Si and O self-diffusion in hydrous forsterite and iron-bearing olivine from the perspective of defect chemistry
Introduction
- Explanation of the new data about the water-content dependence of self-diffusion coefficients in olivine in view of defect chemistry
-
- Si: D ∝ CH2O^(1/3) [Fei et al., 2013]
- O: D independent from CH2O [Fei et al., 2014]
Si diffusion : Why DSiLat ∝ CH2O1/3 ?
–Si diffusion is driven through vacancies in Si sites
• Also DSiLat ∝ [VO･･]
–Jump of VSi”” associated with VO･･ should dominate
• Si is surrounded by O, which makes a barrier
• If one neighbor oxygen ion is missing, VSi”” can jump more easily.
–VSi”” and VO･･ attract with each other due to Coulomb force
• Significant proportions of VSi”” and VO･･ will coupled in a crystal even though [VSi””] and [VO･･] are both low
–This hypothesis should be examined.
• ∴ DSiLat ∝ [VSi””][VO･･]
- Charge compensation of proton incorporation into the olivine structure by Mg vacancy
-
- H2O + OOX = 2(OH)O· + VMg’’
- [VMg”] ∝ fH2O1/3 ∝ CH2O1/3
- K = [(OH)O*]2[VMg” ] / [H2O][OOX ] = [VMg” ]3 / [H2O]
-
- [(OH)O*]~[VMg” ], [OOX ]~1Me
- [VSi””]
-
- charge balance 2[VMg”] ⇔ [VSi””]
- [VSi””] ∝ [VMg”]2 ∝ (fH2O1/3)2 = fH2O2/3 ∝ CH2O2/3
- •[VO··]
-
- Equilibrium constant K = [VO··][VMg”]
- [VO··] ∝ 1/[VMg”] ∝ 1/fH2O1/3 = fH2O-1/3 ∝ CH2O-1/3
- DSiLat ∝ [VSi””] [VO··] ∝ CH2O2/3 CH2O-1/3 = CH2O1/3
O diffusion: Why no water-content dependence on DOLat?
- DOLat ∝ [VO••][(OH) •]
-
- Diffusion coefficient is proportional to defect density
- O at (OH-) predominantly jumps
-
- due to small electric charge
- [VO••] ∝ fH2O-1/3 ∝ CH2O-1/3
-
- [VMg”] ∝ fH2O1/3 ∝ CH2O1/3
-
- H2O + OOX = 2(OH)O· + VMg’’
- K = [(OH)O•]2[VMg” ] / fH2O [OOX] = [VMg” ]3 / fH2O
-
- [(OH)O•] = 2[VMg” ], [OOX ] ~ 1
- K = [VO••][VMg” ] → [VO••] ∝ [VMg”]-1
- [(OH)•] ∝ fH2O1/3 ∝ CH2O1/3
- DOLat ∝ CH2O-1/3CH2O1/3 = CH2O0
Fei, H.-Z., and T. Katsura, Si and O self-diffusion in hydrous forsterite and iron-bearing olivine from the perspective of defect chemistry, Phys. Chem. Miner. 43, 119-126, 2016.