Cole-Davidson dielectric relaxation as a self-similar relaxation process

An effort has been undertaken to understand the nature of one type of non-exponential relaxation, namely Cole-Davidson relaxation. Toward this end, a model of relaxation as a self-similar process is proposed. An equation containing operators of fractional integration and differentiation is obtained and solved, which the relaxation function obeys in this case. Fiz. Tverd. Tela (St. Petersburg) 39, 101–105 (January 1997)     

Proton relaxation in dielectrics

A kinetic equation is found which is written taking account of tunneling transitions for proton relaxation with a potential shape represented by a multiwell model having parabolic barriers. Study of the solution allows one to establish the proton relaxation mechanism in dielectrics and calculate the complex dielectric constant. Comparison with experiment shows acceptable agreement between calculated and experimental charts. Karaganda State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 80–85, February, 1998.     

Nonlinear fractional relaxation

We define a nonlinear model for fractional relaxation phenomena. We use ε-expansion method to analyse this model. By studying the fundamental solutions of this model we find that when t → 0 the model exhibits a fast decay rate and when t → ∞ the model exhibits a power-law decay. By analysing the frequency response we find a logarithmic enhancement for the relative ratio of susceptibility.     

Paramagnetic relaxation of spin polarized 3He at bare glass surfaces

In this first in a series of three papers on wall relaxation of spin polarized, gaseous ³He we investigate both by theory and by experiment surface-induced spin relaxation due to paramagnetic sites in the containing glass. We present experimental and theoretical evidence that — contrary to the traditional opinion — distant dipolar coupling to paramagnetic impurities in the glass, in particular iron ions, cannot be the dominant relaxation mechanism of ³He-spins, although iron dominates the bulk static permeability. Instead dangling-bond type defects in the glass matrix are found to interact much stronger via the isotropic Fermi contact interaction. A model of paramagnetic site controlled ³He relaxation including the Fermi contact interaction is presented. With reasonable semi-empirical assumptions our model allows to describe satisfactorily the measured relaxivities, both in the dissolution-dominated regime of fused silica or borosilicate glasses of the Pyrex type as well as in the surface dominated situation of aluminosilicate glasses which have only a low permeability for He atoms. In a large sample of 1.1 litre cells, built from various aluminosilicate glasses, an average relaxation time of 150 h is reached in case contaminant ferromagnetic particles have been demagnetized beforehand. From the maximum observed value of 250 h we derive after subtraction of dipolar relaxation in the gas phase a paramagnetic surface relaxivity of ρ<0.005 cm/h at room temperature.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

The kinetics of the structural relaxation process in PHEMA-silica nanocomposites based on an equation for the configurational entropy

The enthalpy relaxation of polymer-silica nanocomposites prepared by simultaneous polymerization of poly(2-hydroxyethyl methacrylate) (PHEMA) and tetraethyloxysilane, TEOS, a silica precursor, is investigated. Both the glass transition temperature, T_g, and the temperature interval of the glass transition, ΔT _g , increase as the silica content in the sample does. Structural relaxation experiments show that the temperature interval in which conformational motions take place broadens as the silica content in the hybrid increases. A phenomenological model based on the evolution of the configurational entropy during the structural relaxation process, the SC model, has been used for determining the temperature dependence of the relaxation times during the process. The results show an increase of the fragility of the polymer as the silica content increases, a feature that can be related to the broadening of the distribution of relaxation times characterized by the β parameter of the stretched exponential distribution. On another hand the silica content increase produces a significant change of the relaxation times in the glassy state.     

The kinetics of low-temperature electron-phonon relaxation in a metallic film following instantaneous heating of the electrons

The theoretical analysis of experiments on pulsed laser irradiation of metallic films sputtered on insulating supports is usually based on semiphenomenological dynamical equations for the electron and phonon temperatures, an approach that ignores the nonuniformity and the nonthermal nature of the phonon distribution function. In this paper we discuss a microscopic model that describes the dynamics of the electron-phonon system in terms of kinetic equations for the electron and phonon distribution functions. Such a model provides a microscopic picture of the nonlinear energy relaxation of the electron-phonon system of a rapidly heated film. We find that in a relatively thick film the energy relaxation of electrons consists of three stages: the emission of nonequilibrium phonons by “hot” electrons, the thermalization of electrons and phonons due to phonon reabsorption, and finally the cooling of the thermalized electron-phonon system as a result of phonon exchange between film and substrate. In thin films, where there is no reabsorption of nonequilibrium phonons, the energy relaxation consists of only one stage, the first. The relaxation dynamics of an experimentally observable quantity, the phonon contribution to the electrical conductivity of the cooling film, is directly related to the dynamics of the electron temperature, which makes it possible to use the data of experiments on the relaxation of voltage across films to establish the electron-phonon and phonon-electron collision times and the average time of phonon escape from film to substrate. Zh. éksp. Teor. Fiz. 111, 2106–2133 (June 1997)     

Kinetics of structural relaxation and regularities of plastic flow of metallic glasses

On the basis of a calculation of the structural relaxation rate and an experimental acoustical-emission determination of the temperature of the transition from localized to uniform flow it is argued that the type of plastic deformation of metallic glasses is uniquely determined by the kinetic structure of the relaxation. In the case of a kinetically hindered structural relaxation, which is characteristic for tests of initial samples at temperatures T<380–420 K, a localized dislocational deformation is realized. At higher temperatures, “memory” of the thermal prehistory of the samples is lost (aging at room temperature), the structural relaxation rate grows abruptly and plastic flow becomes uniform viscoplastic flow. Fiz. Tverd. Tela (St. Petersburg) 41, 2167–2173 (December 1999)     

Diffusion and relaxation of the fractional order in fractal media in the classical and quantum cases

Two model examples of the application of fractional calculus are considered. The Riemann–Liouville fractional derivative with 0 < α ≤ 1 was used. The solution of a fractional equation, which describes anomalous relaxation and diffusion in an isotropic fractal space, has been obtained in the form of the product of a Fox function by a Mittag-Leffler function. The solution is simpler than that given in Ref. 6 and it generalizes the result reported in Ref. 7. For the quantum case, a solution of the generalized Neumann–Kolmogorov fractional quantum-statistical equation has been obtained for an incomplete statistical operator which describes the random walk of a quantum spin particle, retarded in traps over a fractal space. The solution contains contributions from quantum Mittag-Leffler (nonharmonic) fractional oscillations, anomalous relaxation, noise fractional oscillations, and exponential fractional diffusion oscillation damping.     

Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, f (t) = f ₀exp - (t/τ)^β , with the exponent β increasing with the temperature. The relaxation time diverges as an Arrhenius law when T→ 0. Received 24 May 2001 and Received in final form 12 September 2001     

Soliton relaxation in antiferromagnets

We study the relaxation two-parameter one-dimensional solitons in antiferromagnets using the phenomenological theory. Allowing for relaxation terms of a relativistic and exchange nature, we set up a system of evolution equations for the constants of the motion of a soliton and calculate the corresponding integral curves, which describe the variation of the soliton parameters in the relaxation process. Zh. éksp. Teor. Fiz. 111, 1633–1650 (May 1997)     

Density matrix formalism for anelastic relaxation

A density matrix formalism is developed for anelastic (mechanical) relaxation in crystalline materials with point defects characterized by elastic dipoles. The time-dependent approach to equilibrium of the strain response under the action of a constant applied stress is deduced. The formalism parallels the one used in nuclear magnetic relaxation. The anelastic relaxation time is determined as a function of the parameters occurring in the defect hopping term in the Hamiltonian. This term is responsible for the dissipation of the anelastic ‘potential’ energy into the host lattice. In a lengthy concluding section, the following aspects are discussed point by point: the advantages of the formalism presented, its scope and special cases; the physical implications of the expression obtained for the relaxation time; the similarities and differences between magnetic relaxation and anelastic relaxation, etc.     

Diffusion relaxation of photoinduced gratings in polyvinyl acetate latex films

The features of the postexposure relaxation of holographic gratings recorded in inhomogeneous polyvinyl acetate latex films with photosensitive agents (photochromic molecules of fulgide dyes and phenanthrenequinone) have been considered. The diffusion coefficients and rms displacements of izomerized probe in polymer latex particles and aqueous environment are determined within the model of two diffusion states. The effective diffusion coefficient of the molecular probe, which is responsible for the relaxation of gratings, increases with an increase in their period in wet films, whereas in dry films, this parameter is independent of the grating period. In the films subjected to high-temperature treatment the effective diffusion coefficient decreases with an increase in the grating period. The successive stages of grating relaxation in latex films with phenanthrenequinone are related to the diffusion of free molecules, radicals, and polymer chains, as well as to the local displacement of macromolecular segments at distances of 5–25 nm.     

Two forms of polarization relaxation in polydomain ferroelectrics in an electric field

The characteristic features of the polarization and depolarization kinetics of polydomain ferroelectrics with square and narrow “extended” dielectric hysteresis loops are investigated for the model of TGS and Rb₂ZnCl₄ crystals. It is shown that for the second crystal, in contrast to the first crystal, the local free energy is asymmetric relative to the direction of polarization, the coercive field does not have a definite value, and only part of the crystal volume participates in the slow thermoactivational relaxation. The slow relaxation follows a universal empirical power law in all cases. The distribution functions of the relaxation times in crystals are constructed on the basis of experimental data, and comparative estimates are made of the relaxation parameters and the parameters of the energy barriers for domain walls. Fiz. Tverd. Tela (St. Petersburg) 41, 499–504 (March 1999)     

Model for vibrational relaxation: Pure-dephasing and depopulation

The three dominant mechanisms giving major contributions to vibrational relaxation in molecular systems are (a) pure dephasing, (b) depopulation (or energy relaxation), and (c) resonant transfer. Here (c) is not considered but the effects due to thesimultaneous occurrence of (a) and (b) are treated within a stochastic model. In dealing with (a), the vibrational frequency is assumed to undergo random uncorrelated ‘jump’, due to fluctuations in the environment of the active molecule between a continuous set of values. The ensuing results are somewhat different from those of the commonly used Kubo model of vibrational dephasing, especially at long times and appear to be better suited in interpreting certain experimental data. The model is next extended to include the simultaneous occurrence of (b). The calculation leads to two important conclusions: (i) the lineshape is not just the convolution of those due to (a) and (b), and (ii) the lineshape is asymmetric, if the intermolecular interactions are not isotropic.     

Structural relaxation in metastable alloys

A mechanism of stress relaxation in metastable alloys is considered. It is demonstrated that structural transformations during a relaxation test lead to anomalously high stress relaxation. Two stages of structural relaxation are revealed: formation of defect-free channels and decomposition of a solid solution. A new method of program hardening of metastable alloys based on the structural relaxation processes is suggested. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 56–61, November, 2007.     

Nuclear magnetic relaxation in rare-earth compound crystals due to fluctuations of hyperfine magnetic fields

Some results on NMR and relaxation studies of the Van Vleck paramagnet TmES (thulium ethylsulphate) and the Ising ferromagnet DyES are summarized. Complicated but regular quasistatic internal magnetic fields are created by Tm and Dy ions in these compounds. These fields fluctuate due to the thermal excitation of tne ions and the energy transfer from one ion to another. Fluctuations give rise to NMR line shifts, broadening of the lines and spin-lattice relaxation, the shifts, linewidth and spin-lattice relaxation rate being proportional to exp(−Δ/kT) at low temperatures (kT≪Δ, Δ is an excitation energy). Pre-exponential factors depend on fluctuating fields in a definite but complicated manner, so estimates of the correlation time (electron spin-spin relaxation time) can be obtained from measurements of nuclear relaxation rates.     

气体声弛豫过程中有效比热容与弛豫时间的分解对应关系

声在多原子分子气体中传播所引起的弛豫过程是探索气体特性的重要方面. 本文通过研究气体声弛豫过程中振动自由度与平动自由度(V-T)以及振动自由度之间(V-V)的分子能量转移模型, 给出了有效比热容与弛豫时间的分解对应关系及其通用获得方法. 该分解模型与现有的声弛豫模型相比, 反映了分解后的V-T 和V-V弛豫过程中振动比热容与弛豫时间的对应关系, 并发现了较高能级是引起对应声弛豫过程的决定因素. 将基于该分解模型获得的气体声弛豫衰减谱经碰撞直径微调改进后, 比现有理论更接近实验数据, 其结果证明了该分解对应关系的正确性和合理性.     

Muon spin relaxation and knight shift in the heavy-fermion superconductor UPt3

Positive muon spin relaxation experiments have been conducted on the heavy-fermion superconductor UPt₃ in both the normal and superconducting states for zero, transverse, and longitudinally applied magnetic fields. Below 6 K in zero applied field, the μ⁺ relaxation rate is approximately twice that expected from¹⁹⁵Pt nuclear dipolar relaxation alone. Transverse- and longitudinal-field measurements show that the observe relaxation rate depends on magnetic field and is quasistatic in origin. It is suggested that the onset of very weak (≈10⁻³ μ_B/U atom) magnetic ordering below approximately 6 K is responsible for the observed increase in the relaxation rate. μ⁺ Knight shift measurements in the normal state of UPt₃ show a temperature dependent shift K_μ which tracks the bulk susceptibility X. From the K_μ vs. X plot, a μ⁺ hyperfine field of approximately 100 Oe/μ_B is extracted.