Temperature of the inner-core boundary of the Earth: Melting of iron at high pressure from first-principles coexistence simulations

Abstract

The Earth's core consists of a solid ball with a radius of 1221 Km, surrounded by a liquid shell which extends up to 3480 Km from the centre of the planet, roughly half way towards the surface (the mean radius of the Earth is 6373 km). The main constituent of the core is iron, and therefore the melting temperature of iron at the pressure encountered at the boundary between the solid and the liquid (the ICB) provides an estimate of the temperature of the core. Here I report the melting temperature of Fe at pressures near that of the ICB, obtained with first principles techniques based on density functional theory. The calculations have been performed by directly simulating solid and liquid iron in coexistence, and show that and at a pressure of ∼ 328 GPa iron melts at ∼ 6370 ± 100 K. These findings are in good agreement with earlier simulations, which used exactly the same quantum mechanics techniques, but obtained melting properties from the calculation of the free energies of solid and liquid Fe [1,2,3]. PACS numbers:The study of iron under extreme conditions has a long hystory. In particular, numerous attempts have been made to obtain its high pressure melting properties [4,5,6,7,8,9,10,11,12]. Experimentally, Earth's core conditions can only be reproduced by shock wave (SW) experiments, in which a high speed projectile is fired at an iron sample, and upon impact high pressure and high temperature conditions are produced. By varying the speed of the projectile it is possible to investigate a characteristic pressure-volume relation known as the Hugoniot [13], and even infer temperatures, although a word of caution here is in order, as temperature estimates are often based on the knowledge of quantities like the constant volume specific heat and the Grüneisen parameter, which are only approximately known at the relevant conditions [10]. If the speed of the projectile is high enough, the conditions of pressure and temperature are such that the sample melts, and it is therefore possible to obtain points on the melting curve, of course with the caveat mentioned above about temperature measurements. An alternative route to high pressure high temperature properties is the use of diamond anvil cells (DAC), in which the sample is surrounded by a pressure medium and statically compressed between two diamond anvils. In DAC experiments pressure and temperatures can be directly measured, and therefore these techniques should in principle be more reliable to investigate melting proeprties. Unfortunately, in the case of iron is it not so, and there is a fairly large range of results obtained by different groups [4,5,6,7,8,9].An alternative approach used for the past ten years or so has been to employ theory -and in particular quantum mechanics techniques based on density functional theory-to calculate the high pressure melting curve of iron. A number of groups have used different approaches to the problem. Our own strategy has been to calculate the Gibbs free energy of solid and liquid iron, and then obtain the melting curve...

Partitioning of Si and O between liquid iron and silicate melt: A two‐phase ab‐initio molecular dynamics study

“…agreement with the density deficit given by Anderson and Isaak [2002]. According to the work, 1% density deficit can be considered by either 1.69 wt% Si or 0.73 wt% O at the iron melting temperature of 6350 K at the inner and the outer core boundary [Alfè, 2009]. Similar value for Si is also given by Chen et al [2007].…”

“…The twophase method, which makes two phases in direct contact in a molecular dynamics (MD) simulation cell, is employed in ab-initio studies of the melting temperatures of iron and MgO [Alfè, 2005[Alfè, , 2009 and the solubility of argon in liquid iron [Ostanin et al, 2006].…”

High-temperature ab initio calculations on FeSi and NiSi at conditions relevant to small planetary cores

“…At a given temperature, the vibrational free energy can be calculated from the phonon frequencies, which were obtained using the small-displacements or "frozen phonon" method as implemented in the program Phon (Alfè 2009). For any system, the most stable structure is that which has the lowest Gibbs free energy, G:…”

Melting temperature of tungsten from twoab initioapproaches

“…The second approach is the direct simulation of the solid-liquid coexistence, i.e., the so-called coexistence approach. [8][9][10][11][12][13][14][15][16][17][18] In this approach, the temperature adjusts spontaneously during the simulation to provide a two-phase equilibrium that satisfies the equality of Gibbs free energies of solid and liquid. In this paper, we use a recently proposed [19][20][21][22] hybrid approach combining the above two approaches.…”