Extrapolation formula for finding the volume of solids at high pressures

The primary objective of theoretical equation‐of‐state work in geophysics has been to provide a framework with which the ultrasonic, X‐ray compression, and shock data can be used in interpreting the seismic velocity and density profiles in the earth. Each of these experimental techniques falls short of the ultimate experiment of reproducing the temperature‐pressure conditions at any depth in the earth and measuring Vp, Vs, and p of mantle‐candidate mineral assemblages for direct comparison with the seismic profiles. The ultrasonic data give Vp, Vs, and p as a function of T and P, but the pressure range has been limited to ∼10 kb. This limit necessitates a large extrapolation for discussion of even the upper mantle. The X‐ray static compression measurements have a pressure range to 300 kb, but are limited to room temperature and to only the pure compression properties KT and p. Finally, although the shock‐wave techniques can generate pressures comparable to those found throughout the earth's mantle and core, the shock‐produced states are characterized by pressure and internal energy. Thus an E(T, P) equation of state is required before the data can effectively be used. Further, like static compression experiments, the shock technique now yields only K and p.

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Empirical equation of state for high compression

Mao¹

1970

J. Geophys. Res.

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An empirical equation of state for high compression is derived from the assumption that K(∂P/∂K) = a + bP where K ≡ ‐V(∂P/∂V). When b = 1, it reduces to the Murnaghan's assumption. The second pressure derivative of bulk modulus is needed in the equation. Since this quantity is generally not available, a method is proposed to estimate it from other readily available data and the relation that the Grüneisen's parameter γ is a function of volume alone as As examples, NaCl, MgO, CsI, and potassium are used to test the equation. Good agreement is found for all of them compared with values in the literature.

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Extrapolation formula for finding the volume of solids at high pressures

Cited by 48 publications

References 20 publications

Thermodynamic assessment of Mg/Zr unary systems

Thermodynamic assessment of Mg/Zr unary systems

Theoretical Equations of State

Empirical equation of state for high compression

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