I. High pressure melting of [gamma]-iron and the thermal profile in the Earth's core. II. High pressure, high temperature equation of state of fayalite (Fe2SiO4)

Citation

Chen, George (Guangqing) (1998) I. High pressure melting of [gamma]-iron and the thermal profile in the Earth's core. II. High pressure, high temperature equation of state of fayalite (Fe2SiO4). Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/z7r2-xf47. https://resolver.caltech.edu/CaltechETD:etd-02262007-141751

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

The melting curve of [...]-iron in the pressure range of 100 to 300 GPa has been derived by computing Gibbs free energies at high pressures and high temperatures from thermodynamic and equations of state (EOS) data for the [...], [...] and liquid-phases. Our calculations indicate the melting curve of iron is very sensitive to the EOS of both the solid [...] and melt phase. Our best estimate of the EOS parameters for [...]-iron are: p0 = 8.775 ± 0.012 Mg/m3, [...] = 205 ± 4 GPa, [...] = 4.80 ± 0.01 (referenced to 12 GPa and 300 K). The calculation favors the melting curve of Boehler [1993] or Saxena et al. [1993]. Shock-wave experiments on pure iron preheated to 1573 K were conducted in 17-73 GPa range. The shock-wave equation of state of [gamma]-iron at 1573 K initial temperature can be fit with [...] = 4.102(0.015) km/s + 1.610(0.014)[...] with [...] = 7.413 ± 0.012 Mg/m3. [Gamma]-iron's bulk modulus and its pressure derivative are 124.7±1.1 GPa and 5.44±0.06 respectively.

We present new data for sound velocities in the [gamma]- and liquid-phases. In the [gamma]-phase, to a first approximation, the longitudinal sound velocity is linear with respect to density: Vp = -3.13(0.72) + 1.119(0.084) [...] (units for Vp and [...] are km/s and Mg/m3 respectively). Melting was observed in the highest pressure (about 70-73 GPa) experiments at a calculated shock temperature of about 2775 ± 160 K. This result is consistent with our calculated [...]-iron melting curve which is close to those measured by Boehler [1993] and Saxena et al. [1993]. The liquid iron sound velocity data yield a Gruneisen parameter value for liquid iron of 1.63±0.28 at 9.37±0.02 Mg/m3 at 71.6 GPa. The quantity [...] from our data is 15.2±2.6 Mg/m3, which is within the bounds of Brown and McQueen [1986] (13.3-19.6 Mg/m3). Based on upward pressure and temperature extrapolation of our melting curve of [gamma]-iron, the estimated inner core-outer core boundary temperature is 5500±400 K, the temperature at the core-mantle boundary on the outer core side is about 3930±630 K, and the thermal boundary layer at the core-mantle boundary has a temperature difference between 400 and 1400 K.

The shock-wave equation of state of initially solid (300 K) and molten (1573 K) fayalite (Fe2SiO4, Fa) are reported in the ranges 23 to 212 GPa and 5 to 47 GPa, respectively. The 300 K data appear to undergo a phase change in the 35-55 GPa range. The density of the high pressure phase (HPP) is consistent with a dense oxide mixture. Although the initially 300 K fayalite may melt along its Hugoniot, this is not explicitly detected. Fitting the HPP Hugoniot data in the shock velocity ([...])-particle velocity ([...]) plane yields:

[...] = 4.375(0.027) Mg/m3, (1)

[...] = 4.07(0.22) km/s + 1.43(0.06) [...], (2)

where [...] is the initial density. The isentropic bulk modulus [...] = 72.4 ± 8.0 GPa, and its pressure derivative [...] = 4.72±0.24.

The 1573 K data set yields: [...] = 3.750(0.018) Mg/m3, (3) [...] = 2.63(0.02) km/s + 1.59(0.01) [...], (4)

and [...] = 25.9 ± 0.4 GPa, [...] = 5.36 ± 0.04. The bulk modulus compares favorably with Agee [1992a]'s result (24.4 GPa), but the pressure derivative is quite different (10.1 from Agee [1992a]).

Above 50 GPa, the high pressure regime of the Hugoniot of the solid fayalite can be fit with oxide mixture models using stishovite and FeO (either LPP or HPP). The fayalitic liquid compression data above 40 GPa are well fit with ideal mixing of partial molar volumes of stishovite and FeO (LPP or HPP), in support of the hypothesis of Rigden et al. [1989].

A model basalt incorporating the liquid fayalite data shows the neutral buoyancy zone of basic silicate melts of plausible terrestrial compositions is at about 250-400 km depth based on the PREM Earth model.

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