Bulk model of rapid thermal oxidation of silicon

A model of rapid thermal oxidation of silicon in dry oxygen based on the reaction of volume oxidation is constructed. It is assumed that the coefficient of oxygen diffusion for silicon dioxide decreases because of internal compressive stress, which is at a maximum near the SiO₂-Si interface; as the distance from the interface increases, this stress decreases according to the time-dependent exponential law because of viscoelastic relaxation from the value of the diffusion coefficient for strained oxide to that for fused quartz. The characteristic relaxation time of the coefficient of oxygen diffusion in silicon dioxide correlates with the relaxation time of internal stress in silicon dioxide films on silicon and with the relaxation time of the refraction index. Because the refraction index is related to the density of silicon dioxide, we arrive at the conclusion that the relaxation of the diffusion coefficient is related not only to the relaxation of internal mechanical stress, but also to the relaxation of the density of silicon dioxide.     

Spin diffusion and nuclear spin-lattice relaxation in irradiated solids: a multiple-pulse NQR study

We present a detailed theoretical and experimental NQR multiple-pulse spin-locking study of spin-lattice relaxation and spin diffusion processes in the presence of paramagnetic impurities in solids. The relaxation function of the nuclear spin system at the beginning of the relaxation process is given by exp , where T_1ρ is spin-lattice relaxation time in rotating frame and =d/6, d is the sample dimensionality. Then the relaxation proceeds asymptotically to an exponential function of time, which was attributed to the spin-diffusion regime. Using the experimental data obtained from the analysis of those two relaxation regimes in γ-irradiated powdered NaClO₃, spin diffusion coefficient has been determined and the radius of the diffusion barrier has been estimated.     

A lattice-Boltzmann scheme for Cattaneo’s diffusion equation

A lattice-Boltzmann (LB) formulation is developed for the simulation of Cattaneo’s diffusion equation. To do this, the collision term is computed from a 1-step back relaxation dynamics which, in turn, induces a hyperbolic-type diffusion effect. The Fickian LB formulation is recovered in the limit as a relaxation time coefficient goes to zero.     

Diffusion-relaxation correlation in simple pore structures

The effects of independent encoding for relaxation and for diffusion using separate time and gradient dimensions are calculated for spins diffusing in plane parallel and spherical pores with relaxing walls. Two-dimensional inverse Laplace transformation is used to obtain computed (D,T(2)) maps for both geometries, in the regime in which the dimensionless diffusion coefficient is less than unity and the dimensionless relaxation parameter of order unity or greater. It is shown that there exist two distinct branches on the (D,T(2)) maps, one with diffusion and relaxation strongly correlated and one in which the diffusion coefficients vary widely independently of relaxation.     

Spin diffusion of dipolar energy in NQR

The theory of spin diffusion was extended to the case of nuclear dipolar order in solids containing paramagnetic impurities and nuclei with spin I > 1/2 having nuclear quadrupole moment. We show that spin diffusion process of dipolar order takes place in solids containing paramagnetic impurities. At the start of relaxation process, the direct relaxation regime is realized with non-exponential time dependence. Then the relaxation regime will be changed to diffusion-limited one. Using obtained expressions for the spin lattice relaxation times for these two relaxation regimes, the diffusion coefficient of the dipolar order in nuclear quadrupole resonance can be estimated from experimental data.     

Cross-Relaxation Effects in Pulsed-Field-Gradient Stimulated-Echo Measurements on Water in a Macromolecular Matrix

Water diffusion in poly[2-hydroxyethyl-methacrylate] hydrogels has been measured by PFG NMR techniques, using both spin-echo and stimulated-echo methods. It is found that the results differ when evaluated using the standard equations for the echo attenuation. Furthermore, an apparent dependence of the diffusion coefficient on the diffusion time was found in stimulated-echo experiments. This effect is shown to be caused by cross relaxation between the protons of the water and those on the polymer matrix. An equation is derived describing the attenuation of a stimulated echo in the presence of cross relaxation. This equation shows that the additional damping due to cross relaxation depends on the gradient amplitude. If this equation is used with the measured cross-relaxation parameters, both methods are found to agree within experimental error, and no diffusion-time dependence is found for the stimulated-echo experiments. The equation predicts the effect of replacing part of the H₂O by D₂O; this has been experimentally verified. It is concluded that macromolecular systems should be checked for cross relaxation when stimulated-echo methods will be used for self-diffusion measurements.     

On the spin-flip line shape in CdS

The longitudinal relaxation time of Spin-Flip Raman scattering (SFRS) in n-CdS is explained in terms of the Elliott mechanism. The energy dispersion of spectroscopic factors of the conduction electrons and the Hasegawa model yield a transversal relaxation time different from the longitudinal relaxation time, but do not reproduce the experimental value. The diffusion coefficient, responsible for the SFRS line width behavior with temperature in n-CdS, is explained based upon hopping effects in the low temperature region.     

Spin diffusion in multiple pulse spin-locking in solids containing paramagnetic impurities

Spin diffusion and spin-lattice relaxation in solids containing paramagnetic impurities under influence of a multiple-pulse spin-locking radio-frequency sequence are studied theoretically and experimentally. The diffusion equation obtained provides a clue for determination of the time dependent magnetization. The spin-lattice relaxation time is calculated as a function of the correlation time and multiple-pulse field parameters. From the experimental data the spin diffusion coefficient, the radius of the spin diffusion barrier, and the correlation time for very slow molecular motion in polycrystalline (C(2)F)(n) system are estimated and found to be D～7.1×10(-12)cm(2)/s, r(c)～4.8×10(-10)m, and τ(c)～10.2μs, respectively.     

Dynamics of a polymer chain confined in a membrane

We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free-membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical structure factor. For large polymer size, both quantities show Zimm-like behavior in the free-membrane case, whereas they are Rouse-like for the sandwiched membrane geometry. We use the scaling argument to discuss the effect of excluded-volume interactions on the polymer relaxation time.     

岩心孔隙介质中流体的核磁共振弛豫

弛豫时间是核磁共振研究中的一个重要参数,岩心孔隙介质流体的弛豫过程是自由流体弛豫机制、表面弛豫机制和流体的扩散弛豫机制共同作用的结果,它包含了丰富的孔隙和流体本身的信息. 弛豫时间和自扩散系数的测量及对弛豫时间的分析是核磁共振技术应用于岩心分析和石油勘测的重要内容.     

Fluctuations and spectral relaxation in dispersion transfer over traps

Based on the self-consistent cluster approximation of an effective medium for random walk over a lattice with stochastically positioned traps in the dispersion regime, the kinetics of the spectral relaxation of the partial populations was analyzed and the self-averaging of the diffusion coefficient was studied. It was demonstrated that the relaxation of partial populations at long time occurs anomalously slow, according to a power law. It was shown that, in the one-dimensional case, no self-averaging of the diffusion coefficient occurs even at long time (its fluctuation amplitude remain comparable with its value) and that in the two- and three-dimensional cases, self-averaging proceeds very slowly, in accordance with a logarithmic and power dependence, respectively.     

Measurement of the nuclear spin diffusion coefficient in organic glasses doped with paramagnetic centers: Orthoterphenyl and polymeric glasses

We have recently developed a method of studying spin diffusion coefficients by doping the materials with paramagnetic centers and measuring the nuclear relaxation in a tilted rotating frame. Using this method, we measure here the spin diffusion coefficient of orthoterphenyl, a molecular organic glass, and of three polymer glasses: poly(4-vinylpyridine), poly(vinylacetate) and poly(methyl methacrylate). We explore a possible dependence of the measured orthoterphenyl spin diffusion coefficient on the electronic relaxation time and concentration of the paramagnetic centers. We conclude that the experiments can be performed at higher concentrations than previously thought. We also show that our method applies to polymers in the glassy state if one works at sufficiently small tilt angle, in spite of a short value ofT _1ρ. We had anticipated that the distribution of proton pairs in these materials precludes the standard dependence of the spin diffusion coefficient on the proton density and free induction decay characteristic decay time. Our results fully confirm such expectation.     

Relaxation time of substance concentration in a medium with an arbitrary space-varying diffusion coefficient

We propose a new method for deriving temporal characteristics of the nonstationary diffusion in a one-dimensional medium without solving the partial differential equation. This method allows the time of relaxation to equilibrium concentration to be determined in a bounded medium with an arbitrary space-varying diffusion coefficient. Some examples are analyzed. State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 7, pp. 886–896, July, 1997.     

Investigation of impurity diffusion in dilute alloys by nuclear magnetic resonance

The diffusion of Al in a Cu: 3.8 at % Al alloy has been investigated by observing the rotating-frame nuclear magnetic relaxation time T_1π of ²⁷Al as a function of temperature. It is shown that relaxation measurements of the solute atoms in a dilute alloy provide the correlation time of the diffusive motion of these atoms, if quadrupolar interactions form the main contribution to the relaxation time. From the correlation times the Al-diffusion coefficient in the alloy has been determined.     

The effect of ultrasound treatment on the interaction of brine with pork meat proteins

The objective of the study is to elucidate the effect of ultrasound treated salt solution on curing of pork meat. The interactions of salt (NaCl) solutions of 3 and 25% with the proteins of pork meat are studied. High intensity ultrasound operating at 20 kHz was used. The differential scanning calorimetry (DSC), NMR spin-spin relaxation time, unfrozen water and water diffusion coefficient measurements were carried out in meat cured with ultrasound treated and untreated salt solutions. The effect of ultrasonication was most evident from measured spin-spin relaxation times T₂₁, the rate of chemical exchange of water protons k and the amount of unfrozen water W_unf in the meat. The measured diffusion coefficient of water D_w in meat cured with ultrasound treated and control salt solution did not show significant difference. The nuclear magnetic resonance (NMR) relaxation data, differential scanning calorimetry (DSC) and the diffusion coefficient data reliably show that the possible action of ultrasound to salt solution was manifested on the first 2 days of the experiment with a 3% salt solution.     

在CP MAS NMR中测量质子自旋扩散速率的方法

自旋扩散在固体核磁共振的许多现象中都起着非常重要的作用。现有几种理论方案以估算扩散系数。然而在实践中这种估算既不实际也不可靠。本文提出了确定自旋扩散速率的新方案,它利用的是CP MAS NMR中的稀核退极化规律。带质子的稀核磁化矢量在退极化中表现出两个阶段,慢衰减的第二阶段是单一指数过程,它提供了自旋扩散速率的直接度量。自旋扩散实质上是极化转移的一种宏观表现形式,这种转移通过一系列成对自旋的flip-flop进行,可以用一维随机走步模型描述。从退磁过程半对数曲线的斜率可以求得平均flip-flop时间。自旋扩散系数可以由此估算。在一些典型的刚性有机固体和结晶高分子聚合物中,求得平均flip-flop的时间是700微秒左右。它比偶极相关时间大一个数量级。这意味着,自旋扩散时间常数与自旋—自旋弛豫时间常数是很不相同的,虽然这两个相应过程虽密切相关的。由质子线宽估计自旋扩散系数是不可靠的。     

Diffusion coefficient for a Brownian particle in a periodic field of force: I. Large friction limit

The diffusion tensor for a Brownian particle in a periodic field of force is studied in the strong damping limit, in which the Smoluchowski equation is valid.A general relation between the diffusion tensor and the Smoluchowski “relaxation operator” is derived; the effect of the periodic force, at least in the simplest situation of diagonal and uniform friction, appears as a dressing of the bare particle mass to an effective tensor mass.From this the explicit form of the diffusion coefficient as a functional of the potential energy in the one-dimensional case is obtained, showing a temperature dependence which deviates at high temperatures from a simple Arrhenius behaviour.Finally, the expression for the mobility of the Brownian particle is derived, and by comparison with the expression for the diffusion coefficient the Einstein relation between diffusion and mobility is proved to be satisfied.     

Effect of atomic hydrogen adsorption on the transport characteristics of semiconducting carbon nanotubes

The effect of atomic hydrogen adsorption on the conduction and diffusion properties of carbon nanotubes of zigzag type in an external electric field is considered. The model of adsorption of atomic hydrogen on the surface of single-walled carbon nanotubes of zigzag type is based on the single-impurity periodic Anderson model. The theoretical calculation of the diffusion coefficient and electrical conductivity of carbon nanotubes of zigzag type doped with hydrogen atoms is carried out in the relaxation time approximation. It has been revealed that the electrical conductivity and electron diffusion coefficient decrease with increasing concentration of adsorbed hydrogen atoms. It has been shown that the dependence of the electrical conductivity and the diffusion coefficient on the amplitude of the constant electric field at the constant concentration of hydrogen adatoms is nonlinear.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

On the kinetic theory of Brownian motion

The influence of fluctuations on the kinetic processes of Brownian motion is investigated. We consider fluctuations for which the correlation time is comparable with the relaxation time of the distribution function. Taking such large scale fluctuations into account is shown to lead to a change of the diffusion coefficient and to the appearance of additional correlations in the motions of Brownian particles. An expression is obtained for the correlation function of a Langevin source in the diffusion equation taking into account the contribution of large scale fluctuations.