Modelling the electrical conductivity of
iron-rich minerals for planetary applications.
P. Vacher∗and O. Verhoeven
December 17, 2004
Laboratoire de Planétologie et Géodynamique, UMR-CNRS 6112; Université de
Nantes, 2 rue de la Houssinière 44322 Nantes cedex3, France
Abstract
In the framework of in situ exploration of planetary interiors, electromagnetic survey is one of the geophysical methods constraining the
structure and composition of the mantle. One of the main parameters which governs the internal structure is the bulk iron content of
the mantle. Unfortunately, the effect of iron on the electrical conductivity of mantle minerals is only known through a few high-pressure
and high-temperature experiments. Reliable measurements on samples with different iron contents were reported for olivine, pyroxene,
magnesiowüstite and perovskite/magnesiowüstite assemblage. In a
first part, we parameterize the effect of iron on the electrical conductivity of these minerals. In a second part, we propose assumptions
∗
Corresponding author: [email protected]
1
to extend this formulation to all minerals considered by the review
of Xu et al (JGR 2000), in order to extrapolate the conductivity of
terrestrial samples (i.e. with iron fraction close to 10%) to the conductivity of iron-rich minerals (up to 40%). In a third part, we apply this
formulation to the computation of a synthetic electrical conductivity
profile of the Martian mantle. Together with a similar description
of the effect of iron on elastic parameters, this paper provides a first
step towards fully joint interpretations of seismic velocities and electromagnetic data.
Keywords: Electrical conductivity, minerals, planetary mantle, Mars.
1
Introduction
A first order description of planetary interiors can be obtained using bulk
observables of the planets, like total mass and moments of inertia. A more
precise knowledge can be derived from in situ geophysical exploration, with
measurements of geodetic anomalies, seismic waves travel times, or components of the magnetic field. On Earth, early seismic measurements revealed
the size and physical state of its different internal layers. More recently, interpretations of mantle seismic profiles (see e.g. Duffy and Anderson, 1989;
Cammarano et al., 2003), and of electrical conductivity profiles (see e.g. Dobson and Brodholdt, 2000a; Xu et al., 2000b) have proved to be successful for
refining the thermal profile and composition of the mantle. Apart from the
Earth, detailed geophysical surveys have been undertaken on the Moon. Seismic travel times measured in the seventies have recently been reinvestigated
and lead to a smaller value of the crustal thickness (Khan and Mosegaard,
2
2002; Lognonné et al, 2003). Magnetometer data have been interpreted in
terms of lunar thermal structure, using assumptions about its composition
(e.g. Duba et al, 1976; Hood et al., 1982). Finally, Mars and Mercury are
the future target planets for in situ and/or orbital geophysical explorations
which are expected to provide a large amount of new data (Harri et al., 1999;
Gold et al, 2001; Dehant et al., 2004).
Each kind of geophysical data requires specific methods to be inverted
and interpreted in terms of planetary structure. But one can reasonably
believe that a joint inversion of all data should be more powerful. For instance, the complementarity between seismic and electromagnetic data has
been demonstrated by Mocquet and Menvielle (2000) in the framework of
a network science mission deployed on Mars. An interdisciplinary group of
researchers has recently developed a global method to invert simultaneously
various geophysical data sets, to get a better insight into the thermal structure and composition of any telluric planet (Verhoeven et al., 2004). The bulk
iron content of the planet is one of the key parameters. It has been shown
to be close to 10% for the Earth’s mantle, but is supposed to be around 25%
for the Martian mantle, using the SNC composition as a guide (e.g. Dreibus
and Wänke, 1985). Therefore the inversion process, proposed by Verhoeven
et al.(2004), has been designed in order to recover this parameter from the
data. The way density and seismic velocities (in fact elastic moduli) depend
upon iron content has been experimentally investigated for many minerals,
(e.g. reviews in Duffy and Anderson, 1989; Cammarano et al., 2003). Unfortunately this is not the case for electrical conductivity for which the effect
of iron-content is poorly constrained.
3
In the present paper we propose a single empirical formulation of the electrical conductivity as a function of iron content. In a first part, we use the few
experimental measurements of the electrical conductivity of iron-rich olivine,
pyroxene, magnesiowüstite and a perovskite/magnesiowüstite assemblage to
build a unique formulation of the effect of iron on the electrical conductivity.
In a second part, we propose assumptions to extend this formulation to all
minerals considered by the review of Xu et al (2000b), in order to extrapolate
the conductivity of terrestrial samples (i.e. with iron fraction close to 10%)
to the conductivity of minerals in planetary mantles, i.e. with higher iron
fractions (up to 40%). In a third part, we use this extrapolation to compute a
synthetic electrical conductivity profile for the Martian mantle characterized
by the mineralogical model of Bertka and Fei (1997).
2
Review of available experimental data
In order to get a mineral data set consistent with density and elastic parameters, the dependence of electrical conductivity upon iron content is expressed
through the variable X:
X=
Fe
Mg + Fe
(1)
where M g and F e are atomic concentrations of magnesium and iron in the
sample, respectively. The electrical conductivity as a function of temperature
T , pressure P and iron content X can be expressed as an Arrhenius-type law:
σ(T, P, X) = σ0 (X)e−
∆U (X)+P ∆V (X)
kT
(2)
where σ0 is a preexponential factor, k is Boltzmann’s constant, ∆U and ∆V
are activation energy at atmospheric pressure and activation volume, respec4
tively (see, e.g., Xu et al, 2000b). For low-pressure phases (low pressure
phases include here phases stable at pressure smaller than 23 GPa, corresponding to the upper mantle in the Earth), reported values of ∆V (see Xu
et al., 2000a for olivine and Lacam, 1985 for ringwoodite) lead to a negligible
effect of pressure compared to the effects of temperature and iron content.
Therefore values of ∆V will be given only for high-pressure phases, for which
pressure leads to a noticeable effect.
Reliable measurements on mineral samples with different iron contents
were reported for olivine (e.g. Hinze et al, 1981), pyroxene (e.g. Seifert et al,
1982), magnesiowüstite (e.g. Dobson and Brodholt, 2000b), perovskite (Peyronneau and Poirier, 1989) and for a perovskite/magnesiowüstite assemblage
(e.g. Shankland et al, 1993). Paying attention to use measurements relevant
for each mineral to the same buffering technique, we have investigated the
effect of iron on the three parameters of equation (2) which can possibly be
iron-dependent: σ0 (X), ∆U (X) and ∆V (X).
In Figure 1 are shown fits of the experimental values of log(σ0 (X)) as a
function of log(X) (left), and of the values of the activation energy ∆U (X) as
a function of X (right). Each line deals with a different phase, namely olivine,
pyroxene, high temperature magnesiowüstite and a magnesiowüstite/perovskite
assemblage. Several general observations can be made before studying phases
independently.
• The choice of the logarithmic scale for the iron dependence of σ0 is
based on theoretical considerations: the electrical conductivity is proportional to point defect concentration, which is itself proportional to
given power α (different for each mineral) of X for iron-bearing phases
5
(e.g. Tyburczy and Fisler, 1995). Corresponding linear trends appear
clearly in Figure 1 (left). For all phases except pyroxene, log(σ0 ) increases linearly with log(X) whereas it decreases linearly for pyroxene
of Seifert et al. (1982).
• To our best knowledge, the iron content dependence of the activation
energy has not been modelled yet at the atomic scale. Therefore, we
merely estimate empirical trend by a linear fit ∆U (X) (right column of
Figure 1). For all phases except magnesiowüstite, ∆U decreases with
iron content.
• Regarding the lack of any reported experiment demonstrating a noticeable effect of iron on ∆V , this dependence will be ignored.
We now focus on the details of the computation, for each phase, of
α = dlog(σ0 )/dlog(X) and β = d∆U/dX from the linear fit of log(σ0 ) with
respect to log(X) and ∆U with respect to X, respectively. Experimental
uncertainties were taken into account in the least square fitting (Press et al,
1990). They are typically of the order of a few percent (e.g. Dobson and
Brodholt, 2000b). When the authors did not reported any uncertainty, we
supplied an estimated error of 10% on both log(σ0 (X)) and ∆U (X).
A systematic study of the electrical conduction of Fe-bearing synthetic
olivine under defined thermodynamic activities has been performed by Hinze
et al. (1981) at temperatures between 600 and 1373 K. Their measurements
of σ0 (X) and ∆U (X) for samples with X = 10 %, 20 % and 40 % (Fa/Q/M
buffer) can be fitted with α = 2.42 ± 0.18 and β = - 0.48± 0.25. These
values are different from the values of α = 1.81±0.02 and β = 0 reported
6
more recently by Hirsch et al (1993). The origin of this different is probably
twofold: first, the latter authors fit their data on a slightly modified Arrhenius
law and second, their measurements were performed in the temperature range
1423-1573 K, which is probably too narrow to discriminate the effect of iron
on both σ0 and ∆U . A more detailed comparison of our formulation with
the results of Hirsch et al (1993) is provided in the next section.
Electrical conductivity of synthetic pyroxenes under defined thermodynamic conditions were measured by Seifert et al (1982) at 1 and 2 GPa and
between 773 and 1273 K. Studying the effect of iron on σ0 (X) and ∆U (X)
on samples with X = 10 %,20 % and 50 %, we find that α = -1.28 ± 0.51 and
β = - 1.41 ± 0.35. To our best knowledge, this study on synthetic pyroxene
is the only experiment on samples with an iron fraction significantly different
from 0.1
In a recent paper, Dobson and Brodholt (2000b) investigated the conductivity of magnesiowüstite up to 10 GPa and 2000 K. They isolated two
dominant conductivity mechanisms, depending on temperature. For temperatures higher than 1000 K , which corresponds to the stability domain of
magnesiowüstite in planetary mantles, the dominant mechanism is a largepolaron process. Among the various samples used in their study, an homogeneous set is found with iron content varying between 4 and 20% and a
constant ferric iron concentration around 4%. Dobson and Brodholt (2000b)
fitted their data on a modified Arrhenius law, with a power law temperature
dependence in the preexponential term. We have therefore recomputed their
data for sampled temperatures within the experimental range of [1000 K,
2000 K] to get the values of σ0 (X) and ∆U (X) within a classical Arrhenius
7
law (2). The power dependence of σ0 (X) is clearly visible in Figure 1 and
we calculated that α = 3.14 ± 0.07. The effect of iron on the activation
energy cannot reasonnably be constrained by the available data as can be
seen on the linear fit of ∆U (X). Therefore we assume that there is no clear
effect of the iron content on the activation energy of magnesiowüstite at high
temperature, i.e. β = 0.
In a series of papers (Peyronneau and Poirier, 1989; Poirier and Peyronneau, 1992; Shankland et al, 1993; Poirier et al, 1996), Poirier and collaborators studied the electrical conductivity of perovskite and a perovskitemagnesiowüstite assembage between room temperature and 673 K at 40 GPa.
The assemblage was prepared from natural olivines with iron fractions between 11 and 20%. Among all their results for the assemblage, we have
chosen to study their conductivity measurements of the freshly ground powder reported in Poirier and Peyronneau (1992) which offers the widest set of
samples prepared with the same method. The fits of log(σ0 ) with respect to
log(X) and ∆U with respect to X lead to values of α = 3.56 ± 1.32 and β =
- 1.72 ± 0.38 for the assemblage. Concerning perovskite, only two different
samples with iron content of 8 and 11 % were investigated. Two measurements cannot be used to constrain our fits, especially for samples with close
iron content, and consequently perovskite is not included at this stage.
8
3
Empirical relationship and extrapolation to
other phases
In the last section, we computed the effect of iron, parameterized by specific
values of α and β from various measurements of the electrical conductivity
of olivine, pyroxene, magnesiowüstite and of a perovskite/magnesiowüstite
assemblage. To take this iron dependence into account, the Arrhenius law
(2) can be rewritten as:
X
σ(T, P, X) = σ0,ref
Xref
!α
e−
∆Uref +β(X−Xref )+P ∆V
kT
(3)
where α gives the iron content power-law dependence of σ0 (X), β gives
the linear iron content dependence of ∆U . σ0,ref is the limiting value of σ
when temperature goes to infinity and when X = Xref , and ∆Uref is the value
of the activation energy when X = Xref and P = 0. We set the iron fraction
reference Xref to 0.1 to ground the Arrhenius law on terrestrial values. Note
that the reference state Xref = 0 classically chosen when describing the irondependence of elastic parameters is not relevant for electrical conductivity,
because iron-free phases show a different conduction mechanism (see e.g.
Seifert et al., 1982, for pyroxene).
Instead of computing the reference values of σ0,ref and ∆Uref from the
various experimental studies listed in Section 2, we propose to calculate them
all from the compilation of Xu et al (2000b) using our values of α and β.
In the latter review, the authors compiled experimental works conducted on
nine different minerals or high pressure phases using the same multianvil
apparatus. Therefore these values are not polluted by the use of different
experimental set up. Samples used had all iron content around 0.1, and
9
the temperature range investigated was 1000-1400
◦
C. We propose in this
work to extrapolate their results to minerals with varying, but non zero iron
contents, using the effect of iron modelled in the last section.
For olivine and pyroxene, values of σ0 (X ∼ 0.1) and ∆U (X ∼ 0.1) of Xu
et al (2000b)’s Arrhenius fits (2) are recast in equation (3) to obtain values
of σ0,ref and ∆Uref . Values of log(σ0,ref ), ∆Uref , α and β computed with this
procedure are given in Table 1.
Concerning olivine, we can now compare our formulation of the conductivity of olivine to the formulation of Hirsch et al (1993). The two formulations
agree very well for temperatures below 1500 K and for iron contents below
30%. At higher iron content, our formulation predicts a conductivity which
is more than one order of magnitude greater than the prediction of Hirsch et
al.
To our best knowledge, the electrical conductivity of wadsleyite (β-phase)
has never been measured for various iron contents. We therefore use the values of σ0 and ∆U of Xu et al. (2000b), to which we apply the same iron
content dependence as for olivine. This approximation is probably not correct: indeed, the polaron hopping conduction mechanism depends on many
parameters, e.g. jump distance of the charge carriers, ferric Fe fraction (e.g.
Hirsch et al, 1993), which take different values for olivine and its high pressure phases. However for the purpose of simulating planetary conductivity
profiles, this approximation will do a better work than ignoring the effect of
iron on wadsleyite conductivity. For ringwoodite (γ-phase), Lacam (1985)
did some measurements on synthetic samples with iron content between 0.5
and 1, at room temperature and pressures up to 20 GPa. Extrapolating the
10
derived iron dependence to Fe-poor samples (X in the range 0 to 0.5) and
to high temperatures seems too hazardous, and we have decided to use for
ringwoodite the log(σ0 ) and ∆U values of Xu et al. (2000b), and the values
of α and β derived for olivine.
Xu et al. (2000b) also give the electrical properties of the high pressure phases of the starting orthopyroxene: clinopyroxene at 13 GPa and the
assemblage garnet + akimotoite (ilmenite phase) at 21 GPa. In the lack
of any other experimental result, we use their values of log(σ0 ) and ∆U ,
with corrections for the iron content dependence using the values of α and
β found for orthopyronexe. Apart from the garnet + akimotoite assemblage
investigated by Xu et al. (2000b), the only experiment made on a garnet
sample is by Kavner et al. (1995). They reported measurements on a meteoritic majorite Mg0.75 Fe0.25 SiO3 and on almandine garnet Mg0.475 Fe0.525 SiO3 ,
at ambient pressure and in the temperature range 290-370 K. These experimental conditions are too far from the expected P-T values in planetary
mantles to allow any extrapolation to be done, and garnet is therefore not
included in Table 1.
The same procedure is applied for the higher pressure phases. As these
phases are stable under much higher pressure that the minerals of the upper
mantle, values of the activation volume ∆V have to be supplied. Dobson and
Brodholt (2000b) measured that ∆V = −0.26 cm3 /mol for magnesiowüstite.
Studying the pressure dependence of Al-free perovskite, Shankland et al
(1993) measured a value ∆V = −0.26 cm3 /mol. Recasting the results of
Xu et al. (2000b) for magnesiowüstite in equation (3) with the above values
of α, β and ∆V , finally gives log(σ0,ref ) = 2.56 and ∆Uref = 0.88 eV. The
11
same method is applied for Al-free perovskite for which the values of α and
β are identical to those of the magnesiowüstite/perovskite assemblage. Two
main reasons motivated this approximation. First, perovskite is the main
phase in the assemblage (70 wt %), whatever temperature and iron content.
Second, Peyronneau and Poirier (1989) noted that, for an iron content equal
to 11 %, the electrical conductivity of perovskite is not significantly different
from that of the mixture of perovskite and magnesiowüstite. The comparison with α and β values for magnesiowüstite (Table 1) suggests that this
approximation underestimates the α value and overestimates the β value of
perovskite.
As Xu et al. (2000b) did, we also consider an Al-bearing perovskite. The
combined effects of Al2 O3 and a high iron content have never been investigated, and we apply the value of α, β and ∆V derived for Al-free perovskite to
the electrical parameters of Al-bearing perovskite given by Xu et al. (2000b).
Figure 2a shows an Arrhenius diagram of electrical conductivity as a function of 10000/T (lower axis) and T (upper axis), for low pressure phases with
X=0.1. Two kinds of temperature dependences can be seen in Figure 2a. On
one hand, olivine, pyroxenes and the assemblage akimotoite+garnet all show
an electrical conductivity in the order of 10−5 - 10−6 S.m at a temperature of
1000 K. These values increase by 4 orders of magnitude when temperature increases to 2000 K. On the other hand, wadsleyite and ringwoodite have higher
electrical conductivities, with values around 10−3 S.m at a temperature of
1000 K. When temperature is increased to 2000 K, electrical conductivity
increases by two orders of magnitude for wadsleyite and ringwoodite. Figure
2b shows the electrical conductivity as a function of temperature for high
12
pressure phases with X=0.1. Dashed and solid lines are computed electrical
conductivity at ambient pressure and 30 GPa, respectively. At a pressure of
30 GPa, Al-free and Al-bearing perovskites show a similar behaviour, with an
electrical conductivity around 10−1.5 S.m for a temperature of 1000 K, rising
to values of around 1 S.m for a temperature of 2000K. Mg-wüstite electrical
conductivity has a similar temperature dependence, with values increasing
from 10−1.5 to 100.5 S.m when temperature increases from 1000 to 2000 K. For
the three phases, increasing the pressure from ambient to 30 GPa increases
electrical conductivity by an order of 0.3 log unit (value slightly depending
on temperature). This identical pressure dependence comes from the values
of ∆V , equal for the three phases (see Table 1).
Figure 3a shows the electrical conductivity of low pressure minerals and
phases as a function of iron content X between 8% and 40%, for a temperature of 1500 K and ambient pressure. Increasing the iron content from 10% to
40% leads to the following results: (1) Electrical conductivity of olivine, wadsleyite and ringwoodite, supposed to have the same iron content dependence,
increases by 2 orders of magnitude; (2) for orthopyroxene, clinopyroxene, and
the akimotoite+garnet assemblage, no significant iron content dependence of
electrical conductivity is observed in the explored range for X. Figure 3b
gives the iron content dependence of electrical conductivity of high pressure
phases, at a temperature of 1800K and a pressure of 30 GPa. For an iron
content increase of 10% to 40%, electrical conductivity increases by 2 orders of magnitude for Mg-Wüstite, and 4 orders of magnitude for perovskite.
Among all the conductivities studied, the conductivity of the perovskite has
the stronger iron dependence.
13
These results are to be considered with caution. All of the samples discussed here have iron content smaller than 50% for low pressure phases and
smaller than 20 % for high pressure phases. Extrapolation of electrical conductivities of samples with iron content well above these upper bound values
is therefore not relevant. The major drawback of this work is that it relies
on very few experimental results, with some of them performed on synthetic
samples. Assuming the same iron dependence as the closest mineral phase
may also be discutable. Nevertheless, our choice to ground the extrapolation
of the conductivity of all phases on the measurements of Xu et al (2000b)
guarantees some confidence in our results. These measurements were indeed
performed on natural terrestrial samples, and the same experimental setup
was used to measure the conductivity of all minerals.
4
Synthetic conductivity profile of the Martian mantle
In this section, we use our modelling of the effect of iron on the electrical conductivity to compute a realistic conductivity profile of the Martian mantle.
Among the various mineralogical models reported in the literature, we have
chosen to represent the mineralogy of the Martian mantle by the model of
Bertka and Fei (1997). They computed the modal mineralogy associated to
the Dreibus and Wänke (1985) composition along given areotherm and pressure profile. This composition was derived from the study of SNC meteorites
which suggested an iron fraction around 25 %.
At a given depth, we compute the conductivity of each phase using for-
14
mula (3) with iron fraction computed from the microprobe analysis of Bertka
and Fei (1997). For garnet, we use the same electrical parameters as the akimotoite+garnet assemblage. Concerning perovskite, we use the values of the
Al-bearing phase in agreement with the reported experimental composition.
The electrical conductivity profile of the aggregate is then computed as the
Hashin-Shtrikman (1962) average of the individual conductivities weighted
by the volume fractions reported by Bertka and Fei (1997) (Figure 4).
In Figure 4, we observe first a monotonous increase of log(σ) from -2.3 at
200 km depth to - 0.8 at 1000 km depth. This is mostly due to the temperature increase, since the transition from orthopyroxene to clinopyroxene is
very smooth and has a small electrical signature (see Figures 2 and 3). Then
the conductivity increases by 1.6 order of magnitude between depths of 1000
and 1200 km. Two successive jumps can be identified and correspond to
phase transitions of olivine to ringwoodite and olivine to wadsleyite, respectively. The first of these transitions is characterized by a small amount of
ringwoodite (less than 15 %), but it is very iron-rich (up to 38 %). This last
feature explains the sharp increase of conductivity. These jumps are followed
by a slight decrease of conductivity (0.2 order of magnitude) between depths
of 1250 and 1390 km. This is due to the decrease of iron content in all phases
during the wadsleyite-ringwoodite and clinopyroxene-majorite transitions. A
final conductivity jump of 0.8 order of magnitude is observed at a depth of
1800 km, due to the breakdown of ringwoodite into perovksite + Mg-wüstite.
This conductivity profile can be compared to previous computations.
Mocquet and Menvielle (2000), in a pioneering work on the complementarity between seismological and electromagnetic data, proposed a very broad
15
range of possible Martian conductivity profiles. The present results, based on
a critical review of available experimental data, fall within their predictions.
Xu et al (2000a) computed a conductivity profile for the Earth’s mantle using a pyrolite-like composition (X = 0.1). A comparison can be made with
our results for each compositional layer: given the respective pressure scales,
the first 1100 km of the Martian model corresponds to the first 400 km of
Earth’s upper mantle, and the discontinuity at 1800 km corresponds to the
upper-lower mantle boundary in the Earth. The Martian profile proposed
here exhibits conductivity values 1 to 1.5 order of magnitude higher than
those of Xu et al (2000a) at all depth. This offset is the signature of the
higher iron content of the Martian mantle. Such a comparison between the
Earth and Mars highlights the efficiency of in situ electromagnetic sounding
for constraining the composition of planetary mantles.
5
Conclusion
In this paper we propose a new formulation of mineral electrical conductivity as a function of temperature, pressure and iron content. With respect to
a classical Arrhenius law, the effect of iron content is included in both the
pre-exponential factor and the activation energy. Various experimental results for olivine, pyroxene, magnesiowüstite and perovskite/magnesiowüstite
assemblage are recast in a common framework based on the data collected
by Xu et al. (2000b). These data concern nine mantle minerals or phases
studied with the same experimental set up. Assuming the same iron dependence as the closest phase for the minerals for which no high-pressure and
high-temperature data are available, we extrapolate the results of Xu et al
16
(2000b) to iron fractions in the range 10-40%. This allows us to compute
realistic electromagnetic signature of iron-rich planetary mantles. As an example, the synthetic conductivity profile associated to the Martian mantle
defined by the Bertka and Fei (1997) model is computed. The main interest
of this new formulation is to get a similar description of elastic and electrical
parameters as a function of iron content. This is a first step towards fully
joint interpretations of results from seismic and electromagnetic surveys.
Acknowledgments
O.V. acknowledges the financial support provided through European Community’s Improving Human Potential Programme under contract RTN22001-00414, MAGE. We thank Antoine Mocquet and Michel Menvielle for
valuable discussions.
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Figure 1: Effect of iron on the preexponential factor σ0 (X) and on the activation energy E(x) for olivine, pyroxene, magnesiowüstite at high temperature
and a magnesiowüstite/perovskite assemblage. For each mineral are shown
a linear fit of the experimental values log(σ0 ) as a function of log(X) (left)
and a linear fit of the values of the activation energy ∆U as a function of X
(right).
Figure 2: Electrical conductivity of minerals as a function of reciprocal temperature 10000/T (lower axis) and temperature (upper axis). For all minerals
the iron content is set to X=0.1. Upper panel (a): upper mantle mineral and
phases. Abbreviations: ol, olivine; opx: orthopyroxene; cpx: clinopyroxene;
ak+gt: assemblage of akimotoite and garnet; wad: wadsleyite; ring: ringwoodite. Lower panel (b): Electrical conductivity of lower mantle phases,
at ambient pressure (dashed lines) and at 30 GPa (solid lines). Abbreviations: Al-pv: Al-bearing perovskite; Al-free pv: Al-free perovskite; mw:
Mg-wüstite.
Figure 3: Electrical conductivity of minerals as a function of iron content
X (upper axis: linear, lower axis: logarithmic). See Fig. 2 caption for
abbreviations. Black dots correspond to conductivities of samples studied
by Xu et al. (2000b). Upper panel (a): upper mantle mineral and phases
at a temperature of 1500 K; lower panel (b): lower mantle phases, at a
temperature of 1800K and a pressure of 30 GPa.
22
Figure 4: Top: Mineralogical composition (wt %) of the Martian mantle, as a
function of depth, from the experiments of Bertka and Fei (1997). See Figure
2 for abbreviations. maj = majorite. Bottom: Computed conductivity of the
Martian mantle as a function of depth.
Table 1: Values of parameters entering equation (3). σ0,ref and ∆Uref are
reference values of the preexponential factor and activation energy for an
iron content X = 0.1. ∆V is the activation volume. α and β give the iron
dependence of σ0 (X) and ∆U (X), respectively.
Mineral name
log(σ
ref )
0,
a
∆U
ref
a
∆V
(eV)
(cm3/mol)
α
β
Ref
(eV)
Olivine
2.69
1.62
-
2.42 ± 0.18
-0.48 ± 0.25
b
Wadsleyite
3.29
1.29
-
2.42 ± 0.18
-0.48 ± 0.25
c
Ringwoodite
2.92
1.16
-
2.42 ± 0.18
-0.48 ± 0.25
c
Orthopyroxene
3.66
1.79
-
-1.28 ± 0.51
-1.41 ± 0.35
d
Clinopyroxene
3.19
1.86
-
-1.28 ± 0.51
-1.41 ± 0.35
e
Akimotoite+garnet
3.29
1.65
-
-1.28 ± 0.51
-1.41± 0.35
e
Al-free Perovskite
1.28
0.68
-0.26
3.56 ± 1.32
-1.72 ± 0.38
f, g, h
Al- Perovskite
2.03
0.76
-0.26
3.56 ± 1.32
-1.72 ± 0.38
f, g, h
Magnesiowüstite
2.56
0.88
-0.26
3.14 ± 0.07
0
i
References: a: Xu et al. (2000b), b: Hinze et al. (1981), c: α and β identical to olivine values, d: Seifert
et al. (1982), e: α and β identical to orthopyroxene values, f: Shankland et al (1993), g: α and β identical
to pv/mw assemblage values, h: Peyronneau and Poirier (1992). i: Dobson and Brodholt (2000b).
23