Semicoherent heterophase interfaces with core-spreading dislocation structures in magneto-electro-elastic multilayers under external surface loads

Using the extended Stroh formalism combining with the Fourier-transform and dual variable and position techniques, semicoherent interfaces are introduced to simulate the appropriate structural interface conditions in three-dimensional magneto-electro-elastic (MEE) multilayered composites under external loads. The field solutions caused by both internal and external actions are expressed in terms of biperiodic Fourier series expansions in multilayered systems that are made of dissimilar, linear and anisotropic plates with planar lattice mismatches. For non-perfectly bonded internal interfaces, the semicoherent heterophase interfaces are atomistically described by infinitely-long, parallel, periodically-spaced, and core-spreading intrinsic dislocation structures in free-standing multilayers. On the other hand, subsequent solutions for general loads on the external surfaces with coherent interfacial conditions are consistently derived and superposed to the former dislocation-induced fields. Three application examples in bi-, tri-, and six-layered MEE systems are investigated. The first bilayered case illustrates the significant effects of the semicoherent interface with dislocation core-spreading widths on the elastic, electric, and magnetic fields in the CoFe₂O₄/BaTiO₃ composite materials. The second example is a trilayered system made of A/B/A with two discrete sets of intrinsic dislocation dipoles on their semicoherent interfaces, analyzed by proposing a novel energy based criterion. Critical dislocation spacings and thicknesses of capped interlayers are quantified in nanoscale MEE heterostructures with different stacking sequences, providing possible guides for stable growth of layered nanostructures. Finally, the complex distribution of field solutions in a six-layered MEE system with a prescribed externally mechanical load shows the crucial role played by the topological defects in localizing the coupled electric and magnetic components at the semicoherent interfaces, which indicates the important interplay between the internal and external actions. These resulting features open up novel opportunities for designing atomic-scale heterostructures with unprecedented MEE properties by engineering the interfacial dislocation patterns when the multilayered structures are free or under external action.