  Motivated by unexpected morphologies of the emerging liquid phase (channels,
bulges, droplets) at the edge of thin, melting alkane terraces, we propose a
new heterogeneous nucleation pathway. The competition between bulk and
interfacial energies and the boundary conditions determine the growth and shape
of the liquid phase at the edge of the solid alkane terraces. Calculations and
experiments reveal a "pre-critical" shape transition (channel-to-bulges) of the
liquid before reaching its critical volume along a putative shape-conserving
path. Bulk liquid emerges from the new shape, and depending on the degree of
supersaturation, the new pathway may have two, one, or zero energy barriers.
The findings are broadly relevant for many heterogeneous nucleation processes
because the novel pathway is induced by common, widespread surface topologies
(scratches, steps, etc.).
