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The motion of microstructural interfaces is important in modeling materialsthat undergo twinning and structural phase transformations. Continuum modelsfall into two classes: sharp-interface models, where interfaces are singularsurfaces; and regularized-interface models, such as phase-field models, whereinterfaces are smeared out. The former are challenging for numerical solutionsbecause the interfaces need to be explicitly tracked, but have the advantagethat the kinetics of existing interfaces and the nucleation of new interfacescan be transparently and precisely prescribed. In contrast, phase-field modelsdo not require explicit tracking of interfaces, thereby enabling relativelysimple numerical calculations, but the specification of kinetics and nucleationis both restrictive and extremely opaque. This prevents straightforwardcalibration of phase-field models to experiment and/or molecular simulations,and breaks the multiscale hierarchy of passing information from atomic tocontinuum.  We present the formulation of a phase-field model -- i.e., a model withregularized interfaces that do not require explicit numerical tracking -- thatallows for easy and transparent prescription of complex interface kinetics andnucleation. The key ingredients are a re-parametrization of the energy densityto clearly separate nucleation from kinetics; and an evolution law that comesfrom a conservation statement for interfaces. This enables clear prescriptionof nucleation through the source term of the conservation law and of kineticsthrough an interfacial velocity field. A formal limit of the kinetic drivingforce recovers the classical continuum sharp-interface driving force, providingconfidence in both the re-parametrized energy and the evolution statement.  We present a number of numerical calculations in one and two dimensions tocharacterize and demonstrate the formulation.

A Dynamic Multiscale Phase-field Model for Structural Transformations  and Twinning: Regularized Interfaces with Transparent Prescription of Complex  Kinetics and Nucleation