Thermodynamic properties of silicate liquids with emphasis on density, thermal expansion and compressibility

In the last five years, there has been a significant influx of new data in the literature on all aspects of the volumetric properties of silicate liquids. Several studies report 1 bar density measurements on a variety of multicomponent silicate liquids (Lange and Carmichael, 1987, Johnson and Carmichael, 1987; Dingwell and Brearley, 1988; Dingwell et al.,1988; Taniguchi, 1989). As a consequence of these recent data, the controversy surrounding the partial molar volume of Al 2 O 3 in multicomponent silicate liquids (Ghiorso and Carmichael,1984; Bottinga et al., 1984) has been resolved, and the partial molar volumes of Fe 2 O 3 and TiO 2 in natural silicate liquids are now well constrained (although they both exhibit a strong compositional dependence in simple three- and four-component liquids). Perhaps most important, the precision of model equations describing the volume and thermal expansion of natural silicate liquids (Lange and Carmichael, 1987) has increased substantially since the original model of Bottinga and Weill (1970). This has extremely important consequences for the precision of model equations describing the compressibility of natural silicate liquids, since the derivation of compressibility data from both acoustic velocity and shock-wave experiments is critically dependent on accurate 1 bar volume and thermal expansion data. The compressibility of natural silicate liquids can now be readily calculated for any anhydrous composition because of the recent measurements of acoustic velocity in silicate liquids as a systematic function of composition (Rivers and Carmichael, 1987, Kress et al., 1988). These sound speed data have been extended to include Fe 2 O 3 -bearing silicate liquids (Kress and Carmichael, 1991) and allow the ferric component to be incorporated into a general model equation describing the volumes of natural liquids as a function of pressure. Perhaps more important, measurements of the compressibilities of both the ferric and ferrous components in silicate melts provide information on how the ferric-ferrous ratio in a natural liquid changes as a function of pressure. Thus the question of whether or not the redox states of erupted lavas reflect the redox states of their source regions (Carmichael, 1991) can be quantitatively addressed. Both the dynamic shock-wave experiments of Rigden et al. (1984, 1988, 1989) to 250 kbar and the static compression measurements of Agee and Walker (1988) between 10-60 kbar provide information on how the compressibility function itself, for silicate liquids, changes with pressure. These experiments allow direct evaluation of the postulate of Stolper et al. (1981) that olivine will float and coexisting melts will sink at sufficiently high pressures in the Earth's interior. More data obtained by these methods will allow further constraints to be placed on how the pressure derivative of the bulk modulus (KT') changes as a function of composition. Preliminary results indicate that values of KT' are more sensitive to composition than values of KT and that KT' increases (compressibility decreases) as the proportion of initially tetrahedrally coordinated cations (e.g., Al 3 + and Si (super 4+) ) decreases in the liquid (Rigden et al.,1989). The volumetric properties of volatile-bearing silicate liquids have a limited experimental basis. Despite the paucity of direct density measurements of H 2 O- and CO 2 -bearing silicate liquids, thermodynamic analysis of solubility curves for both water and carbon dioxide allows estimation of their partial molar volumes in silicate liquids (Spera and Bergman, 1980; Stolper and Holloway, 1980; Silver et al.,1990). Current estimates are VH 2 O = 20 + or - 5 cc/mole and VCO 2 = 33 + or - 1 cc/mole. Further constraints on the temperature, pressure and compositional dependence of these values are highly desirable. The importance of considering the effect of water and carbon dioxide is easily recognized since both components have a dramatic effect on reducing silicate melt densities. Postulated mechanisms of magmatic differentiation, such as compositionally-induced convection or crystal settling in magma chambers, must consider the effect of water on the density of residual liquids. Not only will the concentration of water in the residual liquid steadily increase as crystallization (of anhydrous phases) proceeds, but small amounts of water can significantly alter the composition, proportion and crystallization temperatures of the phenocryst phases and hence, the bulk composition of the residual liquid. This illustrates the necessity of a thermodynamic model (calibrated on accurate thermodynamic data) that can predict crystal-melt equilibria over a wide range of magmatic conditions in order to quantitatively model the physical aspects of a magma's evolution.