Yeah, the mechanism of grain growth and relationship with unit cell...Actually there are different size of grains in real materials while there is a crystal with a defined unit cell. How the orientation impels/induces the systems to choose different numbers of unit cell for the formation of grains with different size?
@ Nita Dragoe: Thank you so much Dear Prof. Dragoe for your great physical based answer, but there is still a question: Is there any relationship between minimum surface energy for grain growth and the number of crystal unit cell (you mentioned that is convention, but physically it is very hard to image different unit cell for a known crystal!)?
The mechanism of recrystallization grain growth is mainly dependent on diffusion characteristics. Indeed, similar to any other diffusion-controlled processes the grain growth leads to the minimization of inner energy of a system. So, theoretically due to the recrystallization you can prepare a single crystal with the minimal surface energy (Prof. N. Dragoe is absolutely true!), but also with the minimal inner energy, that is why it will be without (!) point and linear defects. The problem is only how long you have to wait for this transformation. The kinetics of recrystallization as well as, for example, densification kinetics during powder sintering are similar to the chemical kinetics as the same driving force (minimization of inner energy in a system) is in action. Thus, you can tie/compare your thoughts and ideas with this fundamental principle...