The Liquid and Solid Values of the Grüneisen Ratio for hcp Iron at Core Conditions

Details The Liquid and Solid Values of the Grüneisen Ratio for hcp Iron at Core Conditions The Liquid and Solid Values of the Grüneisen Ratio for hcp Iron at Core Conditions

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003agufm.t11c0409a&link_type=abstract

American Geophysical Union, Fall Meeting 2003, abstract #T11C-0409

Physics

1212 Earth'S Interior: Composition And State (8105), 8124 Earth'S Interior: Composition And State (Old 8105), 8130 Heat Generation And Transport

Scientific paper

Verhoogen first emphasized that the value of the Grüneisen ratio, γ , may be different for solid iron than for liquid iron at core conditions. In calculations involving the adiabatic temperature of the outer core, iron must be considered as in the liquid state. In calculations involving the Hugoniot, however, the measured data up to melting will be taken from the solid state (γ c corresponds to the crystalline state, and γ l to the liquid state). The difference between γ l and γ c for iron at P = 0 is quite large (γ l = 2.44 and γ c = 1.66). Experimental data show that γ l changes considerably with pressure, becoming 1.52 at 135~GPa, according to Alf{è} et al.~(2002). At higher pressures, γ l changes much more slowly with pressure, becoming 1.51 at 330~GPa, according to Alf{è} et al.~(2002). γ c has a component from lattice vibrations that decreases with pressure and a component from free electrons (activated at very high temperatures) that increases strongly with temperature. Along the adiabat of the outer core, the decrease in the vibrational component is almost exactly compensated for by the increase in γ c due to increased temperature. Anderson and Isaak~(2003) have shown that γ c varies from 1.62 at 135~GPa to 1.52 at 330~GPa along the core adiabat. Thus, we see that γ l is only slightly larger than γ c along the adiabat of Earth's outer core. Further, the difference between γ l and γ c decreases as the pressure increases. This is consistent with a decrease in both the volume of melting, Δ Vm, and the heat of crystallization, Δ Hm, with pressure along the core adiabat. Both become quite small at 330~GPa. In the planets Mercury, Mars, and the Moon, the pressure never gets as large as the pressure in the Earth's core, being only about 29~GPa for Mercury. So for these planets, assuming that the core is mostly iron, the value of γ l will be very much larger than the value of γ c. Care must be taken to ensure that the γ used in calculations of core physical properties for these planets is for the liquid state (using values measured for γ c will lead to large errors).

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