Three-body interaction and fluorite structure: Elastic properties of Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Ba${\mathrm{F}}_2$

In spite of the fact that second-order elastic constants of some ionic crystals with fluorite structure can be fitted quite well by the shell model using the two-body interaction only, the situation is still unsatisfactory. In our previous work, it was therefore attempted to provide a satisfactory picture by introducing the three-body interaction. The importance of this interaction was estimated from a study of second-order elastic constants by using mainly the results of a first-principles calculation. In this paper, this investigation is extended to third-order elastic constants. In order to obtain explicit expressions for elastic constants, the terms arising from the Coulomb interaction and shell structure are determined from the work of Srinivasan and those arising from non-Coulomb two- and three-body interactions by the homogeneous deformation theory developed in the preceding paper. The results confirm the importance of the three-body interaction in the study of the elastic properties of Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Ba${\mathrm{F}}_2$.