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1. Wagle, Fabian. Structure-property relations for resistivity of iron alloys at planetary core conditions.

Degree: PhD, 2018, Universität Bayreuth

URL: https://epub.uni-bayreuth.de/3854/

Electronic transport properties of iron alloys under extreme conditions are critical parameters for the generation of magnetic fields in terrestrial planets, and thus of great importance for their evolution and habitability. Like many other material properties, electrical resistivity is closely related to the atomic and electronic structure of the material, both of which change with pressure and temperature. This thesis includes three studies on the relationship between structural properties and electrical resistivity of iron alloys at conditions of planetary cores.
In the first part of the thesis, we use density functional theory based molecular dynamics simulations in combination with the Kubo-Greenwood formalism to self-consistently determine atomic structure and electrical resistivity of potential core forming liquid iron alloys, with several weight per cent of silicon, oxygen and sulfur. We observe that with increasing compression and light element
concentration, the temperature coefficient of resistivity decreases (for all alloys considered), eventually vanishes (Fe-Si) and even changes sign (Fe-S). By analyzing optical
conductivity using a Drude model, we show that the electron mean free path approaches the interatomic distance, causing resistivity to saturate due to a combined effect of temperature, compression and chemical composition. Differences in the degree of saturation between the different alloys are explained by structural observations. In contrast to the interstitial-like incorporation of oxygen, silicon randomly substitutes for iron atoms in the liquid. While the addition of oxygen only marginally shortens the mean free path, silicon does so more efficiently due to its larger scattering cross section. Since the covalent component of bonding between sulfur and iron has been shown to strengthen under pressure, Fe-S alloys exhibit an effective mutual repulsion of sulfur
atoms, resulting in high coordination with iron atoms. This leads to an even distribution of impurity atoms in the liquid with less overlap of impurity scattering cross-sections, causing resistivity to saturate more efficiently. A consequence of the saturation limit is the observation of a secondary electronic effect that leads to a negative temperature coefficient of resistivity for high compression and sulfur concentration. In agreement with Mott's theory, we find that thermal broadening and the associated decrease of the d-electron density of states at the Fermi level leads to a decreasing resistivity with increasing temperature.
Based on this analysis, we conclude that resistivity in the Earth's core cannot exceed 100 μΩcm, largely independent of
temperature. The evolution of a dynamo is therefore only determined by the boundary conditions changed by a growing inner core and not by a variation of the conductivity profile.
In the second part of the thesis, we describe the resistivity discontinuity of iron along the melting curve, representative for potential inner core boundaries of terrestrial planets. Based on…
*Advisors/Committee Members: Steinle-Neumann, Gerd (advisor).*

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APA (6^{th} Edition):

Wagle, F. (2018). Structure-property relations for resistivity of iron alloys at planetary core conditions. (Doctoral Dissertation). Universität Bayreuth. Retrieved from https://epub.uni-bayreuth.de/3854/

Chicago Manual of Style (16^{th} Edition):

Wagle, Fabian. “Structure-property relations for resistivity of iron alloys at planetary core conditions.” 2018. Doctoral Dissertation, Universität Bayreuth. Accessed November 20, 2018. https://epub.uni-bayreuth.de/3854/.

MLA Handbook (7^{th} Edition):

Wagle, Fabian. “Structure-property relations for resistivity of iron alloys at planetary core conditions.” 2018. Web. 20 Nov 2018.

Vancouver:

Wagle F. Structure-property relations for resistivity of iron alloys at planetary core conditions. [Internet] [Doctoral dissertation]. Universität Bayreuth; 2018. [cited 2018 Nov 20]. Available from: https://epub.uni-bayreuth.de/3854/.

Council of Science Editors:

Wagle F. Structure-property relations for resistivity of iron alloys at planetary core conditions. [Doctoral Dissertation]. Universität Bayreuth; 2018. Available from: https://epub.uni-bayreuth.de/3854/