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.     

Fluorescence and REMPI spectroscopy of jet-cooled isolated 2-phenylindene in the S1 state

We investigated the spectroscopy of the first excited singlet electronic state S1 of 2-phenylindene using both fluorescence excitation spectroscopy and resonantly enhanced multiphoton ionization spectroscopy. Moreover, we investigated the dynamics of the S1 state by determining state-selective fluorescence lifetimes up to an excess energy of approximately 3400 cm(-1). Ab initio calculations were performed on the torsional potential energy curve and the equilibrium and transition state geometries and normal-mode frequencies of the first excited singlet state S1 on the CIS level of theory. Numerous vibronic transitions were assigned, especially those involving the torsional normal mode. The torsional potentials of the ground and first excited electronic states were simulated by matching the observed and calculated torsional frequency spacings in a least-squares fitting procedure. The simulated S1 potential showed very good agreement with the ab initio potential calculated on the CIS/6-31G(d,p) level of theory. TDDFT energy corrections improved the match with the simulated S(1) torsional potential. The latter calculation yielded a torsional barrier of V2 = 6708 cm(-1), and the simulation a barrier of V2 = 6245 cm(-1). Ground-state normal-mode frequencies were calculated on the B3LYP/6-31G(d,p) level of theory, which were used to interpret the infrared spectrum, the FDS spectrum of the transition and hot bands of the FES spectrum. The fluorescence intensities of the nu49 overtone progression could reasonably be reproduced by considering the geometry changes upon electronic excitation predicted by the ab initio calculations. On the basis of the torsional potential calculations, it could be ruled out that the uniform excess energy dependence of the fluorescence lifetimes is linked to the torsional barrier in the excited state. The rotational band contour simulation of the transition yielded rotational constants in close agreement to the ab initio values for both electronic states. Rotational coherence signals were obtained by polarization-analyzed, time-resolved measurements of the fluorescence decay of the transition. The simulation of these signals yielded corroborating evidence as to the quality of the ab initio calculated rotational constants of both states. The origin of the anomalous intensity discrepancy between the fluorescence excitation spectrum and the REMPI spectrum is discussed.     

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.