Journal of Geophysical Research: Solid Earth

Influence of protons on Fe-Mg interdiffusion in olivine

Authors


Abstract

[1] We report the experimental measurement of Fe-Mg interdiffusivity in olivine along the [001] crystallographic direction in a water-saturated environment at pressures of 0.1 to 6 GPa and temperatures between 1373 and 1450 K. The concentration of water-derived protons in olivine was controlled by varying the water fugacity. The oxygen fugacity was set by the Ni-NiO solid state reaction, while the activity of silica was controlled by the presence of orthopyroxene. In this work, we report diffusivity as a function of temperature, pressure, and water fugacity following the relation equation imageFe–Mg = image exp [−(Q + PV*)/RT] m2s−1, where log(Do) = (−14.8 ± 2.7), r = 0.9 ± 0.3, Q = 220 ± 60 kJ/mol, and V* = (16 ± 6) × 10−6m3/mol. The approximately linear increase in diffusivity with increasing water fugacity is consistent with incorporation of protons associated with octahedral cation vacancies to form defect complexes. Our results indicate that cation diffusion in water-saturated olivine is ∼50 times faster than under water-absent conditions at a pressure of 5 GPa and a temperature of 1373 K.

1. Introduction

[2] Distribution of water in the earth is heterogeneous as revealed by the water contents in volcanic glasses and mantle xenoliths derived from different source regions in the mantle. For example, lava generated in the Sierra Negro volcanism caused by melting in the central American mantle wedge contains up to 6–8 wt% molecular H2O indicating a high water content in the source region [Roggensack et al., 1997]. In contrast, the volcanic glasses from the Mid-Atlantic Ridge contain <1 wt% water suggestive of a relatively depleted source region [Dixon et al., 2002]. Water content of the silicates in the magma source region can be estimated from the water content of volcanic glasses. For example, the depleted MORB source region in the oceanic upper mantle contains 1600 ppm H/Si dissolved in the silicate minerals [Michael, 1988; Sobolev and Chaussidon, 1996]. The plume source regions in the South Pacific, South and North Atlantic contain 4000–12000 ppm H/Si, as calculated from the water contents of the volcanic glasses [Dixon et al., 2002; Nichols et al., 2002]. The mantle wedge is estimated to contain 32000 ppm H/Si based on the water content of glass inclusions in arc lavas [Sobolev and Chaussidon, 1996]. Because of the differences in the total water content of the sources of these different magmas, the equilibrium concentration of water-derived point defects in the silicate minerals in the magma source region prior to melting will also be different. Olivine megacrysts from spinel lherzolite xenoliths hosted in kimberlites or alkali basalts also reveal spatial variation in hydroxyl concentration, ranging between 10–2200 ppm H/Si, depending on the source region [Bell and Rossman, 1992].

[3] Small concentrations of water derived point defects strongly influence kinetic properties involving ionic diffusion in silicate minerals. In olivine, this effect is well documented in viscosity, grain growth rate, and phase transformation kinetics [Mei and Kohlstedt, 2000a, 2000b; Karato, 1989; Kubo et al., 1998]. Relative to results from experiments carried out under anhydrous conditions, significant enhancement of cation diffusivity in olivine occurred in samples annealed in the presence of water at 0.3 GPa [Wang, 2002; Wang et al., 2004]. To obtain the functional dependence of the diffusivity on concentration of water-derived point defects, laboratory experiments need to be performed over a range of concentration. Under water-saturated conditions the concentration of water-derived point defects in olivine increases systematically with increasing pressure due to the associated increase in water fugacity [Kohlstedt et al., 1996]. For example, at 1373 K, at a confining pressure of 0.3 GPa, hydroxyl solubility in olivine is ∼1000 ppm H/Si [Zhao et al., 2004], while at a confining pressure of 5 GPa, hydroxyl solubility is ∼28000 ppm H/Si [Kohlstedt et al., 1996]. (Note that we have multiplied the reported values of solubility of Kohlstedt et al. [1996] by a factor of 3.5 following the work of Bell et al. [2003] and Koga et al. [2003]).

[4] In the present study, we carried out experiments over a range of water fugacity to obtain the functional dependence of Fe-Mg interdiffusivity on water fugacity. The measured values provide a constraint on the spatial variation of kinetic properties such as diffusivity and electrical conductivity based on the lateral variation of water content in the mantle.

2. Materials and Methods

[5] We report results from 10 successful Fe-Mg interdiffusion experiments at confining pressures of 0.1 to 6 GPa and temperatures of 1373 to 1450 K carried out by annealing olivine bicrystal diffusion couples under water-saturated conditions. Low-pressure experiments between 0.1 and 0.4 GPa were performed in a gas medium apparatus [Paterson, 1990], while high-pressure experiments between 3.5 and 6 GPa were performed in a Walker-type multianvil module mounted on a 1000 ton hydraulic press [Dasgupta et al., 2004]. The oxygen fugacity in all experiments, except for one, was buffered by the Ni-NiO solid state reaction.

2.1. Sample Preparation

[6] Each diffusion couple consisted of a synthetic Fo80 olivine crystal [Tsai et al., 1996] and a natural Fo90 olivine crystal from San Carlos, Arizona. The (010) crystallographic plane of inclusion-free olivine crystals was oriented with a Bruker AXS 5005 X-ray microdiffractometer, and the [100] and [001] crystallographic directions on a polished (010) plane were identified from Laue diffraction pattern obtained with a Siemens D500 Laue camera. Plates were cut from each crystal within ±5° of parallel to the (001) crystallographic plane.

[7] For the experiments performed in the gas medium apparatus, single crystal plates of olivine with dimensions a × b × c ≈ 3 × 2 × 1 mm3 were used. One (001) face on each crystal plate was mechanically polished with lapping films containing 0.5 μm diamond beads and subsequently chemically polished in a colloidal silica suspension of grain size 40 nm to remove the strained layer from the mechanically polished surface. The crystals were placed in a talc crucible created by machining a rectangular cavity into a talc cylinder, with the [100] and [010] axes of each crystal aligned parallel and the polished (001) planes in contact. A mixture of 5:23 moles of talc and brucite powders was used to fill the cavity. Dehydration of the mixture of talc and brucite provided a 9:2:11 molar mixture of olivine, orthopyroxene and water during the run and also controlled the activity of orthopyroxene at unity. The entire assembly was placed in a Ni capsule, and the capsule was welded shut.

[8] For all experiments performed in the multianvil press, similarly oriented and polished single crystal plates of dimension ∼1.5 × 1 × 0.5 mm3 were used. The crystals in all experiments, except for M151, were placed in a rectangular cavity created by cold pressing the mixture of talc and brucite powders into a Au capsule with a steel piston containing a ∼1.5 × 1 mm2 rectangular punch on the end. In experiment M151, a mixture of powdered San Carlos olivine and deionized water was used instead of the talc and brucite mixture. A piece of Ni foil placed in the capsule buffered the oxygen fugacity by the Ni-NiO solid state reaction in all experiments except for M79. No Ni was added to the capsule in the experiment M79. The open end of the gold capsule was subsequently crimped and welded shut. In the experiment M147, a previously annealed bicrystal pair formed the starting sample.

2.2. Diffusion Anneal

[9] All diffusion anneals reported in this work were performed between 1373 and 1450 K. In the internally heated gas medium apparatus, an R-type (Pt-Pt + 13% Rh) thermocouple monitored the temperature. The furnace was calibrated prior to the experiments to ensure that the temperature variation was <4 K along a ∼40 mm long flat zone centered at the 20 mm long sample capsule. The sample was heated at an average rate of ∼45 K/min. Commercial Ar gas with an impurity content of <3 ppm formed the pressure medium. Variation in pressure during the run was ∼2 × 10−3 GPa. After the anneal, the sample was cooled at a rate of 100 K/min.

[10] In the multianvil press, a D-type (3% W + 97% Re-25% W + 75% Re) thermocouple enabled control of the temperature of the assembly. A straight-walled graphite heater was used as the furnace. The vertical temperature gradient, estimated from the temperature difference between two thermocouples in temperature calibration runs, was ∼10 K/mm. The pressure medium was prepared by casting a mixture of MgO-Al2O3-SiO2-Cr2O3 into octahedra of edge length 18 mm with integrated gaskets. The pressure in the assembly was calibrated against the force on the ram by the quartz-coesite (1273 and 1473 K, 3.1 and 3.2 GPa) [Bose and Ganguly, 1995], Fe2SiO4 olivine-wadsleyite (1273 K, 5.3 GPa) [Yagi et al., 1987], CaGeO3 garnet-perovskite (1273 K, 6.1 GPa) [Susaki et al., 1985], and coesite-stishovite (1273 and 1473 K, 8.6 and 9.2 GPa) [Zhang et al., 1993, 1996] phase transitions [Dasgupta et al., 2004]. The pressure uncertainty in the multianvil press was ±0.3 GPa. After reaching the desired pressure level at room temperature, the sample assembly was allowed to adjust itself with the pressure for 5–6 h. Subsequently the temperature was increased to 673 K in a few seconds followed by ramping at the rate of 60 K/min to the temperature of the run. The temperature of the controlling thermocouple was set ∼20 K below the desired temperature, such that the center of the capsule reached the desired temperature. After the diffusion anneal, the sample was cooled at a rate of 60 K/min down to 673 K, after which the furnace power was shut off.

[11] In both sets of experiments, we increased or reduced temperature using slow heating or cooling rates to minimize fracturing along the bicrystal interface due to differential thermal expansion or contraction within the sample assembly. Since the diffusivity decreased rapidly with the falling temperature, diffusion was virtually shut down during cooling. Similarly, the effect of diffusion during heating was also negligible during the entire period of heating. One can estimate the average diffusion length scale during heating or cooling using a time-dependent diffusivity. For example, let us consider the case of temperature varying with time in a linear fashion, given by T = T0 ± αt, where, T0 is the starting temperature, α is the heating/cooling rate and t is the time. Substituting T into equation (3), the average diffusivity during heating or cooling can be determined as ∥D∥ = equation imageD(t)dt/equation imagedt. The change in the length of the concentration profile can be estimated by the average diffusion length scale, l = equation image. For cooling at a rate of 60 K/min starting at 1373 K, using the parameters given in section 3.2, we obtain l ≈ 70 nm, for a cooling period of 10 min. For a heating rate of 45 K/min starting at 278 K, using the same parameters, we obtain l ≈ 70 nm, for a heating period of 24 min. Therefore the total changes in the length of the concentration profile would be ∼140 nm. Such a small variation in the length of the concentration profile, which is below our resolution limit, will not affect the reported values of diffusivity.

[12] After each run, the capsule was pierced under a microscope to test for the presence of water or water vapor. In some of the experiments performed in the gas medium apparatus, a vapor phase bubbled through a leak detecting soap solution, while in some of the experiments performed in the multianvil press, liquid water bubbled out. Further analyses were performed only on samples that retained free water or gas at the end of the run. In some samples, the mixture of talc and brucite powders contaminated the bicrystal interface during capsule preparation; these samples were also rejected. Samples from only 10 out of 45 experiments were thus analyzed. In the initial experiments in the multianvil press that were run for 6–12 h, the olivine single crystals were embayed extensively during the run by Ni-rich olivine. The time of the diffusion anneals for the subsequent multianvil runs was reduced to 1 h to avoid extensive interaction between the diffusion couple and the buffer material.

2.3. Analyses

2.3.1. Chemical Analyses

[13] Multiple diffusion profiles were measured on each sample along the [001] axis of the bicrystals on polished sections cut perpendicular to the interface. Measurements were made both at low-voltage with a field emission gun scanning electron microscope (FEG SEM), employing energy dispersive spectroscopy (EDS), and at higher voltage in an electron microprobe, using wavelength dispersive spectroscopy (WDS). While the data obtained with the low-voltage FEG SEM had very high spatial resolution, the chemical signal was noisy. Therefore data were also acquired at a higher accelerating voltage using an electron microprobe in order to obtain a smooth concentration profile, but with fewer data points due to the lower spatial resolution inherent to the technique.

[14] The EDS analyses were performed at an acceleration voltage of 3 keV with a Philips XL30 FEG SEM using a final beam-defining aperture 30 μm in diameter. Individual diffusion profiles consisted of 256 to 512 pixels uniformly spaced 50–100 nm apart. In these analyses, the beam, rather than the sample stage, was moved. Monte Carlo simulation of the penetration of the electrons within the sample using the software Electron Flight Simulator revealed that the excitation volume under the conditions of data acquisition for the density of olivine has a diameter of ∼300 nm. Background subtracted intensities of the Mg-Kα, Si-Kα, and Fe-Lα characteristic X-ray lines were acquired from spectra obtained at each pixel with a dwell time of 5–10 s. A line of contamination marked the track of the electron beam across the sample surface. A backscattered electron image of the track was acquired after the analysis to ensure that the electron beam did not drift from a straight line path perpendicular to the interface during spectrum acquisition. Data were rejected from acquisitions if the beam drifted from the desired path due to a fault in the algorithm controlling the motion of the beam. Elemental concentrations were extracted from the X-ray intensity data following correction for atomic number and absorption effects using Castaing's approximation [Goldstein et al., 1992]. Matrix corrected concentrations were within 4% of the uncorrected value. X-ray maps of the O-Kα, Mg-Kα, Si-Kα, and Fe-Lα were also acquired using EDS spectral imaging [Kotula et al., 2003]. Maps were 256 × 256 pixels with 100 nm per pixel spacing and 250 ms per pixel dwell time.

[15] Quantitative WDS analyses were performed with a JEOL 8900 electron microprobe at an acceleration voltage of 9 keV and a beam current of 20 nA. A Fo90 standard was used to calculate the concentration at points spaced 1.5 μm apart. Monte Carlo simulation yields an excitation volume of ∼2 μm diameter.

2.3.2. Data Analyses

[16] In general, diffusion coefficients for each sample were determined from the concentration profiles using the Boltzmann-Matano analysis [Glicksman, 2000]. The computer routine used for Boltzmann-Matano analysis was tested for faults by calculating back the diffusivity from an artificial composition profile with a constant diffusivity given by

equation image

where co and c1 are the concentrations of the end-members, t is the time of the anneal and D is a specified concentration-independent diffusivity. The value of diffusivity calculated by the Boltzmann-Matano routine agreed well with the specified constant diffusivity. The position of the Matano interface for each measured concentration profile was numerically determined using the following criterion:

equation image

The analysis was performed iteratively on each profile, starting with an initial guess for the location of the Matano interface, which was updated after each iteration until the constraint given in equation (2) was satisfied.

[17] The starting material for experiment M147 was a bicrystal that had been preannealed at 1373 K and 300 MPa under water-saturated conditions (Z. Wang, personal communication, 2004). It was not possible to calculate diffusivity from this sample using the Boltzmann-Matano analysis because (1) the sample already had a concentration profile from the preanneal and (2) the time of the preanneal was unknown. Thus we employed a technique based on the solution to the diffusion equation provided by Kreyszig [1999]. Using the concentration profile measured from the starting material as an initial condition, the diffusion equation was iteratively solved to match the profile after the anneal by varying the concentration-independent diffusivity between subsequent iterations. The use of a concentration-independent diffusivity is justified since we did not observe any dependence of diffusivity on concentration within the scatter of the data (see section 3.2). The solution, c(x, t), to the diffusion equation in an infinite medium, assuming constant diffusivity, can be obtained by employing a Fourier integral analysis given by Kreyszig [1999],

equation image

where only the initial and final conditions, u(x, 0) and c(x, t), and the time of anneal t are known.

[18] Regression analysis of the calculated values of diffusivity yielded the parameters Do, r, Q, and V* in the diffusivity equation

equation image

where image is the water fugacity, image = 1 Pa is the reference water fugacity used for nondimensionalization, P is the pressure, and T is the temperature. First, the activation energy Q was calculated from a linear fit to the diffusivity-temperature data obtained at P = 0.3 GPa. Second, the preexponential term Do, the fugacity exponent r, and the activation volume V* were calculated from a nonlinear least squares fit of equation (3) to the diffusivity data measured at 1373 K with the activation energy from the previous linear fit. Since the data in Table 1 are heavily biased by the results obtained at 1373 K, a nonlinear least squares fit to the entire diffusivity data set evaluating all parameters (Do, r, V*, and Q) returned an unreasonable value of the activation energy. Hence the two-step regression analysis was necessary.

Table 1. Diffusivity Data From Boltzmann-Matano Analysis
RunP, PaD, m2s−1image PaMethodElement
  • a

    Gas medium.

  • b

    Multianvil press.

  • c

    Used preannealed bicrystals as starting material.

  • d

    Here image was not buffered.

GID-7, 6 h, 1373 Ka100 ± 2 × 1068.33 ± 0.08 × 10−1797 × 106WDSFe
GID-7, 6 h, 1373 Ka100 ± 2 × 1061.50 ± 0.01 × 10−1697 × 106EDSFe
GID-7, 6 h, 1373 Ka100 ± 2 × 1061.69 ± 0.01 × 10−1697 × 106EDSMg
GID-6, 6 h, 1373 Ka200 ± 2 × 1061.00 ± 0.01 × 10−16189 × 106EDSFe
GID-6, 6 h, 1373 Ka200 ± 2 × 1069.99 ± 0.12 × 10−17189 × 106EDSMg
PI-978, 4 h, 1373 Ka300 ± 2 × 1065.56 ± 0.16 × 10−17280 × 106WDSFe
PI-978, 4 h, 1373 Ka300 ± 2 × 1067.41 ± 0.16 × 10−17280 × 106WDSMg
PI-978, 4 h, 1373 Ka300 ± 2 × 1067.50 ± 0.16 × 10−17280 × 106EDSFe
PI-978, 4 h, 1373 Ka300 ± 2 × 1061.31 ± 0.02 × 10−16280 × 106EDSMg
GID-4, 6 h, 1373 Ka400 ± 2 × 1067.39 ± 0.02 × 10−16420 × 106WDSFe
GID-4, 6 h, 1373 Ka400 ± 2 × 1069.06 ± 0.02 × 10−16420 × 106WDSMg
GID-4, 6 h, 1373 Ka400 ± 2 × 1064.66 ± 0.02 × 10−16420 × 106EDSFe
GID-4, 6 h, 1373 Ka400 ± 2 × 1066.50 ± 0.02 × 10−16420 × 106EDSMg
M-147, 1 h, 1373 Kb,c3.5 ± 0.3 × 1091.76 ± 1.45 × 10−16101 × 109WDSFe
M-147, 1 h, 1373 Kb,c3.5 ± 0.3 × 1091.60 ± 1.45 × 10−16101 × 109WDSMg
M-151, 1 h, 1373 Kb3.7 ± 0.3 × 1094.60 ± 1.41 × 10−16133 × 109WDSFe
M-151, 1 h, 1373 Kb3.7 ± 0.3 × 1093.88 ± 1.41 × 10−16133 × 109WDSMg
M-151, 1 h, 1373 Kb3.7 ± 0.3 × 1099.25 ± 1.41 × 10−16133 × 109EDSFe
M-151, 1 h, 1373 Kb3.7 ± 0.3 × 1099.80 ± 1.41 × 10−16133 × 109EDSMg
M132, 6 h, 1373 Kb5 ± 0.3 × 1091.85 ± 1.03 × 10−16708 × 109WDSFe
M132, 6 h, 1373 Kb5 ± 0.3 × 1091.57 ± 1.03 × 10−16708 × 109WDSMg
M132, 6 h, 1373 Kb5 ± 0.3 × 1091.90 ± 1.03 × 10−16708 × 109EDSFe
M132, 6 h, 1373 Kb5 ± 0.3 × 1091.56 ± 1.03 × 10−16708 × 109EDSMg
M79, 12 h, 1373 Kb,d5 ± 0.3 × 1093.10 ± 10.30 × 10−17708 × 109EDSFe
M145, 1 h, 1373 Kb6 ± 0.3 × 1098.34 ± 7.56 × 10−172344 × 109WDSFe
M145, 1 h, 1373 Kb6 ± 0.3 × 1096.49 ± 7.56 × 10−172344 × 109WDSMg
M145, 1 h, 1373 Kb6 ± 0.3 × 1091.35 ± 0.76 × 10−162344 × 109EDSFe
M145, 1 h, 1373 Kb6 ± 0.3 × 1092.68 ± 0.76 × 10−162344 × 109EDSMg
GID-9, 6 h, 1450 Ka300 ± 2 × 1062.29 ± 0.04 × 10−16324 × 106WDSFe
GID-9, 6 h, 1450 Ka300 ± 2 × 1062.07 ± 0.04 × 10−16324 × 106WDSFe

[19] Errors in the reported values of diffusivity in Table 1 were calculated by propagating the uncertainties in temperature and pressure, neglecting any covariance between these two parameters. Temperature and pressure uncertainties of ±1 K with ±2 × 10−3 GPa and ±10 K with ±0.3 GPa were used for the data from experiments performed in the gas medium and the multianvil apparatuses, respectively. To evaluate the error in the measured diffusivity values, we used the parameters Do, r, and V* obtained by the nonlinear least squares fit and Q from the linear fit to the Arrhenius plot.

3. Results

3.1. Bicrystal Interface

[20] The welded interface between the crystals was imaged by backscattered electron imaging (BSE) in the SEM. The BSE image of a sample assembly in Figure 1a displays the welded bicrystal interface adjacent to a cavity occupied by free water during the run. The close-up image of the bicrystal interface in Figure 1b illustrates the gradient in the Fe-Mg ratio along the diffusion zone. Because of the relatively short duration of the anneals, the lengths of the diffusion profiles were ≲20 μm. The variation among values of diffusivities calculated from data acquired along different paths across the bicrystal interface, measured from the same sample, was less than the error associated with the measurement.

Figure 1.

Backscattered electron images of two samples. (a) Low-magnification image of a sample annealed at 6 GPa, 1373 K for 1 hour. The Fe content in the two crystals can be seen by the contrast in gray level in the image. The darker gray rim around the crystals is a mixture of olivine and orthopyroxene produced by the solid state reaction between talc and brucite in the buffer. The asterisk indicates an epoxy-filled cavity that contained free water during the run. The bright outer rim is the Au capsule, whereas the bright phase surrounding the Fo80 crystal is Ni used to buffer image (b) The bicrystal interface in another diffusion couple annealed at 5 GPa, 1373 K for 6 hours. Fe-Mg concentration profiles were measured along the two contamination lines across the interface. The gradient in the gray scale in the image reflects the gradient in Fe-Mg ratio in the crystals.

[21] A fine-grained reaction rim containing orthopyroxene (Mg0.96Fe0.04SiO3) and olivine (Mg1.95 Fe0.01Ni0.04SiO4) formed around the crystals during the diffusion anneals. The circle along the edge of the Fo90 crystal in Figure 1a marks such a reaction rim. The X-ray intensity maps from the EDS spectrum image in Figure 2 illustrate the concentration variations of Fe, Mg, Si, and O within a Fo90 crystal and the surrounding orthopyroxene buffer. Embayments of orthopyroxene, such as the one marked in Figure 2, were observed frequently along the buffer-crystal interface. The intensity variation in the image illustrates the lower metal and higher Si content of orthopyroxene relative to olivine.

Figure 2.

Characteristic X-ray intensity maps for Fe, Mg, Si, and O from a spectrum image of the reaction rim around the Fo90 crystal. The protruding phase is orthopyroxene (marked “en”) created during the run by reaction between brucite and talc in the buffer.

[22] Observation of the reaction rims in the samples indicated that the activity of silica and the fugacity of oxygen were controlled by solid state reactions between olivine-orthopyroxene and Ni-NiO, respectively. We did not detect any silica in the buffer region, while we found both orthopyroxene and olivine in the reaction rim. Therefore the activity of silica during the runs was clearly buffered by orthopyroxene and olivine. A bright green phase adjacent to Ni was also detected under an optical microscope in all runs but M79. This phase is likely to be either a Ni-bearing oxide or silicate. Only the olivine in the fine-grained reaction rim contained a small amount of Ni. However, this olivine was optically distinct from the bright green phase by being nearly colorless. Hence the bright green phase is most likely NiO, which formed from the surrounding Ni, thus buffering the oxygen fugacity during the runs.

[23] The backscattered electron image of the reaction rim in Figure 3 displays the olivine grains in the buffer assemblage. Comparison between the shape and size of the orthopyroxene and olivine grains in Figures 2 and 3 reveals that the olivine grains are more euhedral and significantly larger than the orthopyroxene grains.

Figure 3.

Backscattered electron image of the olivine created by reaction between talc and brucite during the experiment. The diagram in the inset shows the sample assembly with bicrystals, and the square region marked by the dashed line shows the region of the backscattered electron image.

[24] Interaction between the buffer and single crystals resulted in some alteration of the single crystals annealed in the multianvil press. In some cases, such as the one shown in Figure 4, one of the crystals in the diffusion couple has been completely altered, while alteration is less extensive on the other. The remnants of the original crystals are displayed within the boxes in Figure 4. Electron microprobe analyses of the altered crystals reveal compositions of olivine with varying Fe-Mg-Ni ratios among different crystals. Fracturing of the single crystals during pressurization followed by fluid mediated reaction between the buffer material and the fragments of the single crystals during the anneal may have caused the alteration. None of the altered samples were used for diffusion analyses.

Figure 4.

BSE image of interaction between the buffer material and the olivine crystals in the diffusion couple. The broken line indicates the outline of the original crystals. Magnified view of the region enclosed by the boxes reveals the interface between the original crystals and the incursions of Ni-bearing olivine from the buffer. Region marked by the asterisk indicates the original crystal. This sample was not used in the diffusion analysis.

3.2. Diffusivity

[25] The diffusivities calculated using the Boltzmann-Matano analysis from individual profiles exhibited negligible composition dependence, possibly due to the small variation in composition across the profile. The variation in diffusivity between compositions Fo82 and Fo88 was less than ±15%. All diffusivities from the Boltzmann-Matano analysis used for the calculation of the thermochemical parameters were chosen from the center of the profile, corresponding to a composition of Fo85. For this composition, the parameters in the diffusivity relation described by equation (3) are log(Do) = (−14.8 ± 2.7) log(m2s−1), r = 0.9 ± 0.3, Q = 220 ± 60 kJ/mol, and V* = (16 ± 6) × 10−6m3/mol. The values of diffusivity reported in this work lie in the range 10−17–10−16 m2s−1.

[26] Diffusion profiles measured by EDS across good interfaces were noisier than the profiles measured by WDS. A comparison of normalized Fe concentration profiles measured by both techniques is shown in Figure 5a. All profiles, such as the one shown in Figure 5, were symmetric within the resolution of the data. Figure 5b illustrates a plot of equation (1) overlaid by the data from WDS analyses shown in Figure 5a. No variations in the measured Si concentration was observed along the profiles.

Figure 5.

Normalized Fe concentration versus distance measured from the diffusion couple in run M132. (a) Comparison of profiles measured using EDS and WDS techniques. The profiles were measured from the diffusion couple shown in Figure 1b. (b) Solution to the diffusion equation assuming a constant diffusivity, averaged from the values reported in Table 1 for the profiles shown in Figure 5a. Dots are the data from WDS analyses, shown as solid squares in Figure 5a.

[27] To illustrate the dependence of diffusivity on water fugacity, pressure-compensated diffusivity is plotted as a function of water fugacity in Figure 6 for T = 1373 K with the fit to equation (3) overlayed. The slope of this log-log plot indicates that interdiffusivity increases approximately linearly with increasing water fugacity. In the same plot, pressure-compensated diffusivity measured under anhydrous, orthopyroxene-absent conditions [Chakraborty, 1997] is plotted as the horizontal line. The anhydrous diffusivity intersects the fit to equation (3) at image ≈ 15 MPa, which is equivalent to ∼50 ppm H/Si based on equation (7b) of Zhao et al. [2004]. Data from low-pressure experiments [Wang et al., 2004] performed under water-saturated conditions are also included. The complete data set including the diffusivity at 1450 K and the image self-buffered run (M79) are presented in Table 1.

Figure 6.

Plot of pressure-compensated interdiffusion coefficient as a function of water fugacity. Solid symbols are data from [Wang et al., 2004]; open square and open stars are diffusivity values calculated from WDS measurement of Mg and Fe profiles, respectively. Cross and open circles correspond to diffusivity values calculated from EDS measurement of Mg and Fe profiles, respectively.

4. Discussion

4.1. Comparison With Previous Results

[28] Fe-Mg interdiffusion in olivine has been studied extensively under anhydrous conditions (see Bejina et al. [2003] for a compilation of the data from earlier experiments) over a range of temperatures, pressures, and chemical environments. However, no experimental measurement is available for Fe-Mg interdiffusivity under water-saturated conditions at the pressure and temperatures of our experiments.

[29] All but one of the previous investigations were performed under anhydrous conditions. Results from several interdiffusion experiments carried out at atmospheric pressure between temperatures of 1253 and 1573 K indicate that the Fe-Mg interdiffusivity in olivine exhibits an exponential dependence on Fe concentration and a power law dependence on image under anhydrous conditions [Buening and Buseck, 1973; Nakamura and Schmalzried, 1984; Chakraborty, 1997]. Results from Fe-Mg interdiffusion experiments performed between 1173 and 1373 K and 1 and 3.5 GPa under anhydrous conditions yields an activation volume of 5.5 × 10−6m3/mol [Misener, 1974]. In Figure 7 we compare the diffusivity measured under anhydrous conditions to our data. The interdiffusion coefficients for Fo86 from Chakraborty [1997], measured at an oxygen fugacity of 10−7 Pa and atmospheric pressure, were normalized to a pressure of 0.3 GPa using an activation volume of 5.5 × 10−6m3/mol [Misener, 1974] for this comparison.

Figure 7.

Arrhenius plot of diffusivity at P = 0.3 GPa and XFo = 0.85 used to obtain the activation energy of interdiffusion. The open stars are data from [Wang et al., 2004]. The open circles and open diamonds are results from the present study.

[30] Recent data from Fe-Mg interdiffusion experiments carried out under hydrous conditions at 1373 K and 0.3 GPa demonstrate that interdiffusivity is enhanced in the presence of water [Wang, 2002; Wang et al., 2004]. The Arrhenius plot in Figure 7 compares the interdiffusivities measured parallel to the [001] crystallographic direction from our work with those from the studies of Chakraborty [1997] and Wang et al. [2004]. The data from our work and the study of Wang et al. [2004] were acquired under similar experimental conditions. From Figure 7, at a pressure of 0.3 GPa image = 0.28 GPa), the interdiffusivity along the [001] crystallographic direction in olivine is enhanced by almost an order of magnitude under hydrous conditions. It should be noted that the interdiffusion experiments of Chakraborty [1997] were not performed at a controlled level of aopx, which introduces some uncertainty into the comparison.

[31] The diffusivity-water fugacity relation given in equation (3), combined with the solubility-water fugacity relation from Zhao et al. [2004], can be used to calculate the diffusivities in different tectonic environments. As an example, olivines containing 100 and 500 ppm H/Si at 1373 K and 5 GPa will have diffusivities that are factors of ∼50 and 10 smaller, respectively, than olivine containing ∼8100 ppm H/Si at the same temperature and pressure conditions [Kohlstedt et al., 1996]. Characteristic length scales for cation diffusion, given by equation image, will accordingly be shorter by factors of ∼7 and ∼3, respectively.

4.2. Point Defect Chemistry

[32] The reason for the enhancement of Fe-Mg interdiffusion in olivine under hydrous conditions can be understood by comparing the water fugacity dependencies of the interdiffusivity and the concentration of vacancies on octahedral cation sites.

[33] In a water-saturated environment, dissociation of molecular water provides a source of protons. In the olivine lattice, protons bond with oxygen ions, giving rise to hydroxyl absorption bands in transmitted infrared (IR) spectra. Results from experimental measurements as well as ab initio calculation of protonation of forsterite indicate that formation of hydroxyl-cation vacancy point defect complexes is energetically far more favorable than formation of isolated proton interstitials (i.e., OH ions) [Kohlstedt et al., 1996; Kohlstedt and Mackwell, 1998, 1999; Brodholt and Refson, 2000; Wang et al., 2004]. The total octahedral vacancy concentration can be expressed using the Kröger-Vink notation as

equation image

[34] If most of the protons are incorporated in the structure of olivine as the neutral defect complex {2(OH)O − VMe″}x [Kohlstedt et al., 1996], then the total octahedral cation vacancy concentration can be approximated as

equation image

Following a similar logic, it can be shown that, under such a condition, the total hydroxyl concentration, XOH, is given by [Kohlstedt et al., 1996]

equation image

The point defect complex {2(OH)O − VMe″}x can be formed by the reaction [Kohlstedt and Mackwell, 1998]

equation image

where (srg) indicates sites of repeatable growth, such as dislocations and grain boundaries. Applying the law of mass action to reaction (6) and combining equations (4) and (5), we obtain

equation image

The concentration of cation vacancies can thus be determined indirectly by measuring the hydroxyl concentration in olivine [Kohlstedt and Mackwell, 1998].

[35] Fe-Mg interdiffusion in olivine takes place by a vacancy mechanism involving only the octahedral cation sublattice. In olivine, O and Si are much less mobile than the octahedral cations [Bejina et al., 2003]. Under such a condition, the tetrahedral cation and the anion sublattices can be effectively treated as a fixed coordinate frame, and, observing that local charge neutrality is maintained, the interdiffusivity equation imageFe–Mg can be expressed in terms of the Fe and Mg self-diffusivities using the Nernst-Planck relation, which for an ideal solid solution is given by [see Schmalzried, 1981, p. 80; Kohlstedt and Mackwell, 1999]

equation image

where Di is the self-diffusivity of species i and x is the mole fraction of Fe. Also, since cation diffusion in olivine takes place by a vacancy mechanism [Nakamura and Schmalzried, 1984; Wang et al., 2004], both self-diffusivities are proportional to the concentration of cation vacancies, and, for a given value of x, the interdiffusivity can be expressed as the product of the total cation vacancy concentration and an effective vacancy diffusivity equation image [see Schmalzried, 1981, p. 67; Wang et al., 2004]:

equation image

[36] While the hydroxyl solubility is proportional to the concentration of hydroxyls in defect complexes, the interdiffusivity is proportional to the concentration of vacancies in the complexes, as given by equation (8), provided the diffusivity of the complex is similar to the diffusivity of unassociated vacancies and is independent of the concentrations of either of these species. Experimental data indicate that this assumption is reasonable since diffusivity of vacancy associates measured from the rate of proton incorporation in olivine [Kohlstedt and Mackwell, 1998] is similar to the diffusivity of unassociated vacancies measured from the rate of reequilibration of creep rate [Mackwell et al., 1988], electrical conductivity [Wanamaker, 1994], and thermogravimetry [Nakamura and Schmalzried, 1983] following a change in oxygen fugacity or activity of orthopyroxene [see Kohlstedt and Mackwell, 1998, Figure 6]. Therefore, if point defect reaction (6) describes the primary mechanism for incorporation of protons into the olivine lattice, then the interdiffusivity should be proportional to the water fugacity as obtained by combining equations (7) and (8):

equation image

Experimental data indicate that the hydroxyl concentration in hydrothermally annealed olivine crystals increases approximately linearly with an increasing water fugacity [Kohlstedt et al., 1996; Kohlstedt and Mackwell, 1999; Zhao et al., 2004]. The similar water fugacity dependence of interdiffusivity and solubility indicates that protons are incorporated into the olivine structure as neutral point defect complexes with cation vacancies [Kohlstedt et al., 1996].

4.3. Implications for Ionic Conductivity

[37] In this section, we use our results to calculate the cation contribution to electrical conductivity in olivine. We also review the possible contribution of protons to electrical conductivity in olivine.

[38] The cation diffusivity determined from this work can be used to provide an upper limit on the contribution of cations to electrical conductivity of olivine under hydrous conditions. Under anhydrous conditions, electrical conductivity and thermopower measurements indicate that cations on the M site, along with polarons and electrons, are the primary charge carriers [Constable and Roberts, 1997]. Ionic conduction dominates at temperatures above 1573 K [Constable and Roberts, 1997; Wanamaker and Duba, 1993], where the product of mobility times the concentration of polarons is smaller than that for cations. Under hydrous conditions, in addition to octahedral cations and polarons, water-derived point defects can be important charge carrying species [Karato, 1990]. The anomalously high (0.05–0.1 Sm−1) electrical conductivity, observed in the upper mantle beneath northeastern Pacific and central Europe, led to the suggestion that conduction is dominated by diffusion of protons [Lizarralde et al., 1995; Hirth et al., 2000; Duba and Bahr, 2000]. However, this conclusion was reached based on a comparison of proton diffusivity with cation diffusivity, the latter measured under anhydrous conditions [Karato, 1990].

[39] With the cation diffusivity data reported in our study for hydrous conditions, the effect of water on ionic conductivity in olivine can now be more fully addressed. Here we compare the contribution to electrical conductivity from protons with the contribution from cations at a confining pressure of 300 MPa, under both hydrous and anhydrous conditions. The conductivity, σi, due to a species i, is related to its diffusivity, Di, and concentration, ci, by the Nernst-Einstein relation:

equation image

where zi is the dimensionless charge of the species, F is Faraday's constant, R is the universal gas constant, and T is the temperature. The cation contribution to electrical conductivity along the [001] crystallographic direction under water-saturated condition can be calculated using equation (10) and our cation diffusivity. The corresponding values for anhydrous conditions is calculated from Fe-Mg interdiffusivity from the work of [Chakraborty, 1997], normalized to a pressure of 300 MPa using an activation volume of 5.5 × 10−6m3/mol [Misener, 1974].

[40] The Arrhenius plot in Figure 8 illustrates the temperature dependence of ionic conduction calculated for the [001] crystallographic direction under both anhydrous and hydrous conditions. Also shown in the plot are the upper limits of proton conductivities along the [001] and [100] crystallographic directions, calculated using proton diffusivities at a pressure of 0.3 GPa image = 0.28 GPa) [Mackwell and Kohlstedt, 1990] and a hydroxyl concentration appropriate for an olivine of composition of Fo85 [Zhao et al., 2004]. Notice that according to equation (5), the measured hydroxyl concentration is almost entirely equal to the concentration of the neutral defects {2(OH)O − VMe″}x. Consequently, the actual concentration of free protons (i.e., charged protonic defects) is likely to be much smaller than used in the plot, and thus the plot provides only an upper limit for the protonic contribution. The plot indicates that both conduction by protons and conduction by cations under hydrous conditions are larger than conduction by cations under anhydrous conditions. Also, calculated values of σH[001] and σH[100] are ∼1 and 2 orders of magnitude larger, respectively, than σion[001]hydrous at 1600K. The difference is even larger at lower temperatures since the activation energy of cation diffusion is larger than the activation energy of proton diffusion in olivine.

Figure 8.

Arrhenius plot comparing the contributions of octahedral cations and protons to electrical conductivity. For hydrous conditions the conductivities due to protons and ions were calculated under the assumption that all of the protons and all of the cation vacancies contributed to electrical conduction, even those tied up in charge-neutral defect associates.

[41] The similar water fugacity dependencies for cation diffusivity from our work and hydroxyl solubility from [Kohlstedt et al., 1996] combined with results from ab initio calculations of Brodholt and Refson [2000] using DFT method and results from Braithwaite et al. [2002, 2003] using the embedded cluster method indicate that most of the water-derived protons in olivine are likely to reside in neutral point defect complexes. Therefore the protonic contribution to electrical conduction in olivine is likely less than previously calculated values [Karato, 1990] and in the plot in Figure 8. However, on the basis of observation of anisotropic high electrical conductivity in the mantle, suggestions have been made that protonic conduction may play an important role. Magnetotelluric measurements combined with seismic anisotropy observations reveal that, under the SE Pacific Rise (G. Hirth, personal communication, 2004) and the Australian and Fennoscandian plates [Bahr and Simpson, 2002], the direction of the highest electrical conductivity in the upper mantle is coincident with the direction of fastest seismic velocity. This observation is consistent with electrical conduction by protons along the [100] crystallographic direction in olivine. However, if most of the protons reside in neutral point defect complexes, the concentration of available free protons will be too small to contribute significantly to the electrical conductivity. Hence direct experimental measurement of electrical conductivity of olivine under water-saturated conditions need to be carried out to address this apparent disagreement in greater detail.

5. Conclusions

[42] 1. Results from this study demonstrate that Fe-Mg interdiffusivity in olivine is larger in the presence of water than under anhydrous conditions. On the basis of our diffusivity relation given by equation (3) and the relation between hydroxyl solubility and water fugacity from [Kohlstedt et al., 1996], the interdiffusivity increases by a factor of ∼50 at 1373 K and 5 GPa for an increase in hydroxyl content from 100 to 8100 ppm H/Si.

[43] 2. The approximately linear dependence of the divalent cation interdiffusivity on water fugacity suggests that protons are incorporated into olivine as neutral point defect complexes {2(OH)O − VMe″}x.

[44] 3. The increase in divalent cation diffusivity in going from anhydrous to water-saturated conditions is insufficient to explain the observed high electrical conductivities in the mantle olivine by ionic conduction.

Acknowledgments

[45] Tony Withers and Mark Zimmerman kindly assisted us with the experiments. Rüdiger Dieckmann kindly supplied a synthetic iron-rich olivine crystal. Sumit Chakraborty provided insightful suggestions on data analysis. Ellery Frahm in the Microprobe lab in the University of Minnesota helped with the WDS analysis. We appreciate valuable comments and suggestions from Steve Mackwell, Shun Karato, and an anonymous reviewer. Greg Hirth provided insightful comments regarding the electrical conductivity measurements. The research was supported by NSF through grant EAR-0106981. EDS analysis at the SHaRE User Center was sponsored by the Division of Materials Sciences and Engineering, US Department of Energy, under contract DE-AC05-00OR22725 with UT-Battelle LLC.

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