Standard electrical conductivity of isotropic, homogeneous olivine in the temperature range 1200°-1500°C

Abstract

In order to produce electrical conductivity-temperature plots suitable for interpreting mantle conductivity profiles, the authors have used several spatial averaging schemes to reduce the orthorhombic conductivity tensor of olivine to that appropriate for an isotropic material. The starting data were new measurements of electrical conductivity [sigma] in the three orthogonal principal directions of a San Carlos olivine (fayalite 9 per cent) to 1500[degrees]C at 1 atmosphere total pressure. These measurements were made in a CO[sub 2]/CO atmosphere that provided an oxygen partial pressure of 10[sup [minus]4] Pa (10[sup [minus]9] atmosphere) at 1200[degrees]C; this is slightly more reducing than the quartz-fayalite-magnetite (QFM) buffer curve. The highest [001] and lowest [010] conducting directions differ by a factor of 2.3. The next step was to obtain series and parallel bounds from the three principal directions; these absolute upper and lower bounds differ by 15 per cent. A standard conductivity curve comes from applying to the series and parallel curves various averaging schemes such as the Hashin-Shtrikman and Maxwell-Waff bounds or the effective medium, geometric mean, or (a new technique) self-similar methods; these all agree to within 3 per cent. The self-similar calculation demonstrates that the VRH method is a form of parallel averagemore » that is biased toward high values. The standard curve SO1 is given by [sigma] = 46.9 exp ([minus]1.38/kT) + 5.22 [times] 10[sup 8] exp ([minus]3.90/kT) where T is absolute temperature, k is the Boltzmann constant, and the activation energy is in eV. It is valid for the measurement interval of 1200[degrees]-1500[degrees]C and can be used for extrapolation on either side of this range. Uncertainties associated with applying SO1 to inferring mantle temperatures are discussed.« less