Partial Melting of Mafics Rocks from 
Electrical Impedance Spectroscopy Measurements

Jerome MAUMUS 1 (maumus@geophysik.uni-frankfurt.de), 
Nikolai BAGDASSAROV 1, 
Harro SCHMELING 1, 
and Benoit ILDEFONSE 2


(1) Institut für Meteorologie und Geophysik,
Johann Wolfgang Goethe-Universität, 60323 Frankfurt am Main, Deutschland
(2) Laboratoire de Tectonophysique, Universite Montpellier II, France

Abstract

Presence of melt phase with a specific topology may have a large effect on the internal friction and electrical conductivity of rocks. The variations of electrical properties at high temperature have been studied by measuring electrical resistance as a function of frequency, temperature and time in synthetic upper-mantle rocks (olivine crystals and basalt glass) and a natural gabbro from Oman. Gabbro samples show a uniform grain size of 250-300 µm and the absence of cracks and alteration in the starting material. The rock consists of 50-55 vol% Plg, 35% Cpx and 15% Opx. The synthetic upper-mantle rock sample is an aggregate of San Carlos olivine with a grain size of 10-25 µm and 5% of synthetic basalt glass. The electrical impedance measurements have been carried out in a piston cylinder apparatus at 3, 5 and 10 kbar and temperature up to  1200°C. For each temperature, the electrical impedance has been estimated in a frequency range from 10-2 to 105 Hz. The bulk electrical resistance of samples has been estimated from Argand plots (Imaginary vs. real componant of complex impedance). The control of the equilibrium was provided by a monitoring of the electrical impedance as a function of time. At subsolidus temperature, the electrical conductivity of gabbro follows an Arrhenian temperature dependance with the activation energy  1.15 eV. At temperature close to the liquidus (ca. 1215°C at 10 kbar, 1175°C at 5 kbar for gabbro and 1240°C at 10 kbar for olivine), the conductivity increases drastically with time reaching a steady-state value in a few days. This relaxation effect is perhaps due to a slow developing of a better melt interconnection or caused by a chemical reaction between crystals and melt. In a partially molten state with about 15% of melt, gabbro samples are characterised by the electrical conductivity ca. 0.3-0.4 S/m. This value corresponds to the observed electrical conductivity in the lower part of AMC (Sinha et al. 1997). The estimated temperature in this part of AMC may be about 1175-1185°C:

Piston-Cylinder Experiments

Experiments were carried out in a piston-cylinder apparatus with a coaxial cylindrical cell Figure 1 to measure electrical impedance (Khitarov et al., 1970). The measuring cell is situated inside a boron nitride sleeve, graphite heater and a pressure transmitting medium made of CaF2. Boron nitride sleeve insulates the measuring cell from a graphite contamination. The starting sample is a fine powder, pressed between 2 coaxial cylindrical electrodes made from molybdenum foil in order to prevent iron losses from a sample. Inside the inner electrode, we placed a Pt30%Rh-Pt6%Rh thermocouple. For electrical measurements, RC-bridge (Solartron 1260) was connected to the inner electrode by a thermocouple wire and to the outer electrode by the lower piston. Before each measurement, the RC-parameters of the cell were calibrated for open and closed circuite. The geometric factor of the cell Gf was calibrated by measuring the resistance of NaCl-water solutions placed between coaxial electrodes at room temperature and pressure.

Figure 1: Cell Design

Impedance Spectroscopy Measurements

A voltage v(t) = Vm ·sin( wt) at a frequency n = w/2pi is applied to the cell and the resulting current i(t) = Vm ·sin( wt + q) is measured. From the phase shift, we can define the electrical impedance Z(w) = v(t)/i(t) characterised by a magnitude |Z(w)| and a phase angle q(w). The complex impedance Z is calculated from |Z(w)| and q(w). Impedance is a concept more general than resistance because it take the phase shift into account. Complex impedance Z is a complex number composed by an ohmic resistance (real component Re(Z)) and a reactance (imaginary component Im(Z)): Z = Re(Z) + j ·Im(Z) with j2 = -1.
Impedance spectroscopy Figure 2 consists in measuring Re(Z) and Im(Z) in a large range of frequency (10-2 to 105 Hz). As an exemple are plotted some measurement results at different temperatures for a gabbro sample at 10 kbar. The data are represented in Argand diagrams (Im(Z) vs. Re(Z)). At each temperature, data curves show two parts of circles. The left part related to high frequency mesurements describes the sample bulk electrical properties. The second part is related to grain boundary or electrode electrical properties or so-called low frequency dispersion. The data can be fitted to an electrical equivalent circuit model (see Mac Donald, 1987; Roberts and Tyburczy, 1991) to determine the sample bulk resistance R (in W) and to calculate the sample bulk resistivity r (in W.m): r = R ·Gf where Gf is the geometric factor. In first approximation, R is given by the intersection between the Im(Z) curve and the Re(Z) axis. The bulk conductivity s is given by s = 1/r.

Figure 2: Impedance Spectroscopy measurements of a Gabbro Sample at 10 kbar

Frequency range between  to 105 and  10-2 Hz

Two different samples

In order to investigate electrical conductivity of regions where partial melting occurs, we examined 2 samples. The first sample is a natural gabbro rock representating the lower oceanic crust (where magma chamber are located above mid-oceanic ridges). This gabbronorite Table1 from Oman ophiolites is composed of 46%vol. plagioclase feldspar, orthopyroxene (40%vol.) and clinopyroxene (14%vol.). This cumulate rock is caracterised by a homogeneous grain size (ca. 350 mm). The second sample is an aggregate of San Carlos Olivine and 5%weight of a synthetic basalt glass Table2 . Olivine grain size is between 10 and 25 m. We have chosen a basalt glass composition that is in equilibrium with olivine at a temperature range between 1200 and 1300°C and for pressures about 10-20 kbar (Ulmer, 1989).

Tables 1-2: Composition of starting material in oxides weight percent

Results: Olivine+Basalt samples

Figure 3 Green squares show our conductivity measurements (Olivine Fo90+5% basalt). Only one experiment was made on olivine at a pressure of 10 kbar and a temperature about 800 to 1200°. At each temperature we estimated the bulk conductivity of the sample as a function of time. The sample reached a stable value after about 2 or three days. At low temperature, data can be fitted to an Arhennius law s = s0 ·expAe / kT where s (in S/m) is the electrical conductivity, s0 a constant, Ae the activation energy, k the Boltzman constant and T the temperature (in K). For temperature lower than 1200° our sample show the electrical behaviour of a dry polycristalline olivine. However, our measurements show an about 1 order of magnitude higher conductivity than previous works (e. g. Xu, 2000) and our activation energy is lower than what is usually founded for polycristalline sample (1.1 eV vs. 1.4 eV). The difference in conductivity values should be explain by the high dependence of olivine conductivity to the oxygen fugacity conditions. Presence of molybdenum foil and boron nitride may create low oxygen fugacity conditions for temperature between 1000°C and 1200°C. At temperature close to the liquidus, the conductivity increases dramatically (one order of magnitude). At 1200°C, it take 3 days to reach a stable state of conductivity. These may be related to a partial melting occuring in the sample and to a better interconnection of basaltic melt as a function of time. When partial-melting begins, we reach a conductivity of 0.1 S/m.
Circles and triangles show measurements of Roberts and Tyburczy (1999) at atmospheric pressure on an aggregate of olivine (Fo80) and 5% basalt. They prepared their sample at HT-HP conditions and made the electrical measurements in a gaz mixing furnace at 1 atm with a controlled oxygen fugacity. It is difficult to compare their results with our data because olivine and basalt don't have the same composition. Our basalt contains more iron and must be more conductive. The difference in conductivity is about 0.5 order of magnitude for our sample.
The yellow rectangle indicate the range of electrical conductivity from magnetotelluric measurements in the upper mantle above Mid-Atlantic ridge axis where partial melting presumably occurs (Heinson et al., 2000). Our measurements have a good agreement with these data.

Figure3: Electrical conductivity of Olivine+basalt samples

Log of bulk electrical conductivity vs. reciprocal temperature. Green squares: this study, triangles and circles: Roberts and Tyburczy

Results: Gabbro samples

For Oman Gabrro Figure 4, we provided experiments at 10 (circles), 5 (squares) and 3 kbar (triangles). Gabbro samples show a behaviour similar to the olivine-basalt aggregates. At temperature above the liquidus samples follow the behaviour of a dry polycristalline rock. Data can be fitted to an Arhennius law. We don't observe a strong influence of the pressure on the conductivity. At temperature close to the liquidus, the conductivity increases drastically (0.5 to 1.5 order of magnitude). This could be explained by partial melting of the sample and to a better interconnection of the melt as function of time. At 10 kbar and 1240°C, we reached a conductivity (s) of 0.4 S/m. at 5 kbar and 1180°C, s= 0.03 S/m, at 3kbar and 1170°C s= 0.05 S/m.
Microprobing of the sample after quenching shows the presence of a large amount of melt (15 to 30%). Theses observations may indicate that we are not able to detect the beginning of the melting process. From a jump of the electrical conductivity we may only detect a stage of a developed melt inteconnection. The large amount of pyroxene in the sample may not allowed any interconnection of melt for low melt fraction (see e.g. Laporte and Provost (2000)).
The green lines show measurements of Sato and Ida (1984) at atmospheric pressure. The presence of olivine in his gabbro results in a higher conductivity. However, the difference of conductivity is not too large (0.5 order of magnitude).
The lower yellow rectangle shows the range of conductivity from electromagnetic measurements in gabbro far from the axial magma chamber (AMC) at mid-oceanic ridge axis (Sinha et al., 1997). These data are in a good agrement with our measurements of gabbro without interconnected melt. The upper yellow rectangle shows the range of conductivity of gabbro in axial magma chamber at ridge axis (Sinha et al., 1997). Only the measurement made at 10 kbar shows a conductivity value in good agreement with the electromagnetic data.

Figure4: Electrical conductivity of Gabbro samples

Log of bulk electrical conductivity vs. reciprocal temperature. This study: Disk 10kbar, Squares 5 kbar, Triangles 3 kbar

Literature

Heinson, G., S. Constable, A. White, Episodic melt transport at mid-oceanic ridges inferred from magnetotelluric sounding, Geophys. Res. Lett., 27 (2000) 2321-2324.

Khitarov, N.I., A. B. Slutsky, and V.A. Pugin, Electrical conductivity of basalts at high T-P and phase transitions under upper mantle conditions, Phys. Earth Planet. Interiors, 3 (1970) 334-342.

Laporte, D., and A. Provost, The grain scale distribution of silicate carbonate and metallosulfide partial melts: a review of theory and experiments, in: Physics and chemistry of partially molten rocks, edited by N. Bagdassarov, D. Laporte and A.B. Thompson, Kluwer (2000) pp 93-140.

Roberts, J., and J. Tyburczy, Partial-melt electrical conductivity: Influence of melt composition, J. Geophys. Res., 104 (1999) 7055-7065.

Sato, H., and Y. Ida, Low frequency electrical impedance of partially molten gabbro: The effectof melt geometry on electrical properties, Tectonophysics, 107 (1984) 105-134.

Sinha, M.C., D.A. Navin, L. M. MacGregor, S. Constable, C. Pierce, A. White, G. Heinson, and M.A. Inglis, Evidence for accumulated melt beneath the slow-spreading mid-Atlantic ridge, Phil. Trans. Roy. Soc. Lond. A, 355 (1997) 168-172.

Ulmer, P., The dependence of the Fe2+-Mg cation-partioning between olivine and basaltic liquid on pressure, temperature and composition, Contrib. Mineral. Petrol., 101 (1989) 261-273.

Xu, Y., T.J. Shankland, A.G. Duba, Pressure effect on electrical conductivity of mantle olivine, Phys. Earth Planet. Interiors, 118 (2000) 149-161.

Jerome Maumus
6 Apr 2001, 20:10.