Due to variation in the temperature during growth of the material the crystallite size may enhance. Therefore, several physical and mechanical properties may altered.
your question is very interesting but is very complex as well. The growth morphology of a crystal depends on the ratios between the different growth rates of its faces. THe growth rate of a face depends, in turn, on its surface structure, on the supersaturation of the mother phase and on the temperature (when working in the absence of impurities, of course). The dependence on the Temperature is an exponential dependence concerning the activation energies for a growth unit to enter the kinks in the growing steps of a face...and so on. The best way is to study an interesting book:
Crystal Growth for Beginners
Fundamentals of Nucleation, Crystal Growth and Epitaxy
2nd Edition, WORLD SCIENTIFIC
By (author): Ivan V Markov (Bulgarian Academy of Sciences, Bulgaria)
This is the first-ever textbook on the fundamentals of nucleation, crystal growth and epitaxy. It has been written from a unified point of view and is thus a non-eclectic presentation of this interdisciplinary topic in materials science. The reader is required to possess some basic knowledge of mathematics and physics. All formulae and equations are accompanied by examples that are of technological importance. The book presents not only the fundamentals but also the state of the art in the subject. The second revised edition includes two separate chapters dealing with the effect of the Ehrlich-Schwoebel barrier for down-step diffusion, as well as the effect of surface active species, on the morphology of the growing surfaces. In addition, many other chapters are updated accordingly. Thus, it serves as a valuable reference book for both graduate students and researchers in materials science.