Parameter Model of a Rigid Unit Structure

Manoj Gambhir¹ (mg206@cam.ac.uk), Volker Heine¹ (vh200@phy.cam.ac.uk) & Martin T. Dove² (martin@minp.esc.cam.ac.uk)

¹ Cavendish Laboratory, Cambridge University.

² Department of Earth Sciences, Cambridge University.

The Rigid Unit model has been developed to describe phase transitions in which polyhedral units of several atoms maintain their integrity on collective motion. Previously, lattice dynamics calculations have been performed on such structures at zero temperature and with infinitessimal rotations of the rigid units. These calculations are not a true representation of the dynamics of the materials at commonly encountered temperatures.

Molecular Dynamics calculations were carried out on the beta-Cristobalite structure to observe its behaviour under the excitation of several Rigid Unit Modes at finite temperatures. Rigid tetrahedra interacted via harmonic forces at the vertices - the 'one-parameter' model. Rigid Unit Modes (RUMs) are seen, in this model, to freely coexist with no significant preference for one set of RUMs over another.

Volume Coupling in Displacive Phase Transitions

Manoj Gambhir (mg206@cam.ac.uk), Volker Heine (vh200@phy.cam.ac.uk) & Eva R. Myers (erm1001@cam.ac.uk)

Cavendish Laboratory, Cambridge University.

Many displacive phase transitions in framework silicate minerals involve significant volume changes, often as high as 5­10%. These transitions are brought about by coupled rotations of rigid unit molecules and when this is recognised the structural volume change is straightforwardly related to the rotation angle of each unit. Using a simple model of a rigid unit structure it is shown that the forces acting on each unit are strongly dependent upon the volume of the system.

The Order Parameter in these calculations is represented by the set of rotations associated with the soft mode of the transiton. It is seen that the expansion of the structure falls short of the 'ideal' high temperature phase in which the units are notionally at zero rotation. This is explained by the combined effects of thermal agitation of the rigid units and the evolution of the local rotational potential energy profiles as a result of the thermal expansion of the system. As a consequence of these effects, the entropy increases sufficiently to stabilise the high phase.