Fe-Mg diffusion in olivine II: point defect chemistry, change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine

Analysis of existing data and models on point defects in pure (Fe,Mg)-olivine (Phys Chem Miner 10:27-37,1983; Phys Chem Miner 29:680-694, 2002) shows that it is necessary to consider thermodynamic non-ideality of mixing to adequately describe the concentration of point defects over the range of measurement. In spite of different sources of uncertainties, the concentrations of vacancies in octahedral sites in (Fe,Mg)-olivine are on the order of 10(-4) per atomic formula unit at 1,000-1,200 degrees C according to both the studies. We provide the first explicit plots of vacancy concentrations in olivine as a function of temperature and oxygen fugacity according to the two models. It is found that in contrast to absolute concentrations at similar to 1,100 degrees C and dependence on fO(2), there is considerable uncertainty in our knowledge of temperature dependence of vacancy concentrations. This needs to be considered in discussing the transport properties such as diffusion coefficients. Moreover, these defect models in pure (Fe,Mg)-olivine need to be extended by considering aliovalent impurities such as Al, Cr to describe the behavior of natural olivine. We have developed such a formulation, and used it to analyze the considerable database of diffusion coefficients in olivine from Dohmen et al. (Phys Chem Miner this volume, 2007) (Part - I) and older data in the literature. The analysis documents unequivocally for the first time a change of diffusion mechanism in a silicate mineral-from the transition metal extrinsic (TaMED) to the purely extrinsic (PED) domain, at fO(2) below 10(-10) Pa, and consequently, temperatures below 900 degrees C. The change of diffusion mechanism manifests itself in a change in fO(2) dependence of diffusivity and a slight change in activation energy of diffusion-the activation energy increases at lower temperatures. These are consistent with the predictions of Chakraborty (J Geophys Res 102(B6):12317-12331, 1997). Defect formation enthalpies in the TaMED regime (distinct from intrinsic defect formation) lie between -66 and + 15 kJ/mol and migration energies of octahedral cations in olivine are most likely similar to 260 kJ/mol, consistent with previous inferences (Phys Chem 207:147-162, 1998). Plots are shown for diffusion at various constant fO(2) as well as along fO(2) buffers, to highlight the difference in behavior between the two. Considering all the diffusion data and constraints from the point defect models, (Fe-Mg) diffusion in olivine along [001] is best described by the Master equations: (1) At oxygen fugacities greater than 10(-10) Pa: = - 9.21 - 201000 + (P - 10(5)) x 7 x 10(-6) / 2.303RT + 1/6log (fO(2) /10(-7)) + 3X(Fe) where T is in Kelvin, P and fO(2) is in Pascals, X (Fe) is the mole fraction of the fayalite component and R is the gas constant in J/mol/K. (2) At oxygen fugacities less than 10(-10) Pa: log [D-FeMg(m(2) / s)] = - 8.91 - 220000 + (P - 10(5)) x 7 x 10(-6) / 2.303RT + 3X(Fe) These equations reproduce all of the 113 experimental data points within half an order of magnitude. (3) Alternately, a global equation averaging out the change of mechanism may be used, with somewhat larger errors in reproducing the measured diffusion data. It underestimates data at higher temperatures, and overestimates them at lower temperatures on the average. Note that fO(2) is not explicitly considered here, leading to additional sources of error: log [D-FeMg(m(2) / s)] = - 8.27 - 226000 + (P - 105) x 7 x 10(-6) / 2.303RT + 3X(Fe) To obtain diffusion coefficients along [100] and [010], log 6 needs to be subtracted from each of the above equations.