Modeling of non-local interactions on a phase transformation interface

Abstract
If an interaction between phases of different composition at an interface is significant, the classical model of an interface is no longer satisfactory. In such cases, the transition layer has to be modeled as a surface phase with intrinsic non-local properties. The boundary of separation, which defines the interface, must possess its own internal structure in order to allow accommodation of complex phenomena while balancing opposite tendencies on each side of the interface. Consequently, an extended model is needed that is capable of describing the intrinsic properties of the interface. To achieve this goal, we employ a special model of an interface with simple structure, where the mathematical notion of a simple structure corresponds to the material model without rotational degrees of freedom in each lattice point of the interface. By employing characteristic features of the model, we are in a position to describe quantitatively and qualitatively the structural and compositional non-local changes across the interface.