Pressure dependence of the thermal Grüneisen parameter, with application to the earth's lower mantle and outer core

Irvine R.D. and Stacey F.D. (1975) Pressure dependence of the thermal Grüneisen parameter, with application to the earth's lower mantle and outer core. Physics of the Earth and Planetary Interiors, 11 2: 157-165. doi:10.1016/0031-9201(75)90009-6


Author Irvine R.D.
Stacey F.D.
Title Pressure dependence of the thermal Grüneisen parameter, with application to the earth's lower mantle and outer core
Journal name Physics of the Earth and Planetary Interiors   Check publisher's open access policy
ISSN 0031-9201
Publication date 1975
Sub-type Article (original research)
DOI 10.1016/0031-9201(75)90009-6
Volume 11
Issue 2
Start page 157
End page 165
Total pages 9
Subject 1908 Geophysics
1912 Space and Planetary Science
3101 Physics and Astronomy (miscellaneous)
3103 Astronomy and Astrophysics
Abstract By considering high-temperature (classical) thermal oscillations of atoms in certain simple crystal structures with purely central interatomic forces, the treatment of anharmonic oscillations is generalised to random three-dimensional motion, yielding the Vashchenko and Zubarev relationship for the Grüneisen ratio γ at any pressure. If one-dimensional atomic oscillations only are considered the equation reduces to the Dugdale-MacDonald expression. To account for non-central forces additional terms must be introduced, giving: γ= 1 2 dK dP- 5 6+ 2 9 P K- f 18K+ 1 6 df dP 1- 4 3 P K+ f 3K where f = 0 for purely central forces. Calculations of f in terms of the Poisson ratio for different crystal structures have not been made, but for many materials the central-force approximation suffices. This is believed to be true both for the outer core (γ≈1.4) and for the close-packed structures of the lower mantle (γ≈1.0). For the upper mantle non-central atomic forces are important and we have no estimate of (γ independently of laboratory values for plausible minerals which suggest γ ≈ 0.8.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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