Estimation of diffusion coefficients during interdiffusion of geologic melts: Application of transition state theory

Abstract

Two equations for the prediction of non-alkali and alkali, Na and K, diffusivities during the interdiffusion of complex aluminosilicate silicate melts at crustal pressures are proposed. Both equations are derived from transition state theory. The Eyring equation is used to calculate diffusivities for Si from silicate melt viscosities (calculated by the Shaw method). Because previous studies of interdiffusion between silicate melts have reported that non-alkalies appear to chemically diffuse only as rapidly as Si and Al the Eyring equation also predicts the diffusivity of all non-alkali cations during interdiffusion. Alkali diffusivities are orders of magnitude greater than non-alkali diffusivities and therefore are decoupled from melt viscosity; a transition state theory equation which predicts diffusivities from jump distances during diffusion, ionic masses, the free volume of albite melt and the enthalpy of vaporization of Na 2O is used to predict alkali diffusivities. Both diffusivity calculations are demonstrated to typically reproduce measured diffusivities. The relative mean error between measured and predicted diffusivities for non-alkalies is approximately a factor of 2 and less than that for alkalies. The accuracy of these equations in predicting diffusivities during interdiffusion is sufficient to use diffusivities calculated by these equations to constrain and to model interdiffusional processes in melts during igneous petrogenesis.