Thermal regime of the Earth's core |
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| Authors: | John Verhoogen |
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| Institution: | Department of Geology and Geophysics, University of California, Berkeley, Calif. U.S.A. |
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| Abstract: | The outer core is assumed to consist of iron and sulfur, with a small amount of potassium that generates heat by radioactive decay of sim||pre|40 K. Two cases are considered, corresponding respectively to a high rate of heat production (Q = 2 · 1012 cal./sec, about 0.1% K), and to a low rate (Q = 2 · 1011 cal./sec). The temperature at a depth of 2800 km in the mantle is taken to be 3300°K (Wang, 1972). The temperature Tc at the core-mantle boundary depends on whether or not a density gradient in the lowermost layer D″ of the mantle prevents convection in that layer. In the first case, and for high Q, Tc = 4500–5000°K. In the second case, or for low Q, Tc ≈ 3500°K.The heat-conduction equation is used to calculate the temperature Ti at the inner-core boundary in the absence of convection. For high Q, Ti ? Tc ≈ 1600°K; for low Q, Ti ? Tc ≈ 160°K. Corresponding temperature gradients at r = rc and r = ri are listed in Table I.The adiabatic gradient at the top of the core is calculated by the method of Stewart (1970). It strongly depends on the parameters (ρ0, c0, γ0, etc.) that characterize core material at low pressure. Stewart has drawn graphs that allow the selection of sets of parameters that are consistent with seismic velocities and a given density distribution in the core. Some acceptable sets of parameters are listed in Table II. Many sets yield temperatures Tc in the range 3500–5000°K; some give an adiabatic gradient steeper than the conductive gradient and are compatible with convection; others do not. Since properties of FeS melts remain unknown, there is at present no way of selecting any set in preference to another.Properties of the FeS system at low pressure suggest the possible appearance of immiscibility at high temperature in liquids of low sulfur content; accordingly, the inner-core boundary is thought to represent equilibrium between a solid (FeNi) inner core and a liquid layer containing only a small amount of sulfur; layer F in turn is in equilibrium with another liquid (forming layer E) containing more sulfur, and slightly less dense, than F. The temperature Ti at the inner-core boundary is about 6000–6500°K for high Q and Tc ≈ 4500–5000°K. It is consistent with Alder's (1966) and Leppaluoto's (1972) estimates of the melting point of iron at 3.3 Mbar, but not with that of Higgins and Kennedy (1971). |
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