Lattice mismatch and twist partitioning at commensurate dichromatic pattern of two-phase interfaces

Misfit dislocations are formed at a two-phase interface to reduce and even diminish coherency stress in the region far from the interface. Such semi-coherent interfaces are key structural features in a wide range of engineering materials. Burgers vectors of misfit dislocations are defined with the reference lattice named as commensurate dichromatic pattern (CDP) in the topological model. The CDP is not a geometrical average of boundary units as historically used in many examples. In this work, based on the Green’s function and theory of dislocations, both the mechanical effects of interfacial dislocation arrays and coherency strains due to geometry match at the interface are considered to get the CDP. We demonstrated that the mismatch and twist partitioning at a CDP are unequally partitioned in the two adjacent crystals, which only depends on elastic properties of the two crystals regardless of characters of misfit dislocations. Correspondingly, the method to determine the CDP of a two-phase interface in bi-crystal is developed.