Temperature-pressure-composition model for melt viscosity in the Di-An-Ab system

A model for the viscosity (eta) of melts in the system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8 (Di-An-Ab) based on data compiled from the literature is presented. The model is calibrated on 560 measurements of melt viscosity at 1 atm pressure on 40 individual melt compositions and 303 measurements obtained at high pressure on 18 melt compositions. The model is continuous and accounts for variations in melt composition (X), temperature (T) and pressure (P). At ambient pressure, the model spans 15 orders of magnitude of eta, a T range of 933-2450 K, and reproduces the dataset well (RMSE = 0.26 log units). The high-P model is calibrated over a T range of 970-2470 K and pressures of 50 MPa to 13 GPa for viscosities of 10^-1 to 10^14.5 Pa s and reproduces the highpressure dataset to within (larger) experimental uncertainties (RMSE = 0.35 log units). Used in conjunction with chemical proxies for melt structural organization (i.e. SM and NBO/T), the model illustrates the strong coupling between viscosity and changes in melt polymerization as a function of X and P. Di-An-Ab melts with SM values > 25.34 have positive pressure coefficients and show a minimal to strong increase in viscosity with pressure. Model values of glass transition temperatures (Tg) (i.e. eta ~ 10^12 Pa s) range between 930 K and 1130 K at 1 atm; Tg values for highly polymerized melts are depressed by as much as 150 K at 5 GPa at elevated pressures but are higher for more depolymerized melts and higher P. Melt fragility (m) is only weakly affected by increased P as expressed by a slight decrease in m for the most fragile melts versus a slight increase for the least fragile melts. Activation energies (Ea) increase with rising P for depolymerized melts and decrease with rising P for polymerized melts with the crossover at SM = 25.34. Ea values increase at low T for all P conditions and the effects of P are most pronounced at lower T. Lastly, a comparison of the liquidus surface topology for the ternary system to the corresponding isokoms of viscosity shows the relative effects of composition and temperature on melt viscosity at liquidus conditions to be highly varied.