Abstract:
A theoretical approach for the prediction of the growth forms of crystals
is presented on the basis of the kinetics of crystal growth. To describe
the
growth morphology of crystals, the more precise relations between the
relative growth rate of the crystal faces (hkl) R(hkl)(red) and habit-controlling
factors are derived from the Burton-Cabrera-Frank (BCF) models, the
Chernov model, and the two-dimensional crystal growth models. According
to these established relations, the growth morphology of crystals is
directly related to internal and external habit-controlling factors. Among
these
factors, the attachment energy E(hkl)(att), the surface scaling factor
C-l(hkl)* and the molecular orientational factor t(hkl) play an essential
role in
controlling the growth habit of crystals. As the key external habit-controlling
factors, C-l(hkl)* and t(hkl) depend on the structure of the interface,
the
composition of the system, and other parameters affecting the growth
process. Correspondingly, E(hkl)(att) represents the influence of the crystal
structure on the morphology of the crystal. To examine the validity
of our formalisms, the morphology of paraffin crystals grown from n-alkane
solutions and that of C-60 crystals grown from the vapor are predicted.
The results are in excellent agreement with observations. Within the
framework of our approach, the relation R(hkl)(red)similar to E(hkl)(att)
proposed in the Hartman-Perdok theory can be obtained by simplifying our
formulas. Finally, morphological changes resulting from different experimental
conditions are generally discussed based on our formalisms.