Double quantization of CP type orbits by generalized Verma modules

It is known that symmetric orbits in g^* for any simple Lie algebra g are equipped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the “canonical” R-matrix. We realize quantization of the Poisson pencil CPⁿ type orbits (i.e. orbits in sl(n + 1)^* whose real compact form is CPⁿ) by means of q-deformed Verma modules.     

Association energies in Re3+-doped alkaline-earth fluorides studied by computational methods

Association energies of nearest-neighbour and next-nearest-neighbour associates between substitutional, trivalent rare-earth ions and interstitial fluoride ions CaF₂, SrF₂ and BaF₂ are obtained by lattice simulation calculations. The dopant ion-fluoride ion interaction is described (i) with a set of potentials obtained with electron gas methods, and (ii) with a set of potentials derived semi-empirically from the host lattice cation-anion interaction potentials. The calculations successfully simulate the experimentally observed variations of the dopant-interstitial binding energies with the radius of the dopant ion, and with the lattice parameter of the host. The better quantitative agreement is obtained with the semi-empirical potentials. The variations are explained by an evaluation of the displacements of the ions constituting the associates.     

Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation

A correlation-type reciprocity theorem is used to show that the elastodynamic Green's function of any inhomogeneous medium (random or deterministic) can be retrieved from the cross correlation of two recordings of a wave field at different receiver locations at the free surface. Unlike in other derivations, which apply to diffuse wave fields in random media or irregular finite bodies, no assumptions are made about the diffusivity of the wave field. In a second version, it is assumed that the wave field is diffuse due to many uncorrelated sources inside the medium.     

Dielectric relaxation properties of tysonite-type solid solutions La1−xBaxF3−x

Dielectric relaxation properties of solid solutions La_1?xBa_xF_3?x (x ? 0105) have been studied by thermally stimulated depolanzation current (TSDC)- and a c. dielectric loss (DL) techniques.For x < 30 × 10^?3 the dielectric spectra show a relaxation peak which is ascribed to a simple associate of a substitutional dopant ion and a fluoride ion vacancy (Ba_LaV_F)^x in nearest-neighbour position, the vacancy being confined to the B sublattice For x values of about 1.3 × 10^?2 a relaxation peak appears which is tentatively attributed to a similar type of defect associate with the vacancy now confined to the A sublattice of the tysonite anion array One broad relaxation peak dominates the TSDC and DL spectra over the whole concentration range This peak is due to the relaxation of macroscopic space charge, i e ionic conductivity The low-temperature ion conductivity has been determined for several solid solutions, and extrapolates to the high-temperature conductivity determined previously with impedance spectroscopy Below liquid-nitrogen temperature three relaxations are observed, and ascribed to electronic transitions in cenum impurities. A computer programme has been developed to analyse TSDC relaxation peaks, taking dipole-dipole interactions into account Relaxation parameters and dipole concentrations are presented.     

Conductivity enhancement in fluorite-structured Ba1−xLaxF2+x solid solutions

The ionic conductivity of single crystals of the fluorite-structured solid solutions Ba_1?xLa_xF_2+x(10^?3 <×<0.45) has been studied as a function of temperature and composition in the range 300–900 K. Three regions can be discerned in the concentration dependence of the ionic conductivity: a dilute concentration region (x<10^?3), where classic relations between solute content and ionic conductivity hold; an intermediate concentration region (10^?3<x?5×10^?2), where large changes occur in the conductivity activation enthalpy and the magnitude of the conductivity; and a concentrated solid solution region (x?5×10^?2) characterized by enhanced ionic motion. In the dilute region the migration enthalpy for interstitial fluoride ions is determined to be 0.714 eV, while a value of 0.39 eV is found for the (La_BaF_i)^X association enthalpy. The defect chemistry in the intermediate concentration region is shown to be controlled by a superlinear increase of the concentration of mobile defects, while in the concentrated solid solution region a composition-independent amount of ≈1 mole% of interstitial fluoride ions with enhanced mobility, carry the current.     

Surface degradation of fluoride conducting crystals MF2:UF4:CeF3 (M = Ca,Sr, Ba)

The ac electrical response of cell systems composed of single crystals of the concentrated solid solutions M_1?x?yU_xCe_yF_2+2x+y (M = Ca, Sr, Ba and 2.7 < 2x + y < 26.5 m/o), and ionically blocking electrodes has been studied as a function of frequency and temperature. At elevated temperatures the crystals react with traces of oxygen or water vapor. Complex admittance analysis reveals the formation of low-conducting surface layers, contrary to diluted solid solutions which under similar conditions react to form high-conducting surface layers (2). The activation enthalpy for the layer conductivity is substantially larger than that for the bulk conductivity, and equals that for interstitial fluoride ion motion in dilute solid solutions. A mechanism of charge compensation in the layers is presented. After reaction the solid solutions based on CaF₂ show also a surface electronic conductivity. Scanning electron micrographs clearly reveal the surface degradation.     

Small-signal ac response of Ba1−xLaxF2+x crystals

The small-signal ac response of single crystalline Ba_1?xLa_xF_2+x solid solutions has been studied in the temperature region 300–820 K, and in the frequency range 4×10^?2–5×10⁴ Hz. At low temperatures the frequency dispersion is dominated by processes in the bulk. Apart from the bulk conductance these processes include a dielectric response determined by broad distributions of dipole-like relaxations. The increase of the static dielectric constant with increasing solute content is explained. At higher temperatures the frequency dispersion reflects interfacial phenomena. In addition to an almost ideal interface capacitance, phenomena are observed which indicate the growth of a surface layer due to a reaction between the electrolyte, and residual oxygen and/or water vapour from the ambient.