  The phase transition kinetics in three phase systems was investigated using
the numerically efficient cell dynamics method. A phasefield model with a
simple analytical free energy and single order parameter was used to study the
kinetics and the thermodynamics of a three-phase system. This free energy is
able to achieve three phases coexistence, which for simplicity we call \alpha,
\beta and \gamma phases. Our study focused on the kinetics of phase transition
rather than the nucleation of a seed of a new phase that was introduced into
the matrix of the old phase when the relative stability of the three phases
were changed. We found dynamical as well as kinetically arrested static
scenarios in the appearance of the macroscopic metastable phase. A few other
interesting scenarios of the kinetics of phase transition in this three-phase
system will be demonstrated and discussed.
