An electrochemical study of copper diffusion in non-stoichiometric copper sulphide

The diffusion of copper in hexagonal chalcocite (Cu₂S) is not very well-known. In this work electrochemical cells with natural polycrystalline chalcocite working electrodes have been studied by electrochemical impedance spectroscopy (EIS) over a large frequency range at equilibrium potential. To study this phenomenon between 120 and 160°C a solid electrolyte RbCu₄Cl₅ has been used. The impedance spectra present two distinct regions. At high frequencies the general shape of the diagram in the Nyquist plane is a depleted are of a circle. Changes in electrolyte resistance, interfacial capacitance and transfer resistance have been studied as a function of temperature. At low frequencies, a diffusion impedance is observed attributed to the mobility of copper vacancies. Diffusion coefficients, with an activation energy of 1.7 eV, have been deduced from the impedance diagrams (4.7·10⁻⁵cm² s⁻¹ at 130°C). These results are compared with those obtained with orthorhombic chalcocite between 30 and 60 °C by EIS and using an electrochemical cell with a cupric liquid electrolyte. Paper presented at the 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Italy, Sept. 15–22, 1996     

Recombination and charge transfer at the illuminated n-CdTe/electrolyte interface: Simplified kinetic model

The experimental behaviour of the illuminated n-cadmium telluride/aqueous electrolyte interface is presented with a precise analysis of the electrical impedance in acidic medium. Band edge shifts and the photocurrent onset position are observed to depend strongly on the pH value. They are interpreted by considering mainly the kinetics of the different reactions at the interface. An analytical model is then developed allowing the fitting of both current-voltage and impedance curves. The equivalent circuit derived from the model explains the origin and the variation of the recombination resistance observed experimentally.     

Observation of instabilities in a Paul trap with higher-order anharmonicities

Systematic measurements of the relative ion number stored in a Paul trap within the stability diagram given by the solution of the equation of motion reveal many lines, where only few or no ions can be confined. The observations can be explained by the presence of perturbations from higher-order components in the trapping potential, which is a quadrupole potential in the ideal case. The resonances follow the equation (n _r /2) _r + (n _r /2) _z = 1,n _r +n _z =N, where 2N is the order of the perturbation,n _r ,n _z are integer and _r , _z are stability parameters of the trap. The experiments were performed on H⁺ and H ₂ ⁺ ions, which are detected after a storage time of 0.3 s by ejection from the trap.     

Lifetime and collisional depopulation of the metastable 5D 3/2-state of Yb+

The lifetime and collisional depopulation rates of the metastable 5D _3/2 state of Yb⁺ have been determined in a radiofrequency ion trap by observation of the fluorescence count rate after ion excitation by a short laser pulse. From measurements using He, N₂ and H₂ as buffer gases between 10^?8 and 10^?6 mbar pressure and linear extrapolation to zero pressure we obtain a lifetime of τ=52.15±1.00 ms and rate constants ofR(H₂)=(1.02±0.10)×10^?9 cm³/s andR(N₂)=(1.78±0.19)×10^?10 cm³/s. The lifetime is in fair agreement with a calculated value of 74 ms.     

Rotational integral geometry of tensor valuations

We derive a new rotational Crofton formula for Minkowski tensors. In special cases, this formula gives (1) the rotational average of Minkowski tensors defined on linear subspaces and (2) the functional defined on linear subspaces with rotational average equal to a Minkowski tensor. Earlier results obtained for intrinsic volumes appear now as special cases.     

Optical heterodyne measurement of small shift differences between two stimulated Brillouin lines

The beats between two stimulated Brillouin scattering beams issued either from one single crystal or from two differently oriented crystals were observed and this allowed the shift differences to be measured in the range 60 MHz to 1 GHz.     

Bases d'ondelettes adaptées au règlement de la divergence infra-rouge

We propose bi-orthogonal wavelet bases that solve the problem of infrared divergence phenomenon for usual wavelet expansions in the homogeneous Sobolev spaces ${\dot{H}}^s({\mathbb{R}}^n)$. These bases remove the divergence in the case $s?\frac{n}{2}?\mathbb{N}$ since they are also bases of the realization of ${\dot{H}}^s({\mathbb{R}}^n)$. In the critical case $s?\frac{n}{2}\in \mathbb{N}$, they provide a confinement of the infrared divergence in a ‘small’ space. This method of confinement is also applied to the Mumford process. To cite this article: B. Vedel, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Dark resonances as a probe for the motional state of a single ion

Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second-order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. In this paper the motional state of a confined three-level ion is probed, taking advantage of the high sensitivity of observed dark resonances to the trapped ion’s velocity. Excess micromotion is controlled by monitoring the dark-resonance contrast with varying laser-beam geometry. The influence of different parameters such as the cooling laser intensity has been investigated experimentally and numerically.     

Terahertz frequency standard based on three-photon coherent population trapping

A scheme for a terahertz frequency standard based on three-photon coherent population trapping in stored ions is proposed. Assuming the propagation directions of the three lasers obey the phase matching condition, we show that stability of few 10(-14) at 1 s can be reached with a precision limited by power broadening to 10(-11) in the less favorable case. The referenced terahertz signal can be propagated over long distances, the useful information being carried by the relative frequency of the three optical photons.