JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, B02202, doi:10.1029/2004JB003292, 2005
Influence of protons on Fe-Mg interdiffusion in olivine
S. Hier-Majumder1
Department of Geology and Geophysics, University of Minnesota Twin Cities, Minneapolis, Minnesota, USA
I. M. Anderson
Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
D. L. Kohlstedt
Department of Geology and Geophysics, University of Minnesota Twin Cities, Minneapolis, Minnesota, USA
Received 2 July 2004; revised 29 October 2004; accepted 17 November 2004; published 2 February 2005.
[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,
o
~ Fe – Mg = Do( fH O/f H
)r exp [(Q +
pressure, and water fugacity following the relation D
2
2O
2 1
PV*)/RT] m s , where log(Do) = (14.8 ± 2.7), r = 0.9 ± 0.3, Q = 220 ± 60 kJ/mol,
and V* = (16 ± 6) 106m3/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.
Citation: Hier-Majumder, S., I. M. Anderson, and D. L. Kohlstedt (2005), Influence of protons on Fe-Mg interdiffusion in olivine,
J. Geophys. Res., 110, B02202, doi:10.1029/2004JB003292.
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
1
Now at Department of Geology and Geophysics, Yale University, New
Haven, Connecticut, USA.
Copyright 2005 by the American Geophysical Union.
0148-0227/05/2004JB003292$09.00
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 waterderived point defects, laboratory experiments need to be
performed over a range of concentration. Under watersaturated 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
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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 mm 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
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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 2 103 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% Re25% 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 garnetperovskite (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
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HIER-MAJUMDER ET AL.: Fe-Mg INTERDIFFUSION IN OLIVINE
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us consider the case of temperature varying with time in a
linear fashion, given by T = T0 ± at, where, T0 is the starting
temperature, a 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 kDk =
R t2
R t2
t1 D(t)dt/ t1 dt. The change in the length of the concentration profile p
can
be estimated by the average diffusion length
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
scale, l = k D k t . 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.
300 nm. Background subtracted intensities of the Mg-Ka,
Si-Ka, and Fe-La 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-Ka, Mg-Ka, SiKa, and Fe-La 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 mm
apart. Monte Carlo simulation yields an excitation volume
of 2 mm 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
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 mm 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
ð1Þ
pffiffiffiffiffiffiffiffi
cð xÞ co erfc x= 4Dt
¼
;
c1 co
2
where co and c1 are the concentrations of the end-members,
t is the time of the anneal and D is a specified concentrationindependent 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:
Z
c1
xdc ¼ 0:
ð2Þ
co
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
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Table 1. Diffusivity Data From Boltzmann-Matano Analysis
D, m2s1
Run
P, Pa
GID-7, 6 h, 1373 Ka
GID-7, 6 h, 1373 Ka
GID-7, 6 h, 1373 Ka
GID-6, 6 h, 1373 Ka
GID-6, 6 h, 1373 Ka
PI-978, 4 h, 1373 Ka
PI-978, 4 h, 1373 Ka
PI-978, 4 h, 1373 Ka
PI-978, 4 h, 1373 Ka
GID-4, 6 h, 1373 Ka
GID-4, 6 h, 1373 Ka
GID-4, 6 h, 1373 Ka
GID-4, 6 h, 1373 Ka
M-147, 1 h, 1373 Kb,c
M-147, 1 h, 1373 Kb,c
M-151, 1 h, 1373 Kb
M-151, 1 h, 1373 Kb
M-151, 1 h, 1373 Kb
M-151, 1 h, 1373 Kb
M132, 6 h, 1373 Kb
M132, 6 h, 1373 Kb
M132, 6 h, 1373 Kb
M132, 6 h, 1373 Kb
M79, 12 h, 1373 Kb,d
M145, 1 h, 1373 Kb
M145, 1 h, 1373 Kb
M145, 1 h, 1373 Kb
M145, 1 h, 1373 Kb
GID-9, 6 h, 1450 Ka
GID-9, 6 h, 1450 Ka
100 ± 2 106
100 ± 2 106
100 ± 2 106
200 ± 2 106
200 ± 2 106
300 ± 2 106
300 ± 2 106
300 ± 2 106
300 ± 2 106
400 ± 2 106
400 ± 2 106
400 ± 2 106
400 ± 2 106
3.5 ± 0.3 109
3.5 ± 0.3 109
3.7 ± 0.3 109
3.7 ± 0.3 109
3.7 ± 0.3 109
3.7 ± 0.3 109
5 ± 0.3 109
5 ± 0.3 109
5 ± 0.3 109
5 ± 0.3 109
5 ± 0.3 109
6 ± 0.3 109
6 ± 0.3 109
6 ± 0.3 109
6 ± 0.3 109
300 ± 2 106
300 ± 2 106
8.33
1.50
1.69
1.00
9.99
5.56
7.41
7.50
1.31
7.39
9.06
4.66
6.50
1.76
1.60
4.60
3.88
9.25
9.80
1.85
1.57
1.90
1.56
3.10
8.34
6.49
1.35
2.68
2.29
2.07
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
0.08 1017
0.01 1016
0.01 1016
0.01 1016
0.12 1017
0.16 1017
0.16 1017
0.16 1017
0.02 1016
0.02 1016
0.02 1016
0.02 1016
0.02 1016
1.45 1016
1.45 1016
1.41 1016
1.41 1016
1.41 1016
1.41 1016
1.03 1016
1.03 1016
1.03 1016
1.03 1016
10.30 1017
7.56 1017
7.56 1017
0.76 1016
0.76 1016
0.04 1016
0.04 1016
fH2O, Pa
Method
Element
97 106
97 106
97 106
189 106
189 106
280 106
280 106
280 106
280 106
420 106
420 106
420 106
420 106
101 109
101 109
133 109
133 109
133 109
133 109
708 109
708 109
708 109
708 109
708 109
2344 109
2344 109
2344 109
2344 109
324 106
324 106
WDS
EDS
EDS
EDS
EDS
WDS
WDS
EDS
EDS
WDS
WDS
EDS
EDS
WDS
WDS
WDS
WDS
EDS
EDS
WDS
WDS
EDS
EDS
EDS
WDS
WDS
EDS
EDS
WDS
WDS
Fe
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Mg
Fe
Fe
Mg
Fe
Mg
Fe
Fe
a
Gas medium.
Multianvil press.
Used preannealed bicrystals as starting material.
d
Here fO2 was not buffered.
b
c
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 concentrationindependent 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],
1
cð x; t Þ ¼ pffiffiffiffiffiffiffiffiffiffiffi
4pDt
Z
1
uðv; 0Þ exp 1
!
ð x vÞ2
dv;
4Dt
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
~ FeMg ¼ Do fH2 O
D
fHo2 O
!r
Q þ PV *
exp ;
RT
ð3Þ
where fH2O is the water fugacity, f oH2O = 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 diffusivitytemperature 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.
[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 ±2 103 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
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HIER-MAJUMDER ET AL.: Fe-Mg INTERDIFFUSION IN OLIVINE
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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 epoxyfilled 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 fO2. (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.
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.
[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.
[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.
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 mm. 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.
[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
3.2. Diffusivity
[25] The diffusivities calculated using the BoltzmannMatano 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(m2s1), r =
0.9 ± 0.3, Q = 220 ± 60 kJ/mol, and V* = (16 ± 6) 106m3/mol. The values of diffusivity reported in this
work lie in the range 1017 – 1016 m2s1.
[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
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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.
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.
[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 fH2O 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 fO2 self-buffered run (M79)
are presented in Table 1.
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 sev-
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
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.
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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.
eral 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 fO2 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 106m3/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 107 Pa and atmospheric pressure, were normalized to a pressure of 0.3 GPa using an activation volume
of 5.5 106m3/mol [Misener, 1974] for this comparison.
[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 ( fH2O =
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 ex-
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HIER-MAJUMDER ET AL.: Fe-Mg INTERDIFFUSION IN OLIVINE
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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.
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.
ample, 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
pffiffiffiffiffi
cation diffusion, given by
Dt, 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
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.
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HIER-MAJUMDER ET AL.: Fe-Mg INTERDIFFUSION IN OLIVINE
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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 KrögerVink notation as
h
0 i x þ ...
þ 2ðOHÞO V00Me
XV00Me ¼ V00Me þ ðOHÞO V00Me
[34] If most of the protons are incorporated in the structure
of olivine as the neutral defect complex {2(OH).O V00Me}x
[Kohlstedt et al., 1996], then the total octahedral cation
vacancy concentration can be approximated as
XV00Me 2ðOHÞO V00Me
x :
ð4Þ
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]
x XOH 2 2ðOHÞO V00Me :
ð5Þ
The point defect complex {2(OH).O V00Me}x can be formed
by the reaction [Kohlstedt and Mackwell, 1998]
x
MexMe þ 2OxO þ H2 O ¼ 2ðOHÞO V00Me þMeOðsrgÞ;
2ðOHÞO V00Me
x 1
XV00Me ¼ XOH / fH2 O :
2
ð7Þ
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
~ Fe – Mg can be expressed in terms of the Fe
interdiffusivity D
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]
~ FeMg ¼
D
the product of the total cation vacancy concentration and an
~ V00 [see Schmalzried, 1981,
effective vacancy diffusivity D
Me
p. 67; Wang et al., 2004]:
~ FeMg ¼ XV00 D
~ V00 :
D
Me
Me
DFe DMg
;
xDFe þ ð1 xÞDMg
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
ð8Þ
[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):
~ FeMg / fH2 O :
D
ð6Þ
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
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ð9Þ
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 Sm1) 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.,
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HIER-MAJUMDER ET AL.: Fe-Mg INTERDIFFUSION IN OLIVINE
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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.
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, si, due to a species i, is related
to its diffusivity, Di, and concentration, ci, by the NernstEinstein relation:
si ¼
Di ci
ðzi FÞ2
RT
ð10Þ
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 106m3/mol [Misener, 1974].
[40] The Arrhenius plot in Figure 8 illustrates the temperature dependence of ionic conduction calculated for the
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[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 (fH2O = 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 V00Me}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 sH[001] and sH[100] are 1 and 2 orders of magnitude
larger, respectively, than shydrous
ion[001] 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.
[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.
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HIER-MAJUMDER ET AL.: Fe-Mg INTERDIFFUSION IN OLIVINE
[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 V00Me}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.
[45] Acknowledgments. 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-AC0500OR22725 with UT-Battelle LLC.
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I. M. Anderson, Metals and Ceramics Division, Oak Ridge National
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S. Hier-Majumder, Department of Geology and Geophysics, Yale
University, 210 Whitney Avenue, New Haven, CT 06511, USA. (saswata.
[email protected])
D. L. Kohlstedt, Department of Geology and Geophysics, University of
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USA. ([email protected])
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