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The ordering dynamics with a moving plane boundary between ordered and disordered phases is discussed focusing on the instability of disordered material near the plane boundary. The ordered phase is extending steadily. The material is modeled on the infinite state Potts model. A dynamics suitable to the interfacial motion is introduced. The ordered phase may create many grains. Three typical grain morphologies are found by two dimensional numerical simulations, i.e., compact, columnar and huge ones, depending both on the extending speed of the ordered phase and system boundary condition.

Ordering Dynamics with Moving Plane Boundary between Ordered and Disordered Phases