  We characterize both analytically and numerically short-range forces between
spatially diffuse interfaces in multi-phase-field models of polycrystalline
materials. During late-stage solidification, crystal-melt interfaces may
attract or repel each other depending on the degree of misorientation between
impinging grains, temperature, composition, and stress. To characterize this
interaction, we map the multi-phase-field equations for stationary interfaces
to a multi-dimensional classical mechanical scattering problem. From the
solution of this problem, we derive asymptotic forms for short-range forces
between interfaces for distances larger than the interface thickness. The
results show that forces are always attractive for traditional models where
each phase-field represents the phase fraction of a given grain. Those
predictions are validated by numerical computations of forces for all
distances. Based on insights from the scattering problem, we propose a new
multi-phase-field formulation that can describe both attractive and repulsive
forces in real systems. This model is then used to investigate the influence of
solute addition and a uniaxial stress perpendicular to the interface. Solute
addition leads to bistability of different interfacial equilibrium states, with
the temperature range of bistability increasing with strength of partitioning.
Stress in turn, is shown to be equivalent to a temperature change through a
standard Clausius-Clapeyron relation. The implications of those results for
understanding grain boundary premelting are discussed.
