Multicomponent diffusion in garnets I: General theoretical considerations and experimental data for Fe-Mg systems

摘要: We have carried out a combined theoretical and experimental study of multicomponent diffusion in garnets to address some unresolved issues better constrain the behavior Fe Mg almandine–pyrope-rich garnets. (1) improved convolution correction concentration profiles measured using electron microprobes, (2) studied effect thermodynamic non-ideality on (3) explored use mathematical error minimization routine (the Nelder-Mead downhill simplex method) compared visual fitting used earlier studies. conclude that incorporation alters shapes calculated profiles, resulting fits shapes, but retrieved coefficients do not differ from those ideal models by more than factor 1.2 for most natural garnet compositions. Diffusion two kinds only significantly unusual Mg–Mn–Ca-rich found when one becomes much faster or slower rest, couple has composition is dominated component (>75 %), then profile become insensitive tracer coefficients. Visual numerical algorithm give identical results idealized data with strong analytical noise asymmetric returns values closer known inputs. Finally, we four additional experiments (25–35 kbar, 1,260–1,400 °C) piston-cylinder apparatus pyrope- almandine-rich our reanalysis Ganguly et al. (1998) tools developed this work obtain following Arrhenius parameters D = D0 exp{–[Q1bar + (P–1)ΔV+]/RT} DMg* DFe*: Mg: Q1bar 228.3 ± 20.3 kJ/mol, 2.72 (±4.52) × 10−10 m2/s, Fe: 226.9 18.6 1.64 (±2.54) m2/s. ΔV+ were assumed be same as obtained Chakraborty (1992).