Pressure Dependence Of Diffusion Research Articles

Mg tracer diffusion in aluminosilicate garnets at 750-850° C, 1 atm. and 1300° C, 8.5 GPa

Tracer diffusion coefficients of Mg in natural aluminosilicate garnets of composition Alm38Pyr50Gr10Sp2 and Alm73Pyr21Gr5Sp1 have been measured at 1 bar, 750-850° C and at 8.5 GPa, 1300° C by chemically depositing a salt layer enriched in 26Mg on the specially prepared surface of a garnet single crystal. Diffusion anneals at 1 atmosphere (101325 Pa) were carried out at a controlled f O 2 of ∼10−17.5 bars maintained by a flowing gas mix of CO-CO2. Annealing conditions were carefully chosen to avoid decomposition of garnet by redox reactions. High pressure anneals were carried out in a multianvil apparatus. Induced diffusion profiles (0.1–0.6 μm) were measured by an ion-microprobe with SIMS attachment. Diffusion coefficients at 1 atmosphere are in excellent agreement with extrapolation of data from high P-T experiments (Loomis et al. 1985; Chakraborty and Ganguly 1992) and also with the low temperature (750–900° C) dataset of Cygan and Lasaga (1985) if the diffusion coefficients are assumed to be proportional to f O 2 1/6. Such an f O 2 dependence, however, makes this dataset inconsistent with the recent dataset of Schwandt et al. (1995) on garnets of composition (Alm15Pyr72Gr13Sp0) unless a strong compositional dependence of Mg tracer diffusivity for Mg-rich garnets is invoked. The present experimental results show that such a compositional dependence is weak to non-existent for garnets with >38 mole percent almandine component. It is emphasized that the temperature dependence of diffusion coefficients at constant oxygen fugacities (activation energy ≈54 kcal/mol) are different from that along an oxygen fugacity buffer (activation energy ≈64.5 kcal/mol), as already pointed out by Chakraborty and Ganguly (1991). This distinction is of importance for modelling natural processes. The measurements at low temperatures either eliminate the need for, or greatly reduce the uncertainty of, extrapolation of laboratory data for modelling metamorphic processes. The high pressure results combined with those from Chakraborty and Ganguly (1992) and Loomis et al. (1985) indicate that pressure dependence of Mg tracer diffusivity in garnets is much stronger than that in forsterite (Chakraborty et al. 1994). This difference in pressure dependence of diffusivity may be caused by the difference in compressibility of the coordination polyhedra of Mg between olivines and garnets. Activation volumes of Mg tracer diffusion as high as 8 cm3/mol may be estimated using the present data in combination with earlier results. These data suggest that at a temperature of 1300° C, Mg tracer diffusion rates in garnets will decrease by an order of magnitude for every 100 km depth. The pressure effect will be stronger at lower temperatures. For calculations involving diffusion coefficients of garnets at high pressures (e.g. mantle xenoliths, eclogites) the pressure dependence of diffusivity must be taken into account.

The concentration and pressure dependent diffusion of carbon dioxide in nitrile rubbers

The paper reports the results of an experimental and associated analytical study of the time dependent adsorption of carbon dioxide gas into two nitrile elastomers. The mass gas sorption has been measured using a device based on a vibrating reed to a weight fraction accuracy of ca . 0.05 % at 47 °C in the ambient gas pressure range 0.1-34 MPa. The experimental method is described and data are provided. These data are used to compute the most effective description of the diffusion process by invoking a number of different diffusion coefficient, D(θ), characteristics, where θ denotes lapsed time, ambient pressure and local ambient gas concentration within the elastomers. The numerical procedures adopted to perform the fitting of the experimental data with various D(θ) characteristics are described and the quality of the fit is assessed. The D(θ) characteristics chosen have no particular physical basis but follow established empirical precedents. The characteristics of the parameters associated with the various D(θ) functions generally indicate that as the gas is embibed with progressively increasing ambient pressures the diffusion coefficient increases. At high pressures the diffusion is arrested and the coefficient decreases. We have associated the initial increase with gas induced plasticization and the eventual decreases with the effect of the hydrostatic component of the ambient gas pressure. The parameter fitting also indicates that the diffusion is arrested with lapsed time which is tentatively associated with time dependent volumetric relaxations. These interpretations apart, the data and analyses clearly indicate that the transport is not simply fickian and a relatively complex parametric function to describe the sensitivity of the diffusion coefficient to time, concentration and pressure is necessary for these systems.

Diffusion of tin implanted in aluminium

Abstract The temperature and pressure dependence of diffusion of Sn113 implanted in high-purity aluminium single crystals has been investigated by means of the serial-sectioning technique. It was found that tin is a fast diffusing solute in A1. The temperature dependence of the process in the temperature range 649–906 K can be described by The activation volume of diffusion was found to be 0·87 ± 0·01 in atomic volume units at 787·5 K.

Electromigration of fast diffusers in lead

The so-called “fast diffuser” systems consist of dilute solutions of rather insoluble impurities in multivalent metals with broad, relatively undistorted electron bands, such as lead, tin and indium. The impurities include the noble metals and some divalent and transition elements. The initial investigations in this field were performed largely by Turnbull and coworkers [ 11. The pressure dependence of diffusion in these systems has been explored by Decker and colleagues [2]. The rapid diffusivities and small degree of solvent diffusion enhancement suggested at first a simple interstitial mechanism but the simultaneous diffusion of multiple isotopes of the same impurity [3] showed isotope effect coefficient, consistent with a highly cooperative mechanism. Electromigration is the name applied to mass transport caused by high electric currents in media where charge transport is electronic rather than ionic. The strength of the electromigration drive is customarily measured by the dimensionless parameter Z” . It is defined as the number of electron charges the moving entity would have to be subject to a purely electrostatic force in the presence of an electric field equal to the electromigration drive. It is found that the values for Z* vary from a few tenths to possibly a 100 for the electromigration of metal alloys. It appeared that the study of this phenomenon in the fast diffusers might shed additional light on the nature of the mechanism responsible for their high mobility. In addi-

Pressure Dependence of Diffusion in Polymers

The pressure dependence of diffusion of vapors In polymer films arises not only from the concentration dependence of the diffusion coefficient, D, but also because D can vary with the mean pressure within the film. For sufficiently large organic molecule vapors for which a free volume theory of diffusion is applicable one expects that this latter pressure dependence can be obtained also from the pressure dependence of the free volume of the polymer-vapor system.