  A phase-field model that allows for quantitative simulations of low-speed
eutectic and peritectic solidification under typical experimental conditions is
developed. Its cornerstone is a smooth free-energy functional, designed so that
the stable solutions connecting any two phases are completely free of the third
phase. For the simplest choice of this functional, the equations of motion for
each of the two solid-liquid interfaces can be mapped to the standard
phase-field model of single-phase solidification, and all thin-interface
corrections to the dynamics of the solid-liquid interfaces can be eliminated.
This means that simulation results become independent of the thickness W of the
diffuse interfaces. As a consequence, accurate results can be obtained using
values of W much larger than the physical interface thickness, which makes
simulations for realistic experimental parameters feasible. Convergence of the
simulation outcome with decreasing W is explicitly demonstrated. The results
are also compared to a boundary-integral formulation of the corresponding
free-boundary problem. Excellent agreement is found, except in the immediate
vicinity of bifurcation points, where differences arise. These differences
reveal that, in contrast to the standard assumptions of the free-boundary
problem, out of equilibrium the diffuse trijunction region of the phase-field
model can (i) slightly deviate from Young's law for the contact angles, and
(ii) advance in a direction that forms a finite angle with the solid-solid
interface at each instant. While the deviation (i) extrapolates to zero in the
limit of vanishing interface thickness, the small angle in (ii) remains roughly
constant, which indicates that it might be a genuine physical effect, present
even for an atomic-scale interface thickness.
