  Several lines of evidence suggest that fine silicate crystals observed in
primitive meteorite and interplanetary dust particles (IDPs) nucleated in a
supersaturated silicate vapor followed by crystalline growth. We investigated
evaporation of $\mu$m-sized silicate particles heated by a bow shock produced
by a planetesimal orbiting in the gas in the early solar nebula and
condensation of crystalline silicate from the vapor thus produced. Our
numerical simulation of shock-wave heating showed that these {\mu}m-sized
particles evaporated almost completely when the bow shock is strong enough to
cause melting of chondrule precursor dust particles. We found that the silicate
vapor cools very rapidly with expansion into the ambient unshocked nebular
region; the cooling rate is estimated, for instance, to be as high as 2000 K
s$^{-1}$ for a vapor heated by a bow shock associated with a planetesimal of
radius 1 km. The rapid cooling of the vapor leads to nonequilibrium gas-phase
condensation of dust at temperatures much lower than those expected from the
equilibrium condensation. It was found that the condensation temperatures are
lower by a few hundred K or more than the equilibrium temperatures. This
explains the results of the recent experimental studies of condensation from a
silicate vapor that condensation in such large supercooling reproduces
morphologies similar to those of silicate crystals found in meteorites. Our
results suggest strongly that the planetesimal bow shock is one of the
plausible sites for formation of not only chondrules but also other cosmic
crystals in the early solar system.
