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The conventional concept of domain walls is brought into question by asking what happens if the domain wall energy γ→0. In this case, the twin size is conformally miniaturized to near atomic scales and the twin wall density becomes extremely high. This has immense consequences as the symmetry of the domain boundaries is different than the symmetry of the order parameter. This concept is applied to tweed-like structures in morphotropic phase boundary (MPB) piezoelectric crystals, ferromagnetic shape memory alloys (FSMA), and pre-martensitic states (SMA). In particular, an adaptive phase theory is applied to the domain engineered states of MPB piezoelectric crystals that have extremely high properties. Structurally bridging monoclinic phases are predicted, and confirmed, whose values are adjustable values that are combinations of the cubic, rhombohedral/tetragonal phases, and geometrical invariant conditions. The results indicate that the structurally bridging monoclinic phases do not have unique lattice parameters, but rather are a structurally inhomogenous state on the nanometer scale consisting of an ensemble of rhombohedral or tetragonal nano-twins. High properties in nonlinear systems with high twin wall densities seem to be a commonality in MPB, FSMA, and SMA materials. Host: Turab Lookman |