Atomic transport properties of liquid iron at conditions of planetary cores

Stokes-Einstein Relation in Different Models of Water

The purpose of this paper is to discuss to which extent a microscopic version of the Stokes-Einstein (SE) relation without the hydrodynamic radius applies to liquid water. We demonstrate that the self-diffusion and shear viscosity data for five popular water models, recently reported by Ando [J. Chem. Phys. 159, 101102 (2023)], are in excellent agreement with the SE relation. The agreement with experimental results is also quite impressive. The limitations on the applicability of the SE relation are briefly discussed.

Freezing density scaling of transport coefficients in the Weeks-Chandler-Andersen fluid

It is shown that the transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of the Weeks-Chandler-Andersen (WCA) fluid along isotherms exhibit a freezing density scaling (FDS). The functional form of this FDS is essentially the same or closely related to those in the Lennard-Jones fluid, hard-sphere fluid, and some liquefied noble gases. This proves that this FDS represents a quasi-universal corresponding state principle for simple classical fluids with steep interactions. Some related aspects, such as a Stokes-Einstein relation without a hydrodynamic diameter and gas-to-liquid dynamical crossover, are briefly discussed. Simple fitting formulas for the transport coefficients of the dense WCA fluid are suggested.

System Size Dependence of the Diffusion Coefficients in MD Simulations: A Simple Correction Formula for Pure Dense Fluids

A practical correction formula relating the self-diffusion coefficient of dense liquids from molecular dynamics (MD) simulations with periodic boundary conditions to the self-diffusion coefficient in the thermodynamic limit is discussed. This formula applies to pure dense fluids and has a very simple form D = D0(1 - γN-1/3), where D0 is the self-diffusion coefficient in the thermodynamic limit and N is the number of particles in the simulation. The numerical factor γ is dependent on the geometry of the simulation cell. Remarkably, γ ≃ 1.0 is the most popular cubic geometry. The success of this formula is supported by results from MD simulations, including very recent simulations with a "magic" simulation geometry.

Atomic transport properties of liquid iron at conditions of planetary cores

Atomic transport properties of liquid iron are important for understanding the core dynamics and magnetic field generation of terrestrial planets. Depending on the sizes of planets and their thermal histories, planetary cores may be subject to quite different pressures (P) and temperatures (T). However, previous studies on the topic mainly focus on the P-T range associated with the Earth's outer core; a systematic study covering conditions from small planets to massive exoplanets is lacking. Here, we calculate the self-diffusion coefficient D and viscosity η of liquid iron via ab initio molecular dynamics from 7.0 to 25 g/cm³ and 1800 to 25 000 K. We find that D and η are intimately related and can be fitted together using a generalized free volume model. The resulting expressions are simpler than those from previous studies where D and η were treated separately. Moreover, the new expressions are in accordance with the quasi-universal atomic excess entropy (S_ex) scaling law for strongly coupled liquids, with normalized diffusivity D^⋆ = 0.621 exp(0.842S_ex) and viscosity η^⋆ = 0.171 exp(-0.843S_ex). We determine D and η along two thermal profiles of great geophysical importance: the iron melting curve and the isentropic line anchored at the ambient melting point. The variations of D and η along these thermal profiles can be explained by the atomic excess entropy scaling law, demonstrating the dynamic invariance of the system under uniform time and space rescaling. Accordingly, scale invariance may serve as an underlying mechanism to unify planetary dynamos of different sizes.