Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media

We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We obtain fractional integro-differential equations for electromagnetic waves in a dielectric. The electromagnetic fields in dielectrics demonstrate a fractional power-law relaxation. The fractional integro-differential equations for electromagnetic waves are common to a wide class of dielectric media regardless of the type of physical structure, the chemical composition, or the nature of the polarizing species (dipoles, electrons, or ions)

Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently. Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.Comment: 5 pages; 3 figures; corrected versio

Fractional Equations of Curie-von Schweidler and Gauss Laws

The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of noninteger order. We obtain equations that describe "universal" Curie-von Schweidler and Gauss laws for such dielectric materials. These laws are presented by fractional differential equations such that the electromagnetic fields in the materials demonstrate "universal" fractional damping. The suggested fractional equations are common (universal) to a wide class of materials, regardless of the type of physical structure, chemical composition or of the nature of the polarization.Comment: 11 pages, LaTe

Plastic-crystalline solid-state electrolytes: Ionic conductivity and orientational dynamics in nitrile mixtures

Many plastic crystals, molecular solids with long-range, center-of-mass crystalline order but dynamic disorder of the molecular orientations, are known to exhibit exceptionally high ionic conductivity. This makes them promising candidates for applications as solid-state electrolytes, e.g., in batteries. Interestingly, it was found that the mixing of two different plastic-crystalline materials can considerably enhance the ionic dc conductivity, an important benchmark quantity for electrochemical applications. An example is the admixture of different nitriles to succinonitrile, the latter being one of the most prominent plastic-crystalline ionic conductors. However, until now only few such mixtures were studied. In the present work, we investigate succinonitrile mixed with malononitrile, adiponitrile, and pimelonitrile, to which 1 mol% of Li ions were added. Using differential scanning calorimetry and dielectric spectroscopy, we examine the phase behavior and the dipolar and ionic dynamics of these systems. We especially address the mixing-induced enhancement of the ionic conductivity and the coupling of the translational ionic mobility to the molecular reorientational dynamics, probably arising via a "revolving-door" mechanism.Comment: 9 pages, 7 figures; revised version as accepted for publication in J. Chem. Phy

Dielectric response due to stochastic motion of pinned domain walls

We study the contribution of stochastic motion of a domain wall (DW) to the dielectric AC susceptibility for low frequencies. Using the concept of waiting time distributions, which is related to the energy landscape of the DW in a disordered medium, we derive the power-law behavior of the complex susceptibility observed recently in some ferroelectrics below Curie temperature.Comment: 5 pages, 2 figures, revtex

Power-law decay in first-order relaxation processes

Starting from a simple definition of stationary regime in first-order relaxation processes, we obtain that experimental results are to be fitted to a power-law when approaching the stationary limit. On the basis of this result we propose a graphical representation that allows the discrimination between power-law and stretched exponential time decays. Examples of fittings of magnetic, dielectric and simulated relaxation data support the results.Comment: to appear in Phys. Rev. B; 4 figure

Dielectric behavior of Copper Tantalum Oxide

A thorough investigation of the dielectric properties of Cu2Ta4O12, a material crystallizing in a pseudo-cubic, perovskite-derived structure is presented. We measured the dielectric constant and conductivity of single crystals in an exceptionally broad frequency range up to GHz frequencies and at temperatures from 25 - 500 K. The detected dielectric constant is unusually high (reaching values up to 105) and almost constant in a broad frequency and temperature range. Cu2Ta4O12 possesses a crystal structure similar to CaCu3Ti4O12, the compound for which such an unusually high dielectric constant was first observed. An analysis of the results using a simple equivalent circuit and measurements with different types of contact revealed that extrinsic interfacial polarization effects, derived from surface barrier capacitors are the origin of the observed giant dielectric constants. The intrinsic properties of Cu2Ta4O12 are characterized by a (still relatively high) dielectric constant in the order of 100 and by charge transport via hopping conduction of Anderson-localized charge carriers.Comment: 18 pages, 6 figures, submitted to Jouranl of Physical Chemestr

Universal Electromagnetic Waves in Dielectric

The dielectric susceptibility of a wide class of dielectric materials follows, over extended frequency ranges, a fractional power-law frequency dependence that is called the "universal" response. The electromagnetic fields in such dielectric media are described by fractional differential equations with time derivatives of non-integer order. An exact solution of the fractional equations for a magnetic field is derived. The electromagnetic fields in the dielectric materials demonstrate fractional damping. The typical features of "universal" electromagnetic waves in dielectric are common to a wide class of materials, regardless of the type of physical structure, chemical composition, or of the nature of the polarizing species, whether dipoles, electrons or ions.Comment: 19 pages, LaTe

Origin and stability of the dipolar response in a family of tetragonal tungsten bronze relaxors

A new family of relaxor dielectrics with the tetragonal tungsten bronze structure (nominal composition Ba6M3+Nb9O30, M3+ = Ga, Sc or In) were studied using dielectric spectroscopy to probe the dynamic dipole response and correlate this with the crystal structure as determined from powder neutron diffraction. Independent analyses of real and imaginary parts of the complex dielectric function were used to determine characteristic temperature parameters, TVF, and TUDR, respectively. In each composition both these temperatures correlated with the temperature of maximum crystallographic strain, Tc/a determined from diffraction data. The overall behaviour is consistent with dipole freezing and the data indicate that the dipole stability increases with increasing M3+ cation size as a result of increased tetragonality of the unit cell. Crystallographic data suggests that these materials are uniaxial relaxors with the dipole moment predominantly restricted to the B1 cation site in the structure. Possible origins of the relaxor behaviour are discussed.Comment: Main article 32 pages, 8 figures; Supplementary data 24 pages, 4 figure

Evidence of secondary relaxations in the dielectric spectra of ionic liquids

We investigated the dynamics of a series of room temperature ionic liquids based on the same 1-butyl-3-methyl imidazolium cation and different anions by means of broadband dielectric spectroscopy covering 15 decades in frequency (10^(-6)-10^9 Hz), and in the temperature range from 400 K down to 35 K. An ionic conductivity is observed above the glass transition temperature T_{g} with a relaxation in the electric modulus representation. Below T_{g}, two relaxation processes appear, with the same features as the secondary relaxations typically observed in molecular glasses. The activation energy of the secondary processes and their dependence on the anion are different. The slower process shows the characteristics of an intrinsic Johari-Goldstein relaxation, in particular an activation energy E_{beta}=24k_{B}T_{g} is found, as observed in molecular glasses.Comment: Major revision, submitted to Phys. Rev. Let