Journey to the center of the earth: exploring iron’s equation of state

Earth-magnetic-field (Download Image)

Earth is enveloped by a magnetic field that protects life on the planet from exposure to harmful, ionizing radiation in the form of solar wind. This magnetic field is generated and sustained by a geodynamo process that originates from the heat-transport-driven flow of primarily iron, that resides in the planet’s outer core. To get a better idea of how this works, the authors developed a model on the equation of state of iron that involved a critical analysis of more than 100 papers, including past high-profile publications conducted at LLNL. Image by Adobe Stock.

A typical high-school science class teaches that Earth’s core is comprised of two parts: an inner core that is composed mainly of solid iron and an outer core that is composed mainly of molten, liquid iron. Although this is common knowledge, the location of the boundary between the solid inner core and liquid outer core, as well as many other facets of Earth’s deep interior layers, remain unknown.

Earth’s outer core is crucial for life because the flowing metallic liquid present in that layer creates a magnetic field that envelops the planet and helps to shield it from exposure to solar wind, which are high-energy, charged particles generated by the sun that reach Earth. The boundary between the inner and outer cores is largely governed by the melting point of iron at high pressures — approximately three million times atmospheric pressure — that exist within the core.

In a paper recently published in Physical Review B, a team of researchers from Lawrence Livermore National Laboratory (LLNL) present a new equation of state (EOS) for iron to help address some of the uncertainties associated with the composition of Earth’s core structure.

Despite decades of research, there remain many unknowns associated with Earth’s core, which is thought to consist of 90% iron, supplemented by other elements such as nickel, sulfur, silicon, oxygen, carbon, hydrogen and gold. These other elements can affect the phase stability of Earth’s core at various temperatures and pressures.

The melting behavior of iron (and other materials, in general) is a key part of its overall thermodynamic properties, which are encapsulated in the EOS model. This model plays an important role in determining the rate of heat transport from the hot inner core to the somewhat cooler outer core. This heat transport drives the convective flow in the outer core, which is necessary for a geodynamo process to generate and sustain the magnetic field.

The newly developed EOS was specifically designed to address the high pressures and temperatures that are present in Earth’s core, while also accounting for the even more intense, extreme conditions that are found in the core of super-Earths, which are large earth-like planets that may potentially harbor life. In addition to these applications in planetary science, the new EOS can be used to construct models for other iron-rich materials of industrial relevance, such as stainless steel.

To have their EOS cover this broad range of conditions and applications, the team carefully analyzed the extensive literature that exists on the thermodynamic behavior of iron and executed their own first-principles quantum simulations to produce results for certain conditions that are relatively devoid of data. Perhaps most importantly, the team used their critical analysis of the data to produce not just one EOS, but a family of EOS models to address uncertainties in the data and capture different potential scenarios.

“There are a lot of conflicting conclusions and results in the 100-plus studies examined in our work; construction of an EOS is a powerful and useful means to tie these studies together in a coherent way and check for self-consistency among the various data sets,” said the paper’s lead author Christine Wu, a staff scientist in the Physical and Life Sciences’ Physics Division. 

The team focused their EOS development on five key areas: compressibility, shock-and-release behavior, high-pressure melting, thermal expansion and vaporization. The resulting multiphase EOS is designed to fit a diverse and carefully selected set of data that span several orders of magnitude in temperature and density. This data can help address which solid phases are likely to be present in certain regions within Earth — since different phases are expected to transmit seismic waves differently and inform models used to simulate the planetary evolution and geodynamics of Earth and Earth-like planets at various pressure-dependent melt temperatures.

“It is our hope and expectation that the new EOS will prove useful to a broad range of applications involving iron and we are actively seeking to collaborate with experimentalists and theorists to conduct more studies and resolve some of the many uncertainties that still exist.” Wu said.

Other LLNL authors on the paper include Lorin Benedict, Philip Myint, Sebastien Hamel, Carrie Prisbrey and Jim Leek.

– Shelby Conn