Conductivity Relaxation Time Research Articles

Conductivity and Dielectric Relaxation in Concentrated Aqueous Lithium Chloride Solutions

This paper describes a study of the recently recognized phenomenon of conductivity relaxation in liquid electrolytes as it is observed in the system LiCl+water. Advantage has been taken of the supercooling ability of 6–20m solutions in this system to reduce solution temperatures to the vicinity of −100°C and thereby to increase the relaxation time characteristic of the conductance process sufficiently to permit its study with conventional ac conductance bridges operating in the frequency range 0.2–2 000 kHz. Extensive data are presented for four solutions in the concentration range 8.3–11.9m. When the frequency-dependent conductance and capacitance data are analyzed in the dielectric modulus notation developed by Macedo, Bose, and Litovitz, mean relaxation times for conductance are obtained which have a non-Arrhenius temperature dependence identical to that of the dc conductivity. Earlier studies of dielectric relaxation in these solutions, carried out at room temperature and gigahertz frequencies, are re-analyzed and shown to correspond to the high-temperature extension of the same phenomenon examined at low temperatures in the present study. The characteristic migration distance associated with the conductivity relaxation time, assessed using the Nernst—Einstein equation, is of ionic dimensions. The presence of subsidiary higher-frequency relaxations is noted and their origin considered in relation to Goldstein's ubiquitous ``localized motions'' in glasses.

A note on frequency pulling in resonant media

Whether the carrier frequency of an undistorted optical pulse adjusts to the central atomic frequency of the resonant medium in which it propagates is shown to depend on three parameters. Two of these parameters characterize the conductivity and homogeneous relaxation time of the medium, and one is related to the difference between the light phase velocity in the host medium and the assumed pulse velocity.

Comparison of Shear and Conductivity Relaxation Times for Concentrated Lithium Chloride Solutions

Shear viscosity measurements over the temperature interval 23 –− 124 °C (5×10−2– 108 P) and shear impedance measurements at 88 MHz over the interval −75–−130°C have been performed for concentrated aqueous lithium chloride solutions in the concentration range R=4.49 – 5.77 where R is the mole ratio of water to salt. Average shear relaxation times, 〈 τs 〉, have been calculated from these results and compared with average conductivity relaxation times, 〈 τσ 〉, reported previously by Moynihan, Bressel, and Angell. 〈 τs 〉 and 〈 τσ 〉 are within 30% of one another at the low viscosity end ( ∼104 P) of the range of comparison, but at higher viscosities the 〈τs 〉/〈τσ 〉 ratio becomes significantly larger than unity (2–3 at the highest viscosities for which data are available). Estimated 〈τs 〉/〈τσ 〉 ratios for other ionic liquids suggest that the occurrence of 〈τs 〉/〈τσ 〉 ratios greater than unity at high visosities may be a common phenomenon. Description of the shear relaxation process for concentrated LiCl—H2O solutions is found to require a fairly broad, asymmetric (Cole—Davidson) distribution of relaxation times.

Rotational Relaxation in Nonpolar Diatomic Gases

The rotational-translational energy transfer in collisions between homonuclear diatomic molecules and the rotational relaxation time in diatomic gases have been investigated classically. Using Parker's model for the intermolecular potential, numerical solutions were obtained for the rotational-energy transfer in individual collisions. The method of solution for the collision trajectories has been combined with a Monte Carlo integration procedure to evaluate the transport properties for diatomic gases. The formal kinetic-theory expressions derived by Wang Chang, Uhlenbeck, and Taxman for the transport coefficients of gases with internal energy states were used. Results are presented for the shear viscosity, thermal conductivity, and rotational relaxation time in N2 which compare favorably with experimental values. Results are included for both a coplanar and three-dimensional collision model. Approximate solutions for the rotational-energy transfer in coplanar collisions and the rotational relaxation time are also presented. The approximate expression for the relaxation time agrees well with the Monte Carlo calculation and with experimental data for N2 and O2. The effect of unequal rotational and translational temperatures was also studied and found to be significant.

Hole Effective Masses in Highly Doped CdSb Determined from Infrared‐Plasma‐Reflectivity Measurements

AbstractThe infrared plasma reflectivity is measured on heavily Ag‐doped CdSb with hole concentrations of p = (0.7 to 3.0) × 1019 cm−3 in the spectral region λ = 3 to 30 μm at T = 85 and 300 °K. Conductivity effective masses and relaxation times of holes are determined from the plasma frequencies obtained by fitting experimental and theoretical reflectivity spectra. The masses are strongly anisotropic and weakly temperature dependent. The relaxation times for optical frequencies are slightly greater than those according to Hall mobilities. Scattering of holes on ionized impurities is concluded to be predominate in the relaxation mechanism.

Investigation of Germanium conductivity Relaxation in High Microwave Fields

AbstractA method of determining short conductivity relaxation times in semiconductors at high electric fields is presented using the microwave field harmonics due to the nonlinearity of the I‐U characteristic of the bulk of the semiconductor. It is found that the amplitude of these harmonics depends on an additional dc electric field and the semiconductor conductivity relaxation time. The method is applied to the study of conductivity relaxation of n‐type germanium at high microwave fields.

Negative Resistance and Relaxation Effect of Conductivity in Photoconductive CdS at Low Temperature

Negative resistance phenomena are observed in CdS single crystal at temperatures below 222°K and at conductivities larger than 10-3(\\varOmega cm)-1. We are interested here in the change of conductivity σ(t) after sudden removal of the high electric field which caused the negative resistance. The relaxation time of conductivity is very long ranging from a few seconds to several tens seconds and varying linearly with the inverse of conductivity. The relaxation time versus 1/T curve has a kink point at 222°K; this temperature coincides with the critical temperature below which the negative resistance can be observed. From measurements of the spatial distribution of relaxation time and electric field it is found that the negative resistance is not caused by the inhomogeneity but by the decrease of the number of carriers in the sample.

Conductivity, Dielectric Relaxation, and Viscosity of NaCl–Glycerol Solutions

Values of conductivity (σ), viscosity (ηs), and dielectric relaxation time (τD) are reported over several decades for various concentrations of NaCl–glycerol solutions as a function of temperature and concentration. The specific conductivity exhibits a non-Arrhenius temperature dependence of the form A exp[B / (T − T∞)] similar to that of ηs and τD. The dielectric relaxation time was found to be linear with mole-fraction concentration whereas the conductivity saturated at high concentrations (0.07 mole fraction NaCl). The product σηs exhibited a stronger temperature dependence than the product στs, where τs is the shear relaxation time. This suggests that the diffusion of ions is limited by the dynamic structural rearrangement of the solvent rather than simply by a continuous viscous retarding force.

On the Electron Gas Energy Relaxation Mechanisms in n‐Type InSb at Helium Temperatures

AbstractThe relaxation time of the electrical conductivity and the non‐linearity coefficient β in n‐type InSb in the temperature range from 1.8 to 4.1°K are studied as a function of power supplied to the sample from a d.c. source. The results are interpreted by considering energy losses by acoustic piezoelectric and deformation‐potential scattering and by optical polar scattering. The constants of piezoelectric and deformation potentials are estimated.

Study of the Shubnikov-de Haas Effect. Determination of the Fermi Surfaces in Graphite

Measurements of the oscillatory magnetoresistance of a high-quality graphite single crystal were made for all angles $\ensuremath{\theta}$ between the magnetic field and the $c$ axis, for magnetic fields up to 24 kG, and for temperatures from 1.22 to 4.22\ifmmode^\circ\else\textdegree\fi{}K. The results were analyzed by a least-squares fitting to a generalized Landau formula. Oscillations due to electrons were observed for all orientations (including H \ensuremath{\perp} c, where the amplitude dropped by a factor ${10}^{5}$), proving that the electron Fermi surfaces are closed. Although oscillations due to holes were not observed beyond $\ensuremath{\theta}\ensuremath{\simeq}84\ifmmode^\circ\else\textdegree\fi{}$, indirect arguments show that the hole Fermi surfaces are also closed. Both electron and hole surfaces are elongated along the $c$ axis and have anisotropy ratios of 12.1\ifmmode\pm\else\textpm\fi{}1.4 and about 17, respectively. The electron surface is approximately ellipsoidal, whereas the hole surface is similar except for extended ends giving it a diamond-like shape. The results are consistent with a moderate degree of trigonal asymmetry about the $c$ axis. Comparison between the electron density found from the volume of the electron Fermi surfaces and that determined previously from the nonoscillatory galvanomagnetic data confirms the theoretical prediction that there are four electron Fermi surfaces in the Brillouin zone. More indirect arguments show that there are two hole surfaces. Consideration of the size and location of these surfaces along the six zone edges parallel to the $c$ axis leads to a new determination of $\ensuremath{\Delta}\ensuremath{\simeq}\ensuremath{-}0.12$ eV for the band parameter which represents the difference of potential between the two types of atomic sites in the graphite lattice. Analysis of the temperature and magnetic field dependence of the oscillatory amplitude yields effective mass values in the basal plane of $(0.039\ifmmode\pm\else\textpm\fi{}0.001){m}_{0}$ for electrons and $(0.057\ifmmode\pm\else\textpm\fi{}0.002){m}_{0}$ for holes. These masses show an orientation dependence that is consistent with the derived Fermi surface anisotropies. The large amplitude and asymmetric shape of the oscillations in the magnetoconductivity, measured for H\ensuremath{\parallel}c at 1.26 and 4.22\ifmmode^\circ\else\textdegree\fi{}K, are accurately described by the theory of Adams and Holstein. However, there is an unexplained monotonic variation with magnetic field in the total magnetoconductivity. The effective change in temperature due to collision broadening $\ensuremath{\Delta}T$ is about 5 times greater than that estimated from the conductivity relaxation time. This discrepancy in $\ensuremath{\Delta}T$ is qualitatively explained and is related directly to the fact, established from the data of Berlincourt and Steele, that the $\ensuremath{\Delta}T$ found from magnetoresistance oscillations is greater than that found from susceptibility oscillations on the same sample.