Chemical Bonding and Pressure‐Induced Change of the Electron Configuration of Ytterbium in β‐YbAgGa2

Single‐phase polycrystalline samples of the intermetallic compound β‐YbAgGa₂ were synthesized by inductive heating and subsequent annealing for eight weeks at 670 K. Magnetic properties were characterized by susceptibility measurements and indicated intermediate valence of ytterbium at ambient pressure. Angle‐dispersive X‐ray powder diffraction data of orthorhombic β‐YbAgGa₂ indicate stability of the phase in the investigated pressure range from 0.1 MPa (ambient pressure) to 19 GPa. The pressure‐induced volume decrease is accompanied by an increase of the effective valence from 2.17 at ambient conditions to 2.71 at 16 GPa as evaluated by X‐ray absorption spectroscopy at the Yb L_III threshold. Analysis of the chemical bonding in β‐YbAgGa₂ by integrating the electron density of the polyanion in basins as defined by the electron localization function results in an electron count Yb^2.7+[(Ag^0.2—)(Ga1(3b)^1.0—)(Ga2(4b)^1.5—)]. This finding is close to the expected values calculated by means of the Zintl rules and fits well the results of magnetic susceptibility measurements and XAS investigations.     

Unique ergodicity of some flows related to axiom a diffeomorphisms

Continuous flows, whose orbits are the unstable manifolds of certain Axiom A attractors, are shown to be uniquely ergodic. The approach used is symbolic dynamics. Equicontinuity (and lack of it) for these flows is also discussed.     

Boundary value problems for nonuniformly elliptic equations with measurable coefficients

Summary Let A be a symmetric N × N real-matrix-valued function on a connected region in Rⁿ, with A positive definite a.e. and A, A⁻¹ locally integrable. Let b and c be locally integrable, non-negative, real-valued functions on Ω, with c positive a.e. Put a(u, v) = = ((A∇u, ∇v) + buv) dx. We consider in X the weak boundary value problem a(u, v) = = fvcdx, all v ε X; where X is a suitable Hilbert space contained in H _loc ^1,1 (Ω). Criteria are given in order that the Green's operator for this problem have an integral representation and bounded eigenfunctions; in addition, criteria for compactness are given. Entrata in Redazione il 21 giugno 1975. Research was partially supported by the National Science Foundation under Grant GP-28377A2.     

Vessel effects in organic chemical reactions; a century-old,overlooked phenomenon

One of the most intriguing aspects of synthetic chemistry is the interplay of numerous dependent and independent variables en route to achieve a successful, high-yielding chemical transformation. The experienced synthetic chemist will probe many of these variables during reaction development and optimization, which will routinely involve investigation of reaction temperature, solvent, stoichiometry, concentration, time, choice of catalyst, addition sequence or quenching conditions just to name some commonly addressed variables. Remarkably, little attention is typically given to the choice of reaction vessel material as the surface of common laboratory borosilicate glassware is, incorrectly, assumed to be chemically inert. When reviewing the scientific literature, careful consideration of the vessel material is typically only given during the use of well-known glass-etching reagents such as HF, which is typically only handled in HF-resistant, polyfluorinated polymer vessels. However, there are examples of chemical transformations that do not involve such reagents but are still clearly influenced by the choice of reaction vessel material. In the following review, we wish to condense the most significant examples of vessel effects during chemical transformations as well as observations of container-dependent stability of certain molecules. While the primary focus is on synthetic organic chemistry, relevant examples from inorganic chemistry, polymerization reactions, atmospheric chemistry and prebiotic chemistry are also covered.

One of the most intriguing aspects of synthetic chemistry is the interplay of numerous dependent and independent variables en route to achieve a successful, high-yielding chemical transformation.