Water and magmas: application of the Gibbs-Duhem equation: a response

Abstract

A rebuttal is presented to the assertions of Dye and Vogel that the conclusion by Burnham (1975a, b) regarding Raoultian (''ideal'') mixing behavior of the aluminosilicate components in a wide range of melt compositions is valid. It is emphasized that the mixing behavior of one component in a three-component system imposes constraints on the mixing behavior of the other two components, even when the form of the Gibbs--Duhem equation reduces to that for a two-component system. Indeed, the key element in Burnham's conclusion of ideal behavior for the aluminosilicate components in igneous-rock melts is the powerful constraint imposed by the fact that the activity of H/sub 2/O (a/sub H/sub 2/O/), hence its partial molal Gibbs free energy (anti G/sub H/sub 2/O/), is a function only of its mole fraction (X/sub H/sub 2/O/) at a given temperature and pressure (Burnham, 1975b, eqs. 3 and 4). Thus, the objective here is to show, with reference to the generalized ternary system 1-2-3, how imposition of this constraint for component 3 leads to the conclusion that components 1 and 2 mix ideally. (JGB)