Transport coefficients and entropy-scaling law in liquid iron up to Earth-core pressures

Universal Relation between Entropy and Kinetics

Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle configurations. It is universal and applicable to steady states arbitrarily far from thermodynamic equilibrium. Applying the general relation to diffusive dynamics yields a relation between the entropy and the (normal or anomalous) diffusion coefficient. The relation can be used to obtain useful bounds for the late-time diffusion coefficient from the calculated steady-state entropy or, conversely, to estimate the entropy based on measured diffusion coefficients. We demonstrate the validity and usefulness of the relation through several examples and discuss its broad range of applications, in particular, for systems far from equilibrium.

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.

Iron self diffusion in liquid pure iron and iron-carbon alloys

With incoherent quasielastic neutron scattering self-diffusion coefficients [Formula: see text] in pure iron, and iron-carbon alloys containing 8.7 at% and 16.9 at% carbon have been measured. At the melting point [Formula: see text] in liquid iron is [Formula: see text] m² s^-1. For the close-to-eutectic Fe_83.1C_16.9 composition [Formula: see text] m² s^-1 at T[Formula: see text] K. Contradicting conclusions drawn from literature values of tracer diffusion experiments the addition of carbon has only a minor effect on the iron mobility: at a given temperature the self-diffusion coefficient in Fe_83.1C_16.9 is only 10% larger than in liquid iron, although mixing has a drastic effect on liquidus temperature and phase behavior.

Validity of the Stokes-Einstein relation in liquids: simple rules from the excess entropy

It is becoming common practice to consider that the Stokes-Einstein relation D/T~ η ^-1 usually works for liquids above their melting temperatures although there is also experimental evidence for its failure. Here we investigate numerically this commonly-invoked assumption for simple liquid metals as well as for their liquid alloys. Using ab initio molecular dynamics simulations we show how entropy scaling relationships developed by Rosenfeld can be used to predict the conditions for the validity of the Stokes-Einstein relation in the liquid phase. Specifically, we demonstrate the Stokes-Einstein relation may break down in the liquid phase of some liquid alloys mainly due to the presence of local structural ordering as evidenced in their partial two-body excess entropies. Our findings shed new light on the understanding of transport properties of liquid materials and will trigger more experimental and theoretical studies since excess entropy and its two-body approximation are readily obtainable from standard experiments and simulations.

Transport properties and entropy-scaling laws for diffusion coefficients in liquid Fe0.9Ni0.1 up to 350 GPa

Transport properties and entropy-scaling laws for diffusion coefficients in liquid Fe_0.9Ni_0.1 alloy under high pressure conditions have been studied by molecular dynamics simulations based upon the Quantum Sutton and Chen potential.