Coexistence of Two Different Distorted Octahedral [MnF6]3− Sites in K3[MnF6]: Manifestation in Spectroscopy and Magnetism

As a consequence of the static Jahn-Teller effect of the ⁵E ground state of Mn^III in cubic structures with octahedral parent geometries, their octahedral coordination spheres become distorted. In the case of six fluorido ligands, [MnF₆]³⁻ anions with two longer and four shorter Mn−F bonds making elongated octahedra are usually observed. Herein, we report the synthesis of the compound K₃[MnF₆] through a high-temperature approach and its crystallization by a high-pressure/high-temperature route. The main structural motifs are two quasi-isolated, octahedron-like [MnF₆]³⁻ anions of quite different nature compared to that met in ideal octahedral Mn^III Jahn-Teller systems. Owing to the internal electric field of C_i symmetry dominated by the next-neighbour K⁺ ions acting on the Mn^III sites, both sites, the pseudo-rhombic (site 1) and the pseudo-tetragonally elongated (site 2) [MnF₆]³⁻ anions are present in K₃[MnF₆]. The compound was characterized by single-crystal and powder X-ray diffraction, and magnetometry as well as by FTIR, Raman, and ligand field spectroscopy. A theoretical interpretation of the electronic structure and molecular geometry of the two Mn sites in the lattice is given by using a vibronic coupling model with parameters adjusted from multireference ab-initio cluster calculations.     

La3B6O13(OH): The First Acentric High-Pressure Borate Displaying Edge-Sharing BO4 Tetrahedra

La₃B₆O₁₃(OH) was obtained by a high-pressure/high-temperature experiment at 6 GPa and 1673 K. The compound crystallizes in the space group P2₁ (no. 4) with the lattice parameters a=4.785(2), b=12.880(4), c=7.433(3) Å, and β=90.36(10)°, and is built up of corner- as well as edge-sharing BO₄ tetrahedra. It represents the first acentric high-pressure borate containing these B₂O₆ entities. The compound develops borate layers of „sechser“-rings with the La³⁺ cations positioned between the layers. Single-crystal and powder X-ray diffraction, vibrational and MAS NMR spectroscopy, second-harmonic generation (SHG) and thermoanalytical measurements, as well as computational methods were used to affirm the proposed structure and the B₂O₆ entities.     

On a decomposition for a special class of geometric programming problems

Optimization of physical systems consisting of interrelated subsystems which can be formulated as geometric programming problems is considered. Necessary and sufficient conditions are derived for decomposing the optimization of a special class of such systems into a sequence of subsystem optimizations. An example is presented.This research was completed at the Mobil Research and Development Corporation, Central Research Division Laboratory, Princeton, New Jersey.     

Der Einfluß der Elektronenverteilungsfunktion auf Mikrowellenemission und Hochfrequenzleitfähigkeit eines schwach ionisierten Entladungsplasmas

We have investigated the influence of the distribution function on the microwave emission and the rf-conductivity. In the positive column of low current discharges through neon and argon the electrons are Druyvesteyn-like distributed, owing to the absence of Coulomb-interactions. In this case the radiation temperature is a function of the dc-field in the positive column, of the collision frequency for momentum transfer and the radiation frequency. With only elastic and excitation terms in the Boltzmann equation we have computed the distribution functions. These results are used to calculate the radiation temperature by means of Bekefis formula. Agreement is obtained between the experimental and theoretical results. The rf-conductivity does not depend very sensitively on changes in the distribution function; nevertheless the high values of the electron collision frequency obtained from the real part of the rf-conductivity could be explained only with a Druyvesteyn-like distribution.     

Ω-Invariance in control systems with bounded controls

The concepts of weakly Ω-invariant sets and strictly weakly Ω-invariant sets in control systems with bounded controls are defined and analyzed. Computable conditions for weak Ω-invariance are derived, and the question of existence of rest points and stationary points in weakly Ω-invariant sets is considered. For linear dynamics, properties of weakly Ω-invariant sets are studied, and questions of constrained reachability are investigated.