  The basic physics of nucleation in solid \hl{single-crystal} nanoparticles is
revealed by a phase-field theory that includes surface energy, chemical
reactions and coherency strain. In contrast to binary fluids, which form
arbitrary contact angles at surfaces, complete "wetting" by one phase is
favored at binary solid surfaces. Nucleation occurs when surface wetting
becomes unstable, as the chemical energy gain (scaling with area) overcomes the
elastic energy penalty (scaling with volume). The nucleation barrier thus
decreases with the area-to-volume ratio and vanishes below a critical size, and
nanoparticles tend to transform in order of increasing size, leaving the
smallest particles homogeneous (in the phase of lowest surface energy). The
model is used to simulate phase separation in realistic nanoparticle geometries
for \ce{Li_XFePO4}, a popular cathode material for Li-ion batteries, and
collapses disparate experimental data for the nucleation barrier, with no
adjustable parameters. Beyond energy storage, the theory generally shows how to
tailor the elastic and surface properties of a solid nanostructure to achieve
desired phase behavior.
