The attachment energy as a habit controlling factor: I. Theoretical considerations

The habit controlling factors in various crystal growth models (screw dislocation mechanism, two-dimensional nucleation, computer simulation models) are considered and related to the attachment energy Eatt, defined as the energy per molecule released when one slice of thickness dhkl crystallizes onto a crystal face (hkl). It is found that the relative growth rate R of a face always increases with increasing Eatt, although the form of the function R(Eatt) depends on the growth mechanism and on various variables such as supersaturation, temperature and solid-fluid interaction. The crystal habit tends to be isometric in the case of the linear BCF law, while it obtains extreme forms when the quadratic BCF law or a polynucleation model applies. In the region of the quadratic BCF law the habit is independent on supersaturation, while in the linear BCF region or in the polynucleation region a higher supersaturation causes the habit to be more isometric. The fact that crystal habits often follow the geometrical law of Donnay and Harker can be understood from the relatively small orientation dependence of the specific surface energy.