Measurement of the elasticity of pressurized iron

July 17, 2023• Physics 16, 109

Laboratory experiments clarify the directions and speeds at which acoustic waves propagate in the type of iron that probably makes up the earth’s core.

ODA/C. Cain; S. Deemyad/University of Utah

ODA/C. Cain; S. Deemyad/University of Utah

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By exploring uncharted paths within the pressure-temperature phase space, scientists have achieved a revolutionary milestone: the synthesis of single-crystal iron into the structure it likely takes in the Earth’s core [1]. This realization allows precise measurements of the elastic properties of iron in various crystalline directions. Furthermore, the study helps identify a theoretical approach that could uncover the underlying mechanisms responsible for the observed anisotropy in seismic wave propagation across the Earth. By elucidating the properties of iron in its core structure, this research brings us one step closer to unlocking the secrets of our planet’s innermost regions.

Our understanding of the Earth’s composition and structure is based on seismological studies, which analyze how elastic waves propagate through the planet. These studies require knowledge of material properties at relevant densities. The current model of the Earth’s interior is based on an analysis by Sir Harold Jeffreys and Inge Lehmann, who proposed that the Earth’s core consists of a solid inner core surrounded by a liquid outer core. [2, 3]. In the 1980s, researchers discovered that seismic waves exhibit anisotropic behavior, traveling faster in the polar direction than in the equatorial direction [4]. A popular explanation for this phenomenon assumes that the solid inner core is composed predominantly of iron in a tightly packed hexagonal structure known as $\mathrm{????}$-iron [5–7]. This material consists of crystals with preferred orientations which together cause sound waves to propagate differently along different directions [8].

Iron has been extensively studied under high pressure due to its abundance in the Earth’s core [9]. Even so, there has been a crucial lack of experimental data on the elastic properties of $\mathrm{????}$-iron along different crystalline orientations. Determining the elastic properties of anisotropic solids requires measuring the tensor of elasticity, which represents the linear relationship between stress and strain in a material and characterizes the propagation speed of sound in different crystalline orientations. However, measuring the elasticity tensor under pressure is challenging and requires synchrotron X-ray techniques performed on high-quality single crystals.

Unfortunately, when iron is compressed from its initial body-centered cubic crystalline phase ( $\mathrm{????}$-phase) a $\mathrm{????}$-iron, specimens typically fracture into numerous small crystals that undergo plastic deformation. Their tiny size makes them unsuitable for detailed crystallographic analysis and has been a major obstacle in accurately determining the anisotropy in the elastic properties of $\mathrm{????}$-iron.

Agnès Dewaele of the University of Paris-Saclay and her colleagues have successfully met this challenge [1]. They used an innovative experimental approach, taking an alternative route in the phase diagram of iron to synthesize the pure single crystal $\mathrm{????}$-iron. Instead of pressurizing the $\mathrm{????}$-stage on an isothermal path, the researchers heated the sample while still in the $\mathrm{????}$-phase on an isobaric path, or constant pressure, to reach the face-centered cubic phase of iron ( $\mathrm{????}$-phase). Then they switched to $\mathrm{????}$– ironing by isothermal pressurization of $\mathrm{????}$-phase followed by an isobaric cooling. Finally, using inelastic X-ray scattering, they measured the elastic constants of $\mathrm{????}$-iron along different crystalline directions.

Unlike previous studies that relied on powdered iron samples, Dewaele and colleagues’ results provide precise estimates of the anisotropy present in the elastic constants of $\mathrm{????}$-iron. The results of this study qualitatively agree with previous work in identifying the direction in which waves propagate fastest $\mathrm{????}$-the structure of the iron: the fast axis of the material [10]. But they quantitatively show significant deviations from previously obtained data, highlighting the importance of their experimental approach and its impact on our understanding of $\mathrm{????}$-properties of iron.

The study directly verifies that longitudinal waves propagate faster along the lines that connect them $\mathrm{????}$-iron lattice nodes in an orientation known as the c-direction and at a speed approximately 4.4% higher than the waves traveling in the basal plane of the lattice. Furthermore, research successfully demonstrates the pressure dependence of changes in the elastic properties of $\mathrm{????}$-iron, suggesting that these tendencies persist during pressurization. It is important to note that the experiments in this study were performed at room temperature and were limited to pressures up to 30 GPa, which is an order of magnitude lower than the conditions in the Earth’s core. However, the experimental data obtained provide a crucial test for the theoretical models.

Experimental data not only allows researchers to identify the most appropriate theoretical approach, one with superior predictive power for calculating the elasticity tensor of $\mathrm{????}$-iron, but also allow them to extend this knowledge to conditions similar to those inside the Earth’s core. In particular, Dewaele and his colleagues show how the observed anisotropy could persist at a constant magnitude from pressures below the extreme densities characteristic of the Earth’s inner core.

Until we have physical access to the Earth’s core, laboratory measurements of material properties under extreme conditions are crucial to ensure the accuracy of our models. This research brings us closer to realizing the long-standing aspiration of a “virtual journey to the center of the Earth”. The study not only opens new doors to understanding the Earth’s core, but also exemplifies the power of combining experimentation and theory in pushing the boundaries of scientific understanding.

About the author

Shanti Deemyad is an experimental condensed matter physicist who currently serves as an associate professor of physics and head of the High Pressure Research Laboratory at the University of Utah. Deemyad completed his undergraduate studies at the Sharif University of Technology, Iran, and holds a PhD in physics from Washington University in St. Louis. Following the completion of his doctoral studies, he conducted postdoctoral research at Harvard University. Deemyads’ research centers on the exploration of quantum effects in the lattice and electronic properties of condensed matter systems. She is particularly interested in investigating exotic states of matter that emerge under extreme conditions of pressure and temperature.

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