Theoretical consideration of the growth morphology of crystals

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} Rₕₖₗʳᵉᵈ 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 Eₕₖₗᵃᵗᵗ, the surface scaling factor Cₗ₍ₕₖₗ₎* and the molecular orientational factor tₕₖₗ play an essential role in controlling the growth habit of crystals. As the key external habit-controlling factors, Cₗ₍ₕₖₗ{)}*$ and ${t}ₕₖₗ$ depend on the structure of the interface, the composition of the system, and other parameters affecting the growth process. Correspondingly, ${E}ₕₖₗᵃᵗᵗ$ 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 C₆₀ crystals grown from the vapor are predicted. The results are in excellent agreement with observations. Within the framework of our approach, the relation Rₕₖₗʳᵉᵈ{~}Eₕₖₗᵃᵗᵗ 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. {} 1996 The American Physical Society.