Stress and strain mapping of micro-domain bundles in barium titanate using electron backscatter diffraction

Abstract

Cross-correlation of electron backscatter diffraction patterns has been used to generate stress and strain maps of a single crystal of tetragonal barium titanate (BaTiO3) containing bundles of small, (0.2–5) μm, a- and c-domains separated by 90° domain boundaries. The strains peaked at the domain boundaries, and approximately equal, but opposite, values were observed in the a- and c-domains; the peak strain magnitudes were slightly less than half the tetragonal distortion of BaTiO3, about 0.004, consistent with a tendency to a cubic structure at domain boundaries. The strain state was dominated by two normal strains: in-plane, perpendicular to domain wall intersections with the surface, and out-of-plane, perpendicular to the surface. In distinction to larger, lamellar domains, significant shear strains were also observed. Stress maps were constructed from strain maps using a method that does not require zero stress at reference locations. Peak in-plane normal stresses of approximately 700 MPa were observed. The variation of the stress component parallel to the domain walls was used to determine numerically a microstructurally based stress intensity factor for crack propagation perpendicular to the domain walls. The conditions for stable micro-crack formation in the microstructural stress field and unstable crack propagation under the action of a superposed applied stress were considered in the context of multi-layer ceramic capacitor reliability.