Incorporation of H2 in vitreous silica, qualitative and quantitative determination from Raman and infrared spectroscopy

Incorporation mechanisms of H₂ in silica glass were studied with Raman and infrared (IR) microspectroscopy. Hydrogenated samples were prepared at temperatures between 800°C and 955°C at 2 kbar total pressure. Hydrogen fugacities (f_H2) were controlled using the double capsule technique with the iron–wüstite (IW) buffer assemblage generating f_H2 of 1290–1370 bars corresponding to H₂ partial pressures (P_H2) of 960–975 bars. We found that silica glass hydrogenated under such conditions contains molecular hydrogen (H₂) in addition to SiH and SiOH groups. H₂ molecules dissolved in the quenched glasses introduce a band at 4136 cm⁻¹ in the Raman spectra which in comparison to that of gaseous H₂ is wider and is shifted to lower frequency. IR spectra of hydrogenated samples contain a band at 4138 cm⁻¹ which we assign to the stretching vibration of H₂ molecules located in non-centrosymmetric sites. The Raman and IR spectra indicate that the dissolved H₂ molecules interact with the silicate network. We suggest that the H₂ band is the envelope of at least three components due to the occupation of at least three different interstitial sites by H₂ molecules. Both, Raman and IR spectra of hydrogenated glasses contain bands at 2255 cm⁻¹ which may be due to the vibration of SiH groups. Under the assumption that the reaction Si–O–Si + H₂ → Si–H + Si–O–H describes adequately the ‘chemical dissolution' of H₂ molecules, the SiH concentrations in our samples were determined and the molar extinction coefficient for the SiH absorption band in the infrared (₂₂₅₅(SiH)) could then be estimated to be 45 ± 3 l/mol cm. The solubility of molecular H₂ in our hydrogenated samples was determined using the IR absorption band at 4138 cm⁻¹ and the extinction coefficient given by Shelby [J. Non-Cryst. Solids 179 (1994) 138]. Samples quenched with different cooling rates gave nearly identical Raman and IR spectra, suggesting that the chemical dissolution of hydrogen (SiH and SiOH) can be quenched to room temperature without changing relative concentrations and that no exsolution of hydrogen occurred during the quench.     

Cores of partitioning games

A generalization of assignment games, called partitioning games, is introduced. Given a finite set N of players, there is an a priori given set π of coalitions of N and only coalitions in π play an essential role. Necessary and sufficient conditions for the nonemptiness of the cores of all games with essential coalitions π are developed. These conditions appear extremely restrictive. However when N is ‘large’, there are relatively few ‘types’ of players, and members of π are ‘small’ and defined in terms of numbers of players of each type contained in subsets, then approximate cores are nonempty.     

One-pot reactions of 2,4-(dioxobutylidene)phosphoranes. Efficient synthesis of 4-(2-hydroxybenzoyl)salicylic acid derivatives and buta-1,3-diene-1,4-dicarboxylates

4-(2-Hydroxybenzoyl)salicylic esters and amides were prepared by domino ‘Michael-Retro-Michael-Wittig’ reactions of (2,4-dioxobutylidene)triphenylphosphoranes with 3-formylchromones.     

Fast matrix multiplication is stable

We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of Bini and Lotti [Numer. Math. 36:63–72, 1980]. As a consequence of our analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also show that new group-theoretic algorithms proposed in Cohn and Umans [Foundations of Computer Science, 44th Annual IEEE Symposium, pp. 438–449, 2003] and Cohn et al. [Foundations of Computer Science, 46th Annual IEEE Symposium, pp. 379–388, 2005] are all included in the class of algorithms to which our analysis applies, and are therefore numerically stable. We perform detailed error analysis for three specific fast group-theoretic algorithms. J. Demmel acknowledges support of NSF under grants CCF-0444486, ACI-00090127, CNS-0325873 and of DOE under grant DE-FC02-01ER25478. I. Dumitriu acknowledges support of the Miller Institute for Basic Research in Science. R. Kleinberg is supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship     

Dimension-wise integration of high-dimensional functions with applications to finance

We present a new general class of methods for the computation of high-dimensional integrals. The quadrature schemes result by truncation and discretization of the anchored-ANOVA decomposition. They are designed to exploit low effective dimensions and include sparse grid methods as special case. To derive bounds for the resulting modelling and discretization errors, we introduce effective dimensions for the anchored-ANOVA decomposition. We show that the new methods can be applied in locally adaptive and dimension-adaptive ways and demonstrate their efficiency by numerical experiments with high-dimensional integrals from finance.     

Effects of nanoscale defects on critical current density of (Y1−xEux)Ba2Cu3O7−δ thin films

In pulsed laser deposition of YBa₂Cu₃O_7?δ films, defect introduction into the films tends to anisotropically improve the pinning along the H||c direction due to the columnar growth mode of the process. In Eu-substituted samples, however, even though an increase in critical current density (J_c) in the H||c direction was observed for low fields (H = 0.2 T), the improvement was more notable for the H||ab-plane at both low and higher fields. Herein we present detailed TEM microstructural studies to understand these new trends in J_c(H), which are markedly different than flux pinning increases achieved with other methods, for example, with nanoparticle additions. Threading dislocations, observed in the Eu-substituted samples along the c-axis, account for J_c enhancement with H||c at low field. The enhanced ab-planar pinning in the Eu-substituted samples is attributed to the extensive bending of the {0 0 1} lattice planes throughout the film, and the crystal lattice defects with excess Cu–O planes, that were effective in increasing the J_c for H||ab at both low and high fields.     

Comparative PL study of individual ZnO nanorods,grown by APMOCVD and CBD techniques

The photoluminescence properties of individual ZnO nanorods, grown by atmospheric pressure metalorganic chemical vapor deposition (APMOCV) and chemical bath deposition (CBD) are investigated by means of temperature dependent micro-PL. It was found that the low temperature PL spectra are driven by neutral donor bound exciton emission D⁰X, peaked at 3.359 and 3.363 eV for APMOCVD and CBD ZnO nanorods, respectively. The temperature increase causes a red energy shift of the peaks and enhancement of the free excitonic emission (FX). The FX was found to dominate after 150 K for both samples. It was observed that while APMOCVD ZnO nanorods possess a constant low signal of visible deep level emission with temperature, the ZnO nanorods grown by CBD revealed the thermal activation of deep level emission (DLE) after 130 K. The resulting room temperature DLE was a wide band located at 420–550 nm. The PL properties of individual ZnO nanorods can be of importance for their forthcoming application in future optoelectronics and photonics.     

Regio- and diastereoselective synthesis of 2-alkylidenetetrahydrofurans by domino SN/SN' and SN/SN reactions of 1,3-dicarbonyl dianions

The domino C,O-cyclodialkylation reaction of dilithiated 1,3-dicarbonyl compounds with 1,4-dibromo-2-butene resulted in regio- and diastereoselective formation of 2-alkylidene-5-vinyltetrahydrofurans. The cyclization of 1,3-dicarbonyl dianions with 1-bromo-2-chloroethane regio- and diastereoselectively afforded 2-alkylidenetetrahydrofurans under thermodynamic reaction control.