  We propose a natural two-speed model for the phase dynamics of Si(111)
7$\times$7 phase transition to high temperature unreconstructed phase. We
formulate the phase dynamics by using phase-field method and adaptive mesh
refinement. Our simulated results show that a 7$\times$7 island decays with its
shape kept unchanged, and its area decay rate is shown to be a constant
increasing with its initial area. LEEM experiments concerned are explained,
which confirms that the dimer chains and corner holes are broken first in the
transition, and then the stacking fault is remedied slowly. This phase-field
method is a reliable approach to phase dynamics of surface phase transitions.
