  The pathway to forming the iron-rich planet Mercury remains mysterious.
Mercury's core makes up 70% of the planetary mass, which implies a significant
enrichment of iron relative to silicates, while its mantle is strongly depleted
in oxidized iron. The high core mass fraction is traditionally ascribed to
evaporative loss of silicates, e.g. following a giant impact, but the high
abundance of moderately volatile elements in the mantle of Mercury is
inconsistent with reaching temperatures much above 1,000 K during its
formation. Here we explore the nucleation of solid particles from a gas of
solar composition that cools down in the hot inner regions of the
protoplanetary disc. The high surface tension of iron causes iron particles to
nucleate homogeneously (i.e., not on a more refractory substrate) under very
high supersaturation. The low nucleation rates lead to depositional growth of
large iron pebbles on a sparse population of nucleated iron nano-particles.
Silicates in the form of iron-free MgSiO$_3$ nucleate at similar temperatures
but obtain smaller sizes due to the much higher number of nucleated particles.
This results in a chemical separation of large iron particles from silicate
particles with ten times lower Stokes numbers. We propose that such conditions
lead to the formation of iron-rich planetesimals by the streaming instability.
In this view, Mercury formed by accretion of iron-rich planetesimals with a
sub-solar abundance of highly reduced silicate material. Our results imply that
the iron-rich planets known to orbit the Sun and other stars are not required
to have experienced mantle-stripping impacts. Instead their formation could be
a direct consequence of temperature fluctuations in protoplanetary discs and
chemical separation of distinct crystal species through the ensuing nucleation
process.
