High-dimensional generalizations of the kagomé and diamond crystals and the decorrelation principle for periodic sphere packings

In this paper, we introduce constructions of the high-dimensional generalizations of the kagomé and diamond crystals. The two-dimensional kagomé crystal and its three-dimensional counterpart, the pyrochlore crystal, have been extensively studied in the context of geometric frustration in antiferromagnetic materials. Similarly, the polymorphs of elemental carbon include the diamond crystal and the corresponding two-dimensional honeycomb structure, adopted by graphene. The kagomé crystal in d Euclidean dimensions consists of vertex-sharing d-dimensional simplices in which all of the points are topologically equivalent. The d-dimensional generalization of the diamond crystal can then be obtained from the centroids of each of the simplices, and we show that this natural construction of the diamond crystal is distinct from the Dd + family of crystals for all dimensions . We analyze the structural properties of these high-dimensional crystals, including the packing densities, coordination numbers, void exclusion probability functions, covering radii and quantizer errors. Our results demonstrate that the so-called decorrelation principle, which formally states that unconstrained correlations vanish in asymptotically high dimensions, remarkably applies to the case of periodic point patterns with inherent long-range order. We argue that the decorrelation principle is already exhibited in periodic crystals in low dimensions via a 'smoothed' pair correlation function obtained by convolution with a Gaussian kernel. These observations support the universality of the decorrelation principle for any point pattern in high dimensions, whether disordered or not. This universal property in turn suggests that the best conjectural lower bound on the maximal sphere-packing density in high Euclidean dimensions derived by Torquato and Stillinger (2006 Expt. Math. 15 307) is, in fact, optimal.

Source:IOPscience

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High purity germanium crystal growth at the University of South Dakota

High-purity germanium crystal growth is challenging work, requiring the control of individual crystal properties such as the impurity distribution, the dislocation density, and the crystalline structure. Currently, we grow high-purity germanium crystals by the Czochralski method in our laboratory in order to understand the details of the growing process, especially for large diameter crystals. In this paper, we report the progress of detector-grade germanium crystal growth at the University of South Dakota.

Source:IOPscience

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Synthesis of novel liquid crystal compounds and their blood compatibility as anticoagulative materials

The objective of this study was to synthesize new types of cholesteric liquid crystal compounds and study the anticoagulative properties of their composite membranes. Three kinds of cholesteric liquid crystal compounds were synthesized and characterized by infrared spectroscopy, differential scanning calorimetry and optical polarizing microscope. The polysiloxane, as a substrate, was blended with three liquid crystal compounds and was then used as membranes. The anticoagulative property of different polysiloxane liquid crystal composite membranes was identified by the blood compatibility tests. Three cholesteryl liquid crystals synthesized in this work contained hydrophilic soft chains and presented iridescent texture owned by cholesteric liquid crystals in the range of their liquid crystal state temperature, but only cholesteryl acryloyl oxytetraethylene glycol carbonate was in the liquid crystal state at body temperature. When liquid crystals were blended with polysiloxane to form polysiloxane/liquid crystal composite membranes, the haemocompatibility of these membranes could be improved to some extent. The blood compatibility of composite membranes whose hydrophilic property was the best was more excellent than that of other composite membranes, fewer platelets adhered and spread, and showed little distortion on the surface of materials.

Source:IOPscience

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