  A discrete model and the regular solution approximation are applied to
describe the effect of grain boundary motion on grain boundary phase
transformations in a binary alloy. The model predicts all thermodynamic
properties of the grain boundary and the solute drag force, and permits a broad
exploration of the parameter space and different dynamic regimes. The grain
boundary phases continue to exist in the moving grain boundary and show a
dynamic hysteresis loop, a dynamic critical line, and other features that are
similar to those for equilibrium phases. Grain boundary motion strongly affects
the relative stability of the phases and can even stabilize phases that are
absolutely unstable under equilibrium conditions. Grain boundary phase
transformations are accompanied by drastic changes in the boundary mobility.
The results are analyzed in the context of non-equilibrium thermodynamics.
Unresolved problems and future work are discussed.
