Effect of relaxation on the oxygen K-edge electron energy-loss near-edge structure in yttria-stabilized zirconia

The electron energy-loss near-edge structure (ELNES) at the oxygen K-edge has been investigated in a range of yttria-stabilized zirconia (YSZ) materials. The electronic structure of the three polymorphs of pure ZrO2 and of the doped YSZ structure close to the 33 mol %Y2O3 composition have been calculated using a full-potential linear muffin-tin orbital method (NFP-LMTO) as well as a pseudopotential based technique. Calculations of the ELNES dipole transition matrix elements in the framework of the NFP-LMTO scheme and inclusion of core hole screening within Slater's transition state theory enable the ELNES to be computed. Good agreement between the experimental and calculated ELNES is obtained for pure monoclinic ZrO2. The agreement is less good with the ideal tetragonal and cubic structures. This is because the inclusion of defects is essential in the calculation of the YSZ ELNES. If the model used contains ordered defects such as vacancies and metal Y planes, agreement between the calculated and experimental O K-edges is significantly improved. The calculations show how the five different O environments of Zr,Y,O, are connected with the features observed in the experimental spectra and demonstrate clearly the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

Polarization Relaxation in an Ionic Liquid Confined between Electrified Walls

The response of a room temperature molten salt to an external electric field when it is confined to a nanoslit is studied by molecular dynamics simulations. The fluid is confined between two parallel and oppositely charged walls, emulating two electrified solid-liquid interfaces. Attention is focused on structural, electrostatic, and dynamical properties, which are compared with those of the nonpolarized fluid. It is found that the relaxation of the electrostatic potential, after switching the electric field off, occurs in two stages. A first, subpicosecond process accounts for 80% of the decay and is followed by a second subdiffusive process with a time constant of 8 ps. Diffusion is not involved in the relaxation, which is mostly driven by small anion translations. The relaxation of the polarization in the confined system is discussed in terms of the spectrum of charge density fluctuations in the bulk.

Relaxation processes in room temperature ionic liquids: The case of 1-butyl-3-methyl imidazolium hexafluorophosphate

A detailed investigation on the nature of the relaxation processes occurring in a typical room temperature ionic liquid (RTIL), namely, 1-butyl-3-methyl imidazolium hexafluorophosphate ([bmim][PF6]), is reported. The study was conducted using both elastic and inelastic neutron scattering over a wide temperature range from 10 to 400 K, accessing the dynamic features of both the liquid and glassy amorphous states. In this study, the inelastic fixed energy scan technique has been applied for the first time to this class of materials. Using this technique, the existence of two relaxation processes below the glass transition and a further diffusive process occurring above the glass-liquid transition are observed. The low temperature processes are associated with methyl group rotation and butyl chain relaxation in the glassy state and have been modeled in terms of two Debye-like, Arrhenius activated processes. The high temperature process has been modeled in terms of a Kohlraush-Williams-Watts relaxation, with a distinct Vogel-Fulcher-Tamman temperature dependence. These results provide novel information that will be useful in rationalizing the observed structural and dynamical behavior of RTILs in the amorphous state.