  We develop a method for calculating the equilibrium properties of the
liquid-solid phase transition in a classical, ideal, multi-component plasma.
Our method is a semi-analytic calculation that relies on extending the accurate
fitting formulae 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 Horowitz, Berry, & Brown (Phys. Rev. E, 75, 066101, 2007),
who use 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 et al., 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.
