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Melting of Fe Alloys and the Thermal Structure of the Core

Rebecca A. Fischer

Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois, USA

ABSTRACT

The temperature of the Earth's core has significant implications in many areas of geophysics, including applications to Earth's heat flow, core composition, age of the inner core, and energetics of the geodynamo. The temperature of the core at the inner core boundary is equal to the melting temperature of the core's Fe-rich alloy at the inner core boundary pressure. This chapter is a review of experimental results on melting temperatures of iron and Fe-rich alloys at core conditions that can thus be used to infer core temperatures. Large discrepancies exist between published melting curves for pure iron at high pressures, with better agreement on the melting behavior of Fe-light element alloys. The addition of silicon causes a small melting point depression in iron, while oxygen and especially sulfur cause larger melting point depressions. The inner core boundary temperature likely falls in the range 5150-6200 K, depending on the identity of the light element(s) in the core, which leads to a core-mantle boundary temperature of 3850-4600 K for an adiabatic outer core. The most significant sources of uncertainties in the core's thermal structure include the core's composition, phase diagram, and Grüneisen parameter.

1.1. INTRODUCTION

The Earth's core consists primarily of iron-nickel alloy. The presence of several weight percent of one or more lighter elements such as S, Si, O, C, or H is implied by the core's density, and these light elements depress the melting point of the core relative to pure iron [e.g., Birch, 1952; Poirier, 1994]. The thermal structure of the core plays a key role in many deep Earth properties. It affects the magnitude of the temperature difference across the thermal boundary layer at the base of the mantle, heat flow on Earth, and the cooling rate of the core. Faster cooling rates would imply a younger inner core, while slower cooling would imply an older inner core. The age of the inner core corresponds to the onset of compositional convection in the outer core due to the preferential expulsion of light elements during inner core crystallization. The core's temperature structure is also linked to thermal convection in the outer core, with these two types of convection driving the dynamo responsible for Earth's magnetic field [e.g., Lister and Buffett, 1995]. The vigor of thermal convection in the Earth's core depends on both its thermal structure and its thermal conductivity. Recent studies on the thermal conductivity of Fe and Fe-rich alloys at core conditions have revealed a higher thermal conductivity of core materials than previously thought [e.g., Pozzo et al., 2012; Seagle et al., 2013], implying that higher core temperatures and/or stronger compositional convection are required to power the dynamo.

Knowledge of the core's temperature would inform our understanding of these processes and put tighter constraints on the abundances of light elements in the Earth's core, since thermal expansion affects the quantity of light elements needed to match the observed density. The temperature at the inner core boundary (ICB) is equal to the liquidus temperature of the core alloy at that pressure (~330 GPa), since that is the temperature at which the solid inner core is crystallizing from the liquid outer core. Therefore knowledge of the ICB temperature could be combined with measurements of phase diagrams at high pressures and temperatures (P and T) to constrain the identities of the core's light elements. However, the thermal structure of the core is poorly understood.

This chapter reviews the available experimental constraints on the core's temperature. Measuring melting of iron and Fe-rich alloys at core conditions presents significant experimental challenges, leading to discrepancies between studies. Extrapolating melting curves to the ICB pressure provides information about the ICB temperature. Adiabats can be calculated through these P-T points up to the core-mantle boundary (CMB) pressure to determine the thermal structure of the outer core.

1.2. METHODS FOR DETERMINATION OF MELTING

Melting experiments relevant to the Earth's core require the generation of simultaneous extreme pressures and temperatures. This is commonly accomplished through the use of a laser-heated diamond anvil cell, which is capable of reaching inner core conditions. A sample is embedded in a soft, inert pressure-transmitting medium and compressed between two diamond anvils, then heated with an infrared laser until melted. Pressure is typically monitored using an X-ray standard in the sample chamber whose equation of state is well known or by ruby fluorescence or diamond Raman spectroscopy, whose signals shift systematically with pressure. Temperature is measured spectroradiometrically by fitting the thermal emission to the Planck function (see Salamat et al. [2014] for a recent review of diamond anvil cell methodology).

While techniques for generating and measuring extreme P-T conditions in the diamond anvil cell are relatively well established, there is disagreement over the best method for detecting a melt signal. Some studies rely on "speckling," a qualitative detection of movement in the sample visualized by shining a second (visible) laser onto the laser-heated spot during the experiment [e.g., Boehler, 1993]. This movement is thought to be due to convection of the molten sample, though it has recently been proposed that rapid recrystallization of the sample at subsolidus conditions can cause this apparent motion [Anzellini et al., 2013; Lord et al., 2014a]. Other methods rely on discontinuities in physical properties upon melting, such as a change in the emissivity-temperature relationship [Campbell, 2008; Fischer and Campbell, 2010] or in the laser power-temperature relationship [e.g., Lord et al., 2009]. These methods have the advantage of not requiring a synchrotron X-ray source but provide no structural information about subsolidus phases. Synchrotron-based techniques include the use of X-ray diffraction to detect diffuse scattering from the melt and/or disappearance of crystalline diffraction [e.g., Anzellini et al., 2013; Campbell et al., 2007; Fischer et al., 2012, 2013] or, less commonly, time domain synchrotron Mössbauer spectroscopy [Jackson et al., 2013].

In addition to diamond anvil cell methods, the multianvil press has also been used for melting experiments, with analysis of recovered samples used to detect melting [e.g., Fei and Brosh, 2014; Fei et al., 2000]. Previously multianvil press experiments were limited in pressure to ~25 GPa, but recent advances in sintered diamond anvils [e.g., Yamazaki et al., 2012] may allow for higher-pressure melting experiments in the multianvil press in the future. Until recently, shock wave experiments were the standard technique for melting experiments at core conditions [e.g., Brown and McQueen, 1986]. They provide a reliable method for reaching core pressures and temperatures, with melting determined from discontinuities in the sound velocity-pressure relationship. However, temperatures in shock experiments are frequently calculated thermodynamically [e.g., Brown and McQueen, 1986; Nguyen and Holmes, 2004] due to difficulties with direct measurements, making them less accurate, and improvements in diamond cell methods have facilitated the access of core conditions by static methods. Additionally, melting curves can be calculated using ab initio methods [e.g., Alfè et al., 2002] or thermodynamic modeling [e.g., Fei and Brosh, 2014].

1.3. RESULTS ON MELTING OF IRON

Due to its extreme importance to our understanding of the thermal structure of the core, the melting behavior of iron at high pressures has been investigated by many research groups using all of the techniques discussed in Section 1.2. Despite such a large number of results using a variety of methods, there remains no consensus on the melting curve of pure iron at core pressures. Figure 1.1 illustrates some of the many previous results on iron melting obtained using diamond anvil cell [Anzellini et al., 2013; Boehler, 1993; Jackson et al., 2013; Ma et al., 2004; Saxena et al., 1994; Shen et al., 2004; Williams et al., 1987], ab initio [Alfè, 2009; Alfè et al., 2002; Anderson et al., 2003; Belonoshko et al., 2000; Laio et al., 2000; Sola and Alfè, 2009], and shock wave [Ahrens et al., 2002; Brown and McQueen, 1986; Nguyen and Holmes, 2004; Yoo et al., 1993] methods. Below ~50 GPa there is fairly good agreement over the iron melting curve. In the ~50-200 GPa range, readily accessible in the laser-heated diamond anvil cell, Fe melting curves vary by over 1000 K. Where the shock Hugoniot crosses the melting curve at ~240 GPa, reported shock melting temperatures vary by ~1500 K. At the inner core boundary pressure of 330 GPa, ab initio calculations of Fe melting vary by over 1500 K.

Figure 1.1 Selection of the literature results on Fe melting illustrating range of discrepancy in the...