The morphology of quasicrystals, incommensurate composite crystals and modulated crystals derived from the broken-bond model

The broken-bond model for the surface free energy of crystals is considered. The consequences are derived for the morphology of periodic crystals, quasicrystals, incommensurately modulated crystals and intergrowth compounds. It is found that low-index facets on periodic crystals and quasicrystals are the result of finding an optimized position along the vector normal to the surface of the surface plane. The same principle explains the normal facets on modulated crystals and intergrowth crystals. The so-called satellite facets are the result of surface pinning of the phase of the modulated wave. On intergrowth compounds, facets may be found that are stabilized by a combination of both mechanisms. It is shown that the most stable facets on intergrowth crystals are the normal facets that are common to the subsystems, independent of the details of the structure.