  We determine the phase diagram for dense carbon/ oxygen mixtures in White
Dwarf (WD) star interiors using molecular dynamics simulations involving liquid
and solid phases. Our phase diagram agrees well with predictions from Ogata et
al. and Medin and Cumming and gives lower melting temperatures than Segretain
et al. Observations of WD crystallization in the globular cluster NGC 6397 by
Winget et al. suggest that the melting temperature of WD cores is close to that
for pure carbon. If this is true, our phase diagram implies that the central
oxygen abundance in these stars is less than about 60%. This constraint, along
with assumptions about convection in stellar evolution models, limits the
effective S factor for the $^{12}$C($\alpha,\gamma$)$^{16}$O reaction to
S_{300} <= 170 keV barns.
