Sound Velocity Measurements on K2O-Na2O-Al2O3-SiO2 Liquids and the Compressibility of Crustal Melts

Longitudinal acoustic velocities of eight liquids in the K2O-Na2O-Al2O3-SiO2 quaternary system have been measured at one bar between 1215 and 1620°C with an ultrasonic frequency-sweep interferometer at centered frequencies that range from 2.8 to 5.5 MHz. These include the first sound speed measurements on K2O- Al2O3-SiO2 liquids, which tend to be relatively viscous and have therefore been poorly represented in the sound speed data set for magmatic liquids. These new velocity measurements were combined with density data from the literature to calculate the adiabatic compressibility for each liquid. These results were converted to isothermal compressibility using available volume, thermal expansion, and heat capacity data in the literature. The final data set permits the compositional and temperature dependence of the liquid compressibility to be obtained through linear regression. The model equation used in the regression is as follows: βT(liq)=SUM[(XiVi/V)[βi + dβi/dT(T-1673 K)]], where Xi is the mole fraction of each oxide component, Vi is the partial molar volume of each oxide component, V is the molar volume of the liquid, and βi is the partial molar compressibility of each oxide component. The regression leads to fitted values for the partial molar compressibility (units are in 10-2 GPa-1) at a reference temperature of 1673 K (1400°C) of 6.90 ± 0.06 for SiO2, -2.00 ± 0.14 for Al2O3, 8.60 ± 0.10 for Na2O and 15.49 ± 0.15 for K2O. A temperature dependence (units are in 10-4 GPa-1 K-1) is only resolved for the Na2O (1.03 ± .04) and Al2O3 (-0.78 ± .09) components. . The regression has an R-squared value of 0.999 and recovers the measured compressibilities within 0.81 % on average. The inverse of the fitted compressibility terms can be used to obtain a "partial molar" bulk modulus for each oxide component at 1673 K. This exercise leads to values of 14.5 GPa for SiO2, -50.0 GPa for Al2O3, 11.6 GPa for Na2O, and 6.5 GPa for K2O. The results indicate that the K2O component is nearly twice as compressible as the Na2O component, which in turn is slightly more compressible than the SiO2 component. The result for the Al2O3 component indicates a negative compressibility, which should clearly not be extrapolated to the Al2O3 pure end-member. The highly incompressible nature of the Al2O3 component in K2O-Na2O-Al2O3-SiO2 liquids (noted previously by Kress et al., 1988) is in marked contrast to its behavior in the CaO-MgO-Al2O3-SiO2 system (Ai and Lange, 2005), which has a fitted partial molar compressibility of 4.43 10-2 GPa-1 (and thus a partial molar bulk modulus of ~22.6 GPa). This strikingly different compressibility behavior for the Al2O3 component is not found for the SiO2 component. In CaO-MgO-Al2O3-SiO2 liquids, the "partial molar" bulk modulus of the SiO2 component is similar (14.1 GPa) to what is obtained for SiO2 (14.5 GPa) in the K2O- Na2O-Al2O3-SiO2 liquids in this study. The difference in the one-bar compressibility behavior for the Al2O3 component may relate to the tendency for small concentrations of five-coordinated Al3+ to form in one-bar CaO-MgO-Al2O3-SiO2 liquids, but not in one-bar K2O-Na2O-Al2O3-SiO2 liquids (based on NMR results from the literature). Small concentrations of ^{[5]}Al3+ may promote topological mechanisms of compression in the CaO-MgO-Al2O3-SiO2 liquids. The results of this study confirm that the compressibility of silicate liquids is not a linear function of composition, and that compressibility calculations for crustal melts (e.g., rhyolite and dacite) cannot be based on a dataset dominated by more basic liquids.