Water and magmas; a mixing model

Abstract A model for the mixing of H2O and silicate melts has been derived from the experimentally determined effects of H2O on the viscosity (fluidity), volumes, electrical conductivities, and especially the thermodynamic properties of hydrous aluminosilicate melts. It involves primarily the reaction of H2O with those O−2 ions of the melt that are shared (bridging) between adjacent (Al, Si)O4 tetrahedra to produce OH− ions. However, in those melts that contain trivalent ions in tetrahedral coordination, such as the Al3+ ion in feldspathic melts, the model further involves exchange of a proton from H2O with a non-tetrahedrally coordinated cation that must be present to balance the net charge on the AlO4 group. This cation exchange reaction, which goes essentially to completion, results in dissociation of the H2O and is limited only by the availability of H2O and the number of exchangeable cations per mole of aluminosilicate. In the system NaAlSi3O8-H2O, upon which this thermodynamic model is based, there is 1 mole of exchangeable cations (Na+) per mole (GFW) of NaAlSi3O8, consequently ion exchange occurs for H2O contents up to a 1:1 mole ratio (Xmw = mole fraction H2O = 0.5). For mole fractions of H2O greater than 0.5, no further exchange can occur and the reaction with additional bridging oxygens of the melt produces 2 moles of associated OH− ions per mole of H2O dissolved. These reactions lead to a linear dependence of the thermodynamic activity of H2O (amw) on the square of its mole fraction (Xmw) for values of Xmw, up to 0.5 and an exponential dependence on Xmw at higher H2O contents. Thus, for values of X m w ↬ 0.5, a m w = k(X m w ) 2 , where k is a Henry's law constant for the dissociated solute. Extension of the thermodynamic model for NaAlSi3O8-H2O to predict H2O solubilities and other behavior of compositionally more complex aluminosilicate melts (magmas) requires placing these melts on an equimolal basis with NaAlSi3O8. This is readily accomplished using chemical analyses of quenched glasses by normalizing to the stoichiometric requirements of NaAlSi3O8, first in terms of equal numbers of exchangeable cations for mole fractions of H2O up to 0.5 and secondly in terms of 8 moles of oxygen for higher H2O contents. Chemical analyses of three igneous-rock glasses, ranging in composition from tholeiitic basalt to lithium-rich pegmatite, were thus recast and the experimental H2O solubilities were computed on this equimolal basis. The resulting equimolal solubilities are all the same, within experimental error, as the solubility of H2O in NaAlSi3O8 melt calculated from the thermodynamic relations. The equivalence of equimolal solubilities implies that the Henry's law constant (k), which is a function of temperature and pressure, is independent of aluminosilicate composition over a wide range. Moreover, as a consequence of the Gibbs-Duhem relation and the properties of exact differentials, it is clear that the silicate components of the melt, properly defined, mix ideally. Thus, a relatively simple mixing model for H2O in silicate melts has led to a quantitative thermodynamic model for magmas that has far-reaching consequences in igneous petrogenesis.