Volatile solubility in magmas at high pressure

We present a new theoretical approach for the solubility of volatiles in liquid silicates, with special emphasis on the effect of pressure, aiming at better understanding vesiculation processes in ascending magmas. We use the so-called "hard sphere fluid", a reference model widely used in liquid state physics for several decades. This simple model allows describing accurately, up to pressures of several hundreds of kilobars, the equation of state of pure gases. The model also applies very well to liquid silicates under pressure, by comparison to the scarce available experimental data. We use data on the density of melts at 1 bar to constrain the cohesion of such fluids. The hard sphere model also allows studying how a noble gas atom or a CO2 molecule dissolves into a silicate melt, a process governed by the equality of the solute chemical potentials in the melt and gas phase at equilibrium at T and P. The chemical potential consists of an entropic and an energetic contribution. The model enables one to evaluate readily the entropy of cavity formation to accommodate the solute particle through the density fluctuations of the solvent melt. Correlatively, a term describing the solvation energy is added to account for the interaction between the solute and the silicate network. The latter energetic term is directly constrained by the solubilites measured at 1 bar. The hard sphere model shows that compression is important for melt, but even stronger for fluid (for P typically > 10 kbar). We thus show, for the first time, that, when pressure increases, compression of melt is counterbalanced, up to several tens of kbar, by compression of fluid. This explains very well why experiments have seen an almost linear increase of volatile concentration in melt with increasing pressure. At P > 100 kbar, compression of the melt finally dominates and the solubility in melt eventually decreases. Therefore, volatile dissolution in silicate melt at high pressure certainly does not follow Henry's law (where gas is assumed ideal). We use our model to investigate vesiculation of tholeiites at mid-ocean ridges. The until now poorly understood He/Ar elemental fractionation recorded in Mid-Ocean Ridge Basalts is well explained if a melt (with about 0.8% CO2) starts to vesiculate at about 10 kbar (35 km below sea level), and suffers, during ascent, two or three vesiculation stages followed by vesicle loss and a last vesiculation with no loss. If these successive vesiculation events occur at various depths, this explains the large variability of the He/Ar ratios observed in MORBs.