  Although they are rare elements in the Earth's mantle, noble gases (NG) owe
to their strongly varying masses contrasting physical behaviors making them
important geochemical tracers. When partial melting occurs at depth, the
partitioning of NGs between phases is controlled by a distribution coefficient
that can be determined from the solubility of the NGs in each phase. Here we
report quantitative calculations of the solubility of He, Ne, Ar and Xe in
carbonate melts based on molecular dynamics simulations. The NG solubilities
are first calculated in K2CO3-CaCO3 mixtures at 1 bar and favorably compared to
the only experimental data available to date. Then we investigate the effect of
pressure (up to 6 GPa), focusing on two melt compositions: a dolomitic one and
a natrocarbonatitic one (modeling the lava of Ol Doinyo Lengai). The solubility
decreases with the amount of alkaline-earth cation in the melt and with the
size of the noble gas. In the natrocarbonatitic melt, Henry's law is fulfilled
at low pressures (up to ~ 0.1 GPa). At higher pressures the solubility levels
off or even starts to diminish smoothly. In contrast, in molten dolomite the
effect of pressure is negligible on the studied P range (3-6 GPa). At the
pressures of the Earth's mantle, the solubilities of noble gases in carbonate
melts are still of the same order of magnitude as the ones in molten silicates
(~ 1-10 mol%). This suggests that carbonatitic melts at depth are not
preferential carriers of noble gases, even if the dependence with the melt
composition is not negligible and has to be evaluated on a case-by-case basis.
Finally we evaluate the surface tension at the interface between carbonate
melts and noble gases and its evolution with pressure. Whatever the composition
of the melt and of the NG phase, the surface tension increases when P increases
from 0 to 6 GPa.
