Oxygen fugacity, or partial pressure of oxygen (Eugster, 1957), is a thermodynamic variable used to indicate the chemical potential of oxygen in reactions where both reagents and products contain the same element(s) but with different oxidation states. These reactions are termed “redox reactions” and are described by a univariant curve in fo2-temperature diagrams. At a given temperature, above this curve the oxidized phase of an assemblage will be stable whereas, below the reduced phases will be stable.
Figure 1.3 Shown are curves relative to buffer equilibria plotted as function of temperature (Kelvin) versus the logarithm of the oxygen fugacity and calculated at a fixed pressure of 3 GPa. The equilibria are reported with the acronyms explained in the text (Eq. 1.2-1.4).
Rock-forming minerals are widely characterized by the presence of heterovalent elements, such as iron, chromium, vanadium, and carbon. Their occurrence in oxidized or reduced form can be used to infer the redox state at which certain rocks have crystallized. An important goal in experimental
geochemistry is, therefore, to investigate the behavior of these elements with respect to oxygen fugacity and develop interpretative models, for extracting the change of redox conditions in the Earth over the geological time scale from the analysis of heterovalent cation concentrations in mantle rocks (Delano, 2001; Li and Lee, 2004). In figure 1.3 four buffer equilibria are plotted which are extensively used in petrology to describe redox conditions at which common silicates and oxides coexist in the Earth’s interior. These equilibria are conventionally written with the high entropy side, which includes oxygen, on the right and are commonly referenced by their acronyms as follows,
2Fe3O4 + 3SiO2 = 3Fe2SiO4 + O 2 (FMQ; O’Neill and Wall, 1987) (1.2)
The above equilibria can also be used in a natural context. Equilibrium (1.2), for example, could be used to determine the oxygen fugacity from a mineral assemblage (figure 1.3) from consideration of the activity of each component in the phases. The standard Gibbs free energy of the reaction is a function of the oxygen fugacity through the equilibrium condition,
ΔG°(1.2) = -RTlnK = -RTln
⎟ ⎟
with ΔG°[1.2] standard Gibbs free energy of reaction (1.2), R is the gas constant (8.3144 J mol-1K-1), T is the temperature in Kelvin and is the activity of the component i in the phase j (j is omitted in case of pure end members, as in eq. 1.7).
J
a
iIn the case of a pure assemblage of phases such as for equilibrium (1.2), the activity of each phase is 1 and the log fo2 is simply expressed as a function of the Gibbs free energy of the reaction as,
log fo2 =
( )
which requires knowledge of enthalpy, entropy and volume change with pressure and temperature of the given reaction. Thermodynamic databases are provided by Holland and Powell (1990), Robie et al.
(1995) and Fabrichnaya et al. (2004). A simple parameterisation is often used to express the oxygen fugacity as function of pressure and temperature derived from (1.8),
logfo2 =
Since natural minerals are commonly complex solid solutions, in this case the activity is calculated from the chemical composition (by electron microprobe, for example) of each phase in (1.2) as,
i i j
i
x
a = ⋅ γ
(1.10)where xi is the mole fraction of the component in a given phase and γi the activity coefficient which is 1 in case of ideal mixing between sites. In case of non-ideality (γi used) the excess of energy due to the
mixing behaviour between atoms of different elements in a crystalline structure can be described using the general formulation,
(
X)
WRTln
γ
i = 1− i 2 (1.11)with W being an interaction parameter called a Margules parameter, which represents an interchange energy (J mol-1) between cations in case of symmetrical solid solutions (Wood and Fraser, 1977;
Cemič, 2005). Interaction parameters used to calculate the oxygen fugacity in this study are listed in each chapter.
As shown in Figure 1.3 most buffers (1.2), (1.3), (1.4) and (1.5) follow a similar trend as a function of temperature, which results from the enthalpy change associated with oxidation being similar for most assemblages. For this reason fo2 measurements are usually normalized to a given buffer, such as FMQ to eliminate the effect of temperature from the buffer curves.
Figure 1.4 Shown is the oxygen fugacity range calculated from spinel-bearing peridotite rocks from different geological settings (Frost and McCammon, 2008 modified). References are provided by Frost and McCammon (2008).
Figure 1.4 shows the oxygen fugacity measured in natural spinel-bearing peridotites from different localities determined mainly using the following equilibrium calibrated by Nell and Wood (1991),
3Fe2Si2O6 + 2Fe3O4 = 6Fe2SiO4 + O2 (1.12) opx spinel olivine
The oxygen fugacity calculated by (1.12) requires the ferric iron content of spinel to be measured in order to determine the activity of the Fe3O4 component. Fe3+/∑Fe of natural spinel ranges between 15 and 34 wt.%, while in the other phases, particularly olivine, the ferric iron concentration is negligible (Canil and O’Neill, 1996). As shown in figure 1.4, the oxygen fugacity of spinel-bearing xenoliths covers a range between -3 and +2 log units with respect to the FMQ buffer. This wide range reflects in part the heterogeneity of the mantle likely resulting from different processes, such as partial melting or contamination by metasomatic agents. However, it appears that there is also a link to the geological settings with xenoliths from subduction zones being more oxidized as a result of the high activity of water-bearing fluids perhaps, while the most reducing fo2 are recorded by the abyssal peridotites, which are a residue of significant mantle melting (Frost and McCammon, 2008).
Spinel peridotite rocks record pressures corresponding to depths between 30 and 60 km.
Knowledge of the mantle redox state at deeper conditions requires measurements on garnet-bearing peridotites, which are mainly found as xenoliths in kimberlites (Luth et al., 1990). The oxygen fugacity of garnet peridotites can be determined using the equilibrium calibrated by Gudmundsson and Wood (1995),
2Fe3Fe23+Si3O12 = 4Fe2SiO4 + 2FeSiO3 + O2 (1.13) garnet olivine opx
where the oxygen fugacity is,
The volume change of equilibrium (1.13) is positive, which means that increasing pressure stabilizes the Fe3Fe23+Si3O12 skiagitic garnet (Gudmundsson and Wood, 1995; Woodland and Peltonen, 1999). As a consequence, the fo2 will tend to drop with pressure, as shown in figure 1.5 (Frost and McCammon, 2008). This basic trend, which originates from the volume change, has been observed in mantle xenoliths from diamondiferous localities such as Kapvaal and Slave Craton with the conclusion that, the cratonic lithosphere falls mostly into the diamond stability field (Woodland and Koch, 2003;
McCammon and Kopylova, 2004).
Calculations by Frost and McCammon (2008) provide a model (shown as the red line in figure 1.5) for the mantle fo2 profile with depth for a fixed bulk composition and assuming a fixed Fe3+/∑Fe ratio of 0.03 (BSE, McDonough and Sun, 1995). The profile is calculated along a continental geotherm and predicts the depth at which the lowest plausible mantle oxygen fugacity is reached, the so-called nickel precipitation curve (O’Neill and Wall, 1987). Although cratonic xenoliths show that there is a pressure effect on the fo2 of garnet peridotite rocks, this is not related to composition but simply arises from the volume change of the ferric/ferrous equilibria (1.13). This means that, likely, the same pressure effect should operate in the asthenosphere, which is in general made out of the same mineral phases as many cratonic xenoliths, such as PHN1611 (Nixon and Boyd, 1973). This change of fo2 with depth implies that the valence of heterovalent elements other than Fe most likely changes as regions of oceanic mantle undergo adiabatic decompression.