General theory and formula of phase field simulation are discussed to as certain physical meanings of some phenomenological parameters in the basic model. A new concept of boundary range is suggested to explain the physical backgrounds of the phase order parameter gradients at grain boundary and the diffusion grain boundary, separately. It is argued that the boundary range is not the geometrical boundary width of atom disorder and generally believed to be within 3—4 atom sizes. However, the range has an independent boundary feature to represent the grain boundary energy distribution range in which the solute alloy atoms are segregated from interior grain. A model is established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy by using the phase field approach. A set of rules has been proposed to determine the real physical value of all parameters in the model. The simulated results are shown to be in good agreement with reported measurements at the temperatures from 300 to 400 ℃ for up to 100 min. The effect of applied strains field on the microstructure produced during α2 phase to O-phase （orthorhombic phase） transformation in Ti-25Al-10Nb alloy is finally studied by phase field simulation. The effects of strain direction on the volume fraction of O-phase and on the microstructure are investigated. It is also found that a full laminar microstructure can be formed when the applied strain is loaded along 〈1120〉 of α2 phase with magnitude greater than a half of the stress-free transformation strain. The significance and the potential application of the new simulation discovery are discussed.