Activation energy and activation volume

The activation energy for oxygen diffusion in this study is determined to be 352±60 kJ/mol at 8 GPa. This value is lower than that for silicon diffusion (~410-430 kJ/mol, [Fei et al., 2012;

Fei et al., 2013]). By comparing to the activation energy determined at ambient pressure (~302-322 kJ/mol [Andersson et al., 1989; Jaoul et al., 1980] shown in Table 4.2), the activation volume is between 3.8 - 6.3 cm³/mol calculated using the equation: ΔH = ΔE + PΔV, where ΔH

-20.0 -19.5 -19.0 -18.5 -18.0

0 5 10 15 20

Log D

(m

/s)

Duration (hour)

1600 K

1 atm

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is the activation enthalpy at pressure P, ΔE is the activation energy, and ΔV is the activation volume. The ΔV for oxygen diffusion is higher than that for silicon self-diffusion (1.7±0.4 cm³/mol [Fei et al., 2012]), and identical with that for Fe-Mg diffusion (4-7 cm³/mol, [Hier-Majumder et al., 2005]).

Table 4.2. Activation energy for oxygen diffusion determined in forsterite and natural olivine (T:

temperature, P: pressure, ΔE: activation energy).

Sample H2O T (K) P (GPa) ΔE (kJ/mol) Reference Forsterite Wet 1600-1800 8 352±60^*a This study

Forsterite Dry 1423-1873 10^-4 322±42 [Jaoul et al., 1980]

Forsterite Dry 1523-1793 10^-4 302±13 [Andersson et al., 1989]

Olivine Wet 1473-1623 2 437±17^*b [Costa and Chakraborty, 2008]

Olivine Dry 1473-1673 10^-4 266±11 [Ryerson et al., 1989]

Olivine Dry 1363-1773 10^-4 318±17 [Gérard and Jaoul, 1989]

Olivine Dry 1373-1773 10^-4 338±14 [Dohmen et al., 2002]

*a: ΔE is ~296-320 kJ/mol if corrected to ambient pressure using the ΔV =4-7 cm³/mol from Fe-Mg diffusion [Farber et al., 2000; Holzapfel et al., 2007].

*b: ΔE is reported as 324 kJ/mol after pressure correction using ΔV = 7 cm³/mol from Fe-Mg diffusion [Holzapfel et al., 2007] and fO2 correction using an assumed exponent of 1/4 intermediate between the 1/3 and 1/5 exponents determined by Gérard and Jaoul [1989] and Ryerson et al. [1989], respectively.

In Fei et al. [2012], we suppose that the horizontal migration of thin films occurred in previous ambient pressure silicon diffusion experiments, which could also occur in oxygen diffusion studies. However, the activation energy determined in this study agrees well with previous oxygen diffusion studies. This is reasonable because when horizontal migration occurs, there should be a nano size vacant layer between the thin film and substrate which could be an obstacle for silicon diffusion, but not for oxygen since oxygen ions in forsterite (both in the thin film and in substrate) could exchange with that in the vacant layer which is filled with air. As a result, even if the horizontal migration occurred in previous oxygen diffusion studies at ambient

137 pressure, the measured oxygen diffusion coefficient is not influenced and therefore the activation energy determined in this study agrees well with that determined in previous studies.

Costa and Chakraborty [2008] reported an activation energy of ~437 kJ/mol at 2 GPa in hydrous olivine. Additionally, they also pointed out that it is 324 kJ/mol after fO2 and pressure normalization (using ΔV = 7 cm³/mol from Fe-Mg diffusion [Holzapfel et al., 2007] and a fO2

exponent of 1/4 [Gérard and Jaoul, 1989; Ryerson et al., 1989]), which overlaps with that in dry olivine [Dohmen et al., 2002; Gérard and Jaoul, 1989; Ryerson et al., 1989]. Therefore, the activation energy for oxygen diffusion in forsterite and natural olivine is ~ 300-340 kJ/mol under both dry and wet conditions (Table 4.2). Water does not largely affect the activation energy, which agrees with computer simulations by Walker et al. [2003], who proposed the same mechanism for oxygen diffusion in dry and water-bearing forsterite.

4.5.2 Defect chemistry

The zero-CH2O dependence for DO can be understood on the basis of defect chemistry. We use the Kröger-Vink [1956] notation (see Appendix I), e.g. VSi’’’’ indicates four effective negative charges for a vacancy in the silicon site, whereas (OH)O• indicates an H⁺-associated O in the O site with an effective charge of +1. Square brackets [-] denote concentration of the corresponding units. The self-diffusion coefficient of an ion, Dion, is proportional to the vacancy concentration of that ion, [Vion] [Kohlstedt, 2006]. Hence, DO ∝ [VO••]. In a hydrous olivine crystal, water exists as hydroxyl, (OH)O• [Kohlstedt et al., 1996]. Thus, there are two possibilities for the oxygen ions hopping in hydrous olivine: (a) hopping of O in O site, and (b) hopping of O in (OH)O•. Because H⁺-associated O has a lower Coulomb force due to the excess charge by H⁺, the hopping probability of O in (OH)O• should be higher than that of OO×. Thus, the O diffusion should be dominated by O from (OH)O•. Besides, if an O in (OH)O• jumps, the H⁺ cannot remain in an O vacancy because the VO•• already has two excess positive charges, and also the mobility of H⁺ is much higher than that of O^2- [Costa and Chakraborty, 2008; Demouchy and Mackwell, 2003]. Therefore, oxygen diffusion is probably dominated by hopping of OH^- in (OH)O•.

There are mainly three types of (OH)O• in hydrous olivine: (a) (OH)O• associated with metal vacancies, i.e., {(OH)O•-VMg’’}’ and {2(OH)O•-VMg’’}^×; (b) (OH)O• associated with Si vacancies, i.e., {(OH)O•-VSi’’’’}’’’, {2(OH)O•-VSi’’’’}’’, {3(OH)O•-VSi’’’’}’, and {4(OH)O•-VSi’’’’}^×; (c)

138

(OH)O• without associating with any cation vacancies [Brodholt and Refson, 2000]. The third type should have much higher mobility because the association of (OH)O• with VSi’’’’ or VMg’’

should cause lower mobility of (OH)O• due to the additional Coulomb force between (OH)O• and VSi’’’’ or VMg’’. Therefore, oxygen diffusion should be dominated by un-associated (OH)O•,

In wet olivine, the concentration of VMg’’ is much higher than that of VSi’’’’ [Brodholt and Refson, 2000; Kohlstedt, 2006]. Thus, the charge neutrality for H⁺ is mainly kept by VMg’’, namely, [(OH)O•] = 2[VMg’’] [Kohlstedt, 2006]. This charge neutrality condition leads to the relationships between [VO••], [(OH)O•], and water fugacity, fH2O as follows [Costa and Chakraborty, 2008; Kohlstedt, 2006; Mei and Kohlstedt, 2000a]:

3 2004]), which agrees well with our experimental results, DO ∝ CH2O0.06±0.14.

In the enstatite buffered samples, oxygen fugacity (fO2) is relatively higher in comparison with graphite+enstatite buffered samples. However, both systems show almost the same value of DO, which indicates that DO in forsterite is independent with fO2. This observation is consistent with Jaoul et al. , who suggested fO2 has no effect on DO in dry forsterite at ambient pressure.

Natural olivine contains about 10 % of the Fe2SiO4 component. The charge neutrality condition could be different if a significant proportion of ferric iron exists. However, the DO in pure forsterite determined in this study is essentially the same as that obtained in iron-bearing

139 olivine determined by Costa and Chakraborty [2008] after correcting to the same temperature (Fig. 4.3). Therefore, presence of ferric iron in natural olivine is not essential for oxygen diffusion at least at the CH2O levels of several hundred wt. ppm, which is the case for the major part of upper mantle conditions [Dixon et al., 2002; Hirschmann, 2006; Workman and Hart, 2005].