Orthogonal rate and form development

The growth of a face is characterized by its growth rate to the face in question. This is the orthogonal rate R of the face.

Now let us consider two faces A and B that intersect along edge O, examining the rate R on a plane perpendicular to this edge.

Development of crystal faces

Figure 1.1. Development of crystal faces

The orthogonal growth of faces A and B are, respectively, Om and On with, as in the figure:

We can see that face A has increased its surface by mO', whereas face B has lostnO'. The edge has moved from O to O'.

Face A becomes important and, after sufficient time, face B will disappear, thereby becoming a virtual face. Corresponding with the growth progression of the crystal, the number of faces decreases, becoming simpler in form. Important faces have the lowest orthogonal rates.

Here, we can introduce the concept of a face’s morphological importance (MI) as the statistical mean of a face’s surface compared with the mean of the crystals’ total exterior surface. It is consistent to establish MI for a crystal population close in size, since their form increasingly varies as size increases.

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