Growth Mechanism and Crystal Form of Potassium Dichromate
The structure of potassium dichromate (P1, Z = 4) consists of two layers parallel to (001), between which no crystallographic symmetry relation exists. These layers are nearly coincident with each other when rotated through 90° about c * . One question remained unanswered: do the crystals grow parallel to {001} with d(002) or d(001) layers? The pseudo-fourfold axis does not run parallel to a crystallographic direction and acts only between two layers. This means that crystal growth parallel to {001} occurs in d(001) layers, which corresponds to the occurrence of one-sided intergrowths on (001). The layers are also nearly coincident with each other through pseudo-twofold axes parallel to [110] and [110], These axes do not act in the (100) or (010) projections. In the projections along the [110] and [110] directions, the lattice directions are then extended by a factor of approximately √2, and the formula units in the cell of the d(002) layer are doubled. This indicates a further possible growth mechanism. The theoretical growth forms of the crystals were calculated with the Fourier transform method of morphology.
Crystal Growth Mechanism Determined by Crystallographic and Affine Symmetries. Part II
As shown in Part I, in the case of organic substances with two crystallographically independent molecules, crystallographic and affine symmetries determine crystal growth. The Fourier transform method was used to calculate the theoretical growth forms. The morphological lattice necessary for these calculations can be derived from an affine or klassengleiche supergroup of the structural space group. It can be shown that growth is influenced not only by the geometric effectiveness of the symmetry elements but also by physical factors such as differences in conformation and external factors. The theoretical growth forms were also calculated using attachment energies (Hartman method). A better correspondence to the observed crystals is obtained when the affine symmetries are also considered in these calculations. For these investigations, the crystal structures of 2,3-dichloro-1,4-naphthoquinone, amidopyrine (P1 ), glycolic acid, malonamide and cyanoacetamide (P2 1 /c) were used. All of these structures contain two crystallographically independent molecules in the unit cell.
On the enantiomorphism in potassium bichromate crystals
Abstract The occurrence of enantiomorphism and the frequency of occurrence of different planes in contact with the growth vessel are investigated for potassium bichromate crystals grown from aqueous solution by solvent evaporation and temperature difference methods. It was found that left- and right-handed crystals, respectively, grow when the (001) and (00 1 ) faces of self-nucleated seeds are in contact with the bottom of the growth vessel, and that structurally, left- and right-handed crystals are the same. The frequency of occurrence of contact faces corresponds to the morphological importance of potassium bichromate crystals deduced from Bravais-Donnay-Harker law. The observations are discussed from the standpoint of three-dimensional nucleation in the bulk of the supersaturated solution.