A model for silicate melt viscosity in the system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8

Abstract—Five hundred eighty-five viscosity measurements on 40 melt compositions from the ternary system CaMgSi2O6 (Di)-CaAl2Si2O8 (An)-NaAlSi3O8 (Ab) have been compiled to create an experimental database spanning a wide range of temperatures (660 –2175°C). The melts within this ternary system show near-Arrhenian to strongly non-Arrhenian properties, and in this regard are comparable to natural melts. The database is used to produce a chemical model for the compositional and temperature dependence of melt viscosity in the Di-An-Ab system. We use the Vogel-Fulcher-Tammann equation (VFT: logviscosity =A + B/(T- C)) to account for the temperature dependence of melt viscosity. We also assume that all silicate melts converge to a common viscosity at high temperature. Thus, A is independent of composition, and all compositional dependence resides in the parameters B and C. The best estimate for A is -5.06, which implies a high-temperature limit to viscosity of 10^-5.06 Pa s. The compositional dependence of B and C is expressed by 12 coefficients (bi=1,2.6, cj=1,2..6) representing linear (e.g., bi=1:3) and higher order, nonlinear (e.g., bi=4:6) contributions. Our results suggest a near-linear compositional dependence for B (ca. 10% nonlinear) and C (ca. 7% nonlinear). We use the model to predict model VFT functions and to demonstrate the systematic variations in viscosity due to changes in melt composition. Despite the near linear compositional dependence of B and C, the model reproduces the pronounced nonlinearities shown by the original data, including the crossing of VFT functions for different melt compositions. We also calculate values of Tg for melts across the Di-An-Ab ternary system and show that intermediate melt compositions have Tg values that are depressed by up to 100°C relative to the end-members Di-An-Ab. Our non-Arrhenian viscosity model accurately reproduces the original database, allows for continuous variations in rheological properties, and has a demonstrated capacity for extrapolation beyond the original data.