Viscoelasticity of Liquid Iron at Conditions of the Earth's Outer Core

<jats:title>Abstract</jats:title><jats:p>Viscosity and elasticity are material properties essential for understanding the composition, dynamics, and evolution of the Earth's core, yet their intrinsic connection as embedded in the general theory of viscoelasticity is not well explored. Here we use molecular dynamics to determine the viscoelasticity of liquid iron at conditions of the Earth's outer core. The frequency‐dependent viscosity and shear modulus are determined from the power spectrum of the stress autocorrelation function. We find that the stress autocorrelation function is well characterized by a generalized Maxwell model containing two relaxation modes. The mode with shorter relaxation time (<jats:italic>τ</jats:italic><jats:sub>1</jats:sub>) corresponds to the motion of individual atoms; the other with longer relaxation time (<jats:italic>τ</jats:italic><jats:sub>2</jats:sub>) is associated with collective motions. As temperature (<jats:italic>T</jats:italic> ) decreases, the slow‐decaying mode becomes more prominent with increasingly larger <jats:italic>τ</jats:italic><jats:sub>2</jats:sub>. In contrast, <jats:italic>τ</jats:italic><jats:sub>1</jats:sub> remains nearly constant (∼0.016 ps). The infinite frequency shear modulus (<jats:italic>G</jats:italic><jats:sub><jats:italic>∞</jats:italic></jats:sub>), which characterizes the instantaneous shear response, is found to be larger than the static shear modulus of hexagonal close‐packed (hcp) iron of the same density and increases linearly with <jats:italic>T</jats:italic>. Based on these findings as well as seismic analyses (Tsuboi & Saito, 2002, <jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1186/BF03351717">https://doi.org/10.1186/BF03351717</jats:ext-link>; Krasnoshchekov et al., 2005, <jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1038/nature03613">https://doi.org/10.1038/nature03613</jats:ext-link>), the zero frequency viscosity (<jats:italic>η</jats:italic><jats:sub>0</jats:sub>) of the lowermost outer core is inferred as 10<jats:sup>9</jats:sup> Pa·s. The likely material states exhibiting such viscosities are discussed. Moreover, we show that to retain the rigidity consistent with seismic observations, the <jats:italic>η</jats:italic><jats:sub>0</jats:sub> of the inner core should be at least 10<jats:sup>13</jats:sup> Pa·s.</jats:p>