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Register a new userBoundary conditions and heat resistance at the moving solid--liquid interface
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Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at the interface and the quantities characterizing interfacial surface such as the surface temperature and the surface heat flux. Introduction of the surface temperature as an independent variable allows us to describe the scattering energy at the interface. For the steady-state motion of the planar interface the expression for the temperature discontinuity across the phase boundary has been obtained. Effect of Kapitza resistance on the interface velocity is considered. It is shown that heat resistance leads to non-linearity in solidification kinetics, namely, in velocity-undercooling relationship. The conditions of the steady--state motion of the planar interface has been found.
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We present a new technique which allows the fully {em ab initio} calculation of the chemical potential of a substitutional impurity in a high-temperature crystal, including harmonic and anharmonic lattice vibrations. The technique uses the combination of thermodynamic integration and reference models developed recently for the {em ab initio} calculation of the free energy of liquids and anharmonic solids. We apply the technique to the case of the substitutional oxygen impurity in h.c.p. iron under Earths core conditions, which earlier static {em ab initio} calculations indicated to be thermodynamically very unstable. Our results show that entropic effects arising from the large vibrational amplitude of the oxygen impurity give a major reduction of the oxygen chemical potential, so that oxygen dissolved in h.c.p. iron may be stabilised at concentrations up a few mol % under core conditions.
We present analytical results and kinetic Monte Carlo simulations for the mobility and microscopic structure of solid-on-solid (SOS) interfaces driven far from equilibrium by an external force, such as an applied field or (electro)chemical potential difference. The interfaces evolve under a specific stochastic dynamic with a local energy barrier (an Arrhenius dynamic), known as the transition dynamics approximation (TDA). We calculate the average height of steps on the interface, the average interface velocity, and the skewness of the interface as functions of the driving force and the height of the energy barrier. We find that the microscopic interface structure depends quite strongly on the barrier height. As the barrier becomes higher, the local interface width decreases and the skewness increases, suggesting increasing short-range correlations between the step heights.
A general set of methods is presented for calculating chemical potentials in solid and liquid mixtures using {em ab initio} techniques based on density functional theory (DFT). The methods are designed to give an {em ab initio} approach to treating chemical equilibrium between coexisting solid and liquid solutions, and particularly the partitioning ratio of solutes between such solutions. For the liquid phase, the methods are based on the general technique of thermodynamic integration, applied to calculate the change of free energy associated with the continuous interconversion of solvent and solute atoms, the required thermal averages being computed by DFT molecular dynamics simulation. For the solid phase, free energies and hence chemical potentials are obtained using DFT calculation of vibrational frequencies of systems containing substitutional solute atoms, with anharmonic contributions calculated, where needed, by thermodynamic integration. The practical use of the methods is illustrated by applying them to study chemical equilibrium between the outer liquid and inner solid parts of the Earths core, modelled as solutions of S, Si and O in Fe. The calculations place strong constraints on the chemical composition of the core, and allow an estimate of the temperature at the inner-core/outer-core boundary.
The process of rapid solidification of a binary mixture is considered in the framework of local nonequilibrium model (LNM) based on the assumption that there is no local equilibrium in solute diffusion in the bulk liquid and at the solid-liquid interface. According to LNM the transition to complete solute trapping and diffusionless solidification occurs at a finite interface velocity $V=V_D$, where $V_D$ is the diffusion speed in bulk liquid. In the present work, the boundary conditions at the phase interface moving with the velocity $V$ close to $V_D$ ($V lesssim V_D$) have been derived to find the non-equilibrium solute partition coefficient. In the high-speed region, its comparison with the partition coefficient from the work [Phys. Rev. E 76 (2007) 031606] is given.
Interfacial charge transfer is widely assumed to obey Butler-Volmer kinetics. For certain liquid-solid interfaces, Marcus-Hush-Chidsey theory is more accurate and predictive, but it has not been applied to porous electrodes. Here we report a simple method to extract the charge transfer rates in carbon-coated LiFePO4 porous electrodes from chronoamperometry experiments, obtaining curved Tafel plots that contradict the Butler-Volmer equation but fit the Marcus-Hush-Chidsey prediction over a range of temperatures. The fitted reorganization energy matches the Born solvation energy for electron transfer from carbon to the iron redox site. The kinetics are thus limited by electron transfer at the solid-solid (carbon-LixFePO4) interface, rather than by ion transfer at the liquid-solid interface, as previously assumed. The proposed experimental method generalizes Chidseys method for phase-transforming particles and porous electrodes, and the results show the need to incorporate Marcus kinetics in modeling batteries and other electrochemical systems.
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