Contrib Mineral Petrol (1984) 88:260 268 Contributions to Mineralogy and Petrology 9 Springer-Vertag 1984 Activities of olivine and plagioclase components in silicate melts and their application to geothermometry Allen F. Glazner Department of Geology, University of North Carolina, Chapel Hill, NC, 27514, USA Abstract. The activity of a given mineral component in a silicate melt can be calculated from the compositions of coexisting melt and crystals, provided that 1) the compo- nent is an independently variable component of the crystal, and 2) appropriate thermodynamic data for the component are known. This approach is used to calibrate the composi- tional dependence of the activities of forsterite, fayalite, anorthite, and albite from experimental data on natural marie-to-intermediate melts. The natural logarithms of the activities of forsterite and anorthite can be closely approxi- mated as second-degree polynomial functions of the melt composition (r2=0.99 and 0.97, respectively); correspond- ing fits for fayalite and albite are significantly poorer (r 2= 0.81 and 0.87, respectively). The shapes of the fitted activity surfaces yield information about speciation in silicate melts. The activity models for forsterite and anorthite provide ex- cellent geothermometers with standard deviations of tem- perature residuals of approximately 10~ C. These geother- mometers, when combined with the activity models for fayalite and albite, can be used to predict the temperature at which olivine or plagioclase will crystallize from a melt, along with the composition of the crystals. Introduction One of the most vexing problems in igneous petrology is the large number of components and high variance (number of thermodynamic degrees of freedom) of most magmatic systems. The large number of components which must be considered limits the usefulness of graphical techniques for analyzing phase relations. In order to understand how min- erals and complex natural melts interact, petrologists must calculate equilibria that cannot be depicted graphically. Until recently the basic thermodynamic data needed for calculating mineral-melt equilibria did not exist. However, recent calorimetric measurements have provided much of the necessary data on heat capacities and enthalpies of fu- sion of important minerals and melts (e.g., Carmichael et al. 1977; Weill et al. 1980a; Stebbins and Carmichael 1981). In light of these new data a number of models for the thermodynamic behavior of complex natural silicate melts have arisen. Chief among these are the quasi-crystalline model of Burnham (1975, 1981), which has been applied mainly to silicic melts, and the regular-solution model of Offprint requests: A.F. Glazner Ghiorso and Carmichael (1980) and Ghiorso et al. (1983), which has been applied mainly to marie melts. These models have had considerable success in describing mineral-melt equilibria in complex natural systems. One of the main goals of a thermodynamic melt model is to predict the activities of various mineral components in the melt from the composition of the melt. In crystals there is a simple correspondence between activity and com- position (e.g., Wood and Fraser 1977, Ch. 3). In silicate melts a simple correspondence does not exist, because melts do not consist of lattices upon which anions and cations mix freely, and because melts are not bound by the stoichio- metric constraints that restrict the compositional variation of crystals. A lattice approach has been used successfully in some binary melts which have constant ratios of metal oxide to silica (e.g., Richardson 1956), but this approach fails in more complicated and compositionally varied melts. More sophisticated polymer models of the distribution of species in silicate melts have been applied to binary and ternary systems (see reviews in Hess 1980 and Bottinga et al. 1981), but these models have not yet been applied to com- plex natural silicate melts and they cannot be applied to melts that develop ring and network species. In the quasi-crystalline and regular-solution models the melt is divided into mineral-like components and then treated as a crystal in which these components mix either nearly ideally (quasi-crystalline) or nonideally (regular solu- tion). The components are chosen to resemble the actual species that are presumed to mix in the melt. For example, in the regular-solution model of Ghiorso et al. (1983) the melt is divided into 8-oxygen units such as SilO 8, Fe4Si20 8, Al16/308, etc., which are considered to mix molecularly in the melt. Any difference between the distribution of species in the melt and that used in the model is absorbed by the regular-solution coefficients. Regular-solution coefficients are designed to account for excess enthalpy of mixing, but if the components chosen are inadequate to describe the melt then they must model excess entropy of mixing as well. However, because regular-solution theory places tight restrictions on the form of deviation from ideality, the coef- ficients may not be able to adequately absorb the nonidea- lity. This point has been discussed by Ghiorso et al. (1983, p. 114~115). The main difficulty in using a classic thermodynamic approach to model melt activities lies in defining the mole fractions of mineral components such as anorthite, forster- ite, or quartz in the melt. In a relatively simple system