MORPHOLOGY OF MODULATED CRYSTALS

Continuing three recent papers the basic principles of a theory to exp lain the occurrence of faces to be indexed with four integers (hklm) o ccurring on modulated crystals are explained. The theory is rooted in the higher than three-dimensional crystallography of Janner, Janssen, and de Wolff. In higher-dimensional space a continuum of all possible bonds is spanned and from this the so-called principle of selective cu ts is derived. This is the key concept in the new theory. The principl es of the theory are demonstrated for a one-dimensional modulated crys tal embedded in two-dimensional bond space. Using a Wulff-Herring rasp berry-like plot in higher-dimensional space equilibrium forms of modul ated Kossel crystals are presented. It is shown that faces (hklm) and new faces (hkl0) appear on the equilibrium form. In the discussion it is shown that the new theory may be considered as a kind of generalisa tion of the Hartman-Perdok theory integrated with the theory of roughe ning transitions. At the end a confrontation with the ideas of Mermin rejecting the more than three-dimensional crystallography of Janner, J ansen, and de Wolff is presented.