Theory of the Gorsky effect for low interstitial concentrations

The formalism of the preceding paper is applied to work out the theory of the Gorsky effect, or anelastic relaxation due to the long-range diffusion of interstitials in a host lattice, for non-interacting (low-concentration) interstitials (e.g., H in Nb). It is shown how linear response theory (LRT) provides a number of advantages that simplify the solution of the problem and permit the handling of complications due to specimen geometry and stress inhomogeneity. The multiple-relaxation time creep function of Alefeldet al is first re-derived. Next, the dynamic responseand the short-time behaviour of the creep function are deduced exactly, and theω ^−1/2 fall-off of the internal friction at high frequencies is exhibited. Finally, it is pointed out that the true asymptotic behaviour of the dynamic response must be found by going beyond the diffusion equation model. A two-state random walk analysis is used to predict a cross-over to a trueω ⁻¹ asymptotic behaviour, and the physical reasons for this phenomenon are elucidated.     

General linear response analysis of anelasticity

Linear response theory is used to express the anelastic response (creep function and generalized compliance) of a system under an applied stress, in terms of the equilibrium strain auto-correlation. These results extend an earlier analysis to cover inhomogeneous stresses and the tensor nature of the variables. For anelasticity due to point defects, we express the strain compactly in terms of the elastic dipole tensor and the probability matrix governing dipole re-orientation and migration. We verify that re-orientations contribute to the deviatoric strain alone (Snoek, Zener, etc. effects), while the dilatory part arises solely from the long-range diffusion of the defects under a stressgradient (the Gorsky effect). Our formulas apply for arbitrary orientational multiplicity, specimen geometry, and stress inhomogeneity. The subsequent development of the theory in any given situation then reduces to the modelling of the probability matrix referred to. In a companion paper, we apply our formalism to work out in detail the theory of the Gorsky effect (anelasticity due to long-range diffusion) for low interstitial concentrations, as an illustration of the advantages of our approach to the problem of anelastic relaxation.     

3-d Model for strain ordering in steel: II Relaxational effects

The spring-defect model developed by us in the accompanying paper I to discuss ferroelasticity, exhibited in the BCT phase of α-iron (BCC metals), is used to analyse anelastic relaxation across the paraelastic to ferroelastic phase transition. The kinetics of the underlying Hamiltonian representing strain-strain interactions is treated within mean-field theory. The relaxation-response relation of the linear response theory is employed to derive explicit expressions for the anelastic strain, the frequency-dependent compliance and the internal friction in terms of the basic parameters of the spring-defect model.     

Nuclear Spin-Lattice Relaxation of 82BrFe

The field dependence of the nuclear spin-lattice relaxation (SLR) of cold implanted ⁸²Br (T ≤ 25 mK) in α-Fe single crystals was investigated with nuclear magnetic resonance of oriented nuclei (NMR/ON) at low temperatures as experimental technique. The SLR at the lattice sites with the hyperfine fields found by earlier NMR/ON experiments was measured as a function of the applied external magnetic field B _ext parallel to the three principle axes [100], [110] and [111] of the iron single crystal. The data were evaluated with the full relaxation formalism in the single impurity limit and for comparison also with the often employed model of a single exponential function with an effective relaxation time T ₁′. With a phenomenological model the high field values of the relaxation rates r _{∞, [100]′} = 6.6(2) · 10⁻¹⁵ T²sK⁻¹, r _{∞, [110]} = 5.4(2) · 10⁻¹⁵ T²sK⁻¹ and r _{∞, [111]} = 5.2(1) · 10⁻¹⁵ T²sK⁻¹ were obtained.     

Investigation of Relaxation Process of Nylon 1212 Using Dielectric Relaxation Spectroscopy

The relaxation processes of α-form nylon 1212 from 50°C up to 160°C were studied by dielectric relaxation spectroscopy (DRS) in a wide frequency range of 63 Hz to 5 MHz. The α relaxation, the electrode relaxation, and the conductivity relaxation of nylon 1212 were observed and analyzed in detail using permittivity and modulus formalism. Electrode polarization and dc conductivity were the origin of high dielectric permittivity values at low frequencies and high temperatures. The strength of the imaginary part of the electric modulus of conductivity relaxation M″ _max was nearly independent of temperature. The distribution of local conductivity and relaxation time became broader with decreasing temperature.     

Effect of temperature,electric and magnetic field on spin relaxation in single layer graphene: A Monte Carlo simulation study

In this article, we employ the semiclassical Monte Carlo approach to study the spin polarized electron transport in single layer graphene channel. The Monte Carlo method can treat non-equilibrium carrier transport and effects of external electric and magnetic fields on carrier transport can be incorporated in the formalism. Graphene is the ideal material for spintronics application due to very low Spin Orbit Interaction. Spin relaxation in graphene is caused by D'yakonov-Perel (DP) relaxation and Elliott-Yafet (EY) relaxation. We study effect of electron electron scattering, temperature, magnetic field and driving electric field on spin relaxation length in single layer graphene. We have considered injection polarization along z-direction which is perpendicular to the plane of graphene and the magnitude of ensemble averaged spin variation is studied along the x-direction which is the transport direction. This theoretical investigation is particularly important in order to identify the factors responsible for experimentally observed spin relaxation length in graphene.     

Magnetic field dependence of the domain wall resistance in a quantum wire

For an ideal one-dimensional ferromagnetic wire with a magnetic domain wall (DW), contribution of the DW to the resistivity of the system has been investigated. We have studied the resistance due to the magnetic impurities in the domain wall which was suspended in a weak magnetic field for two types of chiralities. The analysis has been based on Boltzmann transport equation, within the relaxation time approximation. Through this formalism, both increasing and decreasing of the resistance due to the DW have been predicted in presence of Zeeman interaction as an extrinsic mechanism.     

Transverse spin relaxation of spin carriers diffusing in spatially periodic magnetic fields

An exact solution of the Bloch–Torrey equation that covers the entire range of relative diffusivities D between the spin carriers and the magnetic structure (due to, e.g., spin‐density waves) is given for the transverse relaxation of an initally uniformly polarized spin system under the influence of a magnetic field varying sinusoidally in space. Explicit closed‐form results for the short‐time relaxation are obtained making use of Laplace transforms, the three‐term recurrence relations associated with Mathieu’s equation, and novel sum rules. At intermediate diffusivities the transverse polarization exhibits a novel long‐time behaviour as a function of D. This revised version was published online in August 2006 with corrections to the Cover Date.     

用于电磁驱动真空-等离子体系统数值模拟的弛豫磁流体力学模型

提出了一个弛豫磁流体力学模型,特别适合电磁驱动真空-等离子体系统的数值模拟。该模型和Seyler采用的弛豫模型有相似之处,即采用全电磁模型,不同的是采用忽略电子惯性项的广义欧姆定律直接作为本构来封闭麦克斯韦方程,减少了独立变量,是适合此类问题的最简模型。分析了磁流体力学模型电磁部分的色散关系,从而论证了其在真空区退化为电磁传播,在等离子体物质区退化为磁扩散近似,并且相速和群速是有上界的。改进了Seyler采用的时间离散方式,从而将时间精度从1阶提高到3阶,时间步长不受刚性源项约束,只受系统最大的特征速度确定的柯朗-弗里德里奇-列维(CFL)条件约束,便于显式计算和大规模并行化。     

Incorporating reversible and irreversible transverse relaxation effects into Steady State Free Precession (SSFP) signal intensity expressions for fMRI considerations

Among the multiple sequences available for functional magnetic resonance imaging (fMRI), the Steady State Free Precession (SSFP) sequence offers the highest signal-to-noise ratio (SNR) per unit time as well as distortion free images not feasible with the more commonly employed single-shot echo planar imaging (EPI) approaches. Signal changes occurring with activation in SSFP sequences reflect underlying changes in both irreversible and reversible transverse relaxation processes. The latter are characterized by changes in the central frequencies and widths of the inherent frequency distribution present within a voxel. In this work, the well-known frequency response of the SSFP signal intensity is generalized to include the widths and central frequencies of some common frequency distributions on SSFP signal intensities. The approach, using a previously unnoted series expansion, allows for a separation of reversible from irreversible transverse relaxation effects on SSFP signal intensity changes. The formalism described here should prove useful for identifying and modeling mechanisms associated with SSFP signal changes accompanying neural activation.     

Intrinsic electron spin relaxation due to the D'yakonov–Perel' mechanism in monolayer MoS2

Intrinsic electron spin relaxation due to the D'yakonov–Perel' mechanism is studied in monolayer Molybdenum Disulphide. An intervalley in-plane spin relaxation channel is revealed due to the opposite effective magnetic fields perpendicular to the monolayer Molybdenum Disulphide plane in the two valleys together with the intervalley electron–phonon scattering. The intervalley electron–phonon scattering is always in the weak scattering limit, which leads to a rapid decrease of the in-plane spin relaxation time with increasing temperature. A decrease of the in-plane spin relaxation time with the increase of the electron density is also shown.     

Anelastic relaxation and around the critical Sr content x = 0.02

Anelastic relaxation and ¹³⁹LaNQR relaxation rates in La_2–xSr_xCuO₄ for Sr content around 2 and 3 percent are discussed in terms of spin and lattice excitations and of the related ordering processes. It is argued how the phase diagram of La_2–xSr_xCuO₄ at the boundary between the antiferromagnetic (AF) and the spin-glass phase (x = 0.02) could be more complicate than previously thought, with a transition to a quasi-long range ordered state at K, as indicated by neutron scattering data. On the other hand, the ¹³⁹LaNQR spectra are compatible with a transition to an AF phase around K, in agreement with the phase diagram commonly accepted in literature. In this case the peaks in NQR and anelastic relaxation rates around 150 K and 80 K respectively in La_1.98Sr_0.02CuO₄, yield the first evidence of freezing process involving simultaneously lattice and spin excitations, possibly corresponding to motion of charged stripes. Received 18 May 2000 and Received in final form 11 July 2000     

Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization

The magnetization under the spin-lattice relaxation and the nuclear magnetic resonance radiofrequency (RF) pulses is calculated for a signal RF pulse train and for a sequence of multiple RF pulse-trains. It is assumed that the transverse magnetization is zero when each RF pulse is applied. The result expressions can be grouped into two terms: a decay term, which is proportional to the initial magnetization M0, and a recovery term, which has no M0 dependence but strongly depends on the spin-lattice relaxation and the equilibrium magnetization Meq. In magnetic resonance pulse sequences using magnetization in transient state, the recovery term produces artifacts and can seriously degrade the function of the preparation sequence for slice selection, contrast weighting, phase encoding, etc. This work shows that the detrimental effect can be removed by signal averaging in an eliminative fashion. A novel fast data acquisition method for constructing the spin-lattice relaxation (T1) map is introduced. The method has two features: (i) By using eliminative averaging, the curve to fit the T1 value is a decay exponential function rather than a recovery one as in conventional techniques; therefore, the measurement of Meq is not required and the result is less susceptible to the accuracy of the inversion RF pulse. (ii) The decay exponential curve is sampled by using a sequence of multiple pulse-trains. An image is reconstructed from each train and represents a sample point of the curve. Hence a single imaging sequence can yield multiple sample points needed for fitting the T1 value in contrast to conventional techniques that require repeating the imaging sequence for various delay values but obtain only one sample point from each repetition.     

Anelastic relaxation of Pr1/2Ca1/2MnO3 at low and medium frequencies in the 350–500 K range

In previous works (Jornadas SAM 2000; J. Magn. Magn. Mater. 226–230 (2001) 988) the low-frequency anelastic effects of two manganite perovskites of La_2/3Sr_1/3MnO₃ and La_2/3Ca_1/3MnO₃ were studied at 1 Hz and temperatures above those of the metal–insulator transition. An important internal friction peak (P1) appears at 414 and 419 K, respectively, with a modulus variation and no appreciable contribution to electrical resistivity. Another compound Pr_1/2Ca_1/2MnO₃ of the same family has been studied by anelastic mechanical spectroscopy in order to add new data which could elucidate the (P1) peak mechanism. The measurements were made in a sub-resonant forced pendulum (0.1–20 Hz) and in a vibrating reed equipment (kHz range). A stable (P1) peak has been detected at 410 K (1 Hz), with a corresponding modulus step. The appearance of this relaxation peak in the Pr_1/2Ca_1/2MnO₃ compound, and its high activation energy value, similar to the other compounds measured, indicates that the microscopic origin of this relaxation does not correspond to an oxygen jump (characteristic activation energy0.8–0.9 eV).     

Spin–Spin Interactions and Nuclear Magnetic Relaxation in Magnetic Solids

The influence of the orientational fluctuations of the electronic magnetization, which modulate nuclear spin–spin interactions (Suhl–Nakamura and dipole–dipole), on the spin-lattice relaxation of magnetic nuclei with spin I = 1/2 in the magnetically ordered solids has been investigated. It has been shown that this mechanism of the spin-lattice relaxation is less effective in comparison with the process of spin-lattice relaxation caused by the direct fluctuations of hyperfine fields, which appear when there are the fluctuations of electronic magnetization direction.     

Relaxation of physical systems in relative-number state representation

The relaxation properties of physical systems in the Liouville space are investigated in terms of the relative-number state representation. An arbitrary state can be expressed by superposition of relative-number states. In the absence of an time-dependent external field, all components with non-zero relative-numbers decay to zero with time, and any stationary state can be expressed only in terms of zero relative-number states. The phase canonically conjugate to the relative-number is completely uncertain in a stationary state. It is thought that relaxation from an arbitrary initial state to a stationary state is described as some kind of phase relaxation process. Such a phase relaxation process is explicitly described by the phase operator formalism within the framework of the relative-number state representation.     

The dielectric function of two- and three-dimensional rotators with permanent electric dipoles

Summary The dynamical theory of the dielectric function of classical dipolar liquids is extended by taking into account the dynamical behaviour of the Kirkwood correction factor and improving the treatment of the relaxation functions. Two- and three-dimensional systems are investigated. It is shown that the Kirkwood correction, related to shortrange interactions, has two dynamical effects: it leads to a viscous force and an orienting force, which decays exponentially with frequency. The formalism developed for liquids is extended for frozen rotators in solids.

---

Riassunto La teoria dinamica della funzione dielettrica dei liquidi dipolari classici è estesa prendendo in considerazione il comportamento dinamico del fattore di correzione di Kirkwood e migliorando la trattazione delle funzioni di rilassamento. Si studiano sistemi bi- e tridimensionali. Si mostra che la correzione di Kirkwood, connessa con le interazioni a corto raggio, ha due effetti dinamici: porta ad una forza viscosa e ad una forza di orientamento, che decade esponenzialmente con la frequenza. Il formalismo sviluppato per i liquidi ⪻ esteso per rotori ghiacciati nei solidi.

     

Effect of flow on the apparent transverse relaxation time in a microfluidic nuclear magnetic resonance chip

The detection of samples in a microfluidic nuclear magnetic resonance chip is generally performed under flow condition. To study the effect of sample flow on the apparent transverse relaxation time in a microfluidic nuclear magnetic resonance chip, theoretical calculations were performed on three microfluidic samples (including deionized water, absolute ethanol, and copper sulfate pentahydrate) for flow velocities in the range 1.7–25?mm/s. A microfluidic nuclear magnetic resonance device with a low cost microfluidic solenoid coil was fabricated to verify the theoretical calculations by experiments. The results show that the apparent transverse relaxation time of the sample is a monoexponential decay with respect to flow velocity. In addition, it was found that the experimental values and the theoretical values of the apparent transverse relaxation time are identical when the samples are prepolarized completely; but for the samples that are not prepolarized completely, all the experimental values are smaller than the theoretical values and their difference increases with the flow velocity of the sample. After further study, it was discovered that the relative error between the experimental values and the theoretical values is a monoexponential decay to the level of the sample to be prepolarized. This discovery is very useful, because it can be used to modify the theoretical calculation model of the apparent transverse relaxation time for the samples that are prepolarized incompletely, as well as improve the application of microfluidics on nuclear magnetic resonance.     

Repeated stress relaxations in Al-2·5% Mg alloy

In a commercial Al-2·5% Mg alloy stress relaxation runs are well described by Hart's low temperature flow law and show essentially friction controlled flow behaviour, ranging from nearly anelastic to plastic flow, depending on the time, temperature and strain. Anelasticity during repeated relaxations indicates substantial strain aging during the initial relaxation run. Initial stages of relaxations show yield point like transients in the temperature/strain regime, where yield points are observed also in the tensile test.The authors are grateful te Drs. C.-Y. Li, D. Stone and M. Hamersky for helpful discussions. Thanks are extended to Nokia Corp. Pikkala Works, for providing the Al-alloy used in this study.