High silicon self-diffusion coefficient in dry forsterite

The plastic deformation of minerals is controlled by diffusion and dislocation creep. The diffusion creep is controlled by diffusion, and dislocation creep is also believed to be controlled by diffusion. Silicon is the slowest diffusion species in most mantle minerals and therefore expected to limit the creep rates. Olivine is the main constituent mineral in the upper mantle and forsterite is the Mg-rich end-member of olivine. Hence, Si self-diffusion coefficient (DSi) in forsterite is essential for understanding the upper mantle rheology. Previous studies of DSi in olivine and forsterite at ambient pressure showed large discrepancy with that estimated from deformation experiments by ~2-3 orders of magnitude. It is necessary to reexamine DSi.

We measured DSi in dry synthetic forsterite single crystals at 1600 and 1800 K, from ambient pressure up to 13 GPa, using an ambient pressure furnace and Kawai-type multi-anvil apparatus. The water contents in the samples were carefully controlled at <1 µg/g. Diffusion profiles were obtained by secondary ion mass spectrometry (SIMS) in depth profiling mode. We obtained much higher values of DSi, which are 2.4 orders of magnitude higher than that determined by Jaoul et al. (1981) (Fig. 1). We speculate that their low DSi might reflect the effects of a horizontal migration of the isotopically enriched thin films applied on the sample surfaces (Fig. 2), which may inhibit diffusion into the substrate during annealing. Our results resolved the inconsistency between DSi measured in diffusion experiments and those deduced from creep rates measured in deformation experiments (Fig. 3).

Small negative pressure dependence of DSi is determined (Fig. 1) with an activation volume of 1.7±0.4 cm3/mol. If we extrapolate our data of DSi at 1600 K to higher pressures, it is almost identical with that in iron and water bearing wadsleyite and ringwoodite (Fig. 3) determined by Shimojuku et al. (2009). The linear relationship of log DSi with pressure in dry forsterite, iron and water bearing wadsleyite and ringwoodite implies the effects of iron, water, and the structural difference among (Mg,Fe)2SiO4 polymorphs on DSi are small.

Fig. 1. logDSi with pressure at 1600 and 1800 K in comparison with Jaoul et al. (1981). Small pressure dependence is found with an activation volume of 1.7±0.4 cm3/mol. DSi at ambient pressure is ~2.4 orders of magnitude higher than that determined by Jaoul et al. (1981).

Fig. 2. The diffusion profile in ZrO2 coated sample (0022) is much longer than that in none-ZrO2 sample (0010) annealed under similar conditions at ambient pressure. We found horizontal shrinkage in none-ZrO2 samples (0010 and 0011), which could cause bad contact between thin film and substrate and lead to short diffusion profile. We speculate that the low DSi reported by Jaoul et al. (1981) might reflect the effect of a horizontal migration of the thin films. Similar DSi were obtained at high pressure in with-ZrO2 and without-ZrO2 samples, which was not too surprising because the thin film was compressed by the surrounding material and had good contact with the substrate at high pressure.

Fig. 3. Log DSi with pressure at 1600 K. Fo: forsterite. Ol: natural olivine. Wd: iron-bearing wadsleyite. Rw: iron-bearing ringwoodite. S2009: Shimojuku et al. (2009); H1990: Houlier et al. (1990); D2002: Dohmen et al. (2002); J1981: Jaoul et al. (1981). G1973: estimated from dislocation data by Goetze and Kohlstedt, (1973). We assume the same activation volume for silicon diffusion in forsterite, wadsleyite and ringwoodite.

Fei, H. Z., C. Hegoda, D. Yamazaki, M. Wiedenbeck, H. Yurimoto, S. Shcheka, and T. Katsura (2012), High silicon self-diffusion coefficient in dry forsterite, Earth Planet. Sci. Lett., 345, 95-103. [Full Text]