The combined effect of F and H2O on interdiffusion between peralkaline dacitic and rhyolitic melts

The effective binary diffusion coefficient (EBDC) of silicon has been measured during the interdiffusion of peralkaline, fluorine-bearing (1.3 wt% F), hydrous (3.3 and 6 wt% H₂O), dacitic and rhyolitic melts at 1.0 GPa and temperatures between 1100°C and 1400°C. From Boltzmann-Matano analysis of diffusion profiles the diffusivity of silicon at 68 wt% SiO₂ can be described by the following Arrhenius equations (with standard errors): $$begin{gathered} {text{with 1}}{text{.3 wt% F and 3}}{text{.3% H}}_{text{2}} {text{O:}} hfill {text{D}}_{{text{Si}}} = begin{array}{*{20}c} { + {text{3}}{text{.59}}} {{text{3}}{text{.66}} times {text{10}}^{ - {text{9}}} } { - {text{1}}{text{.86}}} end{array} {text{exp}}left( {{{ - {text{86}}{text{.1}} pm {text{8}}{text{.9}}} mathord{left/ {vphantom {{ - {text{86}}{text{.1}} pm {text{8}}{text{.9}}} {{text{RT}}}}} right. kern-nulldelimiterspace} {{text{RT}}}}} right) hfill {text{with 1}}{text{.3 wt% F and 6}}{text{.0% H}}_{text{2}} {text{O:}} hfill {text{D}}_{{text{Si}}} = begin{array}{*{20}c} { + {text{3}}{text{.59}}} {{text{3}}{text{.51}} times {text{10}}^{ - {text{8}}} } { - {text{1}}{text{.77}}} end{array} {text{exp}}left( {{{ - {text{109}}{text{.5}} pm {text{8}}{text{.9}}} mathord{left/ {vphantom {{ - {text{109}}{text{.5}} pm {text{8}}{text{.9}}} {{text{RT}}}}} right. kern-nulldelimiterspace} {{text{RT}}}}} right) hfill end{gathered} $$ where D is in m²s^?1 and activation energies are in kJ/mol. Diffusivities measured at 64 and 72 wt% SiO₂ are only slightly different from those at 68 wt% SiO₂ and frequently all measurements are within error of each other. Silicon, aluminum, iron, magnesium, and calcium EBDCs were also calculated from diffusion profiles by error function inversion techniques assuming constant diffusivity. With one exception, silicon EBDCs calculated by error function techniques are within error of Boltzmann-Matano EBDCs. Average diffusivities of Fe, Mg, and Ca were within a factor of 2.5 of silicon diffusivities whereas Al diffusivities were approximately half those of silicon. Alkalies diffused much more rapidly than silicon and non-alkalies, however their diffusivities were not quantitatively determined. Low activation energies for silicon EBDCs result in rapid diffusion at magmatic temperatures. Assuming that water and fluorine exert similar effects on melt viscosity at high temperatures, the viscosity can be calculated and used in the Eyring equation used to determine diffusivities, typically to within a factor of three of those measured in this study. This correlation between viscosity and diffusivity can be inverted to calculate viscosities of fluorine- and water-bearing granitic melts at magmatic temperatures; these viscosities are orders of magnitude below those of hydrous granitic melts and result in more rapid and effective separation of granitic magmas from partially molten source rocks. Comparison of Arrhenius parameters for diffusion measured in this study with Arrhenius parameters determined for diffusion in similar compositions at the same pressure demonstrates simple relationships between Arrhenius parameters, activation energy-E_a, kJ/mol, pre-exponential factor-D_o, m²s^?1, and the volatile, X=F or OH^?, to oxygen, O, ratio of the melt {(X/X+O)}: $$begin{gathered} {text{E}}a = - {text{1533{ }}{{text{X}} mathord{left/ {vphantom {{text{X}} {left( {{text{X}} + {text{O}}} right)}}} right. kern-nulldelimiterspace} {left( {{text{X}} + {text{O}}} right)}}{text{} }} + {text{213}}{text{.3}} hfill {text{D}}_{text{O}} = {text{2}}{text{.13}} times {text{10}}^{ - {text{6}}} {text{exp}}left[ { - {text{6}}{text{.5{ }}{{text{X}} mathord{left/ {vphantom {{text{X}} {left( {{text{X}} + {text{O}}} right)}}} right. kern-nulldelimiterspace} {left( {{text{X}} + {text{O}}} right)}}{text{} }}} right] hfill end{gathered} $$ These relationships can be used to estimate diffusion in various melts of dacitic to rhyolitic composition containing both fluorine and water. Calculations for the contamination of rhyolitic melts by dacitic enclaves at 800°C and 700°C provide evidence for the virtual inevitability of diffusive contamination in hydrous and fluorine-bearing magmas if they undergo magma mixing of any form.