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 datacompiled from the literature is presented. The model is calibrated on 560 measurements of melt viscosity at1 atm pressure on 40 individual melt compositions and 303 measurements obtained at high pressure on 18 meltcompositions. The model is continuous and accounts for variations in melt composition (X), temperature (T) andpressure (P). At ambient pressure, the model spans 15 orders of magnitude of eta, a T range of 933-2450 K, andreproduces the dataset well (RMSE = 0.26 log units). The high-P model is calibrated over a T range of970-2470 K and pressures of 50 MPa to 13 GPa for viscosities of 10^-1 to 10^14.5 Pa s and reproduces the highpressuredataset to within (larger) experimental uncertainties (RMSE = 0.35 log units). Used in conjunction withchemical proxies for melt structural organization (i.e. SM and NBO/T), the model illustrates the strong couplingbetween 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 at1 atm; Tg values for highly polymerized melts are depressed by as much as 150 K at 5 GPa at elevated pressuresbut are higher for more depolymerized melts and higher P. Melt fragility (m) is only weakly affected by increasedP as expressed by a slight decrease in m for the most fragile melts versus a slight increase for the least fragilemelts. Activation energies (Ea) increase with rising P for depolymerized melts and decrease with rising P forpolymerized melts with the crossover at SM = 25.34. Ea values increase at low T for all P conditions and theeffects of P are most pronounced at lower T. Lastly, a comparison of the liquidus surface topology for the ternarysystem to the corresponding isokoms of viscosity shows the relative effects of composition and temperature onmelt viscosity at liquidus conditions to be highly varied.