The pathway for crystallization from dilute vapors and solutions is often observed to take a detourvia a liquid or concentrated-solution phase. For example, in moist subzero air, droplets of liquidwater form, which then freeze. In this example and in many others, an intermediate phase (hereliquid water) is dramatically accelerating the kinetics of a phase transition between two other phases(water vapor and ice). Here we study this phenomenon via exact computer simulations of a simplelattice model. Surprisingly, we find that the rate of nucleation of the new equilibrium phase isactually fastest when the intermediate phase is slightly unstable in the bulk, i.e., has a slightly higherfree energy than the phase we start in, Nucleation occurs at a concave part of the surface andmicroscopic amounts, of the intermediate phase can form there even before the phase is stable in thebulk. As the nucleus of the equilibrium phase is microscopic, this allows nucleation to occureffectively in the intermediate phase before it is stable in the bulk.
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