Multisites Cr3+ in GGG and GSGG garnets

The emission and excitation spectra of Cr³⁺ -doped Gd₃Ga₅O₁₂ (GGG) and Gd₃Sc₂Ga₃O₁₂ (GSGG) are explained in the light of multisite effects. The situation is particularly complicated in the case of GSGG, where the different sites have²E energy levels near each other which overlap with the⁴A₂ ⁴T₂ absorption bands. The spectra obtained under selective excitations are interpreted on the multisite assumption.     

Vaporisation et dissociation thermique des sulfures de phosphore P4S3, P4S7 et P4S10 a l'etat gazeux

Résumé Nous avons montré par spectrométrie Raman à chaud et mesure des tensions de vapeur que P₄S₃ se vaporise de façon congruente tandis que P₄S₇ et P₄S₁₀ se dissocient dès le début de leur vaporisation. P₄S₇ donne réversiblement P₄S₃ et soufre. P₄S₁₀ se dissocie irréversiblement en P₄S₇ et soufre. A l'état de vapeur non saturante, P₄S₃ se dissocie au-dessus de 600° avec formation de phosphore, de soufre et d'autres espèces non identifiées.Nous avons mesuré expérimentalement la capacité calorifique de P₄S₃ liquide, calculé celle de P₄S₃ gazeux et son entropie standard. Nous avons aussi estimé l'enthalpie standard de vaporisation de P₄S₃ à l'aide des mesures des tensions de vapeur saturante. Nous en avons déduit l'entropie standard de P₄S₃ liquide et son point d'ébullition.

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It is shown by Raman spectroscopy at high temperature and by vapor tensimetric measurements that the vaporisation of P₄S₃ is congruent, whereas P₄S₇ and P₄S₁₀ dissociate at the beginning of vaporisation. P₄S₇ gives P₄S₃ and sulfur reversibly. The dissociation of P₄S₁₀ into P₄S₇ and sulfur is irreversible. Above 600°, in non-saturated vapour the dissociation of P₄S₃ gives phosphorus, sulfur and some unidentified gaseous species. The heat capacity of liquid P₄S₃ has been measured. That of gaseous P₄S₃ and its standard entropy have been calculated. The vaporisation standard enthalpy of P₄S₃ has been estimated from the experimental results on the saturated vapour pressures. The standard entropy of liquid P₄S₃ and its boiling point have been derived from these data.

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Zusammenfassung Mittels Raman-Spektrometrie bei erhöhter Temperatur und durch Messung der Dampfdrucke wurde festgestellt, daß sich P₄S₃ verflüchtigt, während P₄S₇ und P₄S₁₀ mit Beginn der Verflüchtigung dissoziieren. P₄S₇ ergibt reversibel P₄S₃ und Schwefel. Im Zustand ungesättigten Dampfes dissoziiert P₄S₃ oberhalb von 600° unter Bildung von Phosphor, Schwefel und anderer nicht identifizierter Substanzen.Die Wärmekapazität von flüssigem P₄S₃ wurde gemessen, während die vom gasförmigem P₄S₃ sowie seine Standard-Entropie berechnet wurden. Die Standard-Enthalpie der Verflüchtigung des P₄S₃ wurde durch Messungen der Sättigungs-Dampfdrucke ermittelt. Daraus wurden die Standard-Entropie des flüssigen P₄S₃ sowie sein Siedepunkt berechnet.

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- - , P₄S₃ , P₄S₇ P₄S₁₀ . P₄S₇ P₄S₃ , P₄S₁₀ P₄S₇ . 600° P₄S₃ , . P₄S₃, P₄S₃ . P₄S₃. P₄S₃ .

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Nous remercions Monsieur Letoffe du laboratoire du Professeur J. Bousquet, INSA de Lyon, 20 Avenue Albert Einstein 401, 69621 Villeurbanne, qui a r6alis6 pour nous les déterminations expérimentales des capacités calorifiques de P₄S₈ liquide.     

Behaviour of water-soluble dinuclear rhodium complexes in the hydroformylation reaction of oct-1-ene

The biphasic hydroformylation reaction of oct-1-ene, has been investigated by using the water-soluble dinuclear complex [Rh₂(μ-S^tBu)₂(CO)₂(TPPTS)₂] as precursor. Addition of ethanol as a cosolvent dramatically improved the yields but the good regioselectivity in linear aldehyde observed for neat oct-1-ene—water systems (97%) decreased to 83% (for 22% ethanol w/w). It is shown that the dinuclear framework cannot be maintained, that the mononuclear complex [RhH(CO)(TPPTS)₃] is formed, and that thiol and significant amounts of [Rh₂(μ-S^tBu)₂(CO)₄] move into the organic phase. This reaction from the dinuclear species requires the simultaneous presence of water and carbon monoxide. Introduction of the water-soluble thiol HS(CH₂)₃NMe₂ in the bridging positions affords the complex [Rh₂(μ-S(CH ₂)₃NHMe₂)₂(CO)₂(TPPTS)₂]Cl₂ which can be kept in the aqueous hase but has a low level of catalytic activity.     

A De Giorgi–Type Conjecture for Minimal Solutions to a Nonlinear Stokes Equation

We study the one-dimensional symmetry of solutions to the nonlinear Stokes equation which are periodic in the d − 1 last variables (living on the torus 𝕋^d−1) and globally minimize the corresponding energy in Ω = ℝ × 𝕋^d−1, i.e., Namely, we find a class of nonlinear potentials W ≥ 0 such that any global minimizer u of E connecting two zeros of W as x₁ → ± ∞ is one-dimensional; i.e., u depends only on the x₁ -variable. In particular, this class includes in dimension d = 2 the nonlinearities with w being a harmonic function or a solution to the wave equation, while in dimension d ≥ 3 , this class contains a perturbation of the Ginzburg-Landau potential as well as potentials W having d + 1 wells with prescribed transition cost between the wells. For that, we develop a theory of calibrations relying on the notion of entropy (coming from scalar conservation laws). We also study the problem of the existence of global minimizers of E for general potentials W providing in particular compactness results for uniformly finite energy maps u in Ω connecting two wells of W as x₁ → ± ∞ . © 2019 Wiley Periodicals, Inc.     

Polymerization of Ethylene by Silica‐Supported Dinuclear CrIII Sites through an Initiation Step Involving C?H Bond Activation

The insertion of an olefin into a preformed metal–carbon bond is a common mechanism for transition‐metal‐catalyzed olefin polymerization. However, in one important industrial catalyst, the Phillips catalyst, a metal–carbon bond is not present in the precatalyst. The Phillips catalyst, CrO₃ dispersed on silica, polymerizes ethylene without an activator. Despite 60 years of intensive research, the active sites and the way the first Cr C bond is formed remain unknown. We synthesized well‐defined dinuclear Cr^II and Cr^III sites on silica. Whereas the Cr^II material was a poor polymerization catalyst, the Cr^III material was active. Poisoning studies showed that about 65 % of the Cr^III sites were active, a far higher proportion than typically observed for the Phillips catalyst. Examination of the spent catalyst and isotope labeling experiments showed the formation of a Si–(μ‐OH)–Cr^III species, consistent with an initiation mechanism involving the heterolytic activation of ethylene at Cr^III O bonds.     

A molecular dynamics investigation of dynamical heterogeneity in supercooled water

We investigate the presence of dynamical heterogeneity in supercooled water with molecular dynamics simulations using the new water model proposed by Mahoney and Jorgensen [M.W. Mahoney, W.L. Jorgensen J. Chem. Phys. 112, 8910 (2000)]. Prompted by recent theoretical results [J.P. Garrahan, D. Chandler, Phys. Rev. Lett. 89, 35704 (2002)] we study the dynamical aggregation of the least and the most mobile molecules. We find dynamical heterogeneity in supercooled water and string-like dynamics for the most mobile molecules. We also find the dynamical aggregation of the least mobile molecules. The two kinds of dynamical aggregation appear however to be very different. Characteristic times are different and evolve differently. String-like motions appear only for the most mobile molecules, a result predicted by the facilitation theory. The aggregation of the least mobile molecules is more organized than the bulk while the opposite is observed for the most mobile molecules.     

A Counter-Example to the Theorem of Hiemer and Snurnikov

A planar polygonal billiard $\mathcal{P}$ is said to have the finite blocking property if for every pair (O, A) of points in $\mathcal{P}$ there exists a finite number of “blocking” points B ₁,...,B _n such that every billiard trajectory from O to A meets one of the B _i 's. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.