A computer simulation study of the effect of pressure on Mg diffusion in forsterite

Abstract

Please cite this article as: B'ejina, F., Blanchard, M., Wright, K., Price, G.D., A computer simulation study of the effect of pressure on Mg diffusion in forsterite, Physics of the Earth and Planetary Interiors (2007), doi:10.1016/j.pepi.2008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d M a n u s c r i p t AbstractComputer simulation techniques were used to investigate the effect of pressure on magnesium diffusion in forsterite between 0 and 10 GPa. We studied the diffusion path along the c crystallographic axis (we always refer to the Pbnm system) via a vacancy mechanism. Using a Mott-Littleton approach within the code GULP, we were able to precisely map the diffusion path of a Mg vacancy and we found the activation energy, E = 3.97 eV at 0 GPa (with E f = 3.35 eV for the formation energy and E m = 0.62 eV for the migration) and E = 4.46 eV at 10 GPa (E f = 3.81 eV and E m = 0.65 eV). Preliminary results using the supercell technique gave the same saddle point coordinates and energies. This saddle point of the Mg vacancy diffusion found with GULP was then introduced in an ab initio code, confirming the values of the migration energy both at 0 and 10 GPa. We were therefore able to estimate the activation volume (∆V ) to be around 5 cm 3 /mol and d(∆V )/dP ≃ 0.The effect of pressure applies mostly on defect formation and little on migration. A c c e p t e d M a n u s c r i p t AbstractComputer simulation techniques were used to investigate the effect of pressure on magnesium diffusion in forsterite between 0 and 10 GPa. We studied the diffusion path along the c crystallographic axis (we always refer to the Pbnm system) via a vacancy mechanism. Using a Mott-Littleton approach within the code GULP, we were able to precisely map the diffusion path of a Mg vacancy and we found the activation energy, E = 3.97 eV at 0 GPa (with E f = 3.35 eV for the formation energy and E m = 0.62 eV for the migration) and E = 4.46 eV at 10 GPa (E f = 3.81 eV and E m = 0.65 eV). Preliminary results using the supercell technique gave the same saddle point coordinates and energies. This saddle point of the Mg vacancy diffusion found with GULP was then introduced in an ab initio code, confirming the values of the migration energy both at 0 and 10 GPa. We were therefore able to estimate the activation volume (∆V ) to be around 5 cm 3 /mol and d(∆V )/dP ≃ 0.The effect of pressure applies mostly on defect formation and little on migration.

Pressure dependence of electrical conductivity in forsterite

“…Pressure dependence of Mg tracer diffusivity in forsterite measured to 10 GPa yields a relatively smaller activation volume of approximately 1–3.5 cm 3 /mol [ Chakraborty et al ., ]. Computer simulation results yielded the large activation volume (Δ V ) for Frenkel defect formation enthalpy of forsterite to be around 5 cm 3 /mol and the small activation volume less than 1 cm 3 /mol for migration [ Jaoul et al ., ; Béjina et al ., ]. Up to 7 GPa, large reduction of the conductivity is in good agreement with strong pressure dependence determined from Mg diffusion studies and indicates that only the migration energy of Mg vacancy, which has almost zero activation volume, cannot account for the large pressure dependence observed in lower pressure range.…”

“…For the high‐temperature regime, the Δ E Mg of the single crystal forsterite is comparable to the Δ E Ox , whereas the Δ V Mg is much higher than the Δ V Ox . The activation volumes for the electrical conduction in association with Mg vacancies (Δ V Mg ) are large and positive (6–18 cm 3 /mol) and are slightly higher or comparable to those of the Mg diffusion experiments [ Béjina et al ., ]. Relatively higher Δ V Mg would be caused by absence of lower pressure data in this study (<3.5 GPa).…”

“…Δ E LT are 0.8–0.9 eV. The small Δ V LT are consistent with that (<1 cm 3 /mol) for migration of Mg self‐diffusion [ Jaoul et al ., ; Béjina et al ., ].…”

“…The fastest crystallographic direction of Fe-Mg interdiffusion and Mg tracer diffusion is also along [001], which is a factor of 4-8 times faster than along [100] and [010] [Chakraborty et al, 1994;Chakraborty, 1997;Dohmen et al, 2007]. Considering the energy of vacancy formation in forsterite, the M1 site for Mg vacancies is more favorable than the M2 site [Béjina et al, 2009]. The diffusion path between two adjacent M1 vacant sites along [001] is predicted to have lower activation energy compared to [100] and [010] [Walker et al, 2009].…”

Lattice Dynamics from Force-Fields as a Technique for Mineral Physics

“…Studies range from investigating the controls on uptake of impurities by mantle silicates (Wright and Catlow 1994;Purton et al 1996Purton et al , 1997Gatzemeier and Wright 2006), though determination of diffusion migration mechanisms (Walker et al 2003;Bejina et al 2009) to modelling the cores of dislocations (Walker et al 2004(Walker et al , 2005.…”