Low-temperature formation and characterization of Cu2O nanoparticles in the binary gold alloys

Thermal analyses, using differential scanning calorimetry (DSC) and dilatometry, reveal an important anomaly at low temperature for Au-25 wt.% Cu composition after homogenization at 700°C during 2 hours under vacuum followed by heating up to 160°C before water quenching. This anomaly has been already observed and not explained. Surface characterization, using scanning electron microscopy (SEM), atomic force microscopy (AFM), and scanning tunneling microscopy (STM), exhibits a specific topography, consisting of a nanostructured surface. The precipitates of nanostructured particles are homogeneously scattered all over the surface for this 18-carat gold alloy. Moreover, X-ray photoelectron spectroscopy (XPS) shows that the composition of the observed particles corresponds to cuprous oxide phase (Cu₂O). The formation of such material can be explained by the diffusion of copper atoms from the lattice to the surface at 160°C. Pulsed radio-frequency glow discharge optical emission spectroscopy (RF GD-OES) further proves the proposed Cu₂O formation through a diffusion process. The appearance of such cuprous oxide nanoparticles on the Au-Cu alloy surface explains the low-temperature DSC and dilatometry anomaly and affects directly the surface electrical resistance at low temperature. These results might open a large gate for new ideas to investigate in catalytic, electronic, and antimicrobial activities.     

Complex Surface Chemistry of an Otherwise Inert Solvent Molecule: Tetrahydrofuran on Si(001)

The reaction of tetrahydrofuran (THF), an otherwise inert solvent molecule, on Si(001) was experimentally studied in ultra‐high vacuum. Using scanning tunneling microscopy (STM) and photoelectron spectroscopy at variable temperature, we could both isolate a datively bound intermediate state of THF on Si(001), as well as the final configuration that bridges two dimer rows of the Si(001) surface after ether cleavage. The latter configuration implies splitting of the O?C bond, which is typically kinetically suppressed. THF thus exhibits a hitherto unknown reactivity on Si(001).     

Multi-layer model of correlated energy prices

In this article we develop an extension of the affine jump-diffusion modeling framework and use it to build an intuitive and tractable model of an energy price complex. The development is motivated by the need to model prices of electricity while capturing their dependence on the price of other energy commodities. Such a model is essential for valuing a range of typical derivatives traded in the electricity markets: cross-commodity spread options, cross-location spread options, fuel-switching powerplants, etc. We give an approximate pricing method for these derivatives together with precise error bound estimates.     

The Quantum and Klein-Gordon Oscillators in a Non-commutative Complex Space and the Thermodynamic Functions

In this work we study the quantum and Klein-Gordon oscillators in a non-commutative complex space. We show that a particle described by such oscillators behaves similarly as an electron with spin in a commutative space in an external uniform magnetic field. Therefore the wave-function $\psi (z,\bar{z} )$ takes values in C ⁴, spin up, spin down, particle, antiparticle, a result which is obtained by the Dirac theory. We obtain the energy levels by exact solutions. We also derive the thermodynamic functions associated to the partition function, and show that the non-commutativity effects are manifested in energy at the high temperature limit.     

Low-frequency variable charge solitary waves in a collisionless dusty plasma with a Cairns-Gurevich ion velocity distribution

In this paper, the problem of large amplitude dust acoustic (DA) solitons has been addressed in a charge varying dusty plasma with ions following a Cairns-Gurevich distribution. Based on the orbit motion limited approach, the correct Cairns-Gurevich ion charging current is presented for the first time. The expression relating the variable dust charge to the plasma potential is given in terms of the Lambert function and we take advantage of this transcendental function to, carefully, analyse DA solitons in a charge varying dusty plasma with trapped nonthermal ions. Our results show that the spatial patterns of the variable charge solitary wave are significantly changed due to the presence of ion population modelled by the Cairns-Gurevich distribution. An addition of a small concentration of trapped nonthermal ions makes the solitary structure less spiky, grows the net negative charge residing on the dust grain surface, and contributes to the electron depletion. Finally, our investigation is extended to highlight the effect of the grain dust charge variation. We have shown that under certain conditions, the impact of dust charge fluctuation may furnish an alternate physical mechanism rasing anomalous dissipation, which becomes more strong and may predominate over the dispersion as the nonthermal character of ions following the Cairns-Gurevich distribution increases.     

The first suberate lanthanum(III) complex without uncoordinated water

catena‐Poly­[[aqua­lanthanum(III)]‐μ‐(8‐carboxy­octanoato)‐μ‐octanedioato], [La(C₈H₁₂O₄)(C₈H₁₃O₄)(H₂O)]_n, is, to our knowledge, the first reported rare‐earth complex containing a flexible long‐chain ligand that crystallizes without water of crystallization. The layered polymeric structure is built from infinite chains of one‐edge‐sharing LaO₈(H₂O) polyhedra, connected through the carbon backbone chains of the ligands. The two chemically different ligands act in the same coordination modes, exhibiting chelating bonds and μ‐1,1‐bridging monodentate linkage, and adopting the same extended conformation. In the relatively limited hydrogen‐bonding network, a very strong hydrogen bond between the deprotonated and protonated ligand ends stabilizes the framework.     

A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

Summary Consider the solution of one-dimensional linear initial-boundary value problems by a finite element method of lines using a piecewiseP ^th -degree polynomial basis. A posteriori estimates of the discretization error are obtained as the solutions of either local parabolic or local elliptic finite element problems using piecewise polynomial corrections of degreep+1 that vanish at element ends. Error estimates computed in this manner are shown to converge in energy under mesh refinement to the exact finite element discretization error. Computational results indicate that the error estimates are robust over a wide range of mesh spacings and polynomial degrees and are, furthermore, applicable in situations that are not supported by the analysis.This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 90-0194; by the U.S. Army Research Office under Contract Number DAAL03-91-G-0215; and by the National Science Foundation under Institutional Infrastructure Grant Number CDA-8805910     

Mixed formulations for a class of variational inequalitiesFormulations mixtes pour une classe d'inéquations variationnelles

This Note is an attempt to extend the mixed finite element method to a class of variational inequalities including the problems of Signorini and of unilateral contact in elasticity with or without friction. Existence and uniqueness for the continuous and the discrete problems as well as error estimates are established in a general abstract framework. As a result, the mixed approximation of the Signorini problem is proved to converge with an error bound in h^3/4. To cite this article: L. Slimane et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 87–92     

Phase transition in ammonium hexafluorovanadate (III)

Heat capacity of ammonium hexafluorovanadate (NH₄)₃ [VF₆] has been measured with a miniaturized adiabatic calorimeter from 20 to 300 K. A phase transition was found at 280.44 ± 0.05 K with the associated entropy change Δ_trs S = 24.9 ± 0.5 JK^?1 mol^?1. The entropy transition is accounted for by the orientational order-disorder changes of hexafluorovanadate ion and ammonium ion occupying respective octahedral sites, as in the cases of (NH₄)₃AlF₆ and (NH₄)₃FeF₆ crystals. Changes in infrared spectra relative to v₃ vibrational mode of [VF₆]^3? ion can be explained by an orientational disorder of the anions in the high-temperature phase (HTP). The dependence of cubic root of the unit-cell volume of a family of ammonium cryolites on their transition temperatures is discussed in relation to the nature of interactions which induce the phase transition.     

Angular Multiplexing Gratings Characterization in Dichromated Gelatin and Thoughts on Diffractive Optical Memory

We were mainly concerned here with multiple exposure gratings that allow interactions and coupling between gratings. We started the study of interactions and coupling with five gratings recorded in dichromated gelatin (DCG). Having determined experimentally the characteristic parameters of these five gratings, we used a method developed by Oxford University to synthesize the modulation profile. Entering these parameters of each grating into our computing programs (based on the alternative theory of diffraction in modulated media) and by varying the amplitude modulation, the latter was deduced by adjusting the numerical curve to the experimental one. We then extended the study to nine multiplexed gratings. This study allowed us to know the range of the amplitude modulation such that a certain number of angular multiplexing can be done in DCG. Several undesirable effects which we had experimentally observed appeared then during the reconstruction of any one of the multiplexed images, such as cross-talk effect. We noted the good concordance between experimental and theoretical results. We finally illustrated cross-talk effect in a diffractive memory where, if the amplitude modulation was first calculated, the number of multiplexing for an angular range could then be determined and the angular separation achieved to avoid cross-talk.