D0 Exp Research Articles

Pressure dependence of Si diffusion in γ-Fe

Abstract The pressure dependence of Si diffusion in γ-Fe was investigated at pressures of 5–15 GPa and temperatures of 1473–1673 K using the Kawai-type multi-anvil apparatus to estimate the rate of mass transportation for the chemical homogenization of the Earth's inner core and those of small terrestrial planets and large satellites. The obtained diffusion coefficients D were fitted to the equation D = D0 exp[−(E* + PV*)/(RT)], where D0 is a constant, E* is the activation energy, P is the pressure, V* is the activation volume, R is the gas constant, and T is the absolute temperature. The least-squares analysis yielded D0 = 10-1.17±0.54 m2/s, E* = 336 ± 16 kJ/mol, and V* = 4.3 ± 0.2 cm3/mol. Moreover, the pressure and temperature dependences of diffusion coefficients of Si in γ-Fe can also be expressed well using homologous temperature scaling, which is expressed as D = D0exp{–g[Tm(P)]/T}, where g is a constant, Tm(P) is the melting temperature at pressure P, and D0 and g are 10-1.0±0.3 m2/s and 22.0 ± 0.7, respectively. The present study indicates that even for 1 billion years, the maximum diffusion length of Si under conditions in planetary and satellite cores is less than ∼1.2 km. Additionally, the estimated strain of plastic deformation in the Earth's inner core, caused by the Harper–Dorn creep, reaches more than 103 at a stress level of 103–104 Pa, although the inner core might be slightly deformed by other mechanisms. The chemical heterogeneity of the inner core can be reduced only via plastic deformation by the Harper–Dorn creep.

Atomistic Modeling of Sulfur Vacancy Diffusion Near Iron Pyrite Surfaces

Through density functional calculations, we investigated the diffusion of isolated sulfur vacancies (VS) from the bulk of iron pyrite (cubic FeS2) to the (100) and (111) surfaces. The influence of vacancy depth on the vacancy formation energy and the activation energy for vacancy diffusion are discussed. Significantly, we find that VS defects tend to migrate toward stoichiometric and sulfur-rich surfaces through sequential “intra-dimer” and “inter-dimer” hops. We find a pre-exponential constant (D0) of 9 × 10–7 m2 s–1 and an activation energy (E) of 1.95 eV for sulfur vacancy diffusion in bulk pyrite, corresponding to a vacancy diffusion coefficient DV = D0 exp(−E/kT) = 9 × 10–40 m2 s–1 at 25 °C and 5 × 10–18 m2 s–1 at 600 °C. The activation energy is smaller near the surface (e.g., E = 1.5 eV near the stoichiometric (100) surface), resulting in faster vacancy diffusion near the surface than in the bulk. Using the formation enthalpy of VS at the (100) surface, E = 2.37 eV, we find a sulfur diffusivity in bulk pyrite DS = 7 × 10–47 m2 s–1 at 25 °C and 2 × 10–20 m2 s–1 at 600 °C. The calculated DS values are in reasonable agreement with experiment only at intermediate temperatures (∼275–625 °C). Our results show that bulk and near-surface sulfur vacancies can be healed in sulfur-rich conditions at reasonably high temperatures. The mechanism of vacancy diffusion presented here should be useful in managing VS defects during the fabrication of high-quality pyrite samples for solar energy conversion applications.

Thermochemical behavior of nano-sized aluminum-coated nickel particles

Molecular dynamics simulations are performed to investigate the thermochemical behavior of aluminum-coated nickel particles in the size range of 4–13 nm, beyond which asymptotic behavior is observed. The atomic interactions are captured using an embedded atom model. Emphasis is placed on the particle melting behavior, diffusion characteristics, and inter-metallic reactions. Results are compared with the corresponding properties of nickel-coated nano-aluminum particles. Melting of the shell, which is a heterogeneous process beginning at the outer surface of the particle, is followed by diffusion of aluminum and nickel atoms and inter-metallic reactions. The ensuing chemical energy heats up the particle under adiabatic conditions. The alloying reactions progressively transform the core–shell structured particle into a homogeneous alloy. The melting temperature of the shell is weakly dependent on the core size, but increases significantly with increasing shell thickness, from 750 K at 1 nm to 1,000 K at 3 nm. The core melts at a temperature comparable to the melting point of a nascent particle, contrary to the phenomenon of superheating observed for nickel-coated aluminum particles. The melting temperature of the core decreases from 1,730 to 1,500 K, when its diameter decreases from 10 to 7 nm. For smaller cores, the majority of nickel atoms participate in reactions before melting. The diffusion coefficient of nickel atoms in aluminum shell exhibits a temperature dependence of the form D = D 0 exp(−E A/RT), with an activation energy of 43.65 kJ/mol and a pre-exponential factor of 1.77 × 10−7 m2/s. The adiabatic reaction temperature, also a size-dependent quantity, increases with increasing core diameter, attains a maximum value of 2,050 K at 5 nm, and decreases with further increase in the core diameter. The calculated values agree reasonably with those obtained via chemical equilibrium analysis. The burning time exhibits strong dependence of particle core size and shell thickness of the form τ b = a d c δ s , where the exponents n and m are 1.70 and 1.38, respectively. The finding further corroborates the fact that the reaction rate is controlled by diffusion process.

Effects of pressure and temperature on the silicon diffusivity of pyrope-rich garnet

We have determined the pressure and temperature dependencies of Si volume diffusion rates in a single crystal of Pyp75Alm15Gr10 garnet at 6–25GPa and 1400–1800°C by the 29Si tracer diffusion method. High-pressure experiments were conducted using the Kawai-type multi-anvil high-pressure apparatus. Diffusion profiles were obtained using secondary ion mass spectrometry in the depth-profiling mode. The Si diffusion coefficient in garnet (Dgt) is expressed by the Arrhenius equation: Dgt=D0 exp(−(E∗+PV∗)/RT), with log10D0=−7.1±1.7m2/s, E∗=345±56kJ/mol, and V∗=4.7±0.5cm3/mol. Si diffusion seems to be the slowest in the major constituent elements in a pyrope-rich garnet and control rates of plastic deformation. The comparison between Si diffusion rates in garnet and wadsleyite/ringwoodite suggests that garnet has similar or slightly lower strength (at most ∼2times) compared with wadsleyite, and has similar or slightly higher strength (at most ∼3times) compared with ringwoodite at temperatures ranging from 900 to 1300°C. Thus, strength contrast between subducted oceanic crust and underlying peridotite layer may be small at the mantle transition zone conditions. This result suggests that the separation of subducted oceanic crust from an underlying peridotite layer may not occur.

Interdiffusion of Earth's core materials to 65 GPa and 2200 K

Diffusion of iron and nickel in an Fe64Ni36 alloy was measured via the use of focused-ion-beam (FIB) milling and energy dispersive x-ray spectroscopy (EDX) to 65GPa and ∼2200K. The experiments were performed using a combination of micro-fabricated samples in the laser-heated diamond-anvil cell (DAC), increasing the pressure range for experimentally determined interdiffusion coefficients in FeNi alloys by >40GPa. Diffusivity in the iron–nickel system follows a homologous temperature relationship D=D0 exp(−19.3(2.7)Tm/T) where D0 is 4.6(7)×10−4m2s−1, with zero-pressure activation energy, 301(40)kJmol−1, consistent with measurements at lower pressures. At inner core conditions, this predicts an inner core solid-state diffusivity of 1×10−14m2s−1 (Tm/T=0.95), with an inner core viscosity of 1020–1022Pas assuming power-law creep (n=3) with a deviatoric stress of 103–104Pa.

Multicomponent diffusion in garnets I: general theoretical considerations and experimental data for Fe–Mg systems

We have carried out a combined theoretical and experimental study of multicomponent diffusion in garnets to address some unresolved issues and to better constrain the diffusion behavior of Fe and Mg in almandine–pyrope-rich garnets. We have (1) improved the convolution correction of concentration profiles measured using electron microprobes, (2) studied the effect of thermodynamic non-ideality on diffusion and (3) explored the use of a mathematical error minimization routine (the Nelder-Mead downhill simplex method) compared to the visual fitting of concentration profiles used in earlier studies. We conclude that incorporation of thermodynamic non-ideality alters the shapes of calculated profiles, resulting in better fits to measured shapes, but retrieved diffusion coefficients do not differ from those retrieved using ideal models by more than a factor of 1.2 for most natural garnet compositions. Diffusion coefficients retrieved using the two kinds of models differ only significantly for some unusual Mg–Mn–Ca-rich garnets. We found that when one of the diffusion coefficients becomes much faster or slower than the rest, or when the diffusion couple has a composition that is dominated by one component (>75 %), then profile shapes become insensitive to one or more tracer diffusion coefficients. Visual fitting and numerical fitting using the Nelder-Mead algorithm give identical results for idealized profile shapes, but for data with strong analytical noise or asymmetric profile shapes, visual fitting returns values closer to the known inputs. Finally, we have carried out four additional diffusion couple experiments (25–35 kbar, 1,260–1,400 °C) in a piston-cylinder apparatus using natural pyrope- and almandine-rich garnets. We have combined our results with a reanalysis of the profiles from Ganguly et al. (1998) using the tools developed in this work to obtain the following Arrhenius parameters in D = D0 exp{–[Q1bar + (P–1)ΔV+]/RT} for DMg* and DFe*: Mg: Q1bar = 228.3 ± 20.3 kJ/mol, D0 = 2.72 (±4.52) × 10−10 m2/s, Fe: Q1bar = 226.9 ± 18.6 kJ/mol, D0 = 1.64 (±2.54) × 10−10 m2/s. ΔV+ values were assumed to be the same as those obtained by Chakraborty and Ganguly (1992).

An integrated approach to optimizing skin delivery of cosmetic and pharmaceutical actives

The academic literature on skin delivery provides countless examples of scientific insights into specific aspects of the overall process. For the practical formulator, however, it is difficult to know how to combine such insights in a way that fits into the realities of commercial formulations. In this study, five key principles are combined into an integrated approach that can be applied to real-world formulations. Given the complexities of skin science, the integrated approach cannot be expected to be highly precise. Instead, it is intended as a way for a formulation team to balance the many conflicting issues. The predictions are sufficiently specific to be examined by those with the appropriate analytical resources and data on formulation efficacy. It is hoped that such challenges will allow the approach to be refined for the future.

Silicon and magnesium diffusion in a single crystal of MgSiO3perovskite

[1] Si and Mg self-diffusion coefficients were measured simultaneously in single crystals of MgSiO3 perovskite under lower mantle conditions. There is little difference in Si volume diffusivity measured directly using single crystals (this study) and those retrieved from experiments with polycrystals (earlier studies). This agreement between studies establishes the reliability of Si diffusion coefficients measured in perovskite. Within the uncertainties of our measurements, no anisotropy in the diffusion of either Si or Mg could be resolved. Diffusion of Si and Mg in perovskite are described by an Arrhenius equation, D = D0 exp (−ΔH/RT) at 25 GPa, with D0 = 5.10 × 10−11 m2/s for Si and 4.99 × 10−11 m2/s for Mg, ΔH = 308 kJ/mol for Si, and 305 kJ/mol for Mg. Mg diffusivity in MgSiO3 perovskite is distinctly lower than those measured in olivine, wadsleyite, and ringwoodite. We find that Mg has very similar diffusivity to Si in perovskite. As a consequence, the rheological properties of the lower mantle may be controlled by the coupled motion of Si and Mg. A point defect–based model is discussed that may account for the diffusion behavior of Si and Mg in MgSiO3 perovskite. Our data indicate that, within realistic ranges of temperature, grain size, and state of stress, both diffusion creep as well as dislocation creep may be observed in the lower mantle.

Applications of an energy‐dispersive pnCCD for X‐ray reflectivity: Investigation of interdiffusion in Fe–Pt multilayers

AbstractA frame store pn‐junction CCD (pnCCD) detector was applied to study thermally induced interdiffusion in Fe/Pt thin film multilayers (MLs) in a temperature range between 300 and 585 K. Based on the energy resolution of the detector the reflectivity was measured simultaneously in a spectral range between 8 keV < E < 20 keV including the Pt L‐edge energies close to 11.5 keV. Above T = 533 K we find a strong drop of intensities at 1st and 2nd order ML Bragg peak interpreted by mutual interdiffusion. Considering a simulated model of interdiffusion it has been found that the concentration of iron that diffuses into the platinum sub layers is higher than that of platinum into iron. The time dependence of inter diffusion was also calculated in the range of 533–568 K and was described by the Arrhenius equation D(T) = D0 exp(−Ha/kBT). The activation energy for the MLs used [Fe 1.7 nm/Pt 2 nm]50 was found to be 0.94 ± 0.22 eV.

Interdiffusion of polymers with glassy bulk

Mechanical properties developing at the contact zone of two samples of linear amorphous polymers with vitrified bulk have been employed to analyze the process of segmental diffusion of reptating chains across polymer–polymer interfaces. The diffusion coefficients (D) of this process have been estimated for polymers with different chain architecture and investigated with respect to healing temperature (T). It has been shown that logD ∼ 1/T at \( T < T_{\text{g}}^{\text{bulk}} \) (\( T_{\text{g}}^{\text{bulk}} \) is the glass transition temperature of the polymer bulk), which implies that the process of segmental diffusion under healing conditions investigated is a thermally activated Arrhenius-like process describing as D = D0 exp[−Ea/(RT)], where D0 and Ea are the activation energy and the pre-exponential factor, respectively. It has been found that logD0 ∼ Ea, which points to the validity of the so-called kinetic compensation effect for the interdiffusion process at the contact zones of polymers with glassy bulk when an increase in Ea is “compensated” by the corresponding increase in D0.

Diffusion of Nanoparticles in Semidilute and Entangled Polymer Solutions

We studied the diffusion of gold nanoparticles in semidilute and entangled solutions of polystyrene (PS) in toluene using fluctuation correlation spectroscopy (FCS). The polymer concentration was varied from approximately 6c* to 20c*, where c* is the overlap concentration. In our experiments, the particle radius (R approximately 2.5 nm) was much smaller compared to the radius of gyration (Rg approximately 18 nm) of the chain but comparable to the average mesh size (xi) of the fluctuating polymer network. The diffusion coefficient (D) of the particles decreased monotonically with polymer concentration and it can be fitted with a stretched exponential function, D=D0 exp(-microcnu), with the value of the scaling parameter, nu approximately 0.9. At high concentration of the polymer, a clear subdiffusive motion of the particles was observed. The results were compared with the diffusion of free dyes (coumarin 480), which showed normal diffusive behavior for all concentrations.

Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep

Diffusion coefficients of Cr and Al in chromite spinel have been determined at pressures ranging from 3 to 7 GPa and temperatures ranging from 1,400 to 1,700°C by using the diffusion couple of natural single crystals of MgAl2O4 spinel and chromite. The interdiffusion coefficient of Cr–Al as a function of Cr# (=Cr/(Cr + Al)) was determined as D Cr–Al = D 0 exp {−(Q′ + PV*)/RT}, where D 0 = exp{(10.3 ± 0.08) × Cr#0.54±0.02} + (1170 ± 31.2) cm2/s, Q′ = 520 ± 81 kJ/mol at 3 GPa, and V* = 1.36 ± 0.25 cm3/mol at 1,600°C, which is applicable up to Cr# = 0.8. The estimation of the self-diffusion coefficients of Cr and Al from Cr–Al interdiffusion shows that the diffusivity of Cr is more than one order of magnitude smaller than that of Al. These results are in agreement with patterns of multipolar Cr–Al zoning observed in natural chromite spinel samples deformed by diffusion creep.

Effects of grown-in defects on interdiffusion dynamics in InAs∕InP(001) quantum dots subjected to rapid thermal annealing

This work investigates the interdiffusion dynamics in self-assembled InAs∕InP(001) quantum dots (QDs) subjected to rapid thermal annealing in the 600–775°C temperature range. We compare two QD samples capped with InP grown at either optimal or reduced temperature to induce grown-in defects. Atomic interdiffusion is assessed by using photoluminescence measurements in conjunction with tight-binding calculations. By assuming Fickian diffusion, the interdiffusion lengths LI are determined as a function of annealing conditions from the comparison of the measured optical transition energies with those calculated for InP∕InAs1−xPx∕InP quantum wells with graded interfaces. LI values are then analyzed using a one-dimensional interdiffusion model that accounts for both the transport of nonequilibrium concentrations of P interstitials from the InP capping layer to the InAs active region and the P–As substitution in the QD vicinity. It is demonstrated that each process is characterized by a diffusion coefficient D(i) given by D(i)=D0(i)exp(−Ea(i)∕kBTa). The activation energy and pre-exponential factor for P interstitial diffusion in the InP matrix are Ea(P–InP)=2.7±0.3eV and D0(P–InP)=103.6±0.9cm2s−1, which are independent of the InP growth conditions. For the P–As substitution process, Ea(P–As)=2.3±0.2eV and (co∕no)D0(P–As)∼10−5−10−4cm2s−1, which depend on the QD height and concentration of grown-in defects (co∕no).

A Fluorescence Correlation Spectroscopy Study on the Self-Diffusion of Polystyrene Chains in Dilute and Semidilute Solution

The self-diffusion coefficient Ds of dye-labeled polystyrene chains having Mw = 3.90 × 105 g/mol and Mw/Mn < 1.10 was measured over almost 4 decades of polymer concentration in toluene solution, from 10-4 to 0.4 g/mL, by fluorescence correlation spectroscopy. In the dilute regime up to 5 × 10-3 g/mL, Ds remains practically constant. The transition to the semidilute regime is observed around 0.01 g/mL, and from 0.02 to 0.4 g/mL Ds decreases strongly with rising concentration. This decrease is well represented by a power law, Ds ∼ c-1.75, as predicted by scaling and reptation theory. As an alternative, a good fit over the whole concentration range can be obtained with a stretched exponential function, Ds = D0 exp(−15c0.65), with D0 = 2 × 10-7 cm2/s and c given in g/mL.

Kinetics of hydrogen extraction and deuteration in grossular

AbstractThe kinetics of hydrogen mobility in grossular with a chemically homogeneous composition of Gr83.2 And14.3 Py2.2 were studied by sequential annealing experiments monitored by Fourier transform infrared spectroscopy. Slices of single crystals &lt;0.5 mm thick were annealed at temperatures in the range 1073–1323 K at ambient pressure in air and in gas mixtures of Ar(90%)/D2(10%) and Ar(90%)/H2(10%). The change of total infrared (IR) absorbance in the OH-stretching region (3700–3500 cm–1) and the OD-stretching region (2750–2580 cm–1) was used to calculate the diffusion coefficients. The law for diffusion of deuterium is given by D = D0 exp[–102±45 kJ mol–1/ RT] with log D0 (m2/s) = –7.6. For hydrogen extraction in air the diffusion law is expressed by D = D0 exp[–323±46 kJ mol–1/RT] with log D0 (m2/s) = 1.0. This activation energy agrees with the values found for Dora Maira pyrope and for other pyropes from mantle xenoliths, but the diffusivity is slower for the grossular. A detailed investigation of the decrease in individual OH bands during hydrogen extraction in air revealed two different kinds of kinetics behaviour, suggesting that at least two different types of OH defects are present in this grossular.

A Possible Approach to Three‐Dimensional Cosmic‐Ray Propagation in the Galaxy. I. Stable Nuclei without Energy Change

We present an analytical solution of the three-dimensional cosmic-ray propagation in our Galaxy, adopting a more realistic structure of the Galaxy than conventional propagation studies. We assume that there is no boundary in both longitudinal distance r from the disk center and the latitudinal distance z from the Galactic plane and that the three critical parameters, the diffusion coefficient D, the gas density n, and the cosmic-ray source density Q, depend on r in the form of D(r) = D0 exp[r/rD + |z|/zD], n(r) = n0 exp[-(r/rn + |z|/zn)], and Q(r) = Q0 exp[-(r/rQ + |z|/zQ)], respectively. We derive analytically the path length distribution P(x) and its mean value , based on the present solution of the cosmic-ray density. Both simple exponential-type and the truncated-type distributions are reproduced by assuming three adequate scale heights, zD, zn, and zQ. Anisotropy amplitudes are also given on the basis of the present model and found to be compatible with the experimental data if we assume adequate scale heights, as well as the diffusion coefficient D0 at the Galactic center. We present empirical formulae for the fragmentation cross sections, reproducing well the accelerator data, with which we perform numerical calculations for several observables. We compare our numerical results with recent experimental data on the stable nuclei, particularly on the energy spectrum of primary components such as protons, helium nuclei, etc., and on the secondary-to-primary ratios such as B/C and sub-Fe/Fe. We find a good agreement between our calculations and experimental data by assuming an adequate set of the scale heights and the ratio of the diffusion coefficient to the gas density at the Galactic center, D0/n0, while we need additional data other than the stable nuclei in order to obtain unique numerical values for the parameters we have introduced.

Self-Diffusion and Tracer Diffusion in Sphere-Forming Block Copolymers

The self-diffusion and tracer diffusion of asymmetric poly(ethylene-alt-propylene-b-dimethylsiloxane), PEP−PDMS, copolymers were measured using forced Rayleigh scattering. Diffusion measurements were made in the disordered state, in disordered micelles, and in the body-centered-cubic (bcc) sphere phase. The FRS intensity decays were fit with a single-exponential function in the disordered state and a stretched exponential function in disordered micelles and bcc spheres. The decays are interpreted as the diffusion of single chains with a broadened distribution of relaxation times when micelles are present, due to the polydispersity of chain lengths. The diffusion coefficients in disordered micelles and bcc spheres are retarded compared to the disordered state. This retardation is consistent with a hindered diffusion process, D ∼ D0 exp(−AχNA), where χ is the Flory−Huggins interaction parameter, D0 is the diffusion coefficient as χ approaches zero, and NA is the length of the core block. The parameter A is found to increase as χNA increases. These results are compared with recent experimental and computational work.

Self‐diffusion of styrene, 2,2′‐azobisisobutyronitrile, and polystyrene in bulk polymerization by pulsed‐gradient spin‐echo nuclear magnetic resonance spectroscopy

AbstractThe self‐diffusion of styrene, polystyrene, and 2,2′‐azobisisobutyronitrile has been determined in the bulk polymerization of styrene with pulsed‐gradient spin‐echo nuclear magnetic resonance at 25 °C. Data on small molecules are discussed with respect to recent diffusion models. They can fit self‐diffusion coefficient data of small molecules in dilute or semidilute polymer solutions; in concentrated solutions, however, there is a breakdown. A semiempirical model based on scaling laws is used to describe the self‐diffusion of styrene and 2,2′‐azobisisobutyronitrile over the whole range of concentrations studied. The dependence of the polystyrene self‐diffusion coefficient on the polymer concentration is described with a stretched exponential function, D = D0 exp(−αcν), where α depends on the molecular weight of the polymer and ν depends on the kind of solvent. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1605–1614, 2003

Model‐free kinetics: Curing behavior of phenol formaldehyde resins by differential scanning calorimetry

AbstractIsoconversional analysis was used to treat nonisothermal DSC data and yield the dependence of activation energy on conversion during the curing process of PF resins. The shape of the dependence revealed that the curing process of PF resins displayed a change in the reaction mechanism from a kinetic to a diffusion regime. In the kinetic regime a comparative DSC experimental analysis between monomer mixtures and PF resins showed that the addition reactions between phenol and formaldehyde had been mostly completed during the synthesis of PF resins and that the main kinetic reactions contained parallel condensations in the curing process. For the diffusion regime a modified equation for the diffusion rate constant, kD= D0 exp(−ED/RT + K1α + K2α2), is proposed. This equation is in good agreement with the experimental dependence of Eα on α in the diffusion regime, which shows the effect of both temperature and conversion on diffusion. A prediction of the conversion advancement with the reaction time under isothermal condition for PF resin has been made. This prediction can be useful in practical applications for evaluating isothermal behavior of thermosetting systems from nonisothermal experimental data. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 433–440, 2003

Hydrogen permeation through mild steel in temperature range 20–500°C measured by hydrogen collection method

Hydrogen permeation through steel plate maintained at various constant temperatures between 20 and 500°C was investigated using the hydrogen collection method. Fused salts were employed at elevated temperatures. Hydrogen entry was induced by step changes in cathodic charging current density. Emanating flux transients obtained at the hydrogen exit face corresponded closely to a model for permeation determined exclusively by bulk hydrogen diffusion through steel, induced by stepped changes in hydrogen concentration at the steel entry face subsurface, and zero hydogen at the exit face subsurface. An Arrhenius plot of log (D) v. 1/T, using diffusion coefficients D derived from permeation transients was approximately linear in the range 20–310°C. The values derived for activation energy Ea of 17 kJ mol -1 and for the pre-exponential factor D0 of 2·6 × 10-3 cm2 s-1, according to D = D0 exp (-Ea/RT) were similar to literature values. Between 310 and 500°C, stable permeation conditions were difficult to obtain, but flux measurements were repeatable and unaffected by moisture in air.