Silicon Self-Diffusion in Stishovite: Calculations of Point Defect Parameters Based on the cBΩ Thermodynamic Model

In the present work we apply the so-called cBΩ thermodynamic model to study the diffusion of Si in stishovite crystal at high pressure and over a wide temperature range. According to this model [1,2], the point defect activation Gibbs free energy is expressed as a function of the bulk properties of the material, i.e. g^act=cBΩ, where B is the isothermal bulk modulus, Ω is the mean atomic volume and c is a dimensionless constant. In this way, other important point defect parameters, such as the activation volume V^act, the activation entropy S^act and the activation enthalpy h^act may be estimated, if the thermoelastic properties of the material are known over a wide temperature and pressure range. Our calculations are based on previously reported self-diffusion coefficients in stishovite single crystals measured at 14 GPa and at temperatures from 1400 to 1800 ^oC, in the [110] and [001] directions, by Shatskiy et al. [3]. Furthermore, the EoS of stishovite, proposed by Wang et al. [4] has been used for the accurate implementation of the cBΩ model. Our results suggest that the aforementioned point defect parameters exhibit considerable temperature dependence over the studied temperature range (1000-2000 ^oC). The estimated activation volumes (4.8-5.8 cm³/mol, in the range 1400-1800 ^oC) are in agreement with the experimental results reported by Xu et al. [5]. Our study confirms the potential of the cBΩ model for the theoretical investigation of diffusion processes in minerals, in order to overcome the experimental difficulties and the lack of experimental data in mantle conditions.

REFERENCES

1. Varotsos P. and Alexopoulos K. Thermodynamics of Point Defects and their Relation with the Bulk Properties, North-Holland, Amsterdam, 1986.
2. Vallianatos, F., Saltas, V. Application of the cBΩ model to the calculation of diffusion parameters of He in olivine, Chem. Miner. 2014, 41, 181-188, Doi: 10.1007/s00269-013-0636-y.
3. Shatskiy, A., Yamazaki, D., Borzdov, Y.M., Matsuzaki, T., Litasov, K.D., Cooray, T., Ferot, A., Ito, E., Katsura, T. Stishovite single-crystal growth and application to silicon self-diffusion measurements, Mineral. 2010, 95, 135–43, Doi: 10.2138/am.2010.3255.
4. Wang, F., Tange, Y., Irifune, T., and Funakoshi, K. P‐V‐T equation of state of stishovite up to mid‐lower mantle conditions, Geophys. Res. 2012, 117, B06209, doi:10.1029/2011JB009100.
5. Xu, F., Yamazaki, D., Sakamoto, N., Sun, W., Fei, H., Yurimoto, H. Silicon and oxygen self-diffusion in stishovite: Implications for stability of SiO₂-rich seismic reflectors in the mid-mantle, Earth Planet. Sci. Lett. 2017, 459, 332–9, Doi: 10.1016/j.epsl.2016.11.044.