Quite Interesting Calculations: The Iron Catastrophe

Written by Nicholas Grundy, PhD | Metallurgist and Application Engineer at Thermo-Calc Software

Sometimes, reading books or journals, I stumble upon materials science problems that make me curious, and I find myself wondering if a thermodynamic calculation might shed some light on the matter. One of the perks of working for Thermo-Calc Software is that I have access to our whole range of state-of-the-art software products and CALPHAD type materials databases. And so, from time to time, I get to set up what I like to call “Quite Interesting Calculations” to investigate unusual materials or processes. Here I would like to share some thermodynamic insight on an event that happened a long, long time ago: The Iron Catastrophe.

(Note: This report is written just for fun and completely without scientific rigor.)

The Iron Catastrophe

Most people probably know that the Earth is built of concentrically arranged units. The three main ones are the metallic core, the silicate mantle-crust system, and the atmosphere-hydrosphere. We live in and rely on the atmosphere-hydrosphere, more specifically the troposphere, which is tiny and fragile. It is only about 1 thousandths of the earth’s diameter and makes up 1 millionth of its mass. The core’s radius is just over 1/2 of the Earth’s radius and its volume is about 1/9 of the Earth’s. However, 1/3 of the mass of the Earth is concentrated in its core. This means the core is almost 3 times as dense as the mantle-crust system, indicating that it must have a completely different chemical composition.

But how do we determine the bulk composition of the Earth? It is obviously not possible to drill a hole deep enough to sample the lower mantle, let alone the core. It turns out that fascinating detective work, involving many different disciplines, is required to decipher the Earth’s composition. Analysis of the propagation of earthquake waves through the Earth’s center provides information on density and the thickness of the Earth’s layers. It also proves that the Earth’s core is liquid. The fact that we have a magnetic field proves that the liquid core must be a good electric conductor and must be moving in a swirling motion.

Direct evidence of the Earth’s mantle composition is given by rare outcrops of rocks that were thrust upward when continental crusts collide. Ophiolites are fragments of the Earth’s oceanic crust that were transported to the surface by a process called obduction. Kimberlites are rocks that originate from deep in the Earth’s mantle where the pressures and temperatures are so high that carbon in the form of graphite is transformed into diamond. They often contain fragments of rocks, so called xenoliths, that originate from even deeper within the mantle.

But surprisingly, it turns out that the most reliable indication of the bulk composition of the Earth comes from outer space: 4.6 billion years ago our solar system was formed out of a slowly rotating disk-shaped cloud of gas and dust, which was left over from the explosion of a supernova. The dust was slowly drawn together by gravity and started to clump up, forming larger and larger clumps, so-called planetesimals, that continued to collide, ultimately forming the planets. This process is termed accretion. During this process, some small clumps of material escaped and continued to circle the sun and still do so today. Sometimes these clumps are trapped by Earth’s gravity field and come hurtling to the surface as meteorites. Analysis of their isotope fingerprint suggests that a certain type of meteorite, the so-called enstatite chondrites, were formed at a similar distance from the sun as the Earth and thus are expected to have a composition that closely resembles the bulk composition of the Earth.

Taking all these pieces of evidence together, so direct and indirect evidence from the earth itself and also the compositions of enstatite meteorites, it turns out the Earth’s mantle consists of about 45% SiO2, 37% MgO, 5% Al2O3, 4% CaO, and 8% FeOx. The core consists of 85% Fe, 5% Ni, and 10% lighter elements including Si, S, P, C, and others. So basically, the Earth consists of an oxide mantle and an Iron-Nickel core.

But how did the Earth’s core form and why does it have such a completely different composition as the mantle? There are a number of theories, but one of the most compelling is the so-called “Iron Catastrophe Theory.” According to this theory, the continued bombardment during the late stages of planetary accretion resulted in partial melting of the early Earth. On melting, two immiscible liquids formed, a dense metallic liquid and a less dense oxidic liquid. The denser metallic liquid started to sink towards the core due to its higher density, driven by gravity. Significant gravitational energy was released, which heated the earth up even more, resulting in a runaway process that resulted in almost complete melting of the earth. Thus, the name “Catastrophe.”

Calculating the Earth’s Core and Mantle Composition with Thermo-Calc

So, if we assume this theory is accurate, and the metallic core of the earth was formed by liquid immiscibility, then we should be able to calculate the resulting core and mantle composition with Thermo-Calc and the TCOX database, which is well suited to calculate the chemical composition of immiscible metallic and oxidic liquids with a similar overall chemistry as the Earth’s. As the database was not developed for geological purposes, the effect of pressure is not included for condensed phases, but we could assume that the compositions of the two liquids is not affected much by pressure. So, for this calculation, I used the bulk earth composition given by W. F. McDonough [1], assuming first a temperature of 2500 K and 1 bar pressure and I compared the calculated composition of the metallic and oxidic liquid with the core and mantle composition taken from the same publication.

Already this calculation shows quite a reasonable agreement for many of the elements. However, the calculation shows that, at a pressure of 1 bar, a gas phase is stable. To suppress the formation of this gas phase, the pressure was increased to 1000 bar and the temperature increased to 3000 K.

This second calculation shows a surprisingly good agreement with the core and mantle composition estimated by McDonough, even though the database was absolutely not developed for this application.

It is interesting to note that calculations at lower temperatures result in a much poorer agreement, indicating that the equilibrium between the two liquids was reached at quite high temperatures. Of course, it cannot be judged if these compositions are still from the original formation of the two liquids during the Iron Catastrophe event, or if the mantle and core composition have gradually changed over time, bringing the overall compositions closer to the equilibrium at the core-mantle boundary.

In spite of the fact that this is just an un-scientific, fun calculation, it still seems to strongly support the theory that the core and mantle compositions are a direct result of liquid immiscibility. The other interesting take-away is that the reactions between the Earth’s liquid metallic core and oxide mantle are eerily similar to the ones happening between liquid steel and oxide slag in all the steel plants around the world.

As a final note, I’d like to add that from a metallurgist’s point of view, I would say that the mantle did not do a good job at desulfurizing the liquid metal core…

References

[1] William F.McDonough, Chapter 1 – The Composition of the Earth, International Geophysics, Volume 76, 2001, Pages 3-23

Nicholas Grundy, PhD

Nicholas originally graduated as a Geologist / Mineralogist before completing a PhD in Materials Sciences from the ETH in Zurich on CALPHAD assessments of functional ceramics for high temperature solid oxide fuel cell (SOFC) materials using Thermo-Calc. After two years as a Post Doc at the ETH, where he supervised two PhD theses, he moved to the Ecole Polytechnique in Montreal, where he developed viscosity models for silicate melts and used the quasi-chemical model to assess the CaO-MgO-B2O3-SiO2 system using FactSage Software. He then left academia and worked in the steel industry for the SMS Group for almost 10 years, before joining Thermo-Calc Software in 2019. At Thermo-Calc he is responsible for the German-speaking market and supports various developments within Thermo-Calc, mainly related to steel and steel processing, such as the Process Metallurgy Module.

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