  Numerous experimental data on the rapid solidification of binary systems
exhibit the formation of metastable solid phases with the initial (nominal)
chemical composition. This fact is explained by complete solute trapping
leading to diffusionless (chemically partitionless) solidification at a finite
growth velocity of crystals. Special attention is paid to developing a model of
rapid solidification which describes a transition from chemically partitioned
to diffusionless growth of crystals. Analytical treatments lead to the
condition for complete solute trapping which directly follows from the analysis
of the solute diffusion around the solid-liquid interface and atomic attachment
and detachment at the interface. The resulting equations for the flux balance
at the interface take into account two kinetic parameters: diffusion speed
$V_{DI}$ on the interface and diffusion speed $V_D$ in bulk phases. The model
describes experimental data on nonequilibrium solute partitioning in
solidification of Si-As alloys [M.J. Aziz et al., J. Cryst. Growth {\bf 148},
172 (1995); Acta Mater. {\bf 48}, 4797 (2000)] for the whole range of
solidification velocity investigated.
