Published Diffusion Coefficients Research Articles

On exhumation velocities of high-pressure units based on insights from chemical zoning in garnet (Tianshan, NW China)

Exhumed high-pressure rocks formed during subduction provide insight into global geodynamic and plate tectonic processes. Their metamorphic history is partially encoded in their mineralogy and mineral chemistry, which can record the P-T evolution and rates of subduction and exhumation. Here, we study a garnet-glaucophane-albite schist from the SW Tianshan in China in which complexly zoned garnet displays a distinct and sharp oscillatory Mn-zonation and irregular, jagged Ca distributions with peak widths of ∼5 μm. Combined Raman quartz-in-garnet barometry and carbonaceous matter thermometry suggests a P-T path that reached ∼2.5 GPa and was followed by ∼0.9 GPa of nearly-isothermal decompression at temperatures of 530–540°C, associated with final garnet growth. This P-T path is largely confirmed by thermodynamic modeling. Three different approaches to modeling coupled Ca, Mn, Mg and Fe diffusion in garnet were used to estimate the duration between establishment of high-resolution Mn, Fe and Ca zoning during growth and cooling below nominal closure conditions upon exhumation. All models agree best with conditions of ∼530°C maintained for around 100 kyr, though slight differences are found depending on published diffusion coefficients. For the constrained exhumation P-T path, we infer that the studied sample experienced exhumation velocities in the range of 40–45 cm/yr from ∼80 km to ∼50 km depth. We propose an exhumation model involving diapiric Stokes flow along the plate interface and low viscosities around the exhumed unit that may facilitate such high exhumation velocities.

Diffusion across the glass transition in silicate melts: Systematic correlations, new experimental data for Sr and Ba in calcium-aluminosilicate glasses and general mechanisms of ionic transport

Viscosity and diffusivity of silicate melts and glasses are related to each other through relaxation timescales. The systematic is explored based on published data. Diffusion coefficients for Sr and Ba were measured in calcium aluminosilicate glasses at conditions near the glass/supercooled liquid boundary in temperature – time space making use of thin film technology and Rutherford Backscattering Spectroscopy (RBS) to measure concentration profiles on nanoscales. These data extend the range of published diffusion coefficients and combined with the systematic noted above allow the nature of change of diffusion coefficients across the glass transition region to be studied. Activation energies for diffusion in the glassy state (~360kJ/mol) are higher than in the molten liquid (~213kJ/mol). A defect based model of glass transition derived by Ojovan and coworkers, where attainment of a percolation threshold of configuron-type defects accounts for the glass – liquid transition, can explain the observed diffusion behaviour. Data treatment using this model yields a defect formation enthalpy of ~146kJ/mol and a migration enthalpy of ~213kJ/mol. The results of this study provide generalized expressions for the prediction of diffusion coefficients of cations in silicate melts for any composition at any temperature.

Analysis of experimental data on divalent cation diffusion kinetics in aluminosilicate garnets with application to timescales of peak Barrovian metamorphism, Scotland

We present a new statistical framework to analyze the diffusion data for divalent cations (Fe, Mg, Mn, and Ca) in aluminosilicate garnet using published experimental data and an Arrhenius relationship that accounts for dependence on temperature, pressure, garnet unit-cell dimension, and oxygen fugacity. The regression is based on Bayesian statistics and is implemented by the Markov chain Monte Carlo approach. All reported experimental uncertainties are incorporated, and the data are weighted by the precision of the experimental conditions. We also include a new term, the inter-experiment bias, to compensate for possible inconsistencies among experiments and to represent any experimental variability not explicitly presented in the Arrhenius relationship (e.g., water content, defect density). At high temperatures where most experiments were conducted, the diffusion coefficients calculated with the new parameters agree well with previous diffusion models (e.g., Chakraborty and Ganguly in Contrib Mineral Petrol, 111:74–86, 1992; Carlson in Am Mineral, 91:1–11, 2006). However, the down-temperature extrapolation leads to notable differences at lower temperatures for common petrological applications. For example, at 600 °C, the diffusion coefficients of Fe and Mn are one half-to-one order of magnitude faster and the diffusion coefficient of Ca is about one order of magnitude slower than calculated with parameters in Carlson (2006). Our statistical analysis also provides well-defined uncertainty bounds for timescale estimates based on garnet diffusion profiles. Application of the newly derived coefficients indicates that the timescale of the thermal peak of Barrovian metamorphism (Dalradian belt of Scotland) is about four to seven times longer than that estimated using previously published diffusion coefficients. The peak is still geologically brief, however—of the order of 106 years (0.75 Myr +0.70/−0.36 Myr; ±1σ). This brevity requires pulsed advective heat input, as provided by syn-orogenic mafic magmatism in these rocks.

Control of Li configuration and electrical properties of Li-doped ZnO

Li-doped ZnO after different thermal treatments was characterized by depth-resolved cathodoluminescence spectroscopy (DRCLS), secondary ion mass spectrometry, surface photovoltage spectroscopy (SPS), coupled with other surface science techniques. It is found that the Li configuration and electrical properties of Li-doped ZnO could be controlled by different thermal processes. Within a 500–600 °C annealing temperature range, subsequent quenching of ZnO leaves Li as interstitial donors, resulting in n-type low room temperature resistivity. In contrast, slower cooling in air enables these interstitials to fill Zn vacancies, forming Li acceptors 3.0 eV below the conduction band edge. Emergence of this acceptor and the resultant resistivity increase agree with the calculated diffusion lengths based on published diffusion coefficients. In general, these acceptors are compensated by residual intrinsic and extrinsic donors, resulting in a semi-insulating material. DRCL spectra exhibit a 3.0 eV optical signature of the LiZn acceptor and its depth distribution in slow-cooled ZnO. A 3.0 eV SPS absorption feature corresponding to a conduction band-to-acceptor level transition confirms this acceptor assignment. Nanoscale SPS spectra reveal p-type band bending localized near ZnO surface nano-mounds, where VZn and LiZn acceptor densities increase. The slow-cooled and quenched Li-doped ZnO spectra display an inverse relationship between the optical emission densities of lithium on zinc versus zinc vacancy sites, demonstrating the time dependence of Li interstitial diffusion to reach zinc vacancies and form substitutional Li acceptors.

Thermobifida fusca cellulases exhibit limited surface diffusion on bacterial micro‐crystalline cellulose

Elucidation of cellulase-cellulose interactions is key to modeling biomass deconstruction and in understanding the processes that lead to cellulase inactivation. Here, fluorescence recovery after photobleaching and single molecule tracking (SMT) experiments are used to assess the surface diffusion of Thermobifida fusca cellulases on bacterial micro-crystalline cellulose. Our results show that cellulases exhibit limited surface diffusion when bound to crystalline cellulose and that a large fraction of the cellulases remain immobile even at temperatures optimal for catalysis. A comparison of our experimental results to Monte Carlo (MC) simulations, which use published diffusion coefficients to model cellulase displacements, shows that even those enzymes that are mobile on the cellulose surface exhibit significantly slower diffusive motions than previously reported. In addition, it is observed that the enzymes that show significant displacements exhibit complex, non-steady surface motions, which suggest that cellulose-bound cellulases exist in molecular states with different diffusive characteristics. These results challenge the notion that cellulases can freely diffuse over cellulose surfaces without catalyzing bond cleavage.

Helium measurements of pore fluids obtained from the San Andreas Fault Observatory at Depth (SAFOD, USA) drill cores

4He accumulated in fluids is a well established geochemical tracer used to study crustal fluid dynamics. Direct fluid samples are not always collectable; therefore, a method to extract rare gases from matrix fluids of whole rocks by diffusion has been adapted. Helium was measured on matrix fluids extracted from sandstones and mudstones recovered during the San Andreas Fault Observatory at Depth (SAFOD) drilling in California, USA. Samples were typically collected as subcores or from drillcore fragments. Helium concentration and isotope ratios were measured 4–6 times on each sample, and indicate a bulk 4He diffusion coefficient of 3.5 ± 1.3 × 10–8 cm2 s–1 at 21°C, compared to previously published diffusion coefficients of 1.2 × 10–18 cm2 s–1 (21°C) to 3.0 × 10–15 cm2 s–1 (150°C) in the sands and clays. Correcting the diffusion coefficient of 4Hewater for matrix porosity (∼3%) and tortuosity (∼6–13) produces effective diffusion coefficients of 1 × 10–8 cm2 s–1 (21°C) and 1 × 10–7 (120°C), effectively isolating pore fluid 4He from the 4He contained in the rock matrix. Model calculations indicate that <6% of helium initially dissolved in pore fluids was lost during the sampling process. Complete and quantitative extraction of the pore fluids provide minimum in situ porosity values for sandstones 2.8 ± 0.4% (SD, n = 4) and mudstones 3.1 ± 0.8% (SD, n = 4).

Diffusion in Minerals: An Overview of Published Experimental Diffusion Data

Although geologists have been thinking and writing about diffusion in minerals, magmas, and rocks since early in the 20th century (e.g., Penrose 1914; Van Orstrand 1915; Bowen 1921; Eskola 1934; Duffell 1937; Reynolds 1947; Garrels 1949), very few experimental measurements of diffusion in minerals by geologists were published until the 1960’s. The development of commercial electron microprobes in the late 1960’s made it possible to measure compositional zoning in minerals on a micron scale, which provided both the motivation for and a means of determining diffusion coefficients. This led to a significant increase in the rate of publication of papers on diffusion in minerals during the 1970’s (see Fig. 1⇓). Other technological advances (e.g., secondary ion mass spectrometry) have further increased interest in diffusion data, leading to a continued growth of published diffusion coefficients and to the application of a host of experimental designs and measurement techniques (e.g., vapor deposition, Rutherford backscattering, nuclear reactions) that have expanded the range of measurable diffusivities (see Watson and Baxter 2007, Fig. 5⇓; Watson and Dohmen 2010; Cherniak et al. 2010). Figure 1. Numbers of published papers in the mineral diffusion database are shown here by date of publication on a bar graph. There were very few publications of experimentally determined diffusion coefficients for minerals until the 1970’s, but there has been significant growth in the publication rate of diffusion papers since then. As interest in diffusion and the number of published diffusion coefficients have grown, several compilations of diffusion data for minerals have been published to assist researchers in finding the data they need (Harrop 1968; Askill 1970; Freer 1980, 1981; Brady 1995). However, such reviews do not provide easy (electronic) access to the data and they become …

Lithium elemental and isotopic disequilibrium in minerals from peridotite xenoliths from far-east Russia: Product of recent melt/fluid–rock reaction

Lithium concentrations and isotopic compositions of coexisting olivine and clinopyroxene (cpx) in well-characterized peridotite xenoliths from Tok (SE Siberian craton) and samples from two other far-east Russian localities reveal strong elemental and isotopic disequilibria, which correlates with bulk rock composition. Lithium concentrations in cpx from Tok (1–12 ppm) are equal to or significantly greater than those in coexisting olivines (1–5 ppm). The Li-rich cpx show core to rim zoning, indicative of Li infiltration from the grain boundaries. Olivines are generally unzoned, although Li concentrations can vary significantly from grain to grain. ol/cpx D varies from 0.2 to 1.0, which is lower than that expected for equilibrium partitioning ( ol/cpx D eq = 1.1 to 2.0), and reflects preferential Li enrichment in cpx. The Li isotopic compositions of both minerals range far beyond normal mantle δ 7Li of ∼ + 4 ± 2. δ 7Li cpx (− 0.8 to − 14.6) is systematically lighter than δ 7Li of coexisting olivine (− 1.7 to + 11.9), and Δ 7Li ol-cpx varies from 2.8 to 22.9‰. The greatest elemental and isotopic disequilibria occur in the most fertile samples (lherzolites) and may reflect longer equilibration times and/or enhanced melt permeability in the more refractory samples. Collectively, these observations suggest that the peridotite minerals experienced Li addition via diffusion from a grain boundary melt or fluid shortly before or coincident with their entrainment into the host basalt (i.e., within tens of thousands of years, based on published diffusion coefficients for Li in cpx at the temperatures of equilibration). This diffusional ingress of Li generated large kinetic isotopic fractionation, leading to unusually light cpx and heavier olivines. Thus, low δ 7Li cpx do not reflect the influence of an exotic mantle component related to crustal recycling.

The influence of non-uniform particle deposition on the 218Po diffusion coefficient measured with the “two-filter” method

The influence of non-uniform 218Po density distribution on the downstream filter was estimated on the basis of a numerical analysis of the aerosol particle transport inside a tube and of a numerical estimation of the efficiency for alpha radioactive particle detectors. For published diffusion coefficients of 0.103, 0.067 and 0.045 cm 2 s −1 , the error was found to be +20%, +25% and +26% respectively, compared with a uniform deposition.

Development of an Apparatus for Mass-Transfer Studies in Supercritical Fluids

A gravimetric analysis apparatus to measure the mass-transfer rates of solid solutes into supercritical solvents has been designed, built, and tested. The heart of the apparatus is a miniature thin film strain gauge load cell which measures the mass of a solid suspended in a flowing fluid continuously over the duration of the experiment. From knowledge of the geometry of the solute pellet, the mass flux at the surface interface is determined directly. In this work, mass flux data was collected for the dissolution of naphthalene into supercritical carbon dioxide at 35 and 55°C and at pressures ranging from 8359 to 12000 kPa. From the data, binary diffusion coefficients were calculated and compared with published values to verify the methodology. As the calculated values fall within the range of the published diffusion coefficients, the apparatus can be considered to have been verified successfully and is fully operational.

Thermal stability of Si/Si 1 − x − yGe xC y/Si heterostructures grown by rapid thermal chemical vapor deposition

High quality pseudomorphic Si 1 − x − y Ge x C y alloy layers were grown on (100) silicon substrates by rapid thermal chemical vapor deposition with 0 or 11 at% Ge and 0.5 or 1 at% C. The relaxation behavior of these strained layers was investigated using rapid thermal annealing between 1000 and 1130°C. Substitutional C gradually precipitated out to form cubic silicon carbide (β-SiC). The in-plane lattice constant remained constant after annealing, indicating that there was no mechanical strain relaxation by misfit dislocations. The perpendicular lattice constant increased due to the decreasing substitutional C concentration. The same behavior was observed for both SiC and SiGeC samples, showing that Ge did not influence C precipitation. C atoms diffused over very short distances before they precipitated. It appears that, once formed, the β-SiC particles stayed put. Germanium out-diffusion was found to be somewhat higher than calculated with published diffusion coefficients.

Site selectivity and cation diffusion in YBa2Cu3O7- delta.

Tracer diffusion of Co, Zn, and Cu has been studied in polycrystals of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ from 600 to 950 \ifmmode^\circ\else\textdegree\fi{}C at an oxygen partial pressure of 1 atm using serial sectioning or the secondary-ion mass spectrometry technique. The present and previously published values of the diffusion coefficient of Cu fall on the same Arrhenius line. The diffusion coefficients of Zn and Cu and published values for Ni are close to each other and the activation energies are almost the same. Measurements of diffusion of Co and Ni in single-crystal c-axis platelets indicate a much greater diffusional anisotropy for Co than for Ni. Diffusion coefficients of Cu are less than published diffusion coefficients of Ag, possibly because Ag attracts oxygen-ion vacancies. The interaction between cations and oxygen vacancies can explain the increase in the diffusion of Cu with decreasing ${\mathit{P}}_{\mathrm{O}2}$ at 850 \ifmmode^\circ\else\textdegree\fi{}C.

Measurement of sorption in polymer membranes with a quartz crystal microbalance

An application of the oscillating quartz crystal microbalance (QCM) in the measurements of sorption rates and equilibria in polymer—vapor systems is presented. The sorption isotherms of methanol, ethanol and n-heptane in cellulose acetate and poly(hexamethylene adipamide) were measured with the QCM at 298K. The results agree reasonably with the Flory model except at low absorbate activities where appreciable deviations due to localized absorption were observed, as verified with IR spectroscopy. The diffusion coefficient of methanol in cellulose acetate was also calculated from the sorption rate data measured with the QCM. The values obtained at different methanol concentrations correlate well with the published diffusion coefficients.

Rapid annealing using the water-wall arc lamp

Rapid annealing techniques using graphite strip heaters [1], tungsten-halogen lamps [2], and conventional arc lamps [3] have been gaining favor to provide controllable activation of ion implants while minimizing the diffusion of the implanted dopant. These conventional heat sources have given good results, but they all suffer from limitations in power output and/or the ability to change power levels rapidly. The water-wall d.c. arc lamp overcomes these limitations and allows precise control and excellent reproducability of the anneal cycle. The high power output and excellent optical coupling of the water-wall lamp allows ilumination from one side of the sample. The wafer temperature can then be directly monitored with a pyrometer and the fast response time of the lamp allows the pyrometer output to control the lamp power and, hence, provide direct feedback control of the wafer temperature. Direct control is important to overcome variations caused by different doping levels or dielectric coatings on the wafers. Annealing experiments using the water-wall lamp have shown that good activation and essentially complete removal of implant damage can be achieved while moving the junction only minimally [4,5]. The degree of dopant diffusion (generally on the order of 1000 Å) is small compared to device dimensions but is somewhat more than would be expected from classical diffusion theory using published diffusion coefficients. The differences depend on the implanted species and models are being developed to explain the discrepancies. The vary rapid heating and cooling rates obtainable with the water-wall lamp offer a great deal of flexibility in the time/temperature cycles used for annealing (or other rapid thermal processes). There are indications that the ability to achieve a rapid cooling rate allows more complete activation of high dose implants and rapid heating rates may reduce the residual damage and amount of diffusion.

A two‐dimensional transport simulation model for trace atmospheric constituents

A two‐dimensional atmospheric transport simulation model is described which is designed to facilitate the interpretation of observed distributions of primary tropospheric trace gases. Transport by large‐scale advection is based on published meridional velocity fields, while the eddy diffusion component of the transport is based on published diffusion coefficients adjusted to produce agreement between model generated and observed global distributions of CCl3F. The observed CCl3F distribution presented here is useful in this context as it is based on recent multiple observations at six globally distributed background monitoring stations which use calibration gases based on a common standard. The model incorporates both northern and southern hemisphere CCl3F release estimates. It is found that in recent years the global rate of increase in tropospheric CCl3F concentration is higher than that consistent with available release data. The model results indicate interhemispheric exchange times (70°N to 70°S) of approximately 8 months.

Isothermal diffusion studies of the H2O-sucrose-KCl system at 25�C

Diffusion coefficients were obtained for two compositions of the system H2O-sucrose-KCl at 25°C. These plus published diffusion coefficients of the same system at two other compositions led to the construction of three-dimensional surface diagrams. Using these diagrams, the diffusion coefficients of the ternary system were compared with those of binary systems of components. The main diffusion coefficient of KCl was estimated from the conductivity data of KCl in aqueous solution of sucrose, and the agreement of these with experimental values was found to be satisfactory. The possible cause for the appreciable size of the cross-term diffusion coefficients is discussed.

Role of the O/U ratio on the sintering of UO2

The sintering of UO2 is a volume diffusion controlled process. The sintering rate as a function of the concentration of hyperstoichiometrie oxygen at the sintering temperature shows the influence of the O/U ratio on the effective uranium diffusion coefficient. Except under atmospheres having a low oxygen capacity, a sintering specimen is in equilibrium with the furnace atmosphere which can therefore be used to set the sample stoichiometry. The resulting diffusion coefficients of stoichiometric material determined from the rate of initial shrinkage of powder compacts are in good agreement with values determined directly from tracer studies. Hyperstoichiometric specimens (O/U= 2.02) show an enhancement of the shrinkage rate and hence the effective uranium diffusion coefficient is several orders of magnitude greater than expected from published diffusion coefficients.