nucleation

Before a raindrop can grow, a first tiny droplet must appear out of the vapor, and getting that very first speck to survive is the hard part. Nucleation is the birth of the first tiny stable particles of a new phase inside the old one. It is like starting a crowd: the first few people to gather feel awkward and tend to disperse; only once enough gather does the group become self-sustaining.

When a new solid particle forms, two energies fight. Building the interior of the new phase lowers the free energy (good, because it is the more stable phase) and scales with volume, roughly r^3. But creating the new surface between old and new phase costs energy (bad) and scales with area, roughly r^2. For a very small cluster the surface cost dominates, so small clusters tend to redissolve. Only clusters that reach a critical size are past the hump and grow spontaneously.

Nucleation comes in two flavours. Homogeneous nucleation happens uniformly in the bulk (rare, and needs large undercooling). Heterogeneous nucleation happens on a pre-existing surface, such as a grain boundary, an impurity particle, or a mould wall, which lowers the barrier and so dominates in practice. This is why real materials transform far more easily than clean thermodynamics predicts.