The phase-field crystal method is used to analysis the dislocation annihilation and grain boundary migration mechanism in the grain shrink process of the circular grain which has three different misorientations from the matrix grain. Results show that when the misorientation between the circular grain and the matrix grain is 17°, the structure of grain boundary is composed of dislocations whose cores is so near that can not find a single dislocation. This grain boundary can not be explained by the dislocation model. However the circular grain area decreases linearly with time, which is in good agreement with the classical boundary migration theory. When the misorientation is 4°, the grain boundary structure is composed of discrete dislocations. Dislocations climb along the radial dierction and the grain rotation occurs for the circular grain to adjust the space of dislocations in the process of circular grain shrinkage. Reactions may take place with the dislocatins becoming closer. For the misorientation of 10°, portion of the grain boundary is composed of discrete dislocations and portion of dislocations with cores overlapped. Dislocations climb along the radial direction and tangential motion occurs at the same time in the grain shrinkage process. The coupled motion lead to the dislocations becoming close and reacting with each other.

The two-mode phase-field-crystal (PFC) method is used to calculate two-dimensional phase diagram and to simulate the process of multistage microstructural evolution in the transformation from hexagonal phase to square phase, which is induced by deformation. And the effect of misorientation and deformation on dislocation, grain boundary, crystal structure and morphology of the new phase is carefully analyzed. Simulation results show that both the nucleation site and growth direction of the square phase are affected by the direction of deformation. Under a tensile deformation, the nucleation of the square phase occurs preferentially in the deformation zone; while under compression deformation, the nucleation of the square phase may begin at dislocations and grain boundary. Moreover, the new phase grows towards the direction along which the degree of atomic mismatch decreases, i.e. the vertical direction of tensile deformation and the parallel direction of compressive deformation. Besides, the free energy varies with misorientation. In small misorientation, the dislocation climbing, slipping and annihilating will result in an energy peak; while in a big misorientation, the dislocation annihilates in several stages and thus offsetting the energy caused by deformation. Furthermore, the process of phase transformation is complex: It is not a pure phase transformation but a composite change of phase transformation and dynamic recrystallization.

The two-mode phase field crystal (PFC) method is used to calculate the phase diagram. And in this paper it is used to simulate the effects of predeformation degree and isothermal temperature on the hexagonal grain boundary evolution and on the hexagonal/square phase transition. Results show that when there is no predeformation in the initial phase, the grain boundary defect causes the pre-melting around the melting point; predeformation increases and the interaction between deformation and defects induces the pre-melting around the melting point; and the predeformation further increases, deformation induces liquid phase and square phase simultaneously at the distortion place. The bigger the predeformation and the closer to melting point the maintained temperature, the more obvious the growth of liquid phase is; on the contrary, the square phase grows obviously. The distortion energy is released with time and the phase of grain finally becomes square phase. It can be concluded that keeping the hexagonal phase isothermal near the melting temperature, the liquid phase appears at the grain boundary or at the other defects because the predeformation leads to the increase of atom activity, thus increasing atom disorder degree. Then with the release of distortion energy, the grain phase finally transforms into an equilibrium square phase. In this way the hexagonal/square transition time is extended.