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.
On crystal growth of ammonium and potassium dichromate. A study of the shubnikov effect
Growth and equilibrium forms of ammonium (A2/a) and potassium dichromate (P 1) have been calculated by means of the Fourier transform method of crystal morphology. Twin laws of potassium dichromate and heteroepitaxial intergrowth of both substances can be explained by partitions of space. According to Shubnikov the (001) planes of potassium dichromate crystals grown in aqueous solutions are always smooth, the parallel opposite planes, however, roughened. Wagner observed that this effect only occurs at temperatures shortly above or below 25 °C. The present investigation has shown that roughening of (001) appears at 25 °C after addition of potassium chromate to the potassium dichromate solutions. This means that the one-sided intergrowth can be explained by a stereospecific adsorption of polychromates. Solution additions like potassium permanganate and Chromotrope 2B generate roughenings on both {001} faces. X-Ray diffraction investigations can be interpreted in such a way that the intergrown plates are mirror symmetric oriented to two planes being normal to the a- and b-axes. This is in accordance with repeated formation of intergrown plates. 
 
 
 
Theoretische Wachstums- und Gleichgewichtsformen von Ammonium- (A2/a) und Kaliumdichromat (P 1) wurden mit Hilfe der Fouriertransformationsmethode der Kristallmorphologie berechnet. Die bekannten Zwillingsgesetze von Kaliumdichromat und die heteroepitaktischen Verwachsungen beider Substanzen lassen sich aus dreidimensionalen Wirkungsbereichsteilungen ableiten. Nach Schubnikow ist die (001)-Flache von Kaliumdichromatkristallen stets glatt, die parallele Gegenflache immer aufgerauht. Dieser Effekt wird nach Wagner allerdings nur unterhalb bzw. oberhalb 25 °C beobachtet. Nach Zugabe von Kalumchromat zu Kaliumdichromatlosungen treten die Aufrauhungen auch bei 25 °C auf. Die einseitigen Aufwachsungen beruhen offensichtlich auf einer stereospezifischen Adsorption von Polychromaten. Verunreinigungen wie Kaliumpermanganat bzw. Chromotrop 2B fuhren zu Aufrauhungen beider Flachen. Rontgenbeugungsuntersuchungen lassen den Schlus zu, das die Aufwachsungen auf (001) spiegelbildlich zu Ebenen orientiert sind, die senkrecht zu den a- und b-Achsen verlaufen. Dies steht nicht im Widerspruch zu der wiederholten Plattchenbildung.
Multi-layer inpainting on Chinese artwork
Digital inpainting uses spatial or frequency information to restore partially damaged/removed photos and artworks. Most restoration algorithms take a picture as a single layer. We propose a new approach, which subdivides a Chinese painting into several layers. Each layer is inpainted separately. The layer fusion mechanism then finds the optimal inpaint among layers, which are restored layer-bylayer. We apply the algorithm on Chinese and western drawing. The result shows a high PSNR value as well as a high user satisfaction. The demonstration of our work is available at: http://www.mine.tku.edu.tw/demos/inpaint.