Direct molecular dynamics simulation of liquid-solid phase equilibria for a three-component plasma.

The neutron-rich isotope ²²Ne may be a significant impurity in carbon and oxygen white dwarfs and could impact how the stars freeze. We perform molecular dynamics simulations to determine the influence of ²²Ne in carbon-oxygen-neon systems on liquid-solid phase equilibria. Both liquid and solid phases are present simultaneously in our simulation volumes. We identify liquid, solid, and interface regions in our simulations using a bond angle metric. In general we find good agreement for the composition of liquid and solid phases between our MD simulations and the semianalytic model of Medin and Cumming. The trace presence of a third component, neon, does not appear to strongly impact the chemical separation found previously for two-component carbon and oxygen systems. This suggests that small amounts of ²²Ne may not qualitatively change how the material in white dwarf stars freezes. However, we do find systematically lower melting temperatures (higher Γ) in our MD simulations compared to the semianalytic model. This difference seems to grow with impurity parameter Q_{imp} and suggests a problem with simple corrections to the linear mixing rule for the free energy of multicomponent solid mixtures that is used in the semianalytic model.

Crystallization of classical multicomponent plasmas.

We develop a method for calculating the equilibrium properties of the liquid-solid phase transition in a classical, ideal, multicomponent plasma. Our method is a semianalytic calculation that relies on extending the accurate fitting formulas available for the one-, two-, and three-component plasmas to the case of a plasma with an arbitrary number of components. We compare our results to those of C. J. Horowitz [Phys. Rev. E 75, 066101 (2007)], who used a molecular-dynamics simulation to study the chemical properties of a 17-species mixture relevant to the ocean-crust boundary of an accreting neutron star at the point where half the mixture has solidified. Given the same initial composition as Horowitz , we are able to reproduce to good accuracy both the liquid and solid compositions at the half-freezing point; we find abundances for most species within 10% of the simulation values. Our method allows the phase diagram of complex mixtures to be explored more thoroughly than possible with numerical simulations. We briefly discuss the implications for the nature of the liquid-solid boundary in accreting neutron stars.