PHASE FIELD THEORY OF POLYCRYSTALLINE FREEZING IN THREE DIMENSIONS

摘要

A phase field theory, we proposed recently to describe nucleation and growth in three dimensions (3D), has been used to study the formation of polycrystalline patterns in the alloy systems. Al-Ti and Cu-Ni. In our model, the free energy of grain boundaries is assumed proportional to the angular difference between the adjacent crystals expressed in terms of the differences of the four symmetric Euler parameters called quaternions. The equations of motion for these fields have been obtained from variational principles. In the simulations cubic crystal symmetries are considered. We investigate the evolution of polydendritic morphology, present simulated analogies of the metallographic images, and explore the possibility of modeling solidification in thin layers. Transformation kinetics in the bulk and in thin films is discussed in terms of the Johnson-Mehl-Avrami-Kolmogorov approach.