Kernrelaxations-Untersuchung der Selbstdiffusion in festem Kupfer

We report on measurements of the⁶³Cu nuclear spin relaxation time in the rotating frame,T _1ρ, in solid copper as a function of temperature and Larmor frequency, from which the temperature dependence of the self-diffusion coefficient was evaluated using Torrey's theory. Within the relatively small temperature range (572 °C ≦ ? ≦ 838 °C) in which diffusion relaxation dominates, the temperature dependence of the diffusion coefficient is compatible with a simple Arrhenius law. However, in an evaluation including recent tracer results in an essentially larger temperature range (353 °C≦?≦1079 °C) clear deviations from this standard interpretation were found, as implied by Seeger's divacancy formalism. From those deviations we have calculated a more reliable set of diffusion parameters than comparable data in the literature.     

Self-diffusion mechanism in solid sodium

The self-diffusion mechanism in sodium is investigated by means of NMR techniques in the temperature range 150–280 K. The temperature dependence of the measured correlation factor confirms the simultaneous migration of mono- and divacancies as the major cause for the curvature of the Arrhenius plot.     

Experimental determination of U diffusion in α-Ti

α-spectrometry was used in order to measure the diffusion of U in bulk α-Ti in the temperature range 863–1123?K (540–850?°C). A straight Arrhenius plot was found, giving diffusion parameters Q?=?297?kJ/mol and D ₀?=?5?×?10^?3?m²/s, which are similar to the α-Ti self-diffusion ones, when measured in Ti samples with a similar impurity content than presently. This behaviour is compatible with the hypothesis of U diffusing via a vacancy-assisted mechanism in the α-Ti lattice and contrasts with older results in which the activation energy is almost a third the self-diffusion one, even lower than the vacancy formation energy.     

Application of the modified electrostatic model to the impurity diffusion in nickel

The modified electrostatic model (Neumann and Tölle 1995) is applied to the impurity diffusion in nickel.Z ₀ = 0.4 is used for the effective charge of the nickel ion.The comparison of calculated and experimental diffusion parameters reveals that the sign of J Q, the difference between impurity diffusion and self-diffusion energy, and the sign of the difference between impurity diffusion and self-diffusion coefficient is correctly predicted in all cases. On the other hand the comparison exhibits some systematic deviations for 5p impurities, which cannot be explained in terms of the current impurity diffusion models.     

Cooperative mechanism of self-diffusion in metals

The atomic mechanism of self-diffusion in a face-centered cubic structure (exemplified by aluminum) is simulated by the molecular-dynamics method without resorting to a priori information. No confirmation of vacancy-jump mechanisms of diffusion has been obtained. The cooperative mechanism of diffusion suggested previously by Khait and Klinger and based on the assumption of possible local melting near vacancies (within one-two nearest coordination shells) appears to be valid. As a result, the preexponential factor proves to depend on the temperature and heat of melting, and the exponential factor depends on the heat of melting and the current temperature.     

An improved theory for temperature-dependent Arrhenius parameters in mesoscale surface diffusion

Experiments on metals typically show an abrupt change in the Arrhenius behavior of surface self-diffusion at temperatures near 60-75% of the bulk melting point. To explain this phenomenon, we propose based on correlational evidence that the most common mechanism for surface self-diffusion is one in which adatoms dominate low-temperature transport, while surface vacancies dominate at high temperatures. The high-temperature dominance of vacancies results from their substantially higher entropy of diffusion, which is a consequence of the large vibrational displacements of surface atoms relative to the bulk. This phenomenon may also explain the Arrhenius behavior on some non-metal surfaces.     

Calculations of vacancy formation and migration energies offcc Cs by the LMTO-method: Application to self diffusion

Vacancy formation and migration energies offcc Cs were calculated from first principles by the LMTO-method. The change in slope of the Arrhenius curve for the diffusion coefficient as a function of temperature is discussed and its occurrence is explained by vacancies concentration dependence of the energy of formation. The frequency of vibration and the jump probability of an atom were calculated and it is shown that they are direction dependent.     

Self-diffusion in copper between 359 and 632°C

The self-diffusion coefficient of copper was determined between 359 and 632°C using a sputtering technique. A slight curvature of the self-diffusion Arrhenius plot was found in agreement with previous calculations.     

Examen de la loi d'arrhenius de la diffusion dans les solides

Validity of the Arrhenius law has been investigated by measuring the influence of temperature on the transport processes in very pure single crystals of sodium iodide. For the first time, due to the high experimental accuracy and the precision of the temperature control, diffusion coefficients could be measured in a solid in steps of a few degrees up to a few tenths of a degree of the temperature of fusion. We have studied: (a) ionic conductivity, (b) self-diffusion of the cation Na⁺ and (c) self-diffusion of the anion I^?. The three transport processes follow the same temperature dependence: (a) strict verification of the Arrhenius law over several orders of magnitude up to about thirty degrees below the melting point and (b) in the last thirty degrees a positive departure from the simple exponential law is observed which increases rapidly to reach 50% at fusion. The different possible reasons of this departure are discussed. The phenomenon seems to be connected with the lattice dynamics before melting.     

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.     

Memory effects in the diffusion of an interacting polydisperse suspension: I. Projection formalism at long wavelength

We consider collective diffusion and self-diffusion in a polydisperse suspension of macroparticles. Using the generalized Smoluchowski equation to describe the interacting suspension we extend Ackerson's work to derive a multispecies projection formalism for the density fluctuations. We include 2-body direct potential interactions as well as accurate 2-body hydrodynamic interactions. We take the long wavelength low density limit of this formalism to obtain an expression for the memory matrix expressed in terms of 2-body interactions and propagators. We show how memory contributions can arise to first order in density from the fact that the correct mobility tensors are not divergenceless.     

Dynamical properties of strongly interacting Brownian particles : II. Self-diffusion

The self-diffusion process of Brownian particles is theoretically investigated for concentrated systems in the presence of strong potential interactions between particles. Starting from an N-particle diffusion equation, a formalism is developed to calculate the self-diffusion coefficient and the velocity autocorrelation function on the basis of the superposition approximation for the three-particle distribution function of non-equilibrium states. Explicit calculations are carried out for model systems of hard spheres with a screened Coulomb potential. Calculated time-dependent self-diffusion coefficients are compared with available data of the Brownian dynamics. Without introducing any phenomenological or adjustable parameters, quantitative agreement is achieved.     

Self-diffusion and nuclear magnetic relaxation of dendritic macromolecules in solutions

The self-diffusion and nuclear magnetic relaxation of poly(butylcarbosilane) and poly(allylcarbosilane) dendrimers dissolved in deuterated chloroform and poly(amidoamine) dendrimers with hydroxyl surface groups in solutions with methanol have been studied. The diffusion rates(D) have been measured by the pulsed-field-gradient nuclear magnetic resonance. It is shown that experimental concentration dependencesD(ϕ) obtained for macromolecules in the dendrimer-solvent systems studied can be reduced to a unified view, and thus, the generalized concentration dependence of the normalized diffusion rates of dendrimers can be obtained. In the macromolecular volume concentration range from 0.01 up to 0.55, the generalized dependence of the normalized diffusion rates for dendrimers coincides with the analogous dependence for globular proteins in aqueous solutions; the last result suggests that self-diffusion features of dendrimers and globular proteins are in general similar. It is also shown that the experimental data obtained permit one to characterize the changes of the own monomer density of dendrimers depending on their molecular weight and, as a consequence, to make a conclusion about the swelling of dendritic macromolecules in the solutions studied.     

Zur Deutung der Protonenspinrelaxation in Glycerin

In contrast with the usual assumption that proton spin relaxation in glycerol originates from rotational molecular diffusion, quantitative evaluation of the temperature and Larmor frequency dependence in the ranges ?30 °C to+70 °C and 10 kHz to 120 MHz, respectively, gives extensive agreement with Fick's translational random walk model. This observation is supported by direct measurements of the self-diffusion constant by means of the pulse gradient method, which reveals the same activation barrier as relaxation spectroscopy.     

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations. Received: 27 April 1998 / Revised: 2 September 1998 / Accepted: 10 September 1998     

Sb diffusion in α-Fe

The effect of the magnetic ordering on the diffusion of Sb in α-Fe was investigated. Measurements were made in an extended temperature range: (673–1073 K), using the ion beam techniques Rutherford backscattering spectrometry (RBS) and heavy ion RBS (HIRBS) in superposed ranges of temperature. By expanding the temperature range with respect to the previous works, the Arrhenius plot shows the variation of the slope at the Curie temperature and a soft-up curvature in the ferromagnetic region. The curvature observed is well fitted by the model developed by Ruch et al. The parameter that takes into account the influence of the magnetic order in the vacancy mobility during the Sb diffusion process is quite similar to that observed in Fe self-diffusion; then, no magnetic interaction between the impurity and the matrix is postulated. PACS 66.30.-h; 66.30.Jt; 61.18.Bn     

Diffusion and rheology in a model of glassy materials

We study self-diffusion within a simple hopping model for glassy materials. (The model is Bouchaud's model of glasses (J.-P. Bouchaud, J. Phys. I France 2, 1705 (1992)), as extended to describe rheological properties (P. Sollich, F. Lequeux, P. Hébraud, M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)).) We investigate the breakdown, near the glass transition, of the (generalized) Stokes-Einstein relation between self-diffusion of a tracer particle and the (frequency-dependent) viscosity of the system as a whole. This stems from the presence of a broad distribution of relaxation times of which different moments control diffusion and rheology. We also investigate the effect of flow (oscillatory shear) on self-diffusion and show that this causes a finite diffusivity in the temperature regime below the glass transition (where this was previously zero). At higher temperatures the diffusivity is enhanced by a power law frequency dependence that also characterises the rheological response. The relevance of these findings to soft glassy materials (foams, emulsions etc.) as well as to conventional glass-forming liquids is discussed. Received 31 August 1998 and Received in final form 25 January 1999     

Diffusion of Hf in α-Zr

The diffusion of Hf in -Zr has been studied in the temperature range 773–1115 K for the first time using the Rutherford backscattering technique. For this purpose we have used 250 Å thick Hf films, which were deposited on two types of Zr samples. Our results show that in both cases, the diffusion coefficients follow curved Arrhenius plots. For the pure Zr material the diffusion coefficients are systematically lower than for Zr samples of lower purity. These results indicate that the Hf diffusion mechanism is at least partially of extrinsic character. Finally it should be mentioned that the present data lie significatively below the values of self-diffusion in -Zr.     

Diffusion of Ta in α-Ti

The diffusion of Ta in the hcp (α) phase of high-purity Ti (99.99%) was studied at different temperatures from 911 K up to 1123 K. The Rutherford Backscattering Spectrometry (RBS) and Heavy Ion RBS (HIRBS) techniques were used to obtain the penetration profiles. The evolution of the diffusion coefficient, D, as a function of temperature follows prediction of the Arrhenius law. The activation energy of the diffusion process is (318±7)kJ/mol, similar to that corresponding to self-diffusion in α-Ti. On the other hand, the measured values of D are systematically lower than those corresponding to self-diffusion by a factor of approximately 5. This reduction could be explained by taking into account the mass difference between Ta and Ti. An increase of the diffusion coefficient was measured when the diffusion proceeds on a less pure Ti (99.9%) matrix. This increment is higher at lower temperatures. Received: 12 November 2001 / Accepted: 12 March 2002 / Published online: 5 July 2002 RID="*" ID="*" RID="*" ID="*" RID="**" ID="**"Corresponding author. Fax: +54-11/6772-7362, E-mail: dyment@cnea.gov.ar RID="*" ID="*"Members of the Carrera del Investigador Científico del Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina     

Generic van der Waals equation of state for polymers, modified free volume theory, and the self-diffusion coefficient of polymeric liquids

In this paper, a molecular theory of self-diffusion coefficient is developed for polymeric liquids (melts) on the basis of the integral equation theory for site-site pair correlation functions, the generic van der Waals equation of state, and the modified free volume theory of diffusion. The integral equations supply the pair correlation functions necessary for the generic van der Waals equation of state, which in turn makes it possible to calculate the self-diffusion coefficient on the basis of the modified free volume theory of diffusion. A random distribution is assumed for minimum free volumes for monomers along the chain in the melt. More specifically, a stretched exponential is taken for the distribution function. If the exponents of the distribution function for minimum free volumes for monomers are chosen suitably for linear polymer melts of N monomers, the N dependence of the self-diffusion coefficient is N⁻¹ for the small values of N, an exponent predicted by the Rouse theory, whereas in the range of 2.3?lnN?4.5 the N dependence smoothly crosses over to N⁻², which is reminiscent of the exponent by the reptation theory. However, for lnN?4.5 the N dependence of the self-diffusion coefficient differs from N⁻², but gives an N dependence, N^−2−δ(0<δ<1), consistent with experiment on polymer melts in the range. For polyethylene δ≈0.48 for the parameters chosen for the stretched exponential. Because the stretched exponential function contains undetermined parameters, the N dependence of diffusion becomes semiempirical, but once the parameters are chosen such that the N dependence of D can be successfully given for a polymer melt, the temperature dependence of the self-diffusion coefficient can be well predicted in comparison with experiment. The theory is satisfactorily tested against experimental and simulation data on the temperature dependence of D for polyethylene and polystyrene melts.