  The motion of microstructural interfaces is important in modeling materials
that undergo twinning and structural phase transformations. Continuum models
fall into two classes: sharp-interface models, where interfaces are singular
surfaces; and regularized-interface models, such as phase-field models, where
interfaces are smeared out. The former are challenging for numerical solutions
because the interfaces need to be explicitly tracked, but have the advantage
that the kinetics of existing interfaces and the nucleation of new interfaces
can be transparently and precisely prescribed. In contrast, phase-field models
do not require explicit tracking of interfaces, thereby enabling relatively
simple numerical calculations, but the specification of kinetics and nucleation
is both restrictive and extremely opaque. This prevents straightforward
calibration of phase-field models to experiment and/or molecular simulations,
and breaks the multiscale hierarchy of passing information from atomic to
continuum.
  We present the formulation of a phase-field model -- i.e., a model with
regularized interfaces that do not require explicit numerical tracking -- that
allows for easy and transparent prescription of complex interface kinetics and
nucleation. The key ingredients are a re-parametrization of the energy density
to clearly separate nucleation from kinetics; and an evolution law that comes
from a conservation statement for interfaces. This enables clear prescription
of nucleation through the source term of the conservation law and of kinetics
through an interfacial velocity field. A formal limit of the kinetic driving
force recovers the classical continuum sharp-interface driving force, providing
confidence in both the re-parametrized energy and the evolution statement.
  We present a number of numerical calculations in one and two dimensions to
characterize and demonstrate the formulation.
