Coherent electron tunneling in triple coupled quantum wells

We present a numerical study of coherent electron tunneling in a triple coupled quantum well system. The evolution of the charge density is described in detail. In this heterostructure the electron will oscillate between the three wells, giving rise to a new type of oscillating luminescence signal. An experiment is proposed.     

(μ‐Oxalato‐O1,O2:O1′,O2′)bis[aqua(diethyl­enetri­amine)nickel(II)] bis(hexafluorophosphate) dihydrate

The title compound, [Ni₂(C₂O₄)(C₄H₁₃N₃)₂(H₂O)₂](PF₆)₂·‐2H₂O, contains a dinuclear oxalato‐bridged nickel(II) complex cation. The structure determination reveals the presence of a centrosymmetric binuclear complex where the oxalate ligand is coordinated in a bis­‐bidentate mode to the Ni atoms. The distorted octahedral environment of each Ni atom is completed by the three N atoms of the diethyl­enetri­amine ligand in a fac arrangement and by one O atom from a water mol­ecule. PF₆^? acts as counter‐anion. A two‐dimensional network of hydrogen bonds links the cations and anions and stabilizes the structure.     

Preparation, characterization, magnetic susceptibility (Eu, Gd and Sm) and XPS studies of Ln2ZrTiO7 (Ln=La, Eu, Dy and Gd)

Bulk and nanosized pyrochlore materials Ln₂ZrTiO₇ (Ln=La, Eu, Dy, Gd and Sm) have been prepared by the sol-gel method. All the samples were characterized by powder X-ray diffraction, Raman and X-ray photoelectron spectroscopy. Magnetic susceptibility (χ) measurements of Gd₂ZrTiO₇, Sm₂ZrTiO₇ and Eu₂ZrTiO₇ were carried out by vibrating sample magnetometer in the temperature range 2-320 K. The variation of χ⁻¹ (or χ) with temperature of Gd₂ZrTiO₇, Sm₂ZrTiO₇ and Eu₂ZrTiO₇ follows the Curie law, intermediate formula and the Curie-Weiss law, respectively. From the linear portion of χT vs. T⁻¹ plot of Eu₂ZrTiO₇ from 2 to 15 K, the classical nearest neighbor exchange (J^cl) and dipolar interactions (D_nn) are obtained. The XPS of Ln₂ZrTiO₇ (Ln=La, Eu, Dy and Gd) gave characteristic peaks for Ln, Ti, Zr and O. The satellite peaks are observed only for 3d La of La₂ZrTiO₇.     

Spectral moments for systems described by an ensemble of hamiltonians

We generalize Van Vleck's method of moments for disordered solid-state that can be described by an ensemble of hamiltonians. Special reference is made to N.M.R. spectroscopy. Inhomogeneous broadening for a sample of free spins and the more complex problem of interacting spins are discussed in detail. The cumulant expansion and the Liouville space formalism are introduced as tools to simplify the expressions for the moments and to obtain physical approximations. As a particular application the Sherrington-Kirkpatrick model for spin glasses is derived and interpreted physically.     

Effect of Cation/Anion Co‐doping on the Photocatalytic Performance of Na3SbO(PO4)2

Silver/copper‐nitrogen co‐doped Na₃SbO(PO₄)₂ were prepared by solid state/ion exchange methods. The materials were characterized by powder XRD, SEM‐EDS, TG analysis, as well as FT‐IR and UV/Vis diffuse reflectance spectroscopy. All the doped materials crystallize in orthorhombic lattice with space group P2₁2₁2₁. The infrared spectra of the samples gave characteristic bands corresponding to PO₄ and SbO₆ groups. The bandgap energy of all the samples was deduced from their UV/Vis DRS profiles. The bandgap energy of doped materials decreased substantially. Visible‐light‐induced photocatalytic oxidation of the methyl violet (MV) and methylene blue (MB) was examined. The influence of cation, anion, and co‐doping on the photoactivity of Na₃SbO(PO₄)₂ was studied. The Ag⁺ and nitrogen co‐doped Na₃SbO(PO₄)₂ exhibited the highest photocatalytic activity among the materials investigated.     

Aurivillius family of layered perovskites,BiREWO6 (RE = La,Pr, Gd,and Dy): Synthesis,characterization, and photocatalytic studies

The present work deals with the synthesis, characterization, and photocatalytic studies of layered perovskites belonging to Aurivillius family. Layered perovskites of various chemical compositions, BiREWO₆ (RE = La, Pr, Gd, and Dy), were synthesized by an ethylene glycol–assisted sol–gel method. These materials were characterized by X-ray diffraction, scanning electron microscopy–energy dispersive spectroscopy (EDS), Fourier transform infrared, Raman, and ultraviolet–visible diffuse reflectance techniques. The composition of all these materials was obtained from EDS. The unit cell lattice parameters were attained from Rietveld refinement program, Fullprof.2k, by refining the d-lines of BiREWO₆. The band gap energy of these samples was obtained from the Kubelka–Munk plot. The photocatalytic activity of all the samples was evaluated by photodegradation of methylene blue. The mechanistic degradation pathway of methylene blue was studied using radical quenchers.     

Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary

In this Note we deduce an explicit Sommerfeld-type radiation condition which is convenient to prove the uniqueness for the time-harmonic outgoing wave problem in an isotropic elastic half-plane with free boundary condition. The expression is obtained from a rigorous asymptotic analysis of the associated Green's function. The main difficulty is that the free boundary condition allows the propagation of a Rayleigh wave which cannot be neglected in the far field expansion. We also give the existence result for this problem. To cite this article: M. Durán et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).