Microscopic elasticity theory of ionic crystal and its application to cubic ZrO2–5.2 mol% Y2O3 system

An analytical expression of the strain energy in an ionic crystalline solid solution was obtained by modifying the microscopic theory of elasticity in metal alloys. The Lorentz field originating in the short-range interaction of dipoles, along with a non-Coulomb force field produces specifically the elastic strain. On the other hand, the macroscopic electric field induced by the long-range interaction of dipoles works on each dipole lattice to produce the piezoelectric strain. The theory was applied to a cubic ZrO2–Y2O3 system of ionic crystalline solid solution in order to estimate the microscopic strain energy of the system. The trace of the minimum points in the energy surface indicates possible spinodal decomposition along [1 1 1] direction. It is also revealed that local electrical neutrality can mostly be preserved during the decomposition due to the macroscopic electric field in the ionic crystal.