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.
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