Electrical conductivity and partial meltingof mafic rocks under pressureJ. Maumus a∗, N. Bagdassarov and H. Schmeling

aArbeitsbereich Geophysik, J. W. Goethe Universitat-Frankfurt,Feldbergstrasse 47, D-60323 Frankfurt am Main, Germany

The paper aims to demonstrate the importance of electric conductivity measurementsof partially molten mafic rocks on the example of Oman gabbro, Karelia olivinite, Rondaand Spitzbergen peridotites. The electrical conductivity of rocks was estimated from theimpedance spectroscopy at temperatures between 800oC and 1450oC and at pressuresbetween 0.3 and 2 GPa in experiments performed in a piston cylinder apparatus. Attemperatures below and above the melting, samples were equilibrated during c. 200 h.It was shown that the jump of electrical conductivity due to the first percentage of melt-ing correlates with the temperature range slightly above the solidus. Thin sections ofquenched samples were used to estimate volume fractions and chemical compositions ofpartial melts. The increase of the electrical conductivity compares well with the connec-tivity of melt in partially molten samples. Above the solidus, the electrical conductivityincreases for about 1 to 2 orders of magnitude in comparison with the conductivity ofnon-melted rock below solidus. When a complete melt connectivity is established, thecharge transport follows the network of the formed melt films at grain boundaries. Ittakes ' 200 h to reach a steady state electrical resistance in a partially molten rock sam-ple.The experimental results were compared with the conductivity data obtained from mag-netotelluric (MT) and electromagnetic (EM) measurements in the Northern part of themid-Atlantic ridge where a series of axial magma chambers (AMC) are presumably lo-cated. There is a good agreement between the measured electric conductivity for gabbrosamples with the melt fraction of 10-13 % vol. and the conductivity estimated at AMC, be-neath the central part of Reykjanes ridge, as well as between the conductivity of partiallymolten peridotites and the source zone beneath the mid-Atlantic ridge at the ' 60km.

1. INTRODUCTION

The electric properties of partially molten peridotite rocks are thought to affect thedepth profile of the electric conductivity in lower lithosphere and upper mantle. Recently,a growing number of electromagnetic field experiments have constrained the electricalstructure of the Earth’s interior, specially in mid-oceanic regions [1,2]. Based on MT and

∗present address : Laboratoire Magmas et Volcans, Universite Blaise Pascal, 5 rue Kessler, 63038Clermont-Ferrand cedex, France

1

2 J. Maumus et al.

EM data, two types of electric conductivity anomalies in the Earth’s crust and the uppermantle may be distinguished: high conductivity zones (HCZ) and low conductivity zones(LCZ). The combination of MT, EM and seismic studies has suggested that the partialmelting of peridotites and gabbro may explain the origin of the high conductivity zonesand axial magma chambers beneath the axe of the mid-Atlantic [1,2]. The interpretationof these field data did not rely on laboratory experiments and theoretical models of partialmelting, which is important in tackling the problems: what and where is the melting andhow does it extend beneath mid-oceanic ridges and other tectonic environments wherepartial melting presumably occurs? Thus, a direct comparison between laboratory mea-surements and field observations of the electrical conductivity of crust and upper mantleis a vital need for a correct interpretation of field geophysical data.

One of the fundamental physical properties of rocks which can be successfully measuredin field and laboratory, is the electrical conductivity σ. The resistance R of a sample de-pends on its geometry and a specific resistance of rock under test ρ. For an homogeneoussample of area A and a length L, having a parallel plate geometry, it follows

R = ρL

A(1)

The reciprocal value of the specific resistance is called specific conductivity σ,

σ =1

ρ(2)

Most of minerals representing rocks in upper mantle and lithosphere are ionic or elec-tronic conductors. Ionic conductivity relates to the diffusion transport process of chargecarriers in bulk of minerals and on the grain boundaries via a diffusion coefficient of thecharged species and the relation

σ =Dz2e2n

kT(3)

which is a form of Nernst-Einstein equation where D is the diffusion coefficient, z thevalence of conducting species, e the charge of electron, n is the concentration of the con-ducting species, k is the Boltzmann constant and T the absolute temperature in Kelvin.In olivine, for example, the contribution from ionic conductivity from Mg vacancies in-creases with temperature and exceeds the contribution from electron-polaron conductionmechanism at T > 1150oC, which is a dominant electric charge transport mechanism atT < 650oC. Several works addressed the question at which conditions differing temper-ature and fO2 dependencies of σ, i.e. ionic and electronic conduction mechanisms, areoperating in olivine (see [3–6] and references therein). The question which still remainsopen is what kind of charge carriers predominates in the overall electrical conductivity inminerals composing peridotitic rocks? The mechanism of a charge carrier transport couldbe discriminated through measurement of the Seebeck coefficient or thermopower, i. e.the voltage generated across a sample in a thermal gradient (e.g. [7]), or from the tem-perature dependence of electrical conductivity σ(T ) in Eq 3 and its activation energy Ea,

Electrical conductivity and melting 3

derived from the Arrhenius dependence of σ. The electrical conductivity measurementsshould be done in this case in a wide range of frequencies ω and temperatures T .The impedance spectroscopy method in application to electrical conductivity of rocksconsists of measuring of R − C parameters of equivalent circuits as a function of T andP at varying frequency ν or cycle-frequency ω = 2 · π · ν. The measured complex electricimpedance which consists of real Z

′(ω) and imaginary components Z

′′(ω) may be pre-

sented in an Argand plot, a graph of −Z′′(ω) vs. Z

′(ω). In a parametric form, the total

electric impedance Z(ω) may be described as a sum of two or more terms as follows

Z(ω) =R1

1 + (j · ω · τ1)α1+

R2

1 + (j · ω · τ2)α2+ ... (4)

where R1,2 is the active resistance, τ1,2 is the dielectric relaxation time, and α1,2 is theexponent characterizing the deviation of a particular relaxation process from a Debyetype of relaxation. The first term in Eq 4 responsible for high frequency behavior (> 103

Hz, usually refers to bulk properties of a tested sample, the second term is attributed tothe grain boundary properties of constituent minerals [8] and attributed to intermediatefrequency properties. The third term, which is omitted in Eq 4, may describe the R− Cproperties of electrodes or low frequency dispersion (< 1 Hz). Under pressure and after areasonable annealing time, the contribution from the grain boundary R−C term becomesnegligible [9] in comparison with a bulk term. Thus, by fitting an observed Argand plotto Eq 4, the bulk properties of a rock sample, resistance R1, dielectric relaxation time τ1

and a parameter of a constant phase element α1, can be estimated. From experimentsconducted at varying T , the temperature dependence of R1(T ), τ1(T ) or σ(T ) may bedetermined which usually follow an Arrhenius equation with the same activation energyEa

σ = σ0 exp(−Ea

kT

)(5)

The use of the impedance spectroscopy (AC-measurements in a wide frequency range)in measurements of natural rock samples is necessary for several reasons: (i) The con-ductivity of polycrystalline materials is always frequency dependent. (ii) Grain interiorand grain boundary conductivities operate at differing frequency ranges, but they canbe overlapped in an impedance spectrum. (iii) By doing experiments in a wide range oftemperatures, contributions from differing charge transport mechanisms corresponding todiffering frequency ranges can be identified.The measured complex impedance is characterized by two components Z

′(ω) and Z

′′(ω).

Impedance spectroscopy (IS) involves the measurement of Z′and Z

′′as a function of ω

in a large frequency range.Until now, only few experimental works were performed to measure the electrical con-ductivity of partially molten peridotite rocks at lower crust or upper mantle conditions.The experiments were mainly conducted on partially molten rocks at atmospheric pres-sure [10,11]. Despite the fact that the electric conductivity of rocks at HP/HT dependsinsignificantly on pressure, the effect of pressure in the case of partially molten rocks isimportant because the solidus temperature directly depends on pressure. In this work in-situ partial melting of mafic and ultramafic rocks was monitored by the use of electrical

4 J. Maumus et al.

conductivity at the crust and the upper mantle P − T conditions.For long monitoring of the variations of electrical conductivity in a piston cylinder a spe-cial construction of a measuring cell was developed and tested. The measuring cell hasbeen used in a form of a concentric cylinder capacitor Fig. 1. This cell was calibrated byusing several standard materials (boron nitride, Al2O3, NaCl, CsCl etc). With the useof this cell the electrical conductivity of natural and analog rocks under pressures up to2 GPa has been investigated. The temperature of experiments varied from 800oC and upto 1470oC. With the help of this measuring cell the partial-melting of some peridotitesand oceanic gabbro was characterized via electric measurements. During the experiments,when a rock sample starts to melt, the occurrence of the first percentage of melt couldbe detected by an abrupt decrease of the electrical resistance. Time variations of themelt fraction and melt topology during progressive melting produce a direct effect on theelectrical conductivity of a rock sample. After melting, the quenched samples were exam-ined, the melt distribution and the melt volume fraction were characterized in order tofind a quantitative relationship between molten rock textures and electrical conductivity.Finally, the electrical conductivity measurements are compared with field electromagneticmeasurements in order to answer the question: Do the electrical measurements realizedin laboratory on molten rock help petrologists and geophysicists to better constrain thedata obtained from deep Earth probing?

2. DESCRIPTION OF EXPERIMENTS

2.1. Measuring cell for electrical conductivityThe pressure experiments were performed in a conventional 1/2 inch end-loaded piston-

cylinder apparatus. The construction of the measuring cell is described elsewhere [12,13]and presented in Fig. 1. The cell assembly consists of a pressure transmitting mediafrom a sleeve of CaF2, of a heater from a sleeve of graphite and of an inner insulatingmaterial from a sleeve of boron nitride. The sample is located in the center of the cellassembly. In all experiments, the pressure was increased manually with a hydraulic pumpup to the desired pressure, then the automatic motorized hydraulic pump was switchedon to control the oil pressure automatically. The pressure calibration of the cell has beendone using standard points. The room temperature calibration has been performed byusing the phase transitions in bismuth: BiI − BiII at 2.56 GPa and BiII − BiIII at2.7 GPa [14]. Standard points for high temperature calibrations were melting curves ofNaCl and CsCl [15] and α-β transition in LiNaSO4 [13]. The melting points of NaCland CsCl as a function of pressure were estimated from in-situ electrical conductivitymeasurements at a fixed electrical frequency of 1 kHz. A jump of conductivity of ca. 2orders of magnitude indicated the melting point of chlorites. The accuracy of the pressurecalibration is ±0.03 GPa. The temperature gradient in the cell was estimated with theuse of Al2O3 powder instead of a sample and by placing three S -type thermocoupleslocated in three different points close to the middle of the graphite furnace (see Fig. 1).The radial temperature gradient is about ' 1oC/mm. The axial temperature gradientwas estimated to ' 2oC/mm in the temperature range up to 900oC, about ' 5oC/mmbetween 900 and 1200oC, and increases up to ' 12oC/mm at 1500oC. This design ofthe measuring cell has been successfully used in previous studies of phase transitions in

Electrical conductivity and melting 5

calcite [16] and in quartz [17].

Figure 1. Design of the cell assembly (not toscale). Outer diameter 1/2 inche.

Figure 2. Variation of electrical conduc-tivity with time for Oman gabbro samplesat 1 GPa and 1240oC (circles), 0.5 GPaand 1188oC (squares) and 0.3 GPa and1196oC (triangles). The large increase ofconductivity is attributed to developmentof a connected network of melt within thesamples.

The sample rock powder was placed between two metallic coaxial cylindrical electrodesmade of Mo -foil (thickness 0.5 mm) having inner and outer diameters 2.1 and 3.9 mm,respectively. Thus, the radial sample thickness is 0.9 mm. The choice of Mo instead oftraditional Pt-foil as an electrode material was dictated by the necessity to prevent thelosses of Fe from a sample into electrodes. The outer electrode was in contact with theboron nitride (BN) sleeve and the inner electrode is wrapped around a Al2O3-ceramicstraw 2mm in diameter. The alumina ceramics has 2-4 inner capillars for thermocouplewires. In the most of experiments S -type and B -type thermocouples were used to monitorthe temperature. The thermocouple junction is located at the end of the Al2O3 ceramicand touched the inner electrode. Thermocouple of B -type (Pt-30%Rh/Pt-6%Rh) aremore stable at high temperatures (T > 1200oC with an accuracy of 0.5% above 800oC).To avoid the contamination of a thermocouple junction from a sample material, the openend of the inner electrode was sealed with a Mo-foil disk preventing the touch between

6 J. Maumus et al.

sample and Al2O3 ceramics. The sample length is 4-5 mm. The rest of the space in theinner BN-sleeve between the sample and the HM-piston was filled with a BN-ceramicplug.The geometry of electrodes consisted of two cylindrical surfaces and one closed with Mo-foil disk end. This geometry of electrodes provides more complicated geometric factorthan in the case of a standard co-axial cylindrical capacitor. The correction of Gf ofelectrodes has been taken into account to calculate the bulk resistance of the sample. Forelectrodes in a form of a standard coaxial cylindrical capacitor having an outer diameterD, inner d and length L,

Gf cylindrical =2πL

ln(

Dd

) (6)

with a typical values of D, d and L in Eq 6 provides Gf ∼ 5 − 7cm. The applicationof coaxial-cylindrical electrodes results in a better measurement precision at low temper-atures. For a same sample volume: Gf parallel−plate ≤ Gf cylindrical, which means that themeasured sample resistance is smaller in the case of a concentric cylinder than in thecase of a parallel plate capacitor. Thus, the ratio of the shunt resistance to the sampleresistance is larger in the case of a co-axial capacitor. From other side, the outer cylin-drical electrode plays a role of electric shield against a noise produced by the graphiteheater. By the use of co-axial cylindrical electrodes, the vertical electrode axis is parallelto the piston motion, and the electrode corrugation during pressurization of a sample isminimized. The changes of the cell geometry measured after the high pressure experi-ments for Linner−electrode and D are 3-4% and 1-2%, respectively. These deformations ofelectrodes did not affect the results of electrical conductivity measurements. Due to asmall deviation of the cell geometry from a co-axial cylindrical geometry (see Fig. 1),the inner electrode has a shorter length than outer electrode and the inner electrode hasan additional surface at the closed end. The deviation of Gf from Gf cylindrical has beenestimated from calibration measurements by using aqueous NaCl solutions of varyingmolality at atmospheric pressure and temperature. The conductivity of aqueous NaClsolutions were measured in a cell identical to the cell used in high pressure experimentsand were compared with the table values [18]. The correction factor of about 25% hasbeen introduced into the final calculation of the geometric factor Gf in Eq 6.Solartron 1260 (Schlumberger Co.), a frequency gain-phase analyzer was used for theimpedance spectroscopy measurements. Solartron 1260 equipped with Novocontrol soft-ware package, which provides measurements of electric impedance over a wide range offrequencies from 10−3 Hz to 32 · 106 Hz with a maximum resolution of 10−3 Hz and anerror of 100 ppm in phase estimations. During the measurements, the ground of thepiston-cylinder press was isolated from the ground of Solartron, and the measurementswere realized in a so called ”free-ground” configuration. One wire of the thermocoupleand the mass of the high pressure autoclave were used to connect inner and outer elec-trodes with input and output of Solartron device. Before starting a piston-cylinder run,the cell (Mo-electrodes without sample) and connecting wires were calibrated for short(space between electrodes was filled with a copper sleeve) and open (space between elec-trodes was empty) circuits in the frequency range 1 MHz - 0.01 Hz. The AC-resistance of

Electrical conductivity and melting 7

the cell in short circuit was typically ≈ 0.4 Ω. A complete description of the impedancespectroscopy method (IS) can be found in [8].

2.2. Sample DescriptionRock samples used in this study were natural rocks from the oceanic crust and the

upper mantle, gabbro and peridotites. A synthetic rock sample prepared from a mixtureof olivine and a synthetic basalt was also used in experiments to model a melting witha fixed melt percentage. After experiments, samples were quenched, cut perpendicularto the electrode axis, mounted in epoxy and polished for electron probe microanalysis(EPMA) to provide sample texture images. Rock samples were prepared by crushingchips of natural rocks. After grinding in the agate mortar, mineral grains have a max-imum size of 40-50 µm that is much smaller than the gap between two electrodes (0.9mm).For sintering of a synthetic rock compact (synthetic basalt + San Carlos olivine), thesynthetic basalt was prepared from high purity oxides (Chempur Co.) and carbonatesgrounded into fine powder under acetone. The powder mixtures were dried at 150oC andthen fired during 10 hours at 1000oC in a CO2/H2 atmospheric furnace with gas flowrates adjusted to yield an oxygen fugacity between magnetite-wustite and iron-wustitebuffers (fO2 = 10−15.9 Pa). The resulting glass was crushed, grind to a grain size ca. 5-10µm. San Carlos olivine grains were grind to a 25 µm maximal grain size. The uniformgrain size in powder compacts was provided by sorting mineral grains in a vertical Erlen-meyer using a selective sedimentation of grains in water. Olivine and basalt were mixedtogether under ethanol and evaporated in order to produce a homogeneous fine powderin the proportion 95 to 5 wt.%.Before cell preparation, all sample powders were kept 24h in a dryer at 150oC. Afterdrying, powders were pressed into the cylindric gap formed by outer and inner electrodesof a measuring cell (Fig. 1). Powders were compacted and pressed with special tools, andthen pressurized in a piston-cylinder.

Two crustal rocks were investigated, an oceanic gabbro rock sample from Oman ophi-olites and a continental olivinite sample from the layered intrusion in Karelia, Russia.Oman gabbro sample is a gabbronorite containing 46 vol.% plagioclase feldspar, 40%orthopyroxene (Opx) and 14% clinopyroxene (Cpx). Chemical composition is presentedin Table 1. Oman ophiolites are interpreted as a material of an ancient oceanic ridgeobducted on Arabic plate platform with a relative small deformation. Probably, Omanophiolites formed at a fast spreading ridge and are differing from the crust formed atslower spreading ridge [19]. This gabbro sample represents a cumulate gabbro formedby a partial crystallization of a melt, from which the residual melt fraction has been re-moved. The formation of this 2-pyroxene gabbro has been discussed in the literature andit is interpreted as a result of the successive intrusions from a perched magma lens [20], orof the crystallization along the floor of the magma lens with a subsequent subsidence, orof both of these two mechanisms [21]. Anyway, this gabbro composition is representativeof the lower crustal rocks formed in magma chambers at a mid oceanic ridge axis.Karelia olivinite sample stems from the large intrusive massif Kivakka-Olanga (NorthKarelia, Russia). It is a product of high temperature differentiation and crystallization

8 J. Maumus et al.

of a magmatic pluton. This pluton was a long lived magma chamber that developedabove a local mantle plume which origin is associated with the activity of the megaplumeresponsible for the formation of Baltic shield province. The age of the pluton is 2.42-2.44Gy estimated from Sm-Nd and U-Pb methods [22]. The sample represents an olivinitecumulate layer with low Mg number in olivine crystals, c. Fo82−84. Karelia olivinite iscomposed of 76% vol. Ol, 3% Cpx, 7% Opx and 14% of plagioclase feldspar, its chemicalcomposition is listed in Table 2.

Table 1Chemical composition of Oman gabbro in wt.%*

Oxides(wt.%) Cpx Opx P lg

SiO2 52.77 54.28 46.17

Al2O3 2.04 1.17 34.23

FeO(total) 7.59 15.76 0.56

CaO 20.96 1.34 17.40

MgO 15.74 26.83 0.06

MnO 0.21 0.37 0.01

Na2O 0.28 0.03 1.54

TiO2 0.35 0.18 −Cr2O3 0.05 0.02 0.02

NiO 0.02 0.03 −P2O5 0.01 − −*Average microprobe analysis on 5-7 grains.

Two natural lherzolites samples, from Ronda (Spain) and from Spitzbergen (Norway),representative of the upper mantle were chosen for electrical conductivity measurements.Spitzbergen sample represents an ”anhydrous” spinel lherzolite from a peridotite xenolithuplifted in the nepheline basanite environment during Pleistocene from the upper mantlethrough a relatively thick continental crust and found in Sverre volcanic center, NW ofSpitzbergen. A summary of the tectonic setting can be found in [23]. The rock is composedof 68 vol.% Ol, 22% Opx, 8% Cpx and 2% Spl. Mineral compositions are presented inTable 3. Ronda peridotite belongs to a large sub-continental peridotite massif located inBetic-Rif chains of SW Spain, which is known to have preserved peridotite metamorphicfacies. It was emplaced during orogeny in Betic-Rif realm. The general feature of themassif is presented in [24,25]. The sample which has been measured is a spinel lherzolitecomposed of 68 vol.% Ol, 25% Opx, 6% Cpx and 1% Spl. Its chemical composition ispresented in Table 4. Unfortunately, some traces of serpentine were presented in thesample.

Electrical conductivity and melting 9

Table 2Chemical composition of Karelia olivinite in wt.%*

Oxides(wt.%) Ol Opx Cpx P lg

SiO2 39.15 51.06 51.17 55.67

Al2O3 0.02 6.47 3.25 26.82

FeO(total) 14.97 6.08 5.09 0.01

CaO 0.05 0.35 20.04 9.91

MgO 44.07 32.03 16.05 0.04

MnO 0.22 0.15 0.14 0.01

Na2O 0.01 0.05 0.61 5.80

TiO2 0.02 0.08 0.49 0.07

Cr2O3 0.01 1.76 0.93 0.02

NiO 0.32 0.08 0.04 0.01

K2O − − − 0.28

P2O5 0.01 − 0.01 0.03

*Average microprobe analysis on 5-7 grains.

The compact powder aggregate consisting of San Carlos olivine and synthetic basalticglass has been used as an analog of a partially molten rock representing a source of themagma beneath a mid-oceanic ridge. The content of the basalt glass recovered from thesample after HP-HT experiments was ≈ 4.5 vol.%. Chemical compositions of the olivineand basalt glass are presented in Table 5. This particular basalt composition has beencalculated according to [26] in order to be close to the equilibrium with San Carlos olivinecrystals during a long sintering process of a powder compact.

3. Results of measurements

For all samples, the experimental procedure was the same:(1) Samples were first pressurized to 0.3 GPa and heated up to 400oC and kept 24h;(2) Samples were heated to a temperature 900−1000oC with a heating rate of 20−25oC/hand kept for 24h in order to obtain a good sintering of samples;(3) Samples were cooled to a temperature of 800oC and kept at this temperature until wereached a stable value of the electrical conductivity which takes ∼ 200h ;(4) Then, electrical measurements started: the temperature was increased stepwise onlyif a constant electrical conductivity was observed during the last 12-24h (the temperaturestep varied between 10o and 50oC). Larger steps were taken when the temperature wasfar from the expected solidus temperature. After each temperature step, IS measurements

10 J. Maumus et al.

Table 3Chemical composition of Spitzbergen lherzolite in wt.%*

Oxides(wt.%) Ol Opx Cpx Spl

SiO2 40.24 55.16 52.11 0.04

Al2O3 0.01 3.07 5.23 52.30

FeO(total) 8.80 5.65 2.14 10.66

CaO 0.03 0.39 21.02 −MgO 48.68 33.10 14.86 19.24

MnO 0.13 0.15 0.08 0.12

Na2O 0.01 0.06 1.52 0.02

TiO2 0.01 0.07 0.35 0.05

Cr2O3 0.01 0.34 1.01 16.27

NiO 0.37 0.08 0.04 0.31

P2O5 0.01 − 0.01 −*Average microprobe analysis on 5-7 grains.

were performed every 15-60 min, and the electrical conductivity was estimated from thefitting of Argand diagrams measured on the sample to the electrical equivalent circuitcomposed of two R-CPE elements connected in series, according to Eq 4. Using thisheating procedure, we were not able to maintain a fixed heating rate. Samples need moretime to reach a stable value of electrical conductivity at low temperatures than at highertemperatures. At each temperature, the last conductivity measurement is kept as a finalvalue and plotted in a Arrhenius plot (log (σ) vs. reciprocal temperature 1/T, K). Theconductivity of ”dry” samples usually demonstrate a linear dependence of log(σ) as afunction of the reciprocal temperature 1/T, K;(5) Temperature is increased stepwise but the measured conductivity does not correspondto the expected extrapolation of the linear Arrhenius plot defined from previous measure-ments (step 4). If the measured electrical conductivity exceeded the extrapolation of thelinear Arrhenius plot, then this temperature was considered corresponding to the occur-rence of melt interconnection in the sample. When melt is interconnected through thesample, a conductivity jump is observed and the procedure continued with the step (6);(6) When a significant conductivity increase was observed, the correspondent temperaturewas kept as constant and the sample electrical conductivity was measured until it reachesa steady state (2-5 days) at a constant temperature (see Fig. 2);(7) Sample were quenched in order to ”freeze” the partially molten textures. Pressurewas carefully set to 0.1 MPa and samples were prepared for the observation of melt dis-tribution.At temperatures lower than 800oC it was not possible to perform a reliable electricalmeasurement in the desired range of frequency (10−2 to 105Hz), the apparent resistanceof the sample was too high and the frequency scans were substantially corrugated. Sev-eral factors may account for the observed disturbances of the electrical signal and a bad

Electrical conductivity and melting 11

Table 4Composition of Ronda lherzolite sample in wt.%*

Oxides(wt.%) Ol Opx Cpx Spl

SiO2 41.11 54.65 53.11 0.03

Al2O3 0.01 4.69 5.36 50.83

FeO(total) 8.54 5.61 2.16 12.10

CaO 0.02 0.96 21.61 −MgO 51.44 33.97 15.89 19.67

MnO 0.13 0.14 0.08 0.13

Na2O 0.01 0.05 1.26 −TiO2 0.01 0.05 0.11 −Cr2O3 0.01 0.72 1.16 17.39

NiO 0.41 0.08 0.03 0.27

P2O5 0.02 0.01 0.02 −*Average microprobe analysis on 5-7 grains.

quality of Argand plots: (i) at low frequencies the quality of the contact between a sampleand electrodes is not perfect; (ii) the electrical noise is produced by the graphite furnaceinterferes with the signal and decreases the resolution of a phase delay of Solartron; (iii)the capacitance of the electrode-sample interface may hide the capacitance of the sample; (iv) the sample conductivity at low temperatures cannot be measured because of thesmaller ratio between shunt and sample resistances.In the temperature range from 800oC for each sample and at each temperature, IS mea-surements were performed in a frequency range of 10−2 Hz to 5·105 Hz. When the meltingtemperature has been reached no significant changes in a shape of impedance spectra wereobserved in Argand diagrams (see example of Oman gabbro in Fig. 3).

Below the solidus, the impedance spectra plotted on Argand diagram are similar plotsto those reported by Roberts and Tyburczy ([27,28] for their polycrystalline compacts andto the results of Huebner and Dillenburg ([9]; (i) a semi circle at high frequencies (HFC),which is related to the bulk grain conductivity, (ii) and only a portion of a semi-circle atlow frequencies (LFC) that may be attributed to electrode-sample interface (left and righthand sides of Fig. 4, respectively). At intermediate frequencies, a contribution from agrain boundary conductivity could be expected but it is not observed due to a good sinter-ing of grain boundaries under pressure during a long annealing time. With the increasingtemperature, the general shape of the impedance spectrum doesn’t change too much butthe size of semi-circles decreases. This is due to an increase of the bulk conductivity. TheHFC maximum and intersection (or cusp in Fig. 4) with the horizontal axis, is progres-sively shifted to higher frequencies, does not display a complete semi-circle but rather asmall portion of this semi-circle. Thus, the contribution from the electrode-sample in-terface becomes more significant at high temperatures and shifts to high frequencies. Atmaximum temperatures of experiments ∼ 1250oC the typical frequencies of the cusp in

12 J. Maumus et al.

Table 5Composition of San Carlos olivine and synthetic basalt glass in wt.%*

Oxides(wt.%) Ol (95%) Synthetic basalt glass (5%)

SiO2 40.86 45.33

Al2O3 − 11.73

FeO(total) 9.53 9.20

CaO 0.06 10.36

MgO 50.07 12.96

MnO − 0.17

Na2O − 2.31

TiO2 − 0.78

Cr2O3 − 2.32

NiO − 0.05

P2O5 − 0.10

K2O − 0.33

*Average microprobe analysis on 5-7 grains.

Fig. 4 is ∼ 103 Hz. At temperatures above the solidus, no significant changes in theshape of spectra are observed in comparison with impedance spectra below solidus. Thiscould indicate that the presence of melt at grain boundaries decreases further the grainboundary resistance and shifts a hidden grain boundary semi-circle into high frequencyrange. In Figs. 3 and 4 at 791, 931 and 1085oC, the estimated conductivity is associatedwith a melt-free rock electrical conductivity. At 1253oC, the lowest value of the sampleresistance and the highest value of conductivity correspond to the presence of melt in thesample. At subsolidus temperatures, the sample conductivity displays a linear increasewith temperature that can be fitted by an Arrhenius equation (Eq 5). The activation en-ergy corresponding to the bulk conductivity mechanism can be estimated from this slope(see Fig. 5). Above solidus, when a jump of conductivity is detected, the correspondenttemperature was kept as constant and the impedance spectra were measured as a functionof annealing time in order to observe the variation of conductivity. The occurrence of meltimplies an important change in the conductivity of a rock due to the contrast betweenthe rock grains interior and the melt conductivities. The melt conductivity is about 2-3order of magnitude higher than the grain interior conductivity. Thus, the melting of arock has been detected from electrical impedance. The melt occurrence will effectivelyincrease the overall conductivity only when the melt phase is interconnected. At smallmelt fractions, the melt may be partially distributed in a form of isolated pockets betweenmineral grains. When the melt fraction is large enough, the geometry of a melt phasebecomes interconnected and the melt network, controls the overall sample conductivity,in this case. Thus, the increase of the electrical conductivity at high temperatures doesnot obviously correspond to the occurrence of the first percentage of melt or starting ofmelting above solidus temperature. This increase may be shifted to higher temperatures

Electrical conductivity and melting 13

due to a delay in the establishing of an interconnected melt network. The establishing ofa steady state electrical conductivity in partially molten rock requires a long time (Fig.2). Only after 2 to 4 days, the conductivity reached a steady-state value which is 1-3order of magnitude higher than the conductivity of melt free samples prior to melting(Fig. 2).Gabbro rock from Oman ophiolites was investigated at 0.3, 0.5 and 1 GPa. The electricalconductivity measurements are presented in Fig. 5. For each sample two stages wereobserved:(i) at temperature below solidus, the gabbro electrical behavior can be fitted toArrhenius Eq 4. At this pressure range, no significant variation of conductivity can beobserved with pressure, and the temperature dependence may be fitted with Ea = 1.38eV and log σ0 = 2.51 S/m. (ii) at temperatures above solidus, the conductivity increasesdramatically: it take several days until it remain stable (Fig. 2). This conductivity jumpis observed at 1240oC (1 GPa), 1196oC (0.5 GPa) and 1188oC (0.3 GPa), and it is about1-2 order of magnitude. This large conductivity change is related to the occurrence of afirst melt in gabbro. At the stage of the formation of interconnected melt network, themelt conductivity starts to control the conductivity of gabbro samples. The conductiv-ity increases with time because (i) the melt reaches chemical and textural equilibriumwith pyroxene grains; (ii) the melt interconnection is delayed due to a slow migrationequilibration processes of the melt phase in presence of pyroxenes. The temperatures as-sociated with the conductivity-jump are more than 50oC higher than the expected solidustemperature of this pyroxene gabbro estimated from the viscoelastic behavior [32].Two experiments were performed at 1 GPa on Karelia olivinite samples. The generalbehavior of the first experiment, presented in Fig. 6, is close to that observed in Omangabbro samples. The melt-free rock can be fitted with the Arrhenius equation withEa = 0.82 eV and logσ0 = 0.67 S/m. Comparing with the conductivity of Oman gabbro(having Ea = 1.38 eV), Karelia olivinite is more conductive, having a smaller activationenergy. This may be explained by compositional differences between these two rocks,olivinite is an olivine-rich rock. The olivine crystals possess higher Fe content (Mg num-ber is 84), and this may explain higher conductivity and lower activation energy in thissample. With the increasing content of Fe in olivine the electron-polaron hopping conduc-tion may extend to higher temperatures [5,6]. Above the solidus, the similar melt effecton the electrical conductivity is observed in olivinite as in gabbro. For Karelia olivinitesample, the conductivity jump is about 2-2.5 orders of magnitude (in comparison with 1.5order of magnitude for Oman gabbro at 1 GPa). This melt effect in olivinite is observedat 1315oC. After reaching a stable conductivity, the sample was quenched. A secondexperiment was provided at the same pressure but the sample was not quenched after themelt occurrence was detected. This second sample was cooled with a constant cooling rateof 20o/h. During cooling the sample shows higher conductivity than during heating. Ifa connected melt network exists in the sample, cooling could transform the basaltic meltinto a glass. The basaltic glass possesses higher conductivity than grains interiors. Thus,this experiment confirms that the melt effect on the electrical conductivity correspondsto the formation of an interconnected melt network above solidus.

The electrical conductivity of Spitzbergen lherzolite has been measured at 1 and 2GPa. Below solidus temperature, the pressure dependence of conductivity on pressure isinsignificant. At 2 GPa the conductivity of a melt-free sample was fitted with the Ar-

14 J. Maumus et al.

rhenius equation having parameters Ea = 2.11 eV and log σ = 4.25 S/m that is slightlylower than Oman Gabbro conductivity. The observed jump in conductivity is about 1-2order of magnitude at 1360oC (1 GPa) and 1465oC (2 GPa). The results of electricalmeasurements are presented in Fig. 7.Ronda lherzolite has been measured at 1 GPa. This rock sample exhibited small traces ofserpentine around olivine crystals. To avoid the influence of a serpentine on the electricalmeasurement, the sample was kept for 24h at 800oC. The conductivity measurementsare presented in Fig. 7. The comparison of the electrical conductivity variations withthe sample texture demonstrated that after sintering the serpentine disappears. Rondalherzolite shows almost the same behavior as Spitzbergen lherzolite. The melt-free rockbehavior can be fitted with the Arrhenius equation (Ea = 1.61 eV and log σ = 2.65 S/m).Above the solidus temperature, the conductivity jump of 1 order of magnitude at 1377oCis observed.Only one experimental work [10] deals with the electrical conductivity of a compact pow-der consisting of olivine + basalt glass, which can be compared with the studied samples ofolivine + basalt aggregates (see Fig. 8). Anyway, (i) In [10] Fo80 olivine was used, versusFo90 in this study, and the basalt glass composition was different. (ii) The experimentsin [10] were made not directly on a starting powder mixture of olivine and basalt glass,which has been done in this study. The compact powder sample in [10] was sintered athigh pressure in a piston cylinder apparatus and, then, the electrical conductivity of a sin-tered sample was measured in the atmospheric furnace with a controlled oxygen fugacity.Thus, in these experiments it was not possible to observe the conductivity increase abovesolidus due to the developing melt interconnection within the sample. In [10] the increaseof the electrical conductivity corresponds to the point of softening of the basalt glass,thus, the magnitude of the conductivity jump does not fully reflect the effect of meltingand spreading of melt between olivine grains. The observed increase of the conductivitydue to the melting in the present sample is about 0.5 order of magnitude higher than in[10] sample, which may be also due to the compositional differences of olivine.A remarkable point is that the small conductivity jump was observed for a melt fractionof only 4.5 vol.% (that is, the maximum melt fraction that was allowed in this sample witha chosen basalt composition). This melt fraction is rather low compared with the meltfraction observed in natural rock samples, gabbro, olivinite and peridotites. This is not asurprise, if one considers, that at textural equilibrium, in the system olivine + basalt, thebasalt melt should be interconnected even at smaller melt fractions in comparison withpyroxene bearing rocks. This fact emphasizes the non-ideal wetting of melt and mineralgrains in natural rocks containing more pyroxene and less olivine. In partially moltenrocks containing pyroxenes and less olivines, a perfect melt interconnection could not bereached when a melt fraction lower than 5-10 vol.% [38,39]. At higher melt fraction, theinterconnection of the melt increases rapidly through grain boundaries adjustment to thepresented melt phase topology.The temperature at which the conductivity jump is detected in peridotites, is higher thanthe expected solidus temperature. Hirschmann [40] compiled experiments made on natu-ral peridotites to constraint the solidus temperature versus pressure. Tsolidus may be fitted

Electrical conductivity and melting 15

with a polynomial relationship:

Tsolidus = a× P 2 + b× P + c (7)

where Tsolidus in oC and P in GPa. Best data fit is obtained with a = −5.104, b = 132.99and c = 132.899. From Eq 7, Tsolidus would be 1153oC (at 1 GPa) and 1167oC (at 2 GPa)with an error of 20oC. This is significantly lower than temperature at which partial meltaffects the electrical conductivity of Spitzbergen lherzolite.Another experimental run was performed with the pure basalt glass compact at 1 GPa.This run was divided into three steps. (1 ) Sample heating: the basalt glass was heateduntil 1170oC where the electric conductivity increases for about one order of magnitude.This can be explained by glass melting. (2 ) After keeping the melt for 12h at 1170oC,the basaltic melt was cooled down with a cooling rate of 25o/h. During cooling basalticmelt exhibits higher conductivity than basalt glass compact during heating that can alsobe explained by a change of the sample geometry due to melting. In the stage (1 ), thesample was a compact powder, and, thus, the conductivity is a sum of the surface andvolume conduction mechanisms. In the stage (2 ) the glass is melted, thus sample becamehomogeneous and the bulk conductivity is a dominant mechanism. (3 ) After keepingthe sample for 12h at 900oC, the glass was reheated up to 1240oC with a heating rateof 20o/h. The sample demonstrated the same temperature behavior than during thestage (2 ). Thus, the conductivity measured during the stages (2 ) and (3 ) represents thereal behavior of the basaltic melt/glass. This behavior shows a good agreement with theconductivity data from [34] measured on basalt glasses. We observed that the basalt glassconductivity is 2.5 order of magnitude higher than the conductivity of San Carlos olivine.The electrical conductivity of San Carlos olivine powder compact (Fig. 8) corresponds toconductivity of Ol crystals without basalt glass measured at 1 GPa, and the results aresimilar to [37].

4. DISCUSSION

4.1. Product of experimentsThe samples from each experimental run were quenched, cut perpendicular to the cell

axis and polished with alumina powder and colloidal silica, and prepared for the analysis ofmelt distribution within samples, which was done with the use of reflected light microscopeand of backscattered electron images obtained on the electron microprobe Jeol JXA-8900.No evidence of melt segregation on the scale of the full sample length was detected.Typically, the equilibrium distribution of melt phase is indicated by the presence of wellformed triple junctions and stable melt wetted crystal faces [41–43]. This texture hasbeen interpreted as an indication of a complete inter-connectivity of the melt [41]. Tables6, 7 and 8 list melt compositions and quenching temperatures of each measured samples(average of 10 microprobe analyzes of glass and crystal with a beam current of 10 kV and20 nA, and an electron beam spot of 5 µm for glass analysis). Quenching temperaturescorrespond to temperatures at which a detectable increase of the electrical conductivitytakes place. Note that in all natural samples the melt occurrence was detected only for amelt fraction ' 10 vol.%.

16 J. Maumus et al.

Table 6Melt content in partially-molten quenched samples

Sample Quenching temperature, oC Melt fraction, vol.%

Oman gabbro

1 GPa 1240 34

0.5 GPa 1188 15

0.5 GPa 1187 12

0.5 GPa 1135 0

0.3 GPa 1196 17

0.3 GPa 1139 0

Karelia olivinite, 1 GPa 1315 10

Spitsbergen lherzolite

2 GPa 1465 22

1 GPa 1360 14

Ronda lherzolite, 1 GPa 1377 11

Olivine+basalt sample 1183 4.5

Microprobe analysis with a beam current of 10 kV and 20 nA

The melt fraction in each sample was estimated from the image processing of SEMpictures of thin sections. The vol.% of melt is extrapolated from the surface % of thinsections without correction to 3D-distribution. To be statistically representative, theseestimations must be obtained from a relatively large surface of a thin section. Table 6shows a melt content estimation and a quenching temperature for each measured samples,except the olivine + basalt sample where the melt content was fixed, and two gabbroexperiments which were quenched below solidus. The estimated melt content is relativelyhigh, larger than few vol.%. This is in agreement with higher temperatures which areneeded to detect an effect of melt affecting the sample conductivity. As it follows fromthe results, the electrical measurements are not very sensitive to detect a melting pointand a first melting fraction < 1− 2%. Larger melt fractions, at least 4-5 % are needed todetect melting via a noticeable increase of the electrical conductivity in olivine rich rocks.For example, in olivine + basalt compacts, where only Ol-Ol-melt triple junctions controlthe melt connectivity, the overall increase of electrical conductivity is moderate. In thecase of pyroxene-rich samples, like pyroxene Oman gabbro, even larger melt fractions areneeded to establish a complete melt interconnection because of the higher pyroxene-meltdihedral angle.

Melt distribution and melt geometry are described from backscattered electrons imagesof quenched samples obtained with a Jeol microprobe. Figs. 9, 10, 12, and 11 showexamples of the melt topology. It should be noticed that in many samples, thermalcracking during quenching correlates with the melt distribution as shown in Fig. 11. Nodihedral angle measurements have been done, but the triple junctions seems to be largerin Oman gabbro samples than in other samples. Different kinds of melt pockets can

Electrical conductivity and melting 17

be detected (e.g. Fig. 10). In all samples, the melt phase or glass occurs both as aninterstitial phase between olivine grains in triple junctions as well as in the form of meltpockets. The melt fraction is large in all studied samples, consequently, the melt fractionis mainly distributed in a form of large pools (see Figs. 9 and 10. We can also observe somewell formed and wetted triple junctions that indicates the developed melt interconnection.In Ol-rich samples, the Ol planar faces (F -faces) control the crystal wetting (Figs. 12and 10). The distribution of the melt phase demonstrates the anisotropy of Ol-basaltinterfacial energies. A similar melt topology is also observed in pyroxene rich samples, i.e.the formation of the non-regular triple junctions as it was described in [44]. In a partiallymolten system with an isotropic interfacial energy of mineral grains, a dihedral angle< 60o implies that the melt should be interconnected at all melt fractions. In the studiedsamples the interfacial energy is anisotropic and this complicates the interpretation ofthe melt topology. If melt fraction is not very high, the possibility of an occurrenceof non-interconnected or poorly interconnected melt geometry increases. The chlorinediffusion has been used as an indicator of a fluid connectivity in H2O-bearing quartzite[45]. Although, the H2O-quartz dihedral angle is 57o, the results suggested a completeconnectivity of a fluid phase at any volume fraction. An abrupt decrease of the bulkdiffusion coefficient for chlorine between 1 vol.% and 0.3 vol.% of fluid was observed in [45].This drop has been interpreted as a result of the elimination of interconnected porosityowing to the presence of a sufficient number of non-wetted grain edges. The similar resultswere obtained for the carbonate-olivine system [46]. The diffusive transport of Fe intodunite as a function of a carbonate melt fraction was studied in [46], and it was concludedthat the melt connectivity was only established above 0.05 wt.% of melt (that is, 0.07vol.%), despite the fact that the dihedral angle is much lower than the critical value 60o

(≈ 25 − 30o). In both studies, the elimination of connectivity at low fluid fractions wasinterpreted as a result of an anisotropy of the solid-fluid interfacial energy, or in otherwords, the differing crystallographic faces possess differing values of the interfacial energy,resulting in a differing thickness of the melt and its curvature on grain-melt interfacesdepending on the crystallographic orientation of grain-faces. The connectivity thresholdin the olivine-basalt system must be larger than in the carbonate-olivine system becauseof the much larger dihedral angle, and may be close to 0.3 vol.% as in the quartz-H2Osystem. The dihedral angle is only slightly larger in this system than in the basalt-olivinesystem, but the degree of the interfacial energy anisotropy is more pronounced for olivinethan for quartz [47]. Therefore, taking into account the presence of pyroxenes in the mostof the studied samples which probably lower the effective connectivity of the samples, itmay be concluded that at low melt fractions, lower than 5 vol.%, a network of grain-edgechannels with a low degree of connectivity can exist. This low degree of connectivity mayexplain the detection-limit of the melt fraction from electrical conductivity measurements.

Due to the lack of melt topology observations from our experiments, it was difficult tobring better constraints to discriminate different mixing models for the electrical conduc-

18 J. Maumus et al.

Tab

le7:

Com

pos

itio

nof

mel

tsan

dm

iner

als

afte

rex

per

imen

talru

ns

at1

GPa

for

Om

anga

bbro

and

Kar

elia

oliv

init

esa

mple

sin

oxid

ew

t.%

Roc

k−

sam

ple

Om

anG

abbro

Kar

elia

oliv

init

e

Oxid

e,w

t%m

elt

Opx

1O

px2

Cpx

quen

ched−

min

eral

mel

tO

l

SiO

250

.96

56.7

555

.19

53.2

949

.33

43.3

740

.39

Al 2

O3

29.3

73.

471.

272.

1417

.78

12.2

90.

04

FeO

(tota

l)2.

4910

.35

15.1

46.

744.

884.

367.

42

CaO

13.5

25.

491.

4021

.39

16.1

121

.86

0.27

MgO

2.05

23.3

426

.42

15.7

610

.96

17.0

551

.14

MnO

0.07

0.29

0.36

0.18

0.17

0.22

0.21

Na 2

O1.

430.

140.

020.

100.

610.

290.

01

TiO

20.

060.

150.

180.

360.

140.

320.

01

Cr 2

O3

−0.

010.

010.

020.

010.

110.

46

NiO

−−

0.01

−−

0.02

0.05

K2O

0.03

−−

−−

0.08

−P

2O

50.

01−

−0.

01−

0.03

0.01

Mic

ropr

obe

anal

ysis

with

abe

amcu

rren

tof

10kV

and

20nA

Electrical conductivity and melting 19

Tab

le8:

Com

pos

itio

nof

mel

tsan

dm

iner

als

afte

rex

per

imen

talru

ns

at1

GPa

for

per

idot

ite

sam

ple

san

dol

ivin

e-bas

alt

com

pac

tin

oxid

ew

t.%

Roc

k−

sam

ple

Spit

zber

gen

Ron

da

Olivin

e+

5w

t.%

bas

alt

Oxid

e,w

t.%

mel

tO

lO

pxm

elt

Ol

mel

tO

l

SiO

242

.75

40.1

256

.03

49.9

139

.95

47.6

340

.00

Al 2

O3

17.9

00.

355.

0717

.40

0.13

9.89

0.15

FeO

(tota

l)1.

5611

.02

1.12

7.21

8.38

5.24

9.86

CaO

2.14

0.36

0.16

15.0

90.

299.

370.

24

MgO

34.5

147

.68

37.2

07.

7650

.77

23.4

849

.07

MnO

0.25

0.21

0.10

0.15

0.14

0.14

0.15

Na 2

O0.

160.

050.

011.

79−

1.85

0.05

TiO

20.

110.

040.

020.

300.

011.

550.

06

Cr 2

O3

0.59

0.10

0.29

0.36

−0.

100.

02

NiO

0.01

0.06

0.01

0.04

0.30

0.13

0.39

K2O

0.06

0.01

−−

0.01

0.47

−P

2O

5−

0.01

−−

0.01

0.16

0.02

Mic

ropr

obe

anal

ysis

with

abe

amcu

rren

tof

10kV

and

20nA

.

20 J. Maumus et al.

Table 9Electrical conductivity of samples below solidus σ = σ0 exp (−Ea/kT )

Sample P ,GPa T ,oC Ea,eV σ0,S/m

Oman gabbro 0.3-1 900-1150 1.38 320.54

Karelia olivinite 1 1050-1250 0.82 4.71

Spitzbergen lherzolite 1-2 1250-1400 2.11 17.68 · 103

Ronda lherzolite 1 1200-1350 1.61 450.34

Olivine San Carlos 1 900-1250 1.53 165.67

tivity of partially molten samples. This is mainly due to a rather large amount of meltpresented in quenched samples. Electrical conductivity measurements obtained on sam-ples with high melt fraction (10 vol.%) was tried to fit with the Hashin-Shtrikman upperbound HS+. This is a well known approach in the analysis of conductivity of a compos-ite medium consisting of two phases or, so called, effective medium theory [48]. In theeffective-medium model, or Maxwell-Wagner model [49,50], the composite is described asa suspension of spheres dispersed in a continuous medium. The model was extended to thecase of ellipsoidal shape inclusions [51]. The method of [52] yields the upper conductivitybound (HS+) and the lower conductivity bound (HS−) and provides more realistic limitsfor the upper and lower limits of a composite conductivity. HS+ and HS− are the pos-sible maximum and minimum limits of the conductivity in medium with an isotropicallydistributed two phases. All models that predict a conductivity higher or lower than HS+

and HS− are automatically non-isotropic effective mediums. This approach provides agood estimations of a possible conductivity range for a system consisting from melt +solid grains, even in the case when the melt is distributed as a complete interconnectednetwork (HS+) or in the case when the melt pockets are isolated in a solid matrix (HS−):

σHS+ = σmelt + Xsolid

(1

σsolid − σmelt

+Xmelt

3σmelt

)−1

(8)

and

σHS− = σsolid + Xliquid

(1

σmelt − σsolid

+Xsolid

3σsolid

)−1

(9)

The results of a relative increase of electrical conductivity versus melt fraction accordingto HS+ model (Eq 8) are shown in Table 10.

It is clear now that the partial melting strongly influences bulk conductivity of rocks, butthe effects of melt composition variation still remains unclear. Melts conductivity increaseswith decreasing SiO2 content and with increasing Fe + Mg and alkali contents [53].Tyburczy and Waff [35] show that at high temperature, ionic conduction via alkali mobilityis the dominant mechanism of charge transport. They measured electrical conductivityof tholeiitic and andesitic melts, with a fixed electrical frequency of 2 kHz, at pressuresup to 2,5 GPa and observed a significant decrease of the electrical conductivity (lessfor tholeiite than for andesite) below 1 GPa that is more pronounced at temperature

Electrical conductivity and melting 21

Tab

le10

:M

elt

conduct

ivity

nee

ded

tom

odel

the

mea

sure

dm

olte

nro

ckco

nduct

ivity

wit

hH

ashin

-Str

ikm

anupper

bou

nd(E

q8)

.

Sam

ple

Tquen

chin

g,oC

log(σ

soli

d),

S/m

σm

elt,

S/m

Xm

eltvo

l.%

log(σ

HS

+),

S/m

log(σ

mes

),S/m

Om

anga

bbro

1G

Pa

1240

-2.0

81.

534

-0.4

1-0

.4

0.5

GPa

1188

-2.2

40.

2915

-1.4

4-1

.45

0.5

GPa

1187

-2.2

50.

3112

-1.5

1-1

.5

0.3

GPa

1196

-2.2

20.

4817

-1.2

0-1

.2

Kar

elia

oliv

init

e,1

GPa

1315

-1.9

228

.810

0.30

0.3

Spit

zber

gen

lher

zolite

2G

Pa

1465

-1.8

64.

922

-0.1

0-0

.1

1G

Pa

1360

-2.2

52.

514

-0.6

0-0

.6

Ron

da

lher

zolite

,1

GPa

1377

-2.2

52.

011

-0.8

0-0

.8

Ol+

bas

alt

sam

ple

,1

GPa

1183

-3.0

62.

94.

5-1

.05

-1.0

5

22 J. Maumus et al.

above 1200oC. Roberts and Tyburczy [10] reported that for a Fo80-basalt melt systemmeasured at 0.1 MPa, the effect of changing melt composition is balanced by the changein temperature. A recent work on basaltic rocks from Mount Etna [36] demonstrate thatwhile melts have higher conductivity due to higher alkali and Fe+Mg contents and lowerSiO2 content, the conductivity of a partially molten rocks is rather more influenced bythe quantity and topology of melt than to the melt composition. If we consider thehigh melt fractions observed in our samples, some effect of pressure or changing meltcomposition may be observed. Despite the difficulty to make a systematic analysis ofmelt chemistry vs. measured conductivity, we compared the calculated melt conductivityneeded to explain the conductivity jumps observed in our experiments (see table 10)and the composition of melts (tables 7 and 8). It should be noted here that (i) Peridotitesamples have a rather high conductivity regarding the alkali content of the produced melts;(ii) From the measurements made on Oman gabbro at 0.3, 0.5 and 1 GPa, the calculatedmelt conductivity increases with pressure increase. This fact contradicts earlier results ofTyburczy and Waff [35].

4.2. Interpretation of field dataThe obtained experimental results can be compared with resistivity profiles estimated

from electromagnetic (EM) and magneto-telluric (MT) field measurements. Recent EMand MT field measurements indicate the existence of high conductivity zones (HCZ) inthe crust [54] and in the upper mantle. Partial melting may be one of the plausibleexplanations of the nature of HCZ in the lower crust beneath Central Andes, Pyreneesand Tibetan Plateau. With the help of the conductivity mixing models it is possible toestimate the amount of melt in HCZ (see e.g. [55,56], and the references therein) for MTmeasurements in Andes, Pyrenees and Tibet. Natural source or magneto-telluric sounding(MT) and controlled source electromagnetism (EM) are two common methods to study thedeep electrical structure of the Earth lithosphere. EM is more appropriate for probing thefirst hundreds kilometers in the Earth. By using MT, it is possible to probe deeper in theEarth. To probe deeper in the Earth one needs to use EM sounding at lower frequencies.By measuring both magnetic (three components Hx, Hy, Hz) and electric (telluric) fields(two component Ex, Ey) in the Earth and determining their ratio at varying frequencies,it is possible to derive the conductivity variation with both depth and distance. Overa half-space, the apparent resistivity gives the true resistivity of the half-space at allfrequencies, and the phase lag is 45o. For a multi-layered Earth, these two parametersvary with frequency, and their variation with frequency can be inverted to explain theunderlying structure. Partial melting and the effect of the electrical conductivity increasedue to the presence of partial melts can be applied to interpret the existing geophysicaldata on oceanic ridges, like Mid-Atlantic or East-Pacific ridges (see e.g. [2,57,58]). Themeasured electrical conductivity of gabbro and peridotites were used to interpret theRAMESSES apparent resistivities [1]. This project integrated the both, field MT andEM measurements with the seismic measurements obtained in the northern part of themid-Atlantic ridge, and demonstrated the existence of two HCZ in the upper mantle andthe oceanic crust.Gabbro samples measured at temperatures below solidus show the same conductivityrange as the conductivity estimated at Reykjanes ridge far from the AMC in the non-

Electrical conductivity and melting 23

melted lower crust (Fig. 13). The same conclusion can be done for the partially moltengabbro at 1 GPa that exhibits the same conductivity range than the conductivity at AMC.Note that the estimated melt fraction measured in this sample after the experiment isc. 34 vol.%, Table 6, which is similar to the melt fraction estimated in the AMC fromRAMESSES projet. The conductivity measured in the same sample at 0.5 and 0.3 GPa are0.5-1 order of magnitude lower than estimated AMC conductivity. Karelia olivinite samplemeasured at 1 GPa demonstrates melt-free rock conductivity slightly higher than theconductivity of the non-melted crust at Reykjanes ridge (Fig. 14). This is probably dueto the high content of olivine in the olivinite samples. Partially molten Karelia oliviniteshows conductivity 0.5 order of magnitude higher than the AMC conductivity. Partiallymolten lherzolite (Ronda and Spitzbergen peridotites) measured at 1 GPa possesses theconductivity that also close to the conductivity range estimated in the partially moltenupper mantle rocks below the AMC (Fig. 15) in a source zone. The same observationcould be done for the olivine-basalt conductivity (Fig. 16). Partially molten Spitzbergenlherzolite measured at 2 GPa is 0.5 order of magnitude more conductive (Fig. 15) thanthe HCZ below AMC. Here again, there is a good agreement between the melt fractionobserved in our samples (respectively 11 and 14 vol.% for Ronda lherzolite and Spitzbergenlherzolite measured at 1 GPa, Table 6)and the melt fractions estimated in the partiallymolten mantle in a source zone 60 km below AMC from seismic and electromagnetic data.The decreapancy between the obtained results on partially molten rocks with the fieldmeasurements of the electrical conductivity from partially molten zones are within theuncertainties of field and laboratory experiments.

5. Conclusions

This experimental work provides some important insights on the electric conductivityin partially molten mafic and ultramafic rocks under pressure up to 2 GPa obtained bythe electrical impedance method.According to the presented experimental results it can be concluded that:(i) Below solidus, electric conductivity increases according to Arrhenius equation σ =σ0 exp (−Ea/kT ). Pressure does not appear to produce any strong effect on rock electri-cal conductivity in the experimental pressure range (0.3 to 2 GPa). log σ0 varies from0.67 to 2.50 S/m and from 2.65 to 4.25 S/m for crustal and mantle rocks respectively.Ea varies from 0.82 to 1.38 eV and from 2.65 to 4.25 eV for crustal and mantle rocksrespectively (see Table 9 for details). Mg number and the relative abundance of olivineand pyroxenes play a decisive role on the electric properties of mafic rocks.(ii) When temperature exceeds the solidus temperature, the conductivity increases abruptlyby 1.5 to 2 orders of magnitude depending on rock conductivity below solidus temper-ature. This sudden increase of conductivity is not observed at the expected Ts (solidustemperature) but at a slightly higher temperature (at least ∼ 50oC above the solidus)and the electric conductivity needs at least 3-4 days to reach a steady-state value due tochemical and textural equilibration of partial melts. Melting of samples and establishingof interconnected network of melt does not influence the impedance spectra. The contri-bution from the grain boundary mechanism in samples where grains are in contact withmelt can not recovered from IS measurements.

24 J. Maumus et al.

(iii) The jump of the electrical conductivity at high temperatures was interpreted by theestablishing of an interconnected network of melt: melts are better electrical conductorsthan mineral grains. Pressure (that controls solidus temperature) does neither influencepartially molten sample conductivity, nor its activation energy, nor the spectrum of elec-trical impedance. The conductivity jump is observed at higher temperatures when thepressure increases according to the pressure dependence of solidus temperature. SEMstudy on polished sections of our quenched samples shows that melt/silicates texturalequilibrium was reached and that the main conductivity jump is related to the large meltfraction (from 10 to 34 vol.%) homogeneously distributed in samples.(iv) A direct comparison between the obtained results and previous experiments aimingto measure electric conductivity of partially molten rocks was not easy to do because ofthe differing measurement strategies of experiments. Practically, all previous experimentswere performed at 0.1 MPa with a fixed heating rate [29,31] or on texturally equilibratedor sintered at high pressure samples [10]. The conductivity jump related to the effectof an interconnected network of melt was also observed in previous studies and meltingfraction less than 5 vol.% [29,31]. In the present study on rocks containing pyroxenes,no influence of melt on partially molten rock conductivity below a melt fraction of 10-15vol.% has been detected. Analysis of these data by using mixing models of composites(effective media theory, brick layer model, etc) demonstrate that the electrical conduc-tivity measured in a sample containing less than 10 vol.% in all previous studies cannotbe adequately explained by a completely connected network of a melt nor by low conduc-tivity of partial melts. It is more realistic to explain the previous results of the electricconductivity measurements vs. melt fraction by a formation of a network of melt witha low degree of connectivity (although, the theory of textural equilibrium in partiallymolten sample predicts that a completely connected network of melt should be reachedat a rather low melt fraction even in the case of an anisotropic distribution of interfacialenergies at melt/mineral grain interfaces). At 10-15 vol.% of melting the connectivityof melt is almost complete. The variation of electric conductivity in olivine + basaltaggregates does not demonstrate this effect. This point is very important, because morerealistic models to calculate the apparent conductivity of a composite medium consistingof melt and mineral grains are needed to be developed in order to get better constraintson the interpretation of MT/EM profiling of partially molten zones in the Earth.

6. Acknowledgements

Project was supported by German Science Foundation (SPP 1150). The authors aregrateful to B. Ildefonse for providing Oman gabbro sample, to F. Brunet for Ronda lher-zolite, to A. Loukanin for Kivakka olivinite and Spitzbergen lherzolite, to H. Hofer fortechnical help with EPMA. This manuscript was significantly improved after the con-structive revisions of J. Roberts, B. Poe and an anonymous reviewer.

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Electrical conductivity and melting 25

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Electrical conductivity and melting 29

0

10

20

30

40

50

-2 -1 0 1 2 3 4 5 60

5

10

15

20-I

m(Z

), k

iloo

hm

s

-2 -1 0 1 2 3 4 5 6

0

2

4

6

8

10

12

-2 -1 0 1 2 3 4 5 60

1

2

3

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3

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5

6

-2 -1 0 1 2 3 4 5 60.0

0.1

0.2

0.3

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0.6

-Im

(Z),

kilo

oh

ms

-2 -1 0 1 2 3 4 5 6

0

10

20

30

40

50

60

-2 -1 0 1 2 3 4 5 6

log (frequency) (freq. in Hz)

0

5

10

-Im

(Z),

ohm

s

-2 -1 0 1 2 3 4 5 6

log (frequency) (freq. in Hz)

791˚C

937˚C

1085˚C

1253˚C

Z’’

Z’

Ω

Z’,

k

ΩZ

’, k

Ω

Z’,

k

Ω

Z’’,

k

Ω

Z’’,

k

ΩZ

’’,

k

ΩZ

’’,

Ω

Z’,

Log ( ), Hzν

Figure 3. Impedance spectrum of Oman gab-bro sample at 791, 931, 1035 and 1253oC at1 GPa. For each temperature, Re(Z) andIm(Z) vs. log(ν) are represented by circlesand squares, respectively.

0

5

10

15

20

10 15 20 25 30 35 40 45 50

Re(Z), kiloOhms

0

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4 6 8 10 12

Re(Z), kiloOhms

0

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2

2 3 4 5 6

Re(Z), kiloOhms

0

10

20

20 30 40 50 60

Re(Z), Ohms

1085˚C

931˚C

791˚C

1253˚C

ΩZ

", k

ΩZ

", k

ΩZ

", k

ΩZ’, k

ΩZ’, k

ΩZ’, k

Ω Z’,

Ω Z

",

Figure 4. Examples of Argand diagram forOman gabbro at 1 GPa. The correspond-ing impedance spectrum is presented inFig. 3

30 J. Maumus et al.

-4

-3

-2

-1

0

1

6 7 8 9

-4

-3

-2

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-4

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6 7 8 9

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-2

-1

0

1

6 7 8 9

9001000110012001300

log

S/m

σ

10000/T, K1

Temperature ˚C

a

b

Figure 5. Electrical conductivity of Omangabbro sample at 0.3 (triangles), 0.5(squares) and 1 GPa (circles) pressure: foreach sample, above solidus, the samples dis-play a behavior that can be fitted the Arrhe-nius dependence σ = σ0 exp (−Ea/kT ). Ageneral fit of data provide Ea = 1.38 eV andlog σ0 = 2.51 S/m. Note the dramatic jumpof conductivity at 1240, 1188 and 1196oCfor 1, 0.5 and 0.3 GPa experiments respec-tively. Measurements on olivine gabbros of:a) - [29]; b) - [11,30,31] are shown for com-parison.

-4

-3

-2

-1

0

1

6 7 8 9

9001000110012001300

10000/T, K−1

log

S/m

Temperature °C

10 kbar, heating

σ

10 kbar, cooling

Figure 6. Electrical conductivity of Kare-lia olivinite sample: two runs were per-formed at 1 GPa. The first run wasquenched at 1315oC corresponding to theconductivity -jump temperature. The sec-ond run was cooled after 24h with a cool-ing rate about 20o/h. The parametersof the Arrhenius dependence for Kareliaolivinite below solidus: Ea = 0.82 eV andlogσ0 = 0.67 S/m.

Electrical conductivity and melting 31

Spitzbergen

10kbar

Spitzbergen, 10 kbar

-4

-3

-2

-1

0

5 6 7 8 9

900100011001200130014001500

Ronda

20 kbar

log

S/m

-1

σ

Temperature ˚C

10000/T, K

Constable and

Duba (1990)

Figure 7. Electrical conductivity of Spitzber-gen (at 1 and 2 GPa) and Ronda (at 1 GPa)lherzolite samples compared with dunite [33].The parameters of the Arrhenius equationfor melt-free rocks: Spitzbergen lherzolite -Ea = 2.11 eV and log σ = 4.25 S/m; Rondalherzolite - Ea = 1.61 eV and log σ = 2.65S/m.

(a)

-4

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6 7 8 9

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9001000110012001300

10000/T, K-1

log

S/m

σ

Temperature ˚C

Presnall

et al. (1972)

(b)Tyburczy and

Waff (1983)(c)

(d)(e)

(i)

(j)(k)

basalt glass

(this study)

(f)

(g)

(h)

Presnall

et al. (1972)

Scarlato et

al. (2004)olivine+basalt

(this study)

Roberts and

Tyburczy

(1999)

Sakamoto et al. (2002)

San Carlos olivine (this study)

(l)

Xu et al. (1998)

Figure 8. Electrical conductivity of syn-thetic basalt glasses measured by Press-nall et al. [34] during (a) heating, and (b)cooling (thin line), tholeiitic basalt glassmeasured by Tyburczy and Waff ([35] atambient pressure (c), 0.43 GPa (d) and1.28 GPa (e), basaltic rocks measured byScarlato et al. ([36], f) and our syntheticbasalt glass during (g) first heating, (h)cooling, (i) second heating; vs. olivine +basalt aggregates (squares, this study) at1 GPa compared to Roberts and Tybur-czy ([10]- open triangles and circles); andSan Carlos olivine at 3-5 GPa (j, [6]), at4 GPa (k, [37]) and at 1 GPa (l, presentstudy).

32 J. Maumus et al.

50 mµ

melt

hole

crack

Figure 9. Oman gabbro, 1 GPa: Backscat-tered electrons image (SEM) of the sampleafter quenching. The area is close to theouter electrode. Cracks are produced dur-ing quenching, cavities are produced duringthe thin section preparation. Melt is a darkgray color and crystals appear in the lightestgray color. Scale in the right upper part ofpicture.

10 mµ

a

b

c

d

e

f

Figure 10. Karelia olivinite, 1 GPa:SEM image of the sample after quenching.Cracks (e) are produced during quench-ing. This picture demonstrate differentkinds of melt pockets and their shapes asdescribed in [44]: Additionally to regulartriple junctions of melt (a), we found outnon-regular triple junction which are con-trolled by planar faces (F -faces) of olivinecrystals (b, c), and larger melt pools (d).(e) Cracks developed during unloadingstage. Some Fe-Ni droplets (f ) indicatethe low level of oxygen fugacity during ex-periment as expected with Mo electrodes.

Electrical conductivity and melting 33

10 mµ

melt

crack

droplet

Figure 11. Ronda peridotite, 1 GPa: Scan-ning electron microscope image of the sampleafter quenching. Cracks due to quenching in-tersect the melt pockets

10 mµ

melt

Figure 12. Spitzbergen peridotite, 2 GPa:Scanning electron microscope image of thesample after quenching. Example of grainintersections that are controlled by a min-imum the surface energy of two F -facesseparated by two grains of different sizes.

-4

-3

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6 7 8 9-4

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6 7 8 9-4

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9001000110012001300

Conductivity in AMC

conductivity far

from AMC

10000/T, K−1

log

S/m

σ

Temperature °C

10 kbar

5 kbar

3 kbar

Figure 13. Oman gabbro conductivity com-pared to σ, which was estimated in the ax-ial magma chamber in the North Atlanticoceanic ridge by RAMESSES group [2,59].

-4

-3

-2

-1

0

1

6 7 8 9-4

-3

-2

-1

0

1

6 7 8 9-4

-3

-2

-1

0

1

6 7 8 9-4

-3

-2

-1

0

1

6 7 8 9-4

-3

-2

-1

0

1

6 7 8 9-4

-3

-2

-1

0

1

6 7 8 9-4

-3

-2

-1

0

1

6 7 8 9

9001000110012001300

Conductivity in AMC

conductivity far

from AMC

10000/T, K−1

log S

/mσ

10 kbar, heating

10 kbar, cooling

Temperature °C

Figure 14. Karelia olivinite conductivitycompared to σ estimated in axial magmachamber in the North Atlantic oceanicridge by RAMESSES group [2,59].

34 J. Maumus et al.

-4

-3

-2

-1

0

5 6 7 8 9

900100011001200130014001500

10000/T, K−1

log

S/m

σ

Conductivity in

partially molten

upper mantle

Temperature °C

Spitzbergen, 10 kbar

Ronda

10kbar

20 kbar

Spitzbergen

Figure 15. Spitzbergen and Ronda lherzo-lite conductivity compared to σ estimatedfrom the partially molten upper mantle be-low AMC beneath the mid-oceanic Atlanticridge at 60 km [2,59].

-3

-2

-1

0

6 7 8 9-3

-2

-1

0

6 7 8 9

9001000110012001300

10000/T, K−1

log

S/m

σConductivity in

partially molten

upper mantle

Temperature °C

Figure 16. Olivine + 5 wt % basalt glassconductivity (squares) compared to [10](triangles) and σ estimated from partiallymolten upper mantle below the AMC be-neath the mid-oceanic Atlantic ridge at 60km [2,59].