Effect of alloying on the self-diffusion activation energy in γ-iron

The experimental data on the self-diffusion coefficient of austenite with different chemical compositions obtained by the radioactive isotope method have been analyzed quantitatively. The self-diffusion activation energy in pure γ-iron is shown to be ∼312 kJ/mol. Alloying of austenite with such elements as Mn, Mo, Nb, Ti, and Si (to a lower degree) increases the self-diffusion activation energy, and alloying with C, V, or Cr (for the element content ≥3 at %) decreases it. The empirical formula is derived for calculation of the self-diffusion activation energy in austenite solid solutions with complex composition.     

Self-Diffusion in Cell Membranes in the Long Time Regime

We consider the process of self-diffusion in the cellular structure in the presence of permeable barriers in long time regime. Based on the most general concepts of the translation mobility and geometry of a heterogeneous system, an expression for the self-diffusion coefficient of liquid molecules in such a medium in a long time regime was derived. We have shown that the value of the self-diffusion coefficient in the long-time limit is determined by the probability of interaction of the diffusant molecule with an obstacle. We obtained an expression for the probability of such interaction as a function of the surface-to-volume ratio (S/V). Comparing the obtained analytical expression with the results of computer simulation was performed. Shown the exponential dependence of the self-diffusion coefficient on the barrier pinning density.     

A statistical-mechanical theory of self-diffusion in colloidal suspensions — application to colloidal glass transitions

A statistical-mechanical theory of self-diffusion in colloidal suspensions is presented. A renormalized linear Langevin equation is derived from a nonlinear Langevin equation by employing the Tokuyama–Mori projection operator method. The friction constant is thus shown to be renormalized by the many-body correlation effects due to not only the direct interactions between particles, but also due to the hydrodynamic interactions between particles. The equations for the mean-square displacement and the non-Gaussian parameter are then derived. The present theory is applied to colloidal glass transitions to discuss the crossover phenomena in the dynamics of a single particle from a short-time self-diffusion process to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of the analyses of the experimental data and the simulation results by the mean-field theory proposed by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that the non-Gaussian parameter is very small, even near the glass transition, because of the existence of the short-time self-diffusion coefficient caused by the hydrodynamic interactions.     

Application of random walk concept to the cyclic diffusion mechanisms for self-diffusion in intermetallic compounds

Huntington–Elcock–McCombie (HEM) mechanism involving six consecutive and correlated jumps, a triple-defect mechanism (TDM) involving three correlated jumps and an anti-structure bridge (ASB) mechanism invoking the migration of an anti-structure atom are the three mechanisms currently in vogue to explain the self- and solute diffusion in intermetallic compounds. Among them, HEM and TDM are cyclic in nature. The HEM and TDM constitute the theme of the present article. The concept of random walk is applied to them and appropriate expressions for the diffusion coefficient are derived. These equations are then employed to estimate activation energies for self-diffusion via HEM and TDM processes and compared with the available experimental data on activation energy for self-diffusion in intermetallic compounds. The resulting activation energies do not favour HEM and TDM for the self-diffusion in intermetallic compounds. A comparison of the sum of experimentally determined activation energies for vacancy formation and migration with the activation energies for self-diffusion determined from radioactive tracer method favours the conventional monovacancy-mediated process for self-diffusion in intermetallic compounds.     

Self-diffusion of aluminium in the intermetallic compound Fe-48 at.% Al

The self-diffusion coefficient of Al in the B2-type intermetallic compound Fe-48 at.% Al has been determined using the intrinsic diffusion coefficients of Fe and Al and the self-diffusion coefficient of Fe with the help of the Darken-Manning relation. The self-diffusion coefficient of Al in Fe-48 at.% Al is estimated to be a factor of about 0.6 smaller than that of Fe, and the activation energy for the self-diffusion of Al is obtained to be 280 kJ mol^?1 which is a little larger than the value of 262 kJ mol^?1 for the self-diffusion of Fe, indicating that the diffusion mechanisms for both components are nearly equal.     

A statistical-mechanical theory of self-diffusion in glass-forming liquids

A statistical-mechanical theory of self-diffusion in glass-forming liquids is presented. A non-Markov linear Langevin equation is derived from a Newton equation by employing the Tokuyama-Mori projection operator method. The memory function is explicitly written in terms of the force-force correlation functions. The equations for the mean-square displacement, the mean-fourth displacement, and the non-Gaussian parameter are then formally derived. The present theory is applied to the glass transitions in the glass-forming liquids to discuss the crossover phenomena in the dynamics of a single particle from a short-time ballistic motion to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of analyses of the simulation results by the mean-field theory proposed recently by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that for times longer than the β-relaxation time the dynamics of a single particle is identical to that discussed in the suspensions.     

Theory of tracer-diffusion in the wurtzite-structure with applications to hexagonal ice

A theory for the tracer self-diffusion by a vacancy mechanism in the wurtzitelattice is developed into which the effects of Bardeen-Herring correlation are included in a rigorous way. The isotope effect parameter is calculated for the limiting case in which the jump process may be treated as the jump of an individual particle and by means of classical statistics.As an interesting example self-diffusion in hexagonal ice is considered which occurs by exchange of entire water molecules with molecular vacancies.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

An Enskog repeated-ring kinetic equation; Long-time tails and the Brownian limit

A kinetic equation for the motion of a particle of arbitrary size and mass through a moderately dense gas is derived and discussed. The “long-time tail” of the velocity correlation function is calculated and found to agree with existing results. For a Brownian particle, the theory gives the Stokes-Einstein law for the self-diffusion coefficient, with the shear viscosity given by its Enskog value.     

Critical anomaly and finite size scaling of the self-diffusion coefficient for Lennardben Jones fluids by non-equilibrium molecular dynamic simulation

We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard-Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ^* = ρσ³ = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T^* = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N^-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of α < 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations from the literature.     

Peculiarities of self-diffusion of alkane molecules in kaolinite

Self-diffusion of alkanes in kaolinite has been explored by pulsed field gradient nuclear magnetic resonance. The concentration dependences of average self-diffusion coefficient (SDC) of liquid have been studied in the wide temperature interval (T=253?383 K). The translational mobility of alkane molecules in kaolinite was shown to have some specific peculiarities. An anomalous rise was found in the average self-diffusion coefficient of the liquid as its content in kaolinite decreased. To explain this we should introduce a new “gas-like” state for the diffusant, whose mobility exceeds that of pure liquid. The possibility of the existence of such a state is explained by kaolinite’s ability to increase the specific surface area of the induced liquid. Analysis of a shape of the spin-echo diffusion attenuation leads one to suppose that there are heterogeneities in the medium’s porous space.     

超高压水的分子动力学模拟

 采用平衡分子动力学（EMD）方法,模拟研究了温度范围为243~348 K、压强范围为0.1~400 MPa条件下水的热力学性质、结构和动力学性质,模拟结果与实验值吻合较好。模拟结果表明,随着压强的增大,水分子间的氢键作用增强,扩散系数减小;随着温度的升高,水分子间的氢键作用减弱,有序程度下降,扩散系数增大。但在过冷水中,扩散系数随压强的增大有增加的趋势。     

On the theory of Brownian motion. I. Interaction between Brownian particles

The molecular theory of the Brownian motion of heavy particles in a homogeneous solvent of light particles is extended to cover the case of interactions between the Brownian particles. This will have physical effects in the concentration dependence of the Brownian particle self-diffusion coefficient. A density expansion for the Brownian particle friction coefficient is derived, and an approximation permitting the first density correction to be calculated is suggested.This work, part of research supported by NSF Grant GP-8497, was done under the tenure of a National Science Foundation Senior Postdoctoral Fellowship, and of a sabbatical leave granted by the University of Oregon.     

Self-diffusion in polycrystalline silver

An experimental study of self-diffusion in polycrystalline silver has been carried out using the radioisotope Ag-110. The electrolytic sectioning technique was used for measuring. This method made it possible to determine the temperature range in which the self-diffusion of silver is not influenced by grain-boundary diffusion. The temperature was found where the grain-diffusion predominates over the volume diffusion so that the grain-boundary diffusion coefficient can be estimated by Fischer's treatment. Finally, it was found that the temperature range of 619°C< <718°C is the transition region where the electrolytic sectioning technique does not permit the volume or grain-boundary diffusion coefficients to be determined.     

Dissipative particle dynamics study of velocity autocorrelation function and self-diffusion coefficient in terms of interaction potential strength

This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters.     

液态纯铁自扩散系数研究

液态金属固有的良好导热性能和很好的流动性能,逐渐受到了工程领域越来越多的重视。但由于液相扩散系数的测量困难,目前未见液态纯铁的自扩散系数报道。本文以液态纯铁正则系综为研究对象,采用分子动力学模拟方法对其自扩散系数进行了模拟分析,研究结果表明液态纯铁自扩散系数随温度增加呈现出了较大的变化,应用自扩散系数与温度存在的Arrhenius关系拟合出了液态纯铁的自扩散系数经验公式,进一步获得了液态纯铁原子的平均自由程计算关系式。     

System size and trajectory length dependence of the static structure factor and the diffusion coefficient as calculated from molecular dynamics simulations: The case of SPC/E water

The effect of the applied trajectory length on the convergence of the self-diffusion coefficient was examined for the SPC/E water model in the NVT ensemble with different system sizes at 293 K. Temperature dependence and isotope effects, via using D₂O instead of H₂O, were also investigated. A simulation for the polarizable SWM4-DP model was also carried out to compare the effect of different potential models. Radial distribution functions and the neutron weighted structure factor were also calculated; they were found to be insensitive to changing the system size in the range of 216 to 16,000 molecules. On the other hand, the diffusion coefficient is rather sensitive to the applied trajectory length, system size and the method of calculation. The diffusion coefficient is therefore not appropriate for assessing, and distinguishing between, potential models of water, whereas the structure factor could serve as a more stable measure.     

The effect of dynamical screening on self-diffusion in a dense magnetized plasma

The coefficient of self-diffusion along an external magnetic field in a dense plasma is evaluated with the use of a kinetic equation that takes dynamical screening effects into account. It is found that the self-diffusion coefficient diminishes monotonously as the magnetic field strength increases. Qualitatively the present calculation corroborates a result obtained recently in a cruder approximation in which only static screening effects are considered.     

Determination of water self-diffusion coefficient in complex food products by low field 1H PFG-NMR: comparison between the standard spin-echo sequence and the T1-weighted spin-echo sequence

In 1990, Van Den Enden et al. proposed a method for the determination of water droplet size distributions in emulsions using a pulsed-field-gradient nuclear magnetic resonance (PFG-NMR) T1-weighted stimulated-echo technique. This paper describes both the T1-weighted spin-echo sequence, an improved method based on this earlier work, and, the standard PFG spin-echo sequence. These two methods were compared for water self-diffusion coefficient measurement in the fatty protein concentrate sample used as a 'cheese model.' The transversal and longitudinal relaxation parameters T1 and T2 were determined according to the temperature and investigated for each sample; fat-free protein concentrate sample, pure anhydrous milk fat, and fatty protein concentrate sample. The water self-diffusion in fat-free protein concentrate samples followed a linear behavior. Consequently, the water self-diffusion coefficient could be easily characterized for fat-free protein concentrate samples. However, it seemed more complicated to obtain accurate water self-diffusion in fatty protein concentrate samples since the diffusion-attenuation data were fitted by a bi-exponential function. This paper demonstrates that the implementation of the T1-weighted spin-echo sequence, using the different T1 properties of water and fat phases, allows the accurate determination of water self-diffusion coefficient in a food product. To minimize the contribution of the 1H nuclei in the fat phase on the NMR echo signal, the fat protons were selectively eliminated by an additional 180 degrees pulse. This new method reduces the standard errors of diffusion data obtained with a basic spin-echo technique, by a factor of 10. The effectiveness of the use of the T1-weighted spin-echo sequence to perform accurate water self-diffusion coefficients measurement in fatty products is thus demonstrated.