EQUILIBRIUM MORPHOLOGY OF INCOMMENSURATELY MODULATED CRYSTALS - A SUPERSPACE DESCRIPTION

The theory for the explanation of equilibrium morphologies of incommen surately modulated one-dimensional crystals, presented in a previous p aper, is extended to the case of incommensurately modulated three-dime nsional crystals. It is shown that, concerning the morphology, there e xists a one-to-one correspondence between faces on the physical crysta l and crystallographic hyperplanes of the embedded crystal in superspa ce. This holds for both main faces and satellite faces. The occurrence of the latter, however, is unique for incommensurately modulated crys tals. It is shown that the stability of satellite faces, as well as ma in faces, can be attributed to a principle of selective cuts. The supe rspace approach that is developed leads to a calculation method for su rface free energies that, in principle, can be applied to incommensura tely modulated structures of arbitrary complexity. Equilibrium morphol ogies are constructed from the calculated surface free energies by mea ns of; a standard Wulff plot. The dependence of the equilibrium morpho logy on several structural parameters is studied for an incommensurate ly modulated simple cubic model crystal. This study allows for a basic understanding of the differences in morphology of AuTe2 crystals and [(CH3)(4)N]2ZnCl4 crystals.