A survey is given of new types of crystallographic faces and forms occurring on modulated crystals which have to be indexed with four integers (hklm). These faces have so far been found on modulated crystals with an average jS-K2S04 structure which can be grown from an aqueous solution and the mineral crystal calaverite (AuTe2) which can be grown from the melt. Interesting data on crystal growth obtained from in situ observations are presented. Among others, spiral-like patterns can be recognized. The occurrence on quasicrystals of crystal forms to be indexed with six integers (hklmno) is discussed and it is shown that these faces can in principle be explained by a generalization of the Hartman- Perdok theory. Crystal forms (hklm) and (hklmno) occurring on modulated and quasicrystals respectively can be explained by the higher than three-dimensional crystallography of de Wolff, Janner and Janssen where these crystals are considered as threedimensional cuts out of a higher than three-dimensional truly translational invariant structure. ... Read more

The anomalous wedge-like shape of KH2PO4-type single crystals, also called tapering, is reconsidered. A reformulation of the problem is given on the basis of a detailed observation of the boundary between prismatic and pyramidal growth sectors by means of transmitted light polarization microscopy. A narrowing of both pyramidal and prismatic sectors can be identified to constitute tapering. The first being due to an overall retardation of prismatic growth layers caused by impurity adsorption, whereas the narrowing of the pyramidal sectors is due to the inability of pyramidal growth layers to reach the prismatic crystal edge. The retardation of pyramidal growth layers can be explained in terms of a change in electrostatic parameters near the crystal edge or by assuming a fundamental roughness of the crystal edge. A connected net analysis shows the presence of two equally stable {022} nets parallel to the pyramidal faces. In a polar environment this equality is broken, favouring a {011} double layer growth mechanism which can also explain in principle the low segregation coefficient for three-valent positive metal ions in the pyramidal growth sector. ... Read more

The morphological consequences of a displacive modulation of the crystal structure have been investigated. The morphology can be divided in a main part, relatively unperturbed by the properties of the modulation wave, and a so-called satellite morphology. In-situ optical microscopy shows that these satellite faces behave as normal F faces, though the bonding nature of these new type of faces is still ill understood. ... Read more

The macroscopic consequences of displacive modulation on the morphology of incommensurate single crystals are confirmed. Bands of faces in the neighborhood of stable normal crystal faces have been observed on spherically shaped Rb2ZnBr4 crystals. An interpretation is given in terms of classical morphological theory extended to include (four-dimensional) superspace group symmetry. This leads to the view that the formation of these bands involves, at least partly, so-called satellite faces and gives a simple explanation of why the set of bands has a lower point-group symmetry than the set of normal faces. ... Read more