Calcium diffusion in a simple silicate melt to 30 kbar

Calcium-45 was used as a radiotracer to measure self-diffusion coefficients for Ca in a sodium-calcium-aluminosilicate melt (29% Na₂O, 5% CaO, 10% Al₂O₃, 56% SiO₂) at temperatures in the range 1100–1400°C and pressures to 30 kbar. Calcium diffusivity (D_Ca) was found to depend upon both temperature and pressure in a complex but systematic manner: $\text{(}\text{?D}{}_{\mathrm{Ca}}\text{?P}\text{)}{}_{\mathrm{T}}$ is always negative and has a larger absolute value at lower temperatures; $\text{(}\text{?D}{}_{\mathrm{Ca}}\text{?T}\text{)}{}_{\mathrm{P}}$ is positive and increases with increasing pressure. The overall dependence of D_Ca upon T and P is given approximately by $\text{D}{}_{\mathrm{caT.P}}\text{= 0.0025 exp(}\text{-23,107}\text{RT}\text{)] exp P}\text{(0.7297T ? 1261.32)}\text{RT}\text{]}$. When expressed in terms of volume (V_a) and energy (E) of activation, the results are as follows: V_a ranges from 2.2 cm³/mole at 1400°C to 11.9 cm³/mole at 1100°C. and E ranges from 25.4 kcal/mole (1 kban to 49.8 kcal/mole (20 kbar).From the systematic dependence of D_Ca upon T and P, it is concluded that diffusion of Ca²⁺ in silicate melts does not take place by means of a vacant site mechanism, but is controlled instead by the amount and distribution of free volume in the melt structure.If it is assumed that the viscosity of the melt used in this study decreases with increasing pressure (Kushiro, 1976, J. Geophys. Res.81, 6351–6356) as D_Ca does, then the Stokes-Einstein inverse relation between viscosity and diffusivity is clearly violated, and its validity for silicate melts must be questioned. Thus, it appears that in silicate melts, unlike many liquids, viscous flow and diffusion are fundamentally different transport processes, involving different structural units.The effect of pressure on calcium diffusion is too small to invalidate kinetic models of upper mantle processes that have been based upon diffusivity values measured at 1 atm. Pressure may, however, induce significant reductions in the diffusion rates of large ions such as Rb⁺ or SiO^4?₄ in silicate melts.