A Model for the Viscosity of Melts in the System Ab-An-Dp.

The prediction of viscosity in natural silicate melts remains one of the most challenging and elusive goals in Earth Sciences. We present a strategy for fitting non-Arrhenian models to viscosity data which can be employed towards a full multicomponent model for melt viscosity. Here, we have adopted the Vogel-Tammann-Fulcher equation (VTF): log $\eta$ = A + B $/$ ( T $-$ C ) which is an effective descriptor of viscosity for most geochemically-important melts. The parameters A, B and C show strong correlations that are a reflection of: i) the nonlinear nature of the VTF equation, ii) the distribution and quality of the experimental data, and iii) co-dependence on composition. Our analysis has shown that the value of A is relatively insensitive to composition implying that the viscosities of silicate melts may converge to a single common value The corollary to this is that the number of compositionally dependent parameters is reduced by a third; all compositional dependencies of melt viscosity are confined to the parameters B and C. We use this strategy to model the non-Arrhenian viscous properties of silicate melts in the chemical system: NaAlSi$_{3}$O$_{8}$ (Ab) : CaAl$_{2}$Si$_{2}$O$_{8}$ (An) : CaMgSi$_{2}$O$_{6}$ (Dp). This system is important because these melts show near-Arrhenian to strongly non-Arrhenian properties. Our modelling is based on experimental data compiled from the literature; the database comprises more than 500 measurements of viscosity on 50 different melt compositions and spanning a temperature range of 960 to 2400 K.The majority of data derive from binary melt compositions. Our optimization fits the full dataset simultaneously based on $\chi$$^{2}$ minimization techniques and returns values of B and C for each melt and a single estimate of A. The optimized value for A deriving from this dataset is $-$4.69 $\pm$ 0.5 (e.g., $\eta$$_{o}$ = 10$^{-4.7}$ Pa s). The original data are reproduced to within error ($\pm$ 0.2 log units) which strongly corroborates our assertion of a common high-T limit for all silicate melts. In conclusion, we will present a complete parameterization for the compositional dependence of the values of B and C