Stevenson, D. J. (1980) Applications of liquid state physics to the Earth's core. Physics of the Earth and Planetary Interiors, 22 (1). pp. 42-52. ISSN 0031-9201. doi:10.1016/0031-9201(80)90099-0. https://resolver.caltech.edu/CaltechAUTHORS:20131120-110757312
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Abstract
By use of the modern theory of liquids and some guidance from the hard-sphere model of liquid structure, the following new results have been derived for application to the Earth's outer core. (1) dK/dP≃5-5.6P/K, where K is the incompressibility and P the pressure. This is valid for a high-pressure liquid near its melting point, provided that the pressure is derived primarily from a strongly repulsive pair potential φ. This result is consistent with seismic data, except possibly in the lowermost region of the outer core, and demonstrates the approximate universality of dK/dP proposed by Birch (1939) and Bullen (1949). (2) dlnT_M/dlnρ = (γC_V^(−1))/(C_V-3/2), where T_M is the melting point, ρ the density, γ the atomic thermodynamic Grüneisen parameter and C_V the atomic contribution to the specific heat in units of Boltzmann's constant per atom. This reduces to Lindemann's law for C -V = 3 and provides further support for the approximate validity of this law. (3) It follows that the “core paradox” of Higgins and Kennedy can only occur if y<2/3. However, it is shown that y<2/3⇔ʃ_0(∂g/∂T)p^r(d/dr)(r^2φ)dr>0, which cannot be achieved for any strongly repulsive pair potential φ and the corresponding pair distribution function g. It is concluded that y<2/3 and that the core paradox is almost certainly impossible for any conceivable core composition. Approximate calculations suggest that γ ∼ 1.3–1.5 in the core. Further work on the thermodynamics of the liquid core must await development of a physically realistic pair potential, since existing pair potentials may be unsatisfactory.
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Additional Information: | © 1980 Elsevier Scientific Publishing Company, Amsterdam. Received July 27, 1979; accepted for publication August 28, 1979. This work was supported by NASA Grant NGL 05-007-002. | |||||||||
Group: | UNSPECIFIED, Division of Geological and Planetary Sciences | |||||||||
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Issue or Number: | 1 | |||||||||
DOI: | 10.1016/0031-9201(80)90099-0 | |||||||||
Record Number: | CaltechAUTHORS:20131120-110757312 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20131120-110757312 | |||||||||
Official Citation: | D.J. Stevenson, Applications of liquid state physics to the Earth's core, Physics of the Earth and Planetary Interiors, Volume 22, Issue 1, April 1980, Pages 42-52, ISSN 0031-9201, http://dx.doi.org/10.1016/0031-9201(80)90099-0. (http://www.sciencedirect.com/science/article/pii/0031920180900990) | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 42594 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Ruth Sustaita | |||||||||
Deposited On: | 20 Nov 2013 21:30 | |||||||||
Last Modified: | 10 Nov 2021 16:25 |
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