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[SIT03-03] Defect chemistry and diffusion in hydrous forsterite
Keywords:defect chemistry, self-diffusion coefficient, silicon, oxygen, water content, forsterite
Fei et al. (2013, 2014) systematically measured silicon and oxygen self-diffusion coefficients (DSi and DO, respectively) in iron-free forsterite as functions of water contents, showing that DSiCH2O0.32(7), DOCH2O0.05(6). These water-content exponents are much smaller than that expected on the basis of the assumption that self-diffusion coefficient of a chemical species is simply proportional to its defect density. Therefore, a new defect chemistry model is required to explain the above relationships.
The DSi should be proportional to the density of silicon defects, namely, DSi[VSi'''']. On the other hand, Si4+ is tightly surrounded by four-coordinated O2-, and therefore, migration of Si4+ should be enhanced if a surrounding O2- is missing. We can expect that a certain proportion of VSi'''' is associated with VO•• due to their excess charges with the opposite signs. As a result, Si migration is probably dominated by VO••-associated VSi''''. DSi is thus also proportional to [VO••] and we have,
DSi [VSi''''] × [VO••].
Under the charge neutrality condition of [(OH)O•] = 2[VMg''] in hydrous forsterite, we have [VSi''''] (fH2O)2/3 and [VO••] (fH2O)-1/3. Therefore,
DSi [VSi''''] ×[VO••] (fH2O)1/3,
which agrees well with the experimental results: DSi (CH2O)0.32(7) (Fei et al., 2013).
In hydrous olivine/forsterite, hydrogen exists as hydroxyl, (OH)-. Oxygen ions could diffuse either by hopping of O2- without H+ or by hopping of O in (OH)-. Because H+-associated O has a lower Coulomb force due to the excess charge by H+, the hopping probability of (OH)- should be higher than that of O2-. Thus, the O diffusion should be dominated by O2- of (OH)-. As a result, we have,
DO [VO] × ([O2-]hopping + [(OH)-]hopping) ≈ [VO••] × [(OH)-]hopping.
There are mainly three types of (OH)- in hydrous olivine/forsterite: (a) (OH)O• associated with VMg''; (b) (OH)O• associated with VSi''''; (c) (OH)O• un-associated with any cation vacancies. The un-associated (OH)O• should have much higher mobility than VSi'''' or VMg'' associated ones due to the Coulomb force and therefore the O diffusion is probably dominated by un-associated (OH)O•. Thus,
DO [VO••] × [(OH)-]hopping ≈ [VO••] × [(OH)O•]un-associated.
Under the charge neutrality condition of [(OH)O•] = 2[VMg''], we have [VO••] (fH2O)-1/3 and [(OH)O•]un-associated (fH2O)1/3. Therefore,
DO [VO••] × [(OH)O•]un-associated (fH2O)0.
This model suggests that DO is independent from CH2O, which agrees well with the experimental results, DO CH2O0.05(6) (Fei et al., 2014).
Fei et al. (2013), Nature 498, 213-215.
Fei et al. (2014), JGR 119, 7598-7606.