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Register a new userAb-initio chemical potentials of solid and liquid solutions and the chemistry of the Earths core
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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.
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Several research groups have recently reported {em ab initio} calculations of the melting properties of metals based on density functional theory, but there have been unexpectedly large disagreements between results obtained by different approaches. We analyze the relations between the two main approaches, based on calculation of the free energies of solid and liquid and on direct simulation of the two coexisting phases. Although both approaches rely on the use of classical reference systems consisting of parameterized empirical interaction models, we point out that in the free energy approach the final results are independent of the reference system, whereas in the current form of the coexistence approach they depend on it. We present a scheme for correcting the predictions of the coexistence approach for differences between the reference and {em ab initio} systems. To illustrate the practical operation of the scheme, we present calculations of the high-pressure melting properties of iron using the corrected coexistence approach, which agree closely with earlier results from the free energy approach. A quantitative assessment is also given of finite-size errors, which we show can be reduced to a negligible size.
Understanding the behavior of molecular systems under pressure is a fundamental problem in condensed matter physics. In the case of nitrogen, the determination of the phase diagram and in particular of the melting line, are largely open problems. Two independent experiments have reported the presence of a maximum in the nitrogen melting curve, below 90 GPa, however the position and the interpretation of the origin of such maximum differ. By means of ab initio molecular dynamics simulations based on density functional theory and thermodynamic integration techniques, we have determined the phase diagram of nitrogen in the range between 20 and 100 GPa. We find a maximum in the melting line, related to a transformation in the liquid, from molecular N_2 to polymeric nitrogen accompanied by an insulator-to-metal transition.
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.
Using event driven molecular dynamics simulations, we study a three dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point and a liquid-liquid critical point. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and give us insight on the mechanisms ruling the dependence of the two critical points on the potentials parameters. The soft core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.
Lattice dynamical methods used to predict phase-transformations in crystals typically evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the $beta$ structure when it appears as a high-temperature phase of the shape memory alloy (SMA) NiTi. Here it is shown by self consistent {it ab initio} lattice dynamical calculations (SCAILD) that the critical temperature for the pre-martensitic $R$ to $beta$ phase-transformation in NiTi can be effectively calculated with good accuracy, and that the $beta$-phase is a result primarily of the stabilizing interaction between different lattice vibrations.
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