Lattice dynamics and vibrational specific heat of MgO microcrystals

In this paper we treat the lattice dynamics of microcrystals (clusters) of MgO in the context of the Kellermann rigid-ion model. Clusters of 180 and 900 ions are studied, both unrelaxed and relaxed. Extensive use of the cluster symmetry (space group $D_{2h}$) allows us to solve the dynamical problem of the large cluster. The effects of size and of relaxation on the dynamics and the vibrational specific heat are evaluated. It is found that size effects are simple, that is, proportional to cluster size and ratio of surface to bulk ions. On the other hand, relaxation effects are very significant in that unrelaxed clusters do not satisfy the condition of rotational invariance; this leads to the wrong behavior of the cluster-excess heat capacity over the entire temperature range.