  The motion of interfaces is an essential feature of microstructure evolution
in crystalline materials. While atomic-scale descriptions provide mechanistic
clarity, continuum descriptions are important for understanding microstructural
evolution and upon which microscopic features it depends. We develop a
microstructure evolution simulation approach that is linked to the underlying
microscopic mechanisms of interface migration. We extend the continuum approach
describing the disconnection-mediated motion of interfaces introduced in Part I
[Han, Srolovitz and Salvalaglio, 2021] to a diffuse interface, phase-field
model suitable for large-scale microstructure evolution. A broad range of
numerical simulations showcases the capability of the method and the influence
of microscopic interface migration mechanisms on microstructure evolution.
These include the effects of stress and its coupling to interface migration,
showing how this leads to important differences from classical microstructure
evolution as, for example, represented by mean curvature flow.
