Ternäre Halogenide vom Typ A3MX6. II. Das System Ag3−xNaxYCl6: Synthese,Strukturen, Ionenleitfähigkeit

Ternary Halides of the A₃MX₆ Type. II. The System Ag_3?xNa_xYCl₆: Synthesis, Structures, Ionic Conductivity . The influence of the substitution of Ag⁺ by Na⁺ ions on the crystal structure and the ionic conductivity of Ag₃YCl₆ (stuffed LiSbF₆-type structure) has been investigated. The system Ag_3?xNa_xYCl₆ forms a complete solid solution. The stuffed LiSbF₆-type structure is stable for all compositions. For compounds with Na⁺ contents of x > 1.67, the cryolite-type structure is observed as the high-temperature form. The transition temperature decreases steadily with increasing Na⁺ content. The “end member” phase Na₃YCl₆ transforms at 243 K from the monoclinic cryolite-type structure to the stuffed LiSbF₆-type structure (trigonal, R3 ; a = 697.3(1), c = 1 868.4(14) pm, Z = 3; R = 0.094; R_w = 0.069). The crystal structures of Ag_1.3Na_1.7YCl₆ (trigonal, R3 ; a = 691.5(2), c = 1 853.7(6) pm, Z = 3; R = 0.099, R_w = 0.081) and AgNa₂YCl₆ (trigonal, R3 ; a = 691.7(1), c = 1 853.9(5) pm, Z = 3; R = 0.099, R_w = 0.064) have also been determined. Both chlorides crystallize like Ag₃YCl₆ and Na₃YCl₆-I in the stuffed LiSbF₆-type structure. The monovalent cations, Ag⁺ and Na⁺, are distributed over the five octahedral voids that are occupied by the Ag⁺ ions alone in Ag₃YCl₆. The ionic conductivity for compounds within the solid solution Ag_3?xNa_xYCl₆ decreases with increasing Na⁺ content. The values for Na₃YCl₆ (σ = 1 · 10^?6 Ω^?1 cm^?1 at T = 500 K) are by 2.5 to 3.5 orders of magnitude smaller than those for Ag₃YCl₆ (σ = 6 · 10^?4 Ω^?1 cm^?1 at T = 500 K).     

Universal deformation rings and self-injective Nakayama algebras

Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring $R(\mathrm{\Lambda },V)$ and we describe $R(\mathrm{\Lambda },V)$ explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups.     

Rb[Li5Si2O7] – A Latecomer in the Family of Alkali Lithosilicates Hiding a Green-Emitting Lithosilicate

In order to expand the field of alkali lithosilicates, a new representative of the substance class with a previously unknown structure type was found based on solid-state synthesis. The novel compound with the sum formula Rb[Li₅Si₂O₇] crystallizes in the orthorhombic space group Pbcm (no. 57) with a=7.6269(3), b=9.5415(4), and c=9.4095(3) Å by means of single-crystal X-ray diffraction. The structure consists of a highly condensed lithosilicate framework, built up of corner- and edge-linked [LiO₄]-tetrahedra and [Si₂O₇]-units, and the rubidium ions aligned in channels. Suitable crystals of the material were obtained using sealed tantalum ampoules as reaction tube at a temperature of 750 °C. The new compound was further characterized via powder diffraction, Rietveld analysis, and EDX measurements. At first glance, Eu²⁺-doped Rb[Li₅Si₂O₇] reveals an intense green luminescence. In-depth crystal analysis shows that a core-shell formation is present even for apparently high quality single-crystals. As a minority phase, the known green phosphor RbLi[Li₃SiO₄]₂:Eu²⁺ is the origin of the luminescence, representing a tiny core inside of the particles surrounded by a large matrix of transparent Rb[Li₅Si₂O₇] dominating the single-crystal diffraction pattern.     

A novel nitridogallate fluoride LiBa5GaN3F5 – Synthesis,crystal structure,and band gap determination

LiBa₅GaN₃F₅ was obtained as red crystals by reaction of Ba, Ga, NaN₃ and EuF₃ in a Na/Li flux at 760 °C in weld-shut tantalum crucibles. The crystal structure (Pnma (no. 62), a = 15.456(3), b = 5.707(1), c = 12.259(3) Å, Z = 4) was solved on the basis of single-crystal X-ray diffraction data. In the solid there are trigonal planar [GaN₃]^6? ions and zigzag chains of vertex sharing LiF₆ octahedrons surrounded by Ba²⁺ ions. Optical measurements and calculations of the electronic structure revealed a band gap of ≤1.9 eV. According to the calculations, the observed transition occurs from a nitrogen state into a hybrid Ba/N state.     

Interpolation on Sparse Grids and Tensor Products of Nikol'skij–Besov Spaces

We investigate the order of convergence of periodic interpolation on sparse grids (blending interpolation) in the framework of tensor products of Nikol'skij–Besov spaces. To this end, we make use of the uniformity of the considered tensor norms and provide a unified approach to error estimates for the interpolation of univariate periodic functions from Nikol'skij–Besov spaces.     

Experimente mit Erdalkalimetallen

Reactions of the alkaline earth metals magnesium, calcium, strontium, and barium with water, phenolphthalein solution, diluted extract of red cabbage, diluted hydrochloric acid, or ammonia are well suited for a demonstration of the increase in reactivity within this group of metals with increasing atomic number. If the alkali metals lithium and sodium are included, the reactivity of six s‐block elements can be demonstrated in test tubes with small amounts of chemicals.     

Simulation-based optimisation of wastewater flow and composition for on-site treatment in the food and beverage industry utilising reference nets in combination with genetic algorithms

This study introduces the concept of computer modelling and simulation of complex bioprocesses and systems using an approach that combines the reference net formalism with machine learning and optimisation techniques. Reference nets are an extension of high level Petri Nets, which can be used as a central visualisation and modelling tool. The net-in-net paradigm used by reference nets makes it possible to model complex processes, such as those found in the food and beverage industry. A plugin/interface system based on the java programming language allows implementation of advanced mathematical modelling techniques at specific points in entire system simulations. Separate optimisation tools can also run and modify existing reference net models for fast solutions to efficiency problems. We present an example system that simulates a specific section of a beer brewery using the reference net formalism, which is optimised using a genetic algorithm. We show in detail how the different software packages can be combined for a simulation based optimisation approach. The optimisation technique specifically addresses the wastewater pollution load in regard to its chemical oxygen demand. A beer brewery was chosen as an example for this study due to the constantly increasing requirements to lower energy and water consumption in this industry. One possibility to lower the energy and water demands is to effectively treat wastewater produced by the brewery, which can introduce cost savings by providing recycled water and biogas. Most approaches to wastewater treatment are end-of-pipe solutions that do not consider the brewery as a whole. A brewery contains many processes that can be running concurrently and interacting with one another (e.g. brewing, clean-in-place and bottling) with each process producing varying amounts of wastewater with different pollution loads. Optimisation of the scheduling of the different processes with respect to the wastewater production will allow for more effective wastewater treatment, and therefore cost and energy savings. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)