CALCULATION OF THE ELASTIC AND ELECTROSTATIC ENERGIES OF AN INCLUSION IN A FERROELECTRIC OR A PIEZOELECTRIC CRYSTAL

Abstract
Previous optical observations have shown that the first order structural phase transitions of some ferroelectric (e.g. KD₂PO₄) or piezoelectric (e.g. quartz) crystals present some similarity with martensitic transformations : two phases with different lattice parameters coexist over a small temperature range and the low temperature phase can be twinned ; (this twinning corresponds to alternate shears and electric polarization in the case of KD₂PO₄). In contrast with martensites both elastic and electric properties are important in determining the morphology of the heterophase structure. In particular the habit plane separating the two phases is no longer a plane without long range strains when electric energies are not negligible. In this case one has to determine the configuration for which the sum of the elastic and electric energies is minimum : this can be done for an inclusion of the new phase in an infinite matrix of the parent phase by extending Khachaturyan's theory to take into account the electric and piezeoelectric properties. We present an outline of this theory in the case of crystals of any symmetry. The effect of a uniform applied stress or of an electric field is also discussed.