Physics – Measuring the elasticity of iron under pressure – Physics
July 17, 2023β’ Physics 16, 109
Laboratory experiments are elucidating the directions and speeds at which acoustic waves propagate in the type of iron that likely forms the Earth’s core.
APS/C. Cain; S. Deemyad/University of Utah
By exploring unknown trajectories within pressure-temperature phase space, scientists have reached a groundbreaking milestone: the synthesis of single-crystalline iron into the structure it likely assumes in the Earth’s core [1]. This achievement allows accurate measurements of the elastic properties of iron in different crystalline directions. In addition, 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 unraveling the secrets of our planet’s inner regions.
Our understanding of 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 consists mainly of iron in a hexagonal close-packed structure known as π-iron [5β7]. This material consists of crystals with preferred orientations that together cause sound waves to propagate in different directions in different ways [8].
Iron has been extensively studied under high pressure due to its abundance in the Earth’s core [9]. Yet there is a critical lack of experimental data on the elastic properties of πiron along different crystalline orientations. Determining the elastic properties of anisotropic solids requires measuring the elasticity tensor, which represents the linear relationship between stress and strain in a material and characterizes the speed of sound propagation 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 ( πΌphase) to πiron, the samples usually break into numerous small crystals that undergo plastic deformation. Their small size makes them unsuitable for detailed crystallographic analysis and has been a major hindrance in accurately determining the anisotropy in the elastic properties of π-iron.
AgnΓ¨s Dewaele from the University of Paris-Saclay and her colleagues successfully met this challenge [1]. They used an innovative experimental approach, following an alternative path in the iron phase diagram to synthesize pure single crystalline π-iron. Instead of putting pressure on the πΌphase on an isothermal path, the researchers heated the sample while it was still in the πΌphase on an isobaric or constant pressure path to achieve the face-centered cubic phase of iron ( πΎ-phase). Then they switched to πiron by isothermal pressure increase of the πΎphase followed by an isobaric cooling. Finally, using inelastic X-ray scattering, they measured the elastic constants of πiron along different crystalline directions.
Unlike previous studies that relied on iron powder samples, Dewaele and colleagues’ findings provide accurate estimates of the anisotropy present in the elastic constants of π-iron. The results of this study are qualitatively consistent with previous work in identifying the direction in which waves propagate fastest πiron structure – the fast axis of the material [10]. But quantitatively they show significant deviations from previously obtained data, highlighting the importance of their experimental approach and its impact on our understanding of πiron properties.
The study directly verifies that longitudinal waves propagate faster along the lines that connect π-iron lattice nodes in an orientation known as the Cdirection, and with a velocity about 4.4% faster than waves traveling in the basal plane of the lattice. In addition, the study successfully demonstrates the pressure dependence of changes in the elastic properties of πiron, suggesting that these trends persist during pressurization. It is important to note that the experiments in this study were conducted at room temperature and limited to pressures up to 30 GPa, which is an order of magnitude lower than conditions in the Earth’s core. However, the experimental data obtained is a crucial test for theoretical models.
The experimental data not only allows the researchers to identify the most appropriate theoretical approach – one with superior predictive power for calculating the elasticity tensor of π-iron – but also allows them to extend this knowledge to conditions similar to those found in the Earth’s core. In particular, Dewaele and her colleagues show how the observed anisotropy could persist with a consistent magnitude, from lower pressures to the extreme densities typical of the Earth’s inner core.
As long as we don’t have physical access to the Earth’s core, laboratory-based 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 ambition 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 illustrates the power of combining experimentation and theory in pushing the boundaries of scientific understanding.
References
- A. Dewaele et al.“Synthesis of Single Crystals of π Iron and Direct Measurements of the Elastic Constants,” Physically. Rev., Lett. 131034101 (2023).
- H Jeffreys, The earth (Cambridge University Press, New York, 1929), p. 265.
- I Lehmann,”PΒ΄,β Bur. Central Seismol. Int. Ser. a 143 (1936).
- S Tateno et al.“The Structure of Iron in the Earth’s Inner Core,” Science 330359 (2010).
- B. Buffett, “The Enigmatic Inner Core of the Earth,” Physically. Today 6637 (2013).
- A. Morelli et al.βAnisotropy of the inner core derived from PKIKP travel times,β Geophysics. Res. Lit. 131545 (1986).
- HK Mao et al.“Static Compression of Iron to 300 GPa and Fe0.8Ni0.2 alloy up to 260 GPa: implications for core composition,β J. Geophys. Res.: solid earth 9521737 (1990).
- A. Deuss, “Heterogeneity and Anisotropy of the Earth’s Inner Core,” Annu. Rev. Planet Earth. Science. 42103 (2014).
- F. Birch, βMantle and Core Density and Composition,β J. Geophys. Res. 694377 (1964).
- WL Mao et al.“Experimental Determination of the Elasticity of Iron at High Pressure”, J. Geophys. Res.: solid earth 11389 (2008).
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