Subinay Dasgupta’s research while affiliated with Jadavpur University and other places

A manifestation of ‘antipiezoelectricity’ in the ionic crystals with fluorite structure is the development of a macroscopic volume distribution of electrostatic quadrupole moment under mechanical strain. We give here microscopic expressions and numerical estimates for the moment and find that it is too feeble to be measured by electrostatic experiments.

It is shown that starting from a Fourier transform relation one can derive, in a surprisingly simple manner, all the well-known results of lattice summation, that have been obtained so far by a complicated use of the Ewald theta transformation. We show that the Ewald transformation follows directly from the Fourier transform relation.

In order to calculate the electrostatic contributions to the elastic constants of piezoelectric crystals, Fuller and Naimon [Phys. Rev. B. 6, 3609 (1972)] used the conventional method of homogeneous deformation by evaluating the lattice sums using the Ewald transformation and omitting the zero-wave-vector term. This procedure, however, lacks justification, since it is well known that the conventional homogeneous deformation theory breaks down for piezoelectric crystals. We develop here the full theory for this case. (The use of a new technique for performing the theta transformation makes the treatment much simpler.) The theory verifies that the procedure of Fuller and Naimon will give the correct contribution to the elastic constants. We also explain why the zero-wave-vector term remained absent in their treatment. Moreover, we derive for an arbitrary crystal structure some relationships between the electrostatic contributions to the different second- and third-order elastic constants. In view of these relationships, one has to calculate a lesser number of electrostatic contributions for a given crystal structure, and some of the evaluations of Fuller and Naimon become redundant.

We derive expressions for the third-order elastic, piezoelectric, and dielectric constants, in terms of the interaction potential, and show that in fluorite structure, equal and opposite dipole moments under homogeneous strain develop. The presence of such latent polarisation is reflected in the dielectric response of the strained crystal.

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 CaF2, SrF2, and BaF2.