Concentration-independent Diffusion Research Articles

Fickian Diffusion Equation—an Unsolved Problem

Two forms of diffusion equation are discussed: (1) the conventional Fick’s law with concentration-independent diffusion coefficient and (2) the flux as proportional to the chemical potential gradient with the proportional constant independent of concentration (which is, in most cases, equivalent to the application of Fick’s law with a diffusion coefficient inversely proportional to concentration). It is shown that appropriate empirical form of the resistant forces could validate both forms thermodynamically. It is concluded that the ideal form of diffusion equation is absent. It is also shown that the second form of the flux equation might describe the self-diffusion flux better.

Application of the dual‐mode model for predicting competitive sorption equilibria and rates of polycyclic aromatic hydrocarbons in estuarine sediment suspensions

We investigated competitive sorption and desorption of phenanthrene, anthracene, and pyrene added to an estuarine sediment from Guilford (CT, USA) on Long Island Sound. The reduction in the equilibrium uptake of a primary solute in the presence of one or both cosolutes was well predicted over the entire isotherm by the dual-mode model, which postulates dissolution and hole-filling domains in sediment organic matter. Isotherms obtained in binary or ternary solute systems were suppressed, and the shapes were more linear than the corresponding single-solute isotherms. In the limit of infinite dilution of the single solute, sorption in the hole-filling domain is a factor of 1.4 to 1.9 times more favorable than sorption in the dissolution domain. A competitive dual-mode radial diffusion model was applied to the batch uptake and sequential-batch desorption rate data. The model captures the uptake and release curves well. The competitive effect slightly accelerates sorption, as predicted. The competitive effect accelerates desorption, but from the existing data it was not possible to decide how much was due to favorable thermodynamic versus favorable kinetic effects. The concentration-independent diffusion rate parameter corresponding to the dissolution domain was approximately the same for sorption and desorption (0.02/h), and little or no sorption hysteresis was observed.

Multilayer TiN/Ti films for high-temperature annealing of GaAs

Gallium arsenide wafers were encapsulated with multilayer films consisting of TiN and Ti layers using an ion beam-assisted deposition technique employing an electron beam evaporator for Ti evaporation and a microwave ion source for ionizing nitrogen gas. The encapsulated GaAs surfaces were heated to 1000 °C and held at that temperature for 15 min. The GaAs surfaces had a desirable surface morphology when covered with a TiN/Ti-rich TiN/TiN multilayer film. A small fraction of the S atom population implanted in the GaAs diffused into the encapsulant during annealing at 1000 °C, while S atoms remained in the GaAs was electrically active. The redistribution profile of S atoms for S-doped GaAs annealed with the desirable composite film of TiN/Ti-rich TiN/TiN is well approximated by a Gaussian distribution function with a concentration-independent diffusion constant.

Effect of electro-chemical properties of chloride salts on their diffusional parameters in symmetrical cellulose acetate membranes

A relation was obtained between electro-chemical properties of alkali, alkali earth and aluminium chlorides (LiCl, NaCl, KCl, RbCl, CsCl, MgCl 2, CaCl 2, AlCl 3) and the distribution coefficient K and the overall diffusion coefficients D in symmetrical cellulose acetate membranes. Symmetrical cellulose acetate membranes were cast to have a wider range of water content, 15–30%. K and D were measured by the unsteady- and steady-state dialysis method. The K values increased with the increase of water content and in the increasing order of CaCl 2, MgCl 2, AlCl 3, LiCl, KCl, NaCl, RbCl and CsCl, and are in the range of 10 −2 for alkali chlorides, 10 −5-10 −4 for alkali earth chlorides, and 10 −4 for AlCl 3. D was found to increase with the increase of the solute concentration, and the extrapolated values of D to zero concentration D (0) were obtained as 0.01-0.1 μm 2/s for membranes cast from a dense dope solution and 0.1–0.4 μm 2/s for thin membranes. D (0) increases with the increase of water content in the membrane and in the order of NaCl, LiCl, MgCl 2, RbCl, CaCl 2, CsCl, KCl and AlCl 3 for dense membranes and NaCl, RbCl, CsCl, KCl and LiCl for thin membranes. D can be divided into the concentration independent diffusion coefficients in the dense part ( D d ), and in the porous ( D p ), applying a two-part (perfect or dense and imperfect or porous) model of the membrane. D d does not depend on the water content in the membrane ( W W ) but on dope composition. Contrary to D d , D p increases with the increase of W W and can be correlated as D p,c = D d exp (γ × W W ). It is shown that the averaged D d , D d increased almost linearly with the increase of the product of valence times ionic mobility u o of the solutes at infinite dilution, and that the parameter γ increased with the increase of Stokes radius of ion r Stokes. The value of K increased slightly with the increase of water content and decreased with the increase of the Flory—Huggics parameter χ, which is calculated from the measured values of distribution coefficients and data from the literature. It was also found that the gradient of linear decrease of χ (λ cation) and of linear increase of χ (λ anion) depend on equivalent ionic conductivity of anion and cation of salt, λ an and λ cat, respectively. It seems possible to predict permeability for some specific solute through a membrane from measured diffusional values such as D (0) and K for NaCl or some standard solute.

Effect of electro-chemical properties of chloride salts on their diffusional parameters in symmetrical cellulose acetate membranes

A relation was obtained between electro-chemical properties of alkali, alkali-earth and aluminium-chlorides (LiCl, NaCl, KCl, RbCl, CsCl, MgCl 2, CaCl 2, AlCl 3) and the distribution coefficient K and the overall diffusion coefficients D in symmetrical cellulose acetate membranes. Symmetrical cellulose acetate membranes was cast to have a wider range of water content, 15–30%. K and D were measured by the unsteady- and steady-state dialysis method. The K values increase with the increase of water content and in the increasing order of CaCl 2, MgCl 2, AlCl 3, LiCl, KCl, NaCl, RbCl and CsCl, and are in the range of 10 −2 for alkali chlorides, 10 −5-10 −4 for alkali earth chlorides, and 10 −4 for AlCl 3. D was found to increase with the increase of the solute concentration and the extrapolated values of D to zero concentration D (0) were obtained as 0.01–0.1 μm 2/s for membranes cast from a dense dope solution and 0.1–0.4 μm 2/s for membranes from a thin one. D (0) increases with the increase of water content in the membrane and in the order of NaCl, LiCl, MgCl 2, RbCl, CaCl 2, CsCl, KCl and AlCl 3 for membranes from dense and NaCl, RbCl, CsCl, KCl and LiCl for membranes from thin. D can be divided into the concentration independent diffusion coefficients in the dense part D d and in the porous D p , applying a two-part (perfect or dense and imperfect or porous) model of the membrane. D d does not depend on the water content in the membrane W w , but on dope composition. Contrary to D d , D p increases with the increase of W w and can be correlated as D p,c = D̄ind exp (γ × W w ). It is shown that the averaged D d , D̄ind increases almost linearly with the increase of the product of valence times ionic mobility u° of the solutes at infinite dilution, and that the parameter γ increases with the increase of Stokes radius of ion r Stokes. The value of K increases slightly with the increase of water content and decreases with the increase of the Flory—Huggins parameter χ. The Flory—Huggins parameter χ is calculated from the measured values of distribution coefficients and data offered from literatures. It was found that the gradient of linear decrease of χ (λ cat) and of linear increase of χ (λ an) depends on equivalent ionic conductivity of anion and cation of salt, λ an and λ cat, respectively. It seems possible to predict permeability for some specific solute through a membrane from measured diffusional values such as D (0) and K for NaCl or some standard solute.

Effect of electro-chemical properties of sodium salts of various anions on their diffusional parameters in symmetrical cellulose acetate membranes

A relation was obtained between electro-chemical properties of sodium salts (NaCl, NaBr, and Na 2SO 4), and the thermodynamic property of permeability in symmetrical cellulose acetate membranes, the distribution coefficient K and the kinetic property, the overall diffusion coefficients D. K and D were obtained by the method we proposed using measured unsteady- and steady-state dialysis data. The K values increase with the increase of water content and are in the range of 10 −2 for sodium halides and 10 −3 for Na 2SO 4. D is found to increase with the increase of the solute concentration, and the extrapolated values of D to zero concentration D (0) are obtained as 0.015–0.03 μm 2/s and increase with the increase of water content in the membrane. D can be divided into the concentration independent diffusion coefficients in the dense part of the membrane D d and in the porous D p , applying a two-part (perfect or dense and imperfect or porous) model of the membrane. Contrary to D d , D p increases with the increase of W w and can be correlated as D p,c = D d exp (γ × W w ). It is shown that the averaged D d , D D increases with the increase of the quantity of the ionic mobility u∘ of the solutes at infinite dilution divided by valence, and that the parameter γ increases with the increase of the ionic mobility u∘. The value of K increases slightly with the increase of water content and decreases with the increase of the Flory—Huggins parameter χ. The Flory—Huggins parameter χ is calculated from the measured values of distribution coefficients and data obtained from the literature. And it was found that the gradient of linear decrease of χ (λ cation) depends on equivalent ionic conductivity of anion of salt, λ an.

Trace element diffusion in andesitic melts: an application of synchrotron X-ray fluorescence analysis

—We have investigated the diffusivity of trace elements in hydrous iron-free andesitic melts containing 4.5 to 5.2 wt.% water at a pressure of 500 MPa and at temperatures between 1100 and 1400°C using the diffusion couple technique. The studied elements can be combined in several groups of particular geochemical interest: low field strength elements (LFSE: Rb, Sr, Ba), transition elements (Cr, Fe, Ni, Zn), rare earth elements (REE: La, Nd, Sm, Eu, Gd, Er, Yb, Y), and high field strength elements (HFSE: Zr, Nb, Hf). The diffusion profiles of the trace elements were measured using the synchrotron X-ray fluorescence (SYXRF) microprobe. H 2O distribution in the samples was analyzed by IR microspectroscopy. Diffusion profiles are excellently reproduced, assuming concentration-independent diffusion coefficients. For all trace elements, the temperature dependence of diffusion in the hydrous melt can be described by a simple Arrhenius law. In general, the diffusivity decreases from the LFSE, to transition elements, to REE, and to the HFSE, a trend that can be correlated to the increase of charge in the same order. The activation energy shows a similar trend, increasing from 129 kJ/mol for Rb to 189 kJ/mol for Zr. For the transition elements Cr and Fe, the activation energy is relatively high (228 and 193 kJ/mol, respectively), which can be explained by increasing contributions of divalent cations to the diffusion flux with increasing temperature. Higher diffusivity of Eu compared to its neighbor elements also is attributed to contributions of divalent cations. Modeling Eu-diffusivity using data of Sr as representative for Eu 2+, and of Sm and Gd as representative for Eu 3+, shows that at all temperatures Eu 3+ is clearly dominating in the hydrous melt. To quantify the effect of water, an additional experiment was performed at 1400°C using a nominally anhydrous melt. The obtained diffusion coefficients are (for most of the elements) by one and a half orders of magnitude lower than for a melt containing 4.5 wt.% H 2O. Chemical diffusion coefficients D η, which were calculated from the viscosity data of Richet et al. (1996) using the Eyring equation, and which assumed a jump distance of 3 Å, are in excellent agreement with the diffusivity of the HFSE for both dry and hydrous melt. Most of the investigated elements show a linear relation between log diffusivity and log viscosity, enabling the prediction of diffusivities in hydrous andesite systems at various conditions. Provided viscosity data are available, we suggest that this relation can be a useful tool to estimate trace element diffusivities for silicate melts with different compositions. The new diffusion data show that water strongly enhances diffusivity of trace elements in andesitic melts. After 10,000 yr at 1200°C, diffusion produces in the dry melt relatively short profiles with lengths (defined as x=( Dt) 1/2) between 0.8 and 0.07 m (for Sr and Zr, respectively), whereas in hydrous melts (5 wt.% water), profiles are much longer with lengths between 3.9 and 0.92 m (for Sr and Zr, respectively).

Mathematical Modeling of the Pervaporative Separation of Methanol−Methylterbutyl Ether Mixtures

This work reports the kinetic modeling of the pervaporative separation of methanol−MTBE mixtures. Using a commercial membrane, Pervap 2256, that presented high selectivity toward methanol permeation, the influence of the operating variables feed composition in the range 1−20 wt % MeOH, feed temperature between 30 and 50 °C, and permeate pressure between 1 and 20 mmHg on the pervaporation flux was experimentally analyzed in a laboratory setup working under pseudo-steady-state conditions. A mathematical model based on the generalized Fick's law and the assumption that transport through the membrane is the rate-limiting step was developed in order to describe the PV flux of both components. The prediction of the flux of methanol needed of a concentration-dependent diffusion coefficient, whereas a simple model with concentration-independent diffusivity was sufficient for the description of the MTBE flux. Finally, the influence of the temperature on the partial fluxes was described through an Arrhenius-type ex...

Identification of vacancy charge states in diffusion of arsenic in germanium

Diffusion of As into Ge from a GaAs overlayer deposited on p-type Ge substrates has been studied by means of secondary ion mass spectrometry. A concentration-dependent diffusion of As atoms was observed in addition to the concentration-independent diffusion of Ga and As atoms. The concentration dependence is explained by a Fermi-level-dependent diffusion model. Arsenic atoms are shown to diffuse through Ge vacancies with the charge states 2− and 0. No presence of the singly negatively charged vacancies was observed, indicating that Ge vacancy could be a negative U center.

Diffusional characteristics of sodium chloride in symmetrical cellulose acetate membranes measured by an unsteady-state dialysis method

Unsteady-state dialysis and steady-state reverse osmosis (RO) experiments for aqueous NaCl solutions were carried out with cellulose acetate (CA) symmetrical membranes. The distribution and overall diffusion coefficients of NaCl, K and D were obtained from the unsteady-state dialysis experimental data, taking the effect of osmosis into consideration. D was found to increase with the increase of the solute concentration. The concentration dependency of D can be explained by applying a two-part (perfect or dense and imperfect or porous) model of the membrane. The concentration independent diffusion coefficients of NaCl in the dense part D d and in the porous D p are obtained from the assumption of the two-part model for the membrane. D d does not depend on the water content in the membrane W w , but on dope composition. Contrary to D d , D p increases with the increase of W w and can be correlated only with W w and D p ( W w =0) is found almost equal to the averaged D d for each type of membrane: D p,c = D d exp ( γ × W w ). It seems from these facts that the structure of membrane becomes tight with the decrease of the ratio of formamide to CA and loose with the decrease the concentration of CA in dope solutions. D c(c = 0) at the zero concentration can be calculated as follows: D c (0) ≈ W w D p,c + (1−W w) D d . Solute permeability ω obtained by RO experiments agrees well with ω c = [K · D c (0)] (ℓ · β) , those calculated from D c (0) and distribution coefficient K.

Praseodymium-doped Ti:LiNbO 3 waveguides

by diffusion doping is investigated by means of secondary neutral mass spectrometry and secondary ion mass spectrometry. The diffusion of praseodymium in LiNbO3 can be described by Fick’s laws of diffusion with a concentration-independent diffusion coefficient and a limited solubility of praseodymium in LiNbO3 increasing exponentially with rising temperature. The diffusion depends on the Li2O content of the LiNbO3 crystal. For LiNbO3 crystals with a nominal slight difference in the congruent composition, the diffusion constants and activation energies for Z-cut LiNbO3 are 3.28×10-5 cm2/s and 2.27 eV, and 1.39×10-5 cm2/s and 2.24 eV, respectively. Titanium-doped waveguides are formed in Pr:LiNbO3 and characterised in relation to waveguide loss and absorption in the visible and near infrared.

Non-metal diffusion coefficients for the Ta–C and Ta–N systems

The diffusivity of carbon in tantalum and tantalum carbides was investigated in the temperature range 1700°C–2200°C, and that of nitrogen in tantalum and tantalum nitrides between 1700°C and 1950°C. The concentration-independent diffusion coefficients were obtained in all phases by investigating the enhanced layer growth in wedge-shaped specimens. In the nonmetal-rich phases having a broad homogeneity range, i.e. in δ-TaC 1− x , β-Ta 2C 1− x and β-Ta 2N 1− x , also the concentration-dependent diffusion coefficients were calculated and compared with the concentration-independent diffusion coefficients. The calculation of the concentration-dependent diffusion coefficients was performed by fitting a modified error function on the measured concentration profiles assuming the nonmetal diffusivity being an exponential function of the nonmetal concentration. Strong dependence of the diffusion coefficient on the nonmetal concentration was found for the δ-TaC 1− x phase, whereas the nonmetal diffusion coefficients were nearly concentration-independent for β-Ta 2C 1− x and β-Ta 2N 1− x .

Combined refinement of diffusion coefficients applied on the Nb-C and Nb-N systems

A novel technique was used for the calculation of diffusion coefficients in the niobium carbides and nitrides prepared by reaction diffusion. The temperature ranges investigated were 1500 °C to 2100 °C for the Nb-C system and 1400 °C to 1800 °C for the Nb-N system. Three independent theoretical approaches were applied and their results are compared. In the metalloid-rich phases, the concentration-dependent diffusion coefficients were calculated from the concentration profiles; two models of layer growth were used to obtain the concentration-independent diffusion coefficients in all phases. It was found that the diffusion coefficient of carbon in δ-NbC1−x shows a decrease with increasing metalloid concentration, whereas the diffusivity of nitrogen in δ-NbN1−x is nearly independent of the nonmetal concentration. The concentration dependence of the carbon diffusion coefficients in δ-NbC1−x is a result of a lower activation energy of carbon diffusion in the substoichiometric δ-NbC1−x than in the δ-NbC. On the contrary, the activation energy of nitrogen in δ-NbN1−x does not change with the nitrogen concentration. This behavior could be explained by the different occupancies of metal sublattices, which remain constant in δ-NbC1−x but decrease with increasing nonmetal concentration in δ-NbN1−x.

Concentration dependent and independent Si diffusion in ion-implanted GaAs

The diffusion of silicon has been studied in $〈100〉$ GaAs implanted with $1\ifmmode\times\else\texttimes\fi{}{10}^{16}$ 40-keV ${}^{30}$Si${}^{+}$ ${\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}/\mathrm{c}\mathrm{m}}^{2}$. The Si concentration profiles were measured by secondary-ion mass spectrometry and nuclear resonance broadening techniques and the defect distributions by the Rutherford backscattering spectrometry channeling technique. The implanted samples were subjected to annealing in argon atmosphere in the temperature range 650 $\ifmmode^\circ\else\textdegree\fi{}$C--850 $\ifmmode^\circ\else\textdegree\fi{}$C. Two independent silicon diffusion mechanisms were observed. Concentration independent diffusion, observed as a broadening of the initial implanted distribution, is very slow and is assigned to Si atoms diffusing interstitially. Concentration dependent diffusion with low solubility and extending deep into the sample is quantitatively explained by diffusion via vacancies of Si atoms in the Ga and As sublattices. Diffusion coefficients together with carrier concentration as a function of Si concentration are given at different temperatures. The solid solubility of Si in GaAs has been determined and an exponential temperature dependence observed. An estimate of the amount of Si atoms residing on either Ga or As sites and the amount of ${\mathrm{Si}}_{\mathrm{Ga}}^{+}{\ensuremath{-}\mathrm{S}\mathrm{i}}_{\mathrm{As}}^{\ensuremath{-}}$ pairs is given. Finally, a fast method is presented for solving the diffusion equation numerically.

Effects of mechanical and chemical properties on transport in fluoropolymers. I. Transient sorption

This is the first part of a study of chemical structure-physical property-performance relationships among several fluoropolymers and liquid penetrants, focusing on their diffusivities and solubilities. Transient sorption experiments conducted with perfluoroalkoxy, fluorinated ethylene propylene, and ethylene tetrafluoroethylene exhibited Fickian diffusion. The first two exhibited concentration-independent diffusivity, while the last displayed concentration-dependent diffusivity. Conversely, polyvinylidene fluoride (PVDF) and ethylene chlorotrifluoroethylene (ECTFE) exhibited non-Fickian behavior, including acceleration as saturation approached. Suspected causes for the unusual sorption behavior were structural characteristics due to processing (e.g., skin or orientation with respect to processing direction), intrinsic chemical structure, and morphological deformation induced by swelling. Stress-strain tests indicated that mechanical properties depend similarly on the presence of penetrants to transport properties. Weak swelling agents exhibited Fickian transport and a negligible change of mechanical properties. In contrast, strong swelling agents induced non-Fickian diffusion and caused significant changes of mechanical properties. A new kinetic model fit the transient sorption results, particularly the observed acceleration in PVDF and ECTFE. The model accounts for structural changes due to swelling and relaxation resulting from free-volume creation, which is assumed to be proportional to the amount of liquid sorbed. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 455–476, 1997

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.

Effect of multiple occupancy upon the diffusivity in zeolites

The traditional hopping model of diffusion in zeolites predicts a concentration-independent diffusivity D, whereas observations almost always yield D(θ) increasing strongly with increasing average occupancy θ of the adsorption sites. An explanation is attempted in terms of a model allowing double occupancy of adsorption wells or “cages.” It is assumed that the repulsion between molecules adsorbed in one well lifts its bottom, whereas the level of the “windows” between wells remains unchanged. The potential barrier from well to window is thereby lowered so that jumps become more frequent at higher density, when double occupancy is more probable. The resulting expression for D(θ) is compared with the main features of existing experimental curves. Although it is possible to fit the observed low density behavior of D(θ), the model is not able to reproduce the steep approach toward saturation.

Effect of Ion Energy on the Diffusion of Si Implanted into GaAs

The diffusion of Si was studied using secondary ion mass spectroscopy and transmission electron microscopy after implantation into at energies ranging from 20 to 200 keV and at doses ranging from followed by furnace annealing. Little or no diffusion occurred in the higher energy implants (>100 keV) while, in general, samples implanted at lower energies (<100 keV) exhibited appreciable dopant redistribution, regardless of peak implant concentration. Both concentration dependent and concentration independent diffusion was observed. Dislocation loop density varied inversely with the amount of diffusion as a function of implant energy. The Monte Carlo computer program TRIM is able to predict the trends of the implant energy dependence of the diffusion by considering the excess point defect dose produced upon implantation. The influence of this excess defect dose together with surface effects on the diffusion of Si is shown to be consistent with a vacancy assisted Si diffusion mechanism.

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.

Experimental dehydration of natural obsidian and estimation of DH2O at low water contents

Water diffusion experiments were carried out by dehydrating rhyolitic obsidian from Valles Caldera (New Mexico, USA) at 510–980°C. The starting glass wafers contained ~0.114 wt% total water, lower than any glasses previously investigated for water diffusion. Weight loss due to dehydration was measured as a function of experiment duration, which permits determination of mean bulk water diffusivity, D w . These diffusivities are in the range of 2.6 to 18 × 10 −14 m 2/s and can be fit with the following Arrhenius equation: In D w ( m 2/s ) = −(25.10 ± 1.29) − (46,480 ± 11,400) ( J/mol)/RT , except for two replicate runs at 510°C which give D w values much lower than that defined by the above equation. When interpreted according to a model of water speciation in which molecular H 2O is the diffusing species with concentration-independent diffusivity while OH units do not contribute to the transport but react to provide H 2O, the data (except for the 510°C data) are in agreement with extrapolation from previous results and hence extend the previous data base and provide a test of the applicability of the model to very low water contents. Mean bulk water diffusivities are about two orders of magnitude less than molecular H 2O diffusivities because the fraction of molecular H 2O out of total water is very small at 0.114 wt% total water and less. The 510°C experimental results can be interpreted as due to slow kinetics of OH to H 2O interconversion at low temperature.