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Applications of liquid state physics to the Earth's core

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. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/0031-9201(80)90099-0DOIArticle
http://www.sciencedirect.com/science/article/pii/0031920180900990PublisherArticle
ORCID:
AuthorORCID
Stevenson, D. J.0000-0001-9432-7159
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.
Funders:
Funding AgencyGrant Number
NASANGL 05-007-002
Issue or Number:1
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:03 Oct 2019 06:00

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