Engineered domain configurations in orthorhombic phase of potassium niobate crystals and their tensor properties

Using general method, we derive macroscopic types of conceivable engineered domain structures of Amm2-phase in KNbO3 single crystals. It appears that piezoelectric domain structures belong to 10 of 15 possible types. We find 9 non-equivalent piezoelectric coherent configurations, each,formed by all domain states lying within same free energy level in the stabilizing field(s); such level, possibly virtual, is given by the relevant term(s) in free energy expansion. Examining macroscopic properties of domain structures, approximated as volume-average over individual states, we establish five cases where additional relationships between tensor components appear compared to single domain crystals with same macroscopic symmetry.