Experimental determination of Fe–Mg interdiffusion in orthopyroxene as a function of Fe content

We have measured the dependence of the Fe–Mg interdiffusion coefficient, D_Fe-Mg, on the ferrosilite component in orthopyroxene, which so far has not been experimentally calibrated. Diffusion couples, consisting of approximately 1 µm thin-films were deposited by pulsed laser ablation on orthopyroxene crystals of En₉₁Fs₉ composition. Diffusion experiments were carried out at atmospheric pressure in vertical gas mixing furnaces (CO-CO₂) at temperatures between 950 and 1100 °C at constant fO₂ = 10^–7 Pa. Using a focused ion beam-scanning electron microscope (FIB-SEM), FIB-foils were cut from diffusion couples before and after annealing. Diffusion profiles were extracted by using combined backscattered electron (BSE) imaging and energy dispersive X-ray (EDXS) mapping on FIB-foils which allowed to resolve concentration gradients within 20 nm. The microstructure of the diffusion experiments was investigated using transmission electron microscopy (TEM). Using this method, we obtained the first experimentally determined data on the dependence of D_Fe-Mg on the ferrosilite content in orthopyroxene at different temperatures, appearing to increase with increasing a temperature. For the temperature range (950 – 1100 °C), log fO₂ = -7 Pa, along [001] in the composition Fs9, the log D_Fe-Mg yields the following Arrhenius equation:

$$D_{Fe - Mg} [m^2 /s] = 3.8 \cdot 10^{ - 9} \exp [ - 261.07 \pm 24[kJ/mol]/(R/T[K])]$$

The effect of X_Fe on D_Fe-Mg, given by \(D(X_{Fe} ) = D(X_{Fe} = 0.09) \cdot {10}^{m (X_{Fe} - 0.09)},\) can be calculated by the following parameterization where m follows a linear regression of m on temperature:

$$m = - 2.711 \cdot 10^4 /T(K) + 23.5408$$

By considering the D_Fe-Mg dependence on X_Fe, the timescales of natural processes obtained from modelling the compositional zoning of natural crystal may considerably differ from previously estimated timescales.