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Concept# Platonic solid

Summary

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra:
Geometers have studied the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato who hypothesized in one of his dialogues, the Timaeus, that the classical elements were made of these regular solids.
History
The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes; however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices of the Platonic solids, there is no ball whose knobs match the 20 vert

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Michèle Bernadette Heeb, Janet Gordon Hering

The heterogeneous precipitation of calcium phosphates on calcium hydroxyapariLe (Ca-10(PO4)(4)OH)(2) or HAP) in the presence arid absence of fluoride is important in the formation of bone and teeth, protection against tooth decay, dental and skeletal fluorosis and defluoridaLion of drinking wafer. Strontium hyclroxyapariLe (Sr-10(PO4)(6)(OH)(2) or SrHAP) and strontium carbonate (SrCO3) were used as calcium free seed templates in precipitation experiments conducted with varying initial calcium-Lophosphate (Ca/P) or calcium-Lo-phosphaLe-Lo-fluoride (Ca/P/F) ratios. Suspensions of SrHAP or SrCO3 seed templates (which were calcium limited for both templates and phosphate limited in the case of SECO3) were reacted at pH 7.3 (25 degrees C) over 3 days. The resulting solids were examined with Scanning Transmission Electron Microscopy (STEM), X-ray Diffraction (XRD), Fourier Transform Infrared (MR), and X-ray Photoelectron Spectroscopy (XPS), X-ray Absorption Near Edge Structure (XANES), and Extended X-ray Absorption Fine Structure spectroscopy (EXAFS). Calcium apatite was the predominant phase identified by all techniques independent of the added Ca/P ratios and of the presence of fluoride. It was not possible to make an unambiguous distinction between HAP and fluorapatite (Ca-10(PO4)(6)F-2, FAP). The apatite was calcium-deficient and probably contained some strontium. (C) 2014 Elsevier B.V. All rights reserved.

Understanding the role of electron correlations in strong spin-orbit transition-metal oxides is key to the realization of numerous exotic phases including spin-orbit–assisted Mott insulators, correlated topological solids, and prospective new high-temperature superconductors. To date, most attention has been focused on the 5d iridium-based oxides. We instead consider the Pt-based delafossite oxide PtCoO2. Our transport measurements, performed on single-crystal samples etched to well-defined geometries using focused ion beam techniques, yield a room temperature resistivity of only 2.1 microhm·cm (μΩ-cm), establishing PtCoO2 as the most conductive oxide known. From angle-resolved photoemission and density functional theory, we show that the underlying Fermi surface is a single cylinder of nearly hexagonal cross-section, with very weak dispersion along kz. Despite being predominantly composed of d-orbital character, the conduction band is remarkably steep, with an average effective mass of only 1.14me. Moreover, the sharp spectral features observed in photoemission remain well defined with little additional broadening for more than 500 meV below EF, pointing to suppressed electron-electron scattering. Together, our findings establish PtCoO2 as a model nearly-free–electron system in a 5d delafossite transition-metal oxide.

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Oksana Banakh, Roland Andreas Bitterli, Laure Jeandupeux

Solid-on-liquid deposition (SOLID) techniques are of great interest to the MEMS and NEMS (Micro- and Nano Electro Mechanical Systems) community because of potential applications in biomedical engineering, on-chip liquid trapping, tunable micro-lenses, and replacements of gate oxides. However, depositing solids on liquid with subsequent hermetic sealing is difficult because liquids tend to have a lower density than solids. Furthermore, current systems seen in nature lack thermal, mechanical or chemical stability. Therefore, it is not surprising that liquids are not ubiquitous as functional layers in MEMS and NEMS. However, SOLID techniques have the potential to be harnessed and controlled for such systems because the gravitational force is negligible compared to surface tension, and therefore, the solid molecular precursors that typically condense on a liquid surface will not sediment into the fluid. In this review we summarize recent research into SOLID, where nucleation and subsequent cross-linking of solid precursors results in thin film growth on a liquid substrate. We describe a large variety of thin film deposition techniques such as thermal evaporation, sputtering, plasma enhanced chemical vapor deposition used to coat liquid substrates. Surprisingly, all attempts at deposition to date have been successful and a stable solid layer on a liquid can always be detected. However, all layers grown by non-equilibrium deposition processes showed a strong presence of wrinkles, presumably due to residual stress. In fact, the only example where no stress was observed is the deposition of parylene layers (poly-para-xylylene, PPX). Using all the experimental data analyzed to date we have been able to propose a simple model that predicts that the surface property of liquids at molecular level is influenced by cohesion forces between the liquid molecules. Finally, we conclude that the condensation of precursors from the gas phase is rather the rule and not the exception for SOLID techniques. (C) 2015 The Authors. Published by Elsevier B.V.