P. Schmoldt, PhD - MTNet - DIAS
P. Schmoldt, PhD - MTNet - DIAS P. Schmoldt, PhD - MTNet - DIAS
5. Earth’s properties observable with magnetotellurics Fig. 5.4.: Arrhenius diagram displaying the relation between log conductivity and reciprocal of the absolute temperature for charge transport by semiconduction. The four lines represent different extrinsic charge transport processes. The variation of the gradient at higher temperatures is due to transition between the two regimes of semiconduction, either dominated by extrinsic or intrinsic charge transport; Figure from Nover [2005]. 5.1.2. Electronic conduction In electronic conduction, charge is transported by the movement of free electrons; the conductivity of media, comprised of good conductors in a more resistive host material, can be described using Ohm’s Law (Eq. 3.5). The presence of a good conductor (metal, graphite, sulphidic ore body, or oxides with a significant amount of graphite or sulphides) in a medium can increase the electric conductivity by orders of magnitude [e.g. Nover, 2005]; again, as in the case of electrolytic conduction, the crucial factor is the interconnection of good conductors. 5.1.3. Semiconduction When a semiconductor is not in an excited state, i.e. it has energy equal to its ground state, it has a full valence band and acts as an insulator. Since semiconduction needs a certain amount of energy to lift one or more electrons from the valence band into the conduction band (activation energy, ∆E), semiconduction is extremely dependent on externally supplied energy that, in the case of Earth’s materials, is usually provided by temperature. Accordingly, charge transport by semiconduction is attributed to two different processes, i.e. extrinsic (also referred to as proton conduction or proton hopping) and intrinsic (also referred to as small polaron conduction or hole hopping). Extrinsic charge transport is due to H + “hopping” between lattice impurities, dominant at low temperatures; whereas intrinsic charge transport is dominantly for high temperatures above the transition point (see Fig. 5.4), when charge is transported through electrons in the conduction band and by “movement of electron holes” in the valence band of exited atoms 2 . For semiconductive 86 2 Electron holes do not actually move, but are filled by electrons from neighbouring atoms, which in turn leave behind new electron holes.
5.2. Variation of electric conductivity with depth Change of electric Description Depth resistivity (Ωm) Type of change (km) from to Moho (oceanic) 5-7 < 103 103 Moho (continental) 33-50 − 105 Material: mafic to ultra-mafic Material: felsic to ultra-mafic LAB 50-160 102 − 103 5-25 Rheology: strong to weak∗ Opx-cpx 300 30-80 100-200 Abundance: ortho- to clinophyroxene MTZ top 410 100-200 20-30 Phase: olivine to Wadsleyite MTZ internal 520 20-30 3-6 Phase: wadsleyite to Ringwoodite MTZ bottom 660-670 3-6 1-3 Phase: ringwoodite to Perovskite Tab. 5.1.: Step like changes in the Earth’s conductivity-depth profile for the depth range potentially observable with magnetotelluric (MT) and geomagnetic deep-sounding (GDS) measurements. Moho: Mohorovi˘cić discontinuity (Crust-mantle boundary), LAB: Lithosphere-Asthenosphere boundary, MTZ: Mantle transition zone. Values from Heinson [1999], Jones [1999], Xu et al. [2000a], Yoshino et al. [2008], and Eaton et al. [2009]. See Figures 5.5, and 5.6 for further details about the electric conductivity values of the different regions. *: note that electric conductivity properties of the LAB are controversial; see Section 5.2.2 for a discussion of this issue. charge transport processes, an Arrhenius-like description of the conductivity–temperature relation has be found, i.e. σ = σ1 exp (−∆H1/kBT) + σ2 exp (−∆H2/kBT) , (5.9) with σi: pre-exponential factor, kB: Boltzmann’s constant, T: Temperature in Kelvin, and the activation enthalpy ∆Hi = ∆Ei + P · ∆Vi, (5.10) with ∆Ei: activation energy, P: pressure, ∆Vi: activation volume, and the index i ∈ [1, 2] referring to intrinsic and extrinsic charge transport, respectively. In laboratory experiments, values of pre-exponential factors, activation energies, and activation volumes of a sample can be derived by determining slopes and axis intercepts of the two regimes in the Arrhenius diagram (Fig. 5.4). Given that (the intrinsic part of) semiconduction appears to dominate conductivity of mantle materials at local P − T conditions, numerous studies were carried out in order to determine these parameters for the relevant materials [Duba and Shankland, 1982; Duba et al., 1994; Karato, 1990; Constable et al., 1992; Xu et al., 1998a; Xu and Shankland, 1999; Yoshino et al., 2008, e.g.]; see Section 5.3 for a detailed discussion of semiconduction at mantle conditions. 5.2. Variation of electric conductivity with depth The Earth is commonly divided into crust, mantle, and core; however, due to enhanced measurements and modern techniques, these three layers can be subdivided into smaller regions (Tab. 5.1). Despite the afore-mentioned difficulties to create 1D models for the 87
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5. Earth’s properties observable with magnetotellurics<br />
Fig. 5.4.: Arrhenius diagram displaying the relation between log conductivity and reciprocal of the absolute temperature for charge<br />
transport by semiconduction. The four lines represent different extrinsic charge transport processes. The variation of the gradient at<br />
higher temperatures is due to transition between the two regimes of semiconduction, either dominated by extrinsic or intrinsic charge<br />
transport; Figure from Nover [2005].<br />
5.1.2. Electronic conduction<br />
In electronic conduction, charge is transported by the movement of free electrons; the<br />
conductivity of media, comprised of good conductors in a more resistive host material,<br />
can be described using Ohm’s Law (Eq. 3.5). The presence of a good conductor (metal,<br />
graphite, sulphidic ore body, or oxides with a significant amount of graphite or sulphides)<br />
in a medium can increase the electric conductivity by orders of magnitude [e.g. Nover,<br />
2005]; again, as in the case of electrolytic conduction, the crucial factor is the interconnection<br />
of good conductors.<br />
5.1.3. Semiconduction<br />
When a semiconductor is not in an excited state, i.e. it has energy equal to its ground state,<br />
it has a full valence band and acts as an insulator. Since semiconduction needs a certain<br />
amount of energy to lift one or more electrons from the valence band into the conduction<br />
band (activation energy, ∆E), semiconduction is extremely dependent on externally<br />
supplied energy that, in the case of Earth’s materials, is usually provided by temperature.<br />
Accordingly, charge transport by semiconduction is attributed to two different processes,<br />
i.e. extrinsic (also referred to as proton conduction or proton hopping) and intrinsic (also<br />
referred to as small polaron conduction or hole hopping). Extrinsic charge transport is<br />
due to H + “hopping” between lattice impurities, dominant at low temperatures; whereas<br />
intrinsic charge transport is dominantly for high temperatures above the transition point<br />
(see Fig. 5.4), when charge is transported through electrons in the conduction band and by<br />
“movement of electron holes” in the valence band of exited atoms 2 . For semiconductive<br />
86<br />
2 Electron holes do not actually move, but are filled by electrons from neighbouring atoms, which in turn<br />
leave behind new electron holes.
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