Dynamics and Thermochemistry of Oxygen Uptake by a Mixed Ce–Pr Oxide

The dynamics of oxygen uptake by mixed Ce_0.55Pr_0.45O_2–x oxide is studied in a pulsed oxygen supply mode using in situ high-temperature heat flow differential scanning calorimetry. It is stated that the oxidation proceeds in two regimes: a fast one at the beginning of the oxidation process, and a slow one, which is controlled by the diffusion of oxygen through the bulk of the solid at the later stages of the process. Analysis of the shape of calorimetric profiles reveals some processes, accompanied by heat release, that occur in the sample in the absence of oxygen in the gas phase. These could be due to both the redistribution of consumed oxygen in the oxide lattice and the lattice relaxation associated with the transformation of phases with different arrangements of oxygen vacancies in them. The heat effect (which diminishes from ~60 to ~40 kJ/mol in the course of oxygen uptake) associated with the oxidation of the reduced form of mixed Ce–Pr oxide, corresponds to the oxidation of praseodymium ions from (3+) to (4+).     

Exceptional elastic anisotropy of hybrid organic–inorganic perovskite CH3NH3PbBr3 measured by laser ultrasonic technique

The results of the direct experimental evaluation of all elastic constants of single crystal hybrid organic–inorganic perovskite (HOIP) methylammonium lead bromide, a material known due to its possible solar‐energy, optoelectronics, X‐ray detector and thermoelectricity applications, are reported. The measurements of anisotropic elasticity of CH₃NH₃PbBr₃by the technique of laser ultrasonics demonstrate that properties of HOIPs can be even more remarkable than the theoretical expectations: the extracted shear modulus is more than twice smaller, the universal anisotropy is more than twice higher, while the Debye temperature is more than 50° lower. Thus HOIPs can exhibit extremely low shear rigidity and extremely high anisotropy, both strongly overrunning the parameters which have been expected based on earlier first principles theoretical predictions. A simple theoretical model of granular crystal indicates that these observations could be related to the contributions of rotations/tilts of PbBr₆octahedra to elastic response of cubic CH₃NH₃PbBr₃. Another experimental observation is strong stiffening of shear rigidity with temperature increase from its room value up to 120 °C. Discovered elastic properties of HOIPs characterize them as exceptionally ductile/flexible/adaptive materials which could be deposited on corrugated/structured surfaces. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Effects of substituents in the cationic and anionic η<Superscript>3</Superscript>-allylpalladium complexes according to data from <Superscript>13</Superscript>C NMR spectroscopy and quantum chemical calculations

A linear correlation of chemical shifts (δ) of signals in the ¹³C NMR spectra of the unsubstituted terminal carbon atom of the allyl ligand in [(1-R-η³-C₃H₄)Pd]NO₃ (R = Me, CH₂OMe, CO₂Me, COMe, CHO) with the substituent constants σ⁺ and σ^s- in acetone solutions was found. A considerable deviation from linearity was observed for R = Ph. The ¹³C nuclear magnetic screening constants were calculated by the DFT method in the GIAO approximation for equilibrium geometries of the cations [(1-R-η³-C₃H₄)Pd(Me₂C=0)₂]⁺ and anions [(1-R-η³-C₃H₄)PdCl₂]^s-. In the latter case, the theoretical and experimental δ values are consistent. The influence of the substituent R on the geometric parameters and charges on atoms in the neutral, anionic, and cationic η³-allylpalladium complexes is discussed.     

Invariant Subspaces for Commuting Operators on a Real Banach Space

It is proved that the commutative algebra A of operators on a reflexive real Banach space has an invariant subspace if each operator T ∈ A satisfies the condition

$${\left\| {1 - \varepsilon {T^2}} \right\|_e} \leqslant 1 + o\left( \varepsilon \right)as\varepsilon \searrow 0,$$

where ║ · ║ _e denotes the essential norm. This implies the existence of an invariant subspace for any commutative family of essentially self-adjoint operators on a real Hilbert space.

     

The properties of anions which determine the extractability of their associates with triarylmethane dyes

Conclusions Some properties of anions which affect the extraction of their ionic associates with organic cations have been studied in the present paper. A comparison of these properties is exceedingly difficult even for ions of a single type. Almost any change in the composition of the ion (for example, the substitution of one ligand for another with similar properties: Cl and Br) involves the simultaneous change of the size and effective charge of the ion, the metal-ligand bond stability, and so on. It is not always possible to isolate the factor which has the main influence on the properties of the associate. Besides, the maximum activity of various ions is observed at various acidities in the aqueous phase, and the acidity strongly affects the activity of the dye and its tendency toward association [5]. Nevertheless, the relationships developed herein allow us to interpret the experimental material in several cases and do not exclude the possibility of making predictions for the trends studied.Ural Scientific Research Chemical Institute, Sverdlovsk; Institute of Inorganic Chemistry, Siberian Division, Academy of Sciences, USSR, Novosibirsk. Translated from Zhurnal Strukturnoi Khimii, Vol. 8, No. 2, pp. 216–220, March–April, 1967.     

An extension of Burnside’s Theorem to infinite-dimensional spaces

The classical Burnside’s Theorem guarantees in a finite dimensional space the existence of invariant subspaces for a proper subalgebra of the matrix algebra. In this paper we give an extension of Burnside’s Theorem for a general Banach space, which also gives new results on invariant subspaces. Partially supported by a grant from the National Science Foundation.