Boundary influence on the fields and arrangement of the needle domains in barium titanate single crystals

Abstract

The superposition theory is adopted to study the boundary value problem of needle domains in barium titanate single crystals, which decomposes into an infinite-medium solution and a complementary solution. The model of an equivalent edge dislocation and line charge is adopted to calculate the fields due to the discrete needle domains in an infinite medium. The complementary solutions are obtained from a linear elastic boundary value problem using the finite element method. The influence of boundaries on the fields and arrangement of the needles in thin barium titanate single crystals is analysed, by considering traction-free boundaries and using the plane stress approximation. According to the principle of minimum potential energy, it is found that pairs of parallel needle domains can be stabilized if the effective charge associated with the needle tips is reduced to 48% of the material’s full polarization charge. The evolution of comb-like arrays of needle domains under compressive mechanical load is simulated, and the results are found to be qualitatively similar to experimental observations which have not previously been explained theoretically.