Relaxation Time Tau Research Articles

Optical Properties of Bi2Se3-xAsx Single Crystals

Bi2Se3-xAsx single crystals with the As content of cAs = 0 to 2.0x1019 atoms/cm3 prepared from the elements of 5N purity by means of a modified Bridgman method were characterized by measurements of infrared reflectance and transmittance. Values of the plasma resonance frequency omegap, optical relaxation time tau, and high-frequency permittivity were determined by fitting the Drude-Zener formulas to the reflectance spectra. It was found that the substitution of As atoms for Se atoms in the Bi2Se3 crystal lattice leads to a decrease in the omegap values. This effect is accounted for by a model of point defects in the crystal lattice of Bi2Se3-xAsx. The dependences of the absorption coefficient K on the energy of incident photons were determined from the transmittance spectra. The optical width of the energy gap is found to decrease with increasing As content. The values of the exponent b from the relation of K ∼ lamdab for the long-wavelength absorption edge range within the interval 2.0 to 2.3, i.e. the dominant scattering mechanism of free current carriers in Bi2Se3-xAsx crystals is the scattering by acoustic phonons.

Dynamical Properties near the Metal-Insulator Transition: Evidence for Electron-Assisted Variable Range Hopping

We report independent measurements (between 20 and 200 mK) of the electronic specific heat C(e), the electron-phonon coupling G(e-ph), and the electron-phonon relaxation time tau(e-ph) (from 10(-2) to 10(-5) s) for NbxSi1-x Anderson insulator thin films. We show that the usual equation tau(e-ph) = C(e)/G(e-ph) holds only if the resistance is solely related to the electron temperature. We conclude that at sufficiently low temperatures variable range hopping transport is assisted by electron-electron interactions alone and is independent of the phonon distribution.

Glass transitions and dynamics in thin polymer films: dielectric relaxation of thin films of polystyrene

The glass transition temperature T(g) and the temperature T(alpha) corresponding to the peak in the dielectric loss due to the alpha process have been simultaneously determined as functions of film thickness d through dielectric measurements for polystyrene thin films supported on glass substrate. The dielectric loss peaks have also been investigated as functions of frequency for a given temperature. A decrease in T(g) was observed with decreasing film thickness, while T(alpha) was found to remain almost constant for d>d(c) and to decrease drastically with decreasing d for d<d(c). Here, d(c) is a critical thickness dependent on molecular weight. The relaxation time tau(alpha) of the alpha process, which was measured as the frequency at which the dielectric loss realizes its peak value at a given temperature, was found to have a d dependence similar to that of T(alpha). The relaxation function for the alpha process was obtained by using the observed frequency dependence of the peak profile of the dielectric loss. The exponent beta(KWW), which was obtained from the relaxation functions, decreases as thickness decreases. This suggests that the distribution of relaxation times for the alpha process broadens with decreasing thickness. The thickness dependence of T(g) is directly related to the distribution of relaxation times for the alpha process, not to the relaxation time itself. The value of the thermal expansion coefficient normal to the film surface was found to increase with decreasing film thickness below T(g), but to decrease with decreasing film thickness above T(g). These experimental results are discussed in the context of a three-layer model in which within thin films there are three layers with different mobilities and glass transition temperatures.

Model for dynamics in supercooled water.

We propose a phenomenological model for the intermediate scattering function (ISF) associated with density fluctuation in low temperature water. The motivation is twofold: to extract various physical parameters associated with the ISF computed from extended simple-point-charge model water at supercooled temperatures, and to apply this model to analyze high resolution inelastic x-ray scattering data of water in the future. The ISF of the center of mass of low temperature water computed from 10 M-step molecular dynamics (MD) data shows clearly time-separated two-step relaxation with a well-defined plateau in-between. We interpret this result as due to the formation of a stable hydrogen-bonded, tetrahedrally coordinated cage around a typical molecule in low temperature water. We thus model the long-time cage relaxation by the well-known Kohlrausch form exp[-(t/tau)(beta)] with an amplitude factor which is a k-dependent Debye-Waller factor A(k), and treat the short-time relaxation as due to molecular collisional motions within the cage. The latter motions can be described by the generalized Enskog equation, taking into account the confinement effect of the cage. We shall show that the effect of the confinement changes the collisional dynamics by modifying certain input parameters in the kinetic theory by a factor [1-A(k)](1/2). We solve the generalized Enskog equation approximately but analytically by a Q-dependent triple relaxation time kinetic model. This kinetic model was previously shown to account for the large k behavior of Rayleigh-Brillouin scattering from moderately dense, simple fluids. We find that our model fits well with the MD generated collective as well as single-particle ISFs. For the short-time collisional dynamics, we fix values of the hard sphere diameter sigma and pair correlation function at contact g(sigma), without introducing any adjustable parameters. The calculated ISFs reproduce the correct Brillouin peak frequencies at low k values. From the long-time dynamics, we deduce values of the Debye-Waller factor A(k), the Kohlrausch exponent beta(k), and the cage relaxation time tau(k).

Similarity of relaxation in supercooled liquids and interacting arrays of oscillators.

Dielectric relaxation and dynamic light scattering of small molecule glass-forming liquids invariably show that the fractional exponent beta(alpha) of the Kohlrausch-Williams-Watts correlation function, exp[-(t/tau(alpha))(beta(alpha))], used to fit the alpha-relaxation data is temperature dependent, increasing towards the value of unity as temperature is raised and the relaxation time tau decreased. Comparing different glass formers, another property is the existence of a correlation between the value of (1-beta(alpha)) at the glass temperature, T(g), and the T(g)-scaled temperature dependence of tau(alpha). We analyze a system of interacting arrays of globally coupled nonlinear oscillators. Each array has its oscillators coupled among themselves with a coupling strength K. The coupling between arrays is characterized by the interarray coupling strength K'. The decay of the phase coherence r for each array is slowed down by the interarray coupling and its time dependence is well approximated at sufficiently long times by exp[-(t/tau)(beta)]. For a fixed K', on increasing K the results exhibit a decrease of tau and a concomitant increase of beta, similar to the properties of dielectric relaxation and dynamic light scattering of glass-forming liquids on increasing temperature. For each K' we define K(g) to be the value of K at which tau is equal to an arbitrarily chosen long time. We find that beta(K(g)) is correlated with the K(g)-scaled K dependence of tau. The results obtained in this manner at various fixed values of K' reproduce the relaxation properties and temperature dependencies of strong, intermediate, and fragile glass-forming liquids.

Synthesis, Structure, Magnetic Properties, and (1)H NMR Studies of a Moderately Antiferromagnetically Coupled Binuclear Copper(II) Complex.

A binuclear Cu(II) complex of [(Cu(2)(HAP)(2)IPA)(OH)(H(2)O)](ClO(4))(2).H(2)O (HAP = 3-amino-1-propanol; IPA = 2-hydroxy-5-methylisophthalaldehyde) has been synthesized and characterized by X-ray crystallography, by solid state magnetic susceptibility, and in solution by (1)H NMR studies. The binuclear copper(II) complex crystallizes in the orthorhombic system, space group Pbcn, a = 27.9972(9) Å, b = 8.8713(3) Å, c = 19.5939(6) Å, and Z = 8. The two copper(II) atoms in this binuclear Cu(II) complex are bridged by the oxygen atoms of the phenolate and hydroxy groups. The axial position at one Cu atom is occupied by a water molecule while another Cu has weak interaction with a perchlorate group. The coordination geometries around the two Cu atoms are distorted square pyramid and square planar. The solid state magnetic susceptibility measurement reveals a moderate antiferromagnetic exchange interaction between the two Cu atoms with a -2J value of 113 +/- 9 cm(-)(1). The variable-temperature (1)H NMR studies in CD(3)CN solution show that the observed relatively sharp hyperfine shifted signals follow a Curie behavior. The exchange coupling constant (-2J) obtained in solution by using chemical shift as a function of temperature also reveals a moderate antiferromagnetic exchange interaction between two Cu(II) ions. An analysis of the relaxation data shows that the reorientational correlation time (tau(c)) is dominated probably by a combination of electronic relaxation time tau(s) and rotational correlation time (tau(r)) due to an exchange-modulated dipolar mechanism for this moderately antiferromagnetically coupled binuclear copper(II) system.

Atomic diffusion, step relaxation, and step fluctuations.

We show that the dynamics of the pair correlation function in a step train can pinpoint the dominant relaxation mechanism occurring at a crystal surface. Evaporation-condensation and step-edge diffusion do not produce dynamical correlations between neighboring steps, while terrace diffusion may lead to correlations which fall off like a power law with distance and which are peaked at a characteristic time. We derive these results within a "real space" Langevin formalism which is based on diffusion kernels which are different for each mass transport process. We validate this formalism by reproducing the step fluctuation autocorrelation function. We then derive results on the pair correlation between different steps. Results for solvable limiting cases are summarized in Tables I and II of the paper. As an intermediate step in the analysis we also find expressions for the relaxation time tau(pq) of a mode of wave number q along the steps and wave number p perpendicular to the steps, which we also discuss and compare with prior work.

Exact solutions of some urn models of relaxation in glassy dynamics.

We consider two simple models, called "urn models," for a general N-ball, M-urn problem. These models find applications in the study of relaxation in glassy dynamics. We obtain exact analytical results in these two cases for the average relaxation time tau to reach the ground state. In model I we also obtain the functional dependence of tau for large N, and in model II we obtain an asymptotic (N-->infinity) dependence of tau as a function of the number of urns M.

Long-time dynamics of de Gennes’ model for reptation

Diffusion of a polymer in a gel is studied within the framework of de Gennes’ model for reptation. Our results for the scaling of the diffusion coefficient D and the longest relaxation time τ are markedly different from the most recently reported results, and are in agreement with de Gennes’ reptation arguments: D∼N−2 and τ∼N3. The leading exponent of the finite-size corrections to the diffusion coefficient is consistent with the value of −2/3 that was reported for the Rubinstein model. This agreement suggests that its origin might be physical rather than an artifact of these models.

Dielectric studies of trans-4-n-octyl-(4-cyanophenyl)cyclohexane (8PCH) at ambient and high pressure

Dielectric relaxation studies have been performed on trans -4- n -octyl-(4-cyanophenyl)is cyclohexane (8PCH) at ambient and high pressure (0.1-175MPa). Two experimental set-ups were applied: a time domain spectrometer (TDS) covering the frequency range 10 MHz-5 GHz, was used to study the relaxation processes in the isotropic phase (at ambient pressure); an impedance analyser (1 kHz-13MHz) was used for high pressure measurements on both the nematic (N) and isotropic (I) phases. The low frequency (l.f.) relaxation process connected with molecular rotations about the short axis is hindered by the activation enthalpy of 70 kJ mol-1 and 32.6kJ mol-1 in the N and I phases, respectively, whereas the high frequency process (rotations about the long axis) has an activation enthalpy of 22.6kJ mol-1 (isotropic phase). From the pressure and temperature dependencies of the l.f. relaxation time tau, the activation volume, enthalpy and energy were calculated. It was found that the energy barrier hindering the molecular rotations around the short axis in the nematic phase is influenced to about one half by the volume effects. The nematic potential q was estimated at various pressures and comprises 10 20% of the total energy barrier. The pressure dependence of q enabled the calculation of the order parameter S (p) with the aid of old (Maier and Saupe) as well as recent (Coffey et al.) theoretical formulae.

Stability and kinetics of unfolding and refolding of cAMP receptor protein from Escherichia coli.

cAMP receptor protein (CRP) is involved in regulation of expression of several genes in Escherichia coli. The protein is a homodimer and each monomer is folded into two distinct structural domains. The mechanism of the biological activity of the protein may involve the interaction between the subunits and domains. In order to determine the interaction between the subunits or domains of CRP, we have studied the reversible denaturation of the protein by guanidine hydrochloride. The unfolding and refolding kinetics of CRP was monitored using stopped-flow fluorescence spectroscopy at 20 degrees C and pH 7.9. The results of CRP denaturation indicate that the transition can be described by a three-state model: (CRP native)2<=> 2 (CRP native)<=>2 (CRP denatured). The faster process, characterized by the relaxation time tau 2 = 80 +/- 3 ms, corresponds to the dissociation of CRP dimer into monomers. The slower process has the relaxation time tau t = 1.9 +/- 0.1 s and corresponds to the cooperative unfolding of CRP monomer. The free energy change in the absence of denaturant upon CRP dissociation is delta G dis degrees = 46.9 +/- 2.5 kJ/mol and for monomer unfolding delta G unf degrees = 30.9 +/- 1.3 kJ/mol. The thermal unfolding of CRP was studied by circular dichroism and fluorescence spectroscopy at various guanidine hydrochloride concentrations. It has been found that the native protein is maximally stable at about 21 +/- 0.3 degrees C and is denatured upon heating and cooling from this temperature. The apparent free energy change for CRP unfolding at 21 degrees C is equal to 30.5 +/- 0.4 kJ/mol and the apparent specific heat change is equal to delta Cp, app = 10.7 +/- 0.7 kJ mol-1 K-1. The predicted values of cold denaturation midpoint is equal to tau G = -18.8 +/- 1.5 degrees C and for high-temperature transition tau G = 63.1 +/- 1.5 degrees C. The predicted midpoint of high-temperature unfolding transition is about the same as determined experimentally.

Relationships between paramaters describing low-frequency electrical admittance locus plot of human palmar skin

Using a two-frequency three-electrode method, unipolar electrical admittance was measured in the palmar skin of 48 normal healthy humans. Characteristics of and relationships between the phase angle pi alpha/2, the conductance extrapolated at zero frequency G(O) and ion relaxation time tau obtained from the Cole-Cole equation were examined in a low-frequency region (up to 354 Hz). At base-line resting values, the three admittance parameters were interrelated according to the regression model; log tau i = A + B alpha i + D log G(O)i + epsilon i with R2 > or = 0.7434 (p < or = 0.0001), where A, B and D determined from regression analysis showed inter- and intra-individual variation. Multi-factor analyses of variance showed that alpha was greater in women than men (0.8025 versus 0.7545, p < 0.0023), and log G(O) decreased significantly with age (covariate coefficient = -0.0058 log microS cm-2 per year, p < 0.04). For evoked responses, alpha showed a very small change (maximum < 5%), tau decreased while G(O) increased. With increasing frequency, conductance responses increased in absolute amplitudes but decreased in relative changes (amplitude change divided by static level). Statistical analyses from clinical experimental materials (total 130 subjects) showed that the capacitive behaviour of admittance (due to alpha) presented significant variation between controls and patient groups. This may shed new light on the nature of the skin electrical admittance/impedance.

Flux-flow conductivity in high-Tc superconductors

Using an early theory by Houghton and Maki based on the BCS model, which assumes a temperature-independent relaxation time tau , we compute the flux-flow magnetoresistivity rho S(T,H) of layered superconductors near H(c2) in the clean limit. Then we use our results to analyse the magnetoresistivity curves of single-crystal YBaCuO. Extending the validity of the calculation to a temperature-dependent tau , we find that for constant tau , or for relaxation times obtained from experiments, the theory reproduces qualitatively the saturation-like behaviour of the observed magnetoresistance, and also the broadening of the resistive transition, as well as the changes in the slope d rho S(T)/dT with field. However, quantitative agreement with experiments is not achieved. This allows an estimate to be made of the contribution of the thermal vortex line fluctuations to the total dissipation; we find the former to be about 10% of the latter.

Energy relaxation at THz frequencies in AlxGa1-xAs heterostructures

We report 4.2 K studies of the dependence of the in-plane, DC conductivity of a quasi 2D electron gas on the amplitude Eomega of applied fields with frequencies from 0.25 THz to 3.5 THz. We analyse the dependence of sigma DC on Eomega assuming that electron-optical phonon scattering dominates energy relaxation, that the absorbed power has a Drude form and that the electron distribution is thermal. This simple analysis is self-consistent: Arrhenius plots of the estimated energy loss rate have a slope near -h omega LO/k8, for all frequencies, as expected for energy loss by optical phonon emission. We find that the effective energy relaxation time tau epsilon varies with the frequency of the applied field, from tau epsilon approximately 4 ps at 0.34 THz to tau epsilon approximately 0.3 ps at 3.45 THz. This may indicate a frequency-dependent form for the hot-phonon distribution.

Double relaxation times of non-spherical polar liquids in non-polar solvent: a new approach based on single frequency measurement

A new approach based on single frequency measurement is suggested to estimate the double relaxation times, tau 1 and tau 2 of some highly non-spherical polar liquids in solvents benzene and carbon tetrachloride. The smaller relaxation time tau 1 refers to the smallest flexible part attached to the parent molecule while the larger one tau 2 is due to end-over-end rotation of the polar molecule. The weighted contributions c1 and c2 towards relaxations are calculated from Frohlich's equations as well as by a new technique adopted here. The dipole moments mu 1 and mu 2 are also computed from the slope beta of the ultra-high-frequency conductivity Kij against the weight fraction omega j for the compounds in terms of tau 1 and tau 1. The close agreement of mu 2 values thus computed with those of existing methods immediately indicates that the approach suggested is correct.

Characteristics of phase angle, extrapolated conductance and ion relaxation time in the low-frequency admittance locus plot of human palmar skin.

The Cole-Cole equation can be used to model the electrical admittance of human skin. Using a previously published two-frequency (AC excitation) three-electrode method, the admittance locus plot (ALP) in the low-frequency region (< 1000 Hz) has been shown to be very well approximated by a straight line and can be described with frequency-independent parameters; phase angle alpha pi/2, conductance at extrapolated zero frequency G0 = 1/R0, and ion relaxation time tau. The aim of the paper is to study characteristics of alpha pi/2, G0 and tau in the low-frequency ALP of human palmar skin. The measured data are calculated off-line on a personal computer. Relative changes in alpha pi/2 are small (< 2%) even during a heavy physical-exercise period. G0 corresponds well with GDC obtained by the traditional DC method at excitations up to 200 mV (relative differences < or = 5% during baseline registration). Based on these findings, two comparatively simpler methods using only one lock-in amplifier are suggested: either measuring simultaneously with DC and at one frequency with AC excitation, or measuring at two different frequencies successively. The low-frequency part of the ALP can then be determined. G0, alpha and tau estimated by these simplified methods are in good agreement with the simultaneous two-frequency method and should therefore be suited for clinical applications.

Electron paramagnetic resonance studies of Zn1-xMnxTe

Electron paramagnetic resonance has been studied in Zn1-xMnxTe over a wide temperature range 20 K<or=T<or=290 K and a wide manganese concentration range 0.013<or=x<or=0.81. Our results show that, for lower manganese concentrations x<or=0.23, the EPR line can be represented by the Bloch model modified for broad resonance in the entire range of temperatures. For x>or=0.37 the resonance is detected at higher temperatures. The values of the relaxation time tau and the g-factor are obtained by fitting an expression for the EPR absorption line in the modified Bloch model to the experimental data. The high-temperature linewidth for x<or=0.37 is analysed within the exchange narrowing model. The calculated infinite-temperature linewidths are in good agreement with the extrapolated experimental values. It is found that the main contribution to the linewidth arises from the anisotropic superexchange.

A new decoupled algorithm for nonstationary, transient simulations of GaAs MESFETs

Simulation of devices for which nonlocal, hot carrier transport cannot be ignored requires solution of the Poisson equation and at least the first three moments of the Boltzmann transport equation or the use of Monte Carlo techniques. These equations form nonlinear, coupled, time-dependent partial differential equations. In conventional decoupled solvers, decoupling of the equations puts a limit on the maximum allowable time step Delta t, which should be kept smaller than the dielectric relaxation time tau /sub d/ of the material. This constraint makes these solvers very inefficient, especially for obtaining steady-state solutions. A highly efficient decoupled numerical algorithm which allows Delta t as large as 20-50 times tau /sub d/ is presented. Results of simulations of GaAs MESFETs using both a conventional and the new decoupled solver and CPU time taken on a CRAY Y-MP by the two solvers are discussed. >

Ultrasonic attenuation due to H in a Pd85Pt15 single crystal

Ultrasonic attenuation has been measured as a function of temperature approximately over the range 10-300 K at 5, 10, 15 and 45 MHz in a single crystal of a Pd85Pt15 alloy. The measurements have been carried out for five different propagation modes, both in the H-free and the H-loaded (H/(Pd+Pt)=0.29 at.%) state of the material. An anelastic relaxation has been observed at around 225 K (f=10 MHz), whose activation energy W and limit relaxation time tau 0 are: W=0.24+or-0.02 eV; tau 0=(1.4+or-0.5)*10-14 s. The mode dependence of the relaxation strength reveals the existence of a hydrostatic relaxation due to reactions between dipoles associated with H-H and H-Pt complexes. The results can be accounted for in terms of stress-induced changes in the short-range order of both the H-H and the H-Pt bonds (or antibonds) as well as of the occupancy probabilities of octahedral interstitial sites by H.

Calorimetric study of isothermal relaxation in a quenched beta -Cu-Zn-Al alloy

The isothermal relaxation process in a beta -Cu-Zn-Al single crystal which follows quenches from different Tq temperatures has been studied by means of an isothermal calorimetric technique at three Ta temperatures. The relaxation has been attributed mainly to a reordering process which takes place through a vacancy mechanism. The dissipated energy during the process has been measured for the different Ta and Tq temperatures. The authors have found that the relaxation process is not of a single exponential type and that, in all cases, the recorded curves giving the dissipated thermal power, W(t), against time show long tails. The kinetics of the process have then been characterized by means of a relaxation time tau , defined as the time at which the product tW(t) versus time shows a maximum. Assuming an Arrhenius law dependence of tau on Ta and Tq, they have obtained effective activation energies of 0.76+or-0.03 eV and 0.43+or-0.03 eV for vacancy migration and formation respectively.