Concentration-independent Diffusion Coefficients Research Articles

Erbium incorporation in LiNbO 3 by diffusion-doping

The erbium incorporation into LiNbO3 by diffusion doping is investigated in detail by means of Secondary Ion Mass Spectrometry, Secondary Neutral Mass Spectrometry, Rutherford Backscattering, Atomic Force Microscopy, X-ray Standing Wave technique and optical site-selective spectroscopy. The diffusion of erbium in LiNbO3 can be described by Fick’s laws of diffusion with a concentration-independent diffusion coefficient. The diffusion constants and activation energies for Z-cut (X-cut) LiNbO3 are 4.8×10-5 cm2/s (12.0×10-5 cm2/s) and 2.28 eV (2.44 eV), respectively. A limited solubility of erbium in LiNbO3 has to be taken into account increasing exponentially with rising temperature. During the first step of diffusion an Er x Nb y -oxide layer is formed at the surface of the sample acting as diffusion reservoir. Erbium is incorporated into LiNbO3 on vacant Li-sites slightly shifted from the original Li-position along the (-c)-direction. Site-selective spectroscopy found four distinguishable energetically different erbium centres at this lattice site resulting from locally different symmetries of the crystal field.

Differential permeation ? Part I: A method for the study of solvent diffusion through membranes

We describe the differential permeation method for the study of the diffusion of solvents from a liquid (or liquid mixture) through flat or tubular membranes. This method consists of measuring the transient permeation rates through the membrane when one of its faces is suddenly put into contact with the liquid medium. The change in the transient rate with time is analyzed by numerical best fitting methods to determine the Fickian diffusion coefficient. A simplified equation is proposed for the fitting of the response of a tubular membrane. Deviations from the Fickian transport mechanism with concentration-independent diffusion coefficient can be evidenced and eventually analyzed by using other mechanistic models.

Diffusion kinetics of Si in GaAs and related defect chemistry

The diffusion of Si in GaAs was investigated using diffusion sources from different tie triangle regions on the Si-Ga-As ternary phase diagram which provide constant chemical potentials for the three components under isothermal conditions. The Si profiles are measured with secondary ion mass spectrometry and differ significantly for the different sources. The Ga-Si-GaAs tie triangle source produces p-type Si doping with concentration independent diffusion coefficients, and a neutral As or Ga vacancy is proposed as the dominant mobile defect for these conditions. Arsenic-rich sources from two tie triangle regions and also a Si-GaAs tie line source produce Si donor diffusion with concentration-dependent diffusion behavior. The concentration-dependent diffusion coefficients of donor Si for As-rich source diffusion are related to the net ionized donor concentration showing three different regimes: intrinsic regime, intermediate regime, and saturation regime. Ga vacancies are proposed to be responsible for donor Si diffusion in GaAs: a V0Ga and/or V−Ga mechanism for the intrinsic regime; and a V−Ga related mechanism for the extrinsic and saturation regimes. The Si-GaAs tie line source resulted in two branch type profiles, intermediate between the As-rich and the Ga-rich source diffusion cases.

On the mechanism of separation of ethanol/water mixtures by pervaporation I. Calculations of concentration profiles

A solution—diffusion model for the permeation of liquid mixtures through polymeric membranes taking into account coupling of fluxes has been developed. The model is applied to the separation by pervaporation of ethanol—water mixtures through cellulose acetate. In order to determine the activities of the permeating components in the polymeric membrane, values of polymer—liquid and liquid—liquid interaction parameters are needed; polymer—liquid interaction parameters have been determined from swelling experiments and liquid—liquid interaction parameters have been calculated from excess free energy of mixing data taken from the literature. Concentration profiles of water and ethanol in cellulose acetate membranes have been calculated using (a) apparent concentration independent diffusion coefficients, and (b) diffusion coefficients with exponential concentration dependence and two adjustable parameters. It is discussed that the transport of ethanol—water mixtures by pervaporation cannot be explained by using concentration independent diffusion coefficients.

Solubility and diffusion of propane in blends of polystrene and poly(vinyl methyl ether) at T > Tg

The solubility and diffusion of propane in rubbery blends of polystyrene and poly(vinyl methyl ether) were investigated at low diffusant pressure. Solubibity is characterized by Henry's law and diffusion by Fick's law with concentration-independent diffusion coefficients. The composition dependence of the solubility and diffusion parameters is presented. The diffusion coefficients for propane in the blends are related to those for the component polymers by using the glass transitions as reference temperatures.

Mechanism of diffusion and sorption of carbon dioxide in poly(vinyl acetate) above and below the glass transition temperature

The pressure dependence below 1 atm of the apparent diffusion and permeation coefficients were observed by using the permeation time lag method for carbon dioxide in poly(vinyl acetate), which has a glass transition near room temperature, at temperatures ranging from 8 to 50°C. Above the glass transition temperature, pressure dependence of the diffusion and permeation coefficient has not been observed; hence, Fick's law with a concentration independent diffusion coefficient applies. On the other hand, in the glassy state, the apparent diffusion coefficient shows pressure dependence. Moreover, the behavior of the pressure dependence does not show a clear curve in the ranges between 30°C to 17°C. Above 17°C, the apparent diffusion coefficients show discontinuities, but below 17°C increase with pressure is regular. Using the theoretical prediction of Paul, a computer was used in the numerical calculation to determine the true diffusion coefficient and other dual sorption parameters. p]The compensated diffusion coefficients controlled only by Henry's law dissolution was described by three straight lines with two intersection in the form of Arrhenius plots, which give good agreement with both our results for He and Ar and those of Meares. It is assumed that beside the dual sorption mechanism, another effect, for instance some relaxation effect may also contribute to the diffusion for carbon dioxide in poly(vinyl acetate) near the glass transition temperature region.

Selective permeation of hydrocarbon gases in poly(tetrafluoroethylene) and poly(fluoroethylene–propylene) copolymer

AbstractThe permeabilities and diffusivities of methane, ethane, propane, n‐butane, and isobutane in commercially available poly(tetrafluoroethylene) (TFE) and poly(fluoroethylene–propylene) (FEP) Teflon have been measured in a Pasternak‐type permeation cell. Experiments were carried out at upstream hydrocarbon partial pressures up to 50 torr (1000–60,000 ppm gas phase concentration) and temperatures from 40 to 195°C with films of 0.0508 and 0.127 mm thickness using nitrogen as carrier gas on the upstream and downstream sides of the membrane. The transient and steady‐state permeation data are described well by a combination of Henry's law and Fick's law with a concentration‐independent diffusion coefficient. Linear Arrhenius plots of both permeabilities and diffusivities were obtained. Linear correlations were found both between the activation energy for diffusion and the square of the gas molecule diameter, and between the logarithm of solubility at 90°C and the penetrant boiling point. Separation factors for binary mixtures of hydrocarbons were measured for TFE at 140°C and found to be similar to those predicted by individual permeabilities in most cases. Measurements with mixed gases were not made for FEP Teflon, but selectivities of FEP are expected to be similarly well described by the ratios of the pure gas permeabilities at the low partial pressures studied. The effect of annealing FEP Teflon for 24 hr at 200°C was found to produce an average of 20–30% reduction in solubility as well as a 9% increase in the activation energy for diffusion compared to as‐received films. These effects are believed to be due to increased crystallinity in the sample upon annealing.

Differential equation for transport along parallel linear successions of identical symmetrical potential barriers

The differential equation for transport of non-interacting species along parallel paths, each consisting of a linear succession of identical symmetrical potential barriers, is expanded as an infinite series in the derivatives of the electrostatic potential and concentration. The first order expression is shown to represent the model adequately for all but extremely high space charge concentrations and/or extreme departures from steady-state conditions. Under the appropriate limiting conditions it reduces to the well-known linear transport equation, and to the Mott–Cabrera equation, but extends these to higher concentrations since the formulation forbids hops into occupied sites. The treatment leads to a concentration independent diffusion coefficient, but to a concentration dependent mobility.

Diffusion of 45Ca in bovine enamel.

The penetration of 45Ca ions into whole bovine enamel from an aqueous solution was studied as a function of the Ca content in the solution. A sectioning technique was employed to measure the penetration of 45Ca into the enamel. Probably only Ca ions occupying surface positions in the hydroxyapatite crystallites participate in the exchange process at the solution-enamel interface. The fraction of Ca ions participating in the exchange was 2% of the total number of Ca ions. Two different diffusion processes occur; firstly, a process governed by a diffusion coefficient, D1 ranging from about 5 x 10(-14) to 2 x 10(-12) cm2/s and strongly dependent on the calcium concentration in the solutions; and secondly a process with a concentration-independent diffusion coefficient, D2, with a value of 2.8 x 10(-12) cm2/s. It is assumed that the 2 diffusion types correspond to intra- and interprismatic transport, respectively. A model based on the pore structure of dental enamel and on surface charges on hydroxyapatite crystallites is discussed.

Interdiffusion of hydrogen and alkali ions in a glass surface

Experimental data on the interdiffusion of hydrogen and alkali ions in glass are examined using a concentration-dependent interdiffusion coefficient, taking into account surface dissolution. The comparisons between calculated and experimental concentration profiles and diffusion coefficients are more satisfactory than for a concentration-independent diffusion coefficient, and support the use of the interdiffusion coefficient.

A Study of the Diffusion of Oxygen in Alpha‐Zirconium by Means of Nuclear Microanalysis

Polycrystalline zirconium samples were oxidized in pure oxygen under atmospheric pressure at temperatures ranging from 700° to 845°C and for times up to 400 hr. The diffusion of oxygen in the metal, beneath the oxide layer formed, was studied using a direct quantitative method of analysis based on the observation of the nuclear reaction . It was found that at a given temperature the oxygen concentration profiles, referred to the oxidemetal interface, may be superimposed after scaling by a factor . The results may be fitted assuming a concentration independent diffusion coefficient , the oxygen concentration at the oxide‐metal interface being constant and nearly equal to the saturation value, around 30 atom per cent. An activation energy was found for the process. Identical results were obtained in air, showing that, at atmospheric pressure, nitrogen in the air plays a negligible role in the dry corrosion of zirconium.

Homogenization of compacted blends of nickel and tungsten powders

The diffusional homogenization of compacted blends of elemental Ni and W powders was studied using quantitative metallography and X-ray compositional line broadening. Homogenization treatments were carried out in the temperature range from 1156 to 1271°C (in the region of the Ni-W phase diagram where only the terminal solid solutions exist). The mean compositions of the compacts studied ranged from 0.06 to 0.14 atomic fraction tungsten (in the Ni-rich solid solution). Other variables studied included the size and shape of the W particles, compaction pressure, and the effect of applied load during the homogenization treatment. Experimental measurements of the solution of the unstable W-rich phase and the increase in W concentration in the Ni-rich matrix were compared to calculated values obtained from a concentric-sphere mathematical model which assumed volume interdiffusion (concentration-independent diffusion coefficients) and local equilibrium at the heterophase interface. The model provided a fairly good approximation of the homogenization kinetics and the effects of the major processing and powder parameters investigated. The primary sources of discrepancy between model predictions and experimental data appeared to result from modest surface diffusion contributions to homogenization and imperfect powder blending.

Diffusion of 51Cr in NiO Single Crystals

The diffusion of 51Cr into single crystals has been investigated as a function of temperature in the region 1100°°1250°C and under oxygen partial pressures from one to 10−4 atm. At high chromium concentrations the diffusion is concentration dependent, probably as a result of self‐doping by the trivalent chromium cations. At 1 atm of oxygen the concentration independent diffusion coefficients can be represented by . At 1150° and 1250°C chromium diffusivities decrease with decreasing oxygen partial pressure.