Effects of cooperative diffusion on rheological and mechanical behavior of bcc Fe: A combined approach using elastically collective nonlinear Langevin equation  theory and statistical moment method

Anomalous seismic data on Earth's inner core have challenged our understanding of mineral physics for decades. According to recent ab initio studies, bcc Fe may be a key to solving this long-standing problem. However, simulating the bcc phase requires an enormous supercell, a long simulation time, and a prohibitive computational cost. Consequently, available information about bcc Fe is very limited. Herein, we introduce a more convenient approach for investigating the rheological and mechanical properties of the bcc structure under deep-Earth conditions. Since bcc Fe behaves similarly to a liquid system while remaining within the solid state, we treat it as a hard-sphere glass former in the elastically collective nonlinear Langevin equation theory. On that basis, we can readily evaluate the contribution of local and nonlocal interactions to the motion of atoms at various packing fractions. To consider finite-temperature and hydrostatic-pressure effects, we utilize the statistical moment method. The mentioned strategy enables us to determine the diffusivity, viscosity, and rigidity of bcc Fe without strenuous computational efforts. In addition, we discover a close connection between the glass and superionic transitions. Our theoretical calculations agree quantitatively well with cutting-edge large-scale molecular dynamics simulations. Therefore they would be valuable for unlocking the mysteries of Earth's inner core, such as the low shear resistance, the high Poisson ratio, and the strong seismic-wave attenuation.