- © The Mineralogical Society Of America
Whether the redox state, quantified as oxygen fugacity, recorded in a planetary basalt is an accurate representation of the redox state of the planetary interior from which it was derived through partial melting, ascent, eruption and emplacement is a fundamental question in planetary geology. In the absence of mantle xenoliths in samples from the Moon, Mars and differentiated asteroids, the basalt-mantle source relationship must be extrapolated from what is known about the Earth in order to probe the redox state of these planetary interiors. A review of current knowledge regarding the basalt-mantle source relationship for the Earth provides insights into the advantages and pitfalls of determining mantle redox state. The range of currently available oxybarometers, including thermodynamic models based on ferrous-ferric mineral equilibria and multivalent cation analysis are surveyed and their limitations presented. The result is a basis for the informed interpretation of the oxygen fugacity of planetary basalts, and new insights into the role of C-H-O volatiles in the terrestrial planets.
For the purpose of elucidating the redox evolution of terrestrial planet interiors, the Earth represents a natural, if not ideal, laboratory in which to examine the relationship between the oxygen fugacity (fO2) of a basaltic sample and the redox state of its mantle source. Partial melting of terrestrial planet interiors to produce basaltic eruptives is a fundamental process that was initiated on the terrestrial planets shortly after their formation and has continued in some cases to the present day. The redox characteristics of a basalt are the direct results of the physical and chemical conditions of partial melting, ascent and eruption.
The oxygen fugacity of a basalt from the Earth can be determined by the judicious selection of one or more pertinent oxybarometers based on ferrous-ferric mineral equilibria or multivalent trace element characteristics; comparison of its oxygen fugacity with that of a related mantle xenolith, complemented perhaps by insights from laboratory experiments, places constraints on the behavior of multivalent elements (and redox-sensitive volatiles) during partial melting. In this way, the influence of the physical and chemical conditions of partial melting of the mantle source on the oxygen fugacity of the basaltic product can be quantified, or at least characterized.
The same cannot be done for samples of the Moon, Mars and differentiated asteroids (e.g., 4 Vesta), due to the apparent absence of mantle xenoliths from our samples of these suites. Instead, the basalt-mantle source relationship, as quantified from studies of terrestrial samples, must be adapted for and extrapolated to the suite of basaltic samples from these other planetary bodies. For this reason, summaries of the oxidation state of the Earth’s mantle, the array of available oxybarometers applicable to basaltic samples, and a discussion of whether the oxygen fugacity of a basalt is reflective of the oxidation state of its mantle source are important precursors to the presentation of data for planetary basalts, and are essential to their proper interpretation.
Oxygen fugacity is not a straightforward concept. A summary of the origin of the concept and a discussion of common misconceptions is provided by Frost (1991). The misconception most relevant to the following discussion is that oxygen is present as a fluid species in natural systems. Although we express oxygen fugacity in units of gas pressure (for example, 10−9.3 bars of O2), oxygen fugacity does not represent the partial pressure of a gas, but instead monitors the chemical potential, and can therefore be used to describe a condensed system in which no free oxygen is present (Frost 1991). Therefore, the “O2” term in many of the equations presented in this chapter does not necessarily indicate involvement of free oxygen.
Oxygen fugacity is most often expressed relative to an assemblage of pure phases that define a specific oxygen fugacity for a given temperature. These assemblages are known as solid oxygen buffers or petrologic buffers; they are not necessarily present in natural systems, but represent convenient references to describe the oxygen fugacity of a natural system. Common examples are iron-wüstite (IW), fayalite-magnetite-quartz (FMQ), nickel-nickel oxide (NNO), and magnetite-hematite (MH). A number of studies have been carried out over the past several decades to define the buffer equations, resulting in a number of formulations. A selection is given in Table 1⇓, and other compilations can be found in Frost (1991) and Chou (1987). The oxygen fugacity defined by the buffers increases with increasing temperature, and the slopes of the buffers are nearly the same in all cases. An oxygen fugacity estimate calculated using an oxybarometer (see below) can be expressed relative to one of the buffers, obviating the need to state both the absolute oxygen fugacity and temperature. For example, an oxygen fugacity estimate of log fO2 = −9.3 at a temperature of 1200 °C and a pressure of 1 bar corresponds to 1 log unit below FMQ, or “FMQ − 1”. The most recent data for solid oxygen buffers come from O’Neill and Pownceby (1993); regression of their data for the IW and NNO buffers is provided in Table 1⇓. Also provided are regressions of data from O’Neill (1987a) for NNO, O’Neill (1988) for IW, and O’Neill (1987b) for FMQ. The latter equation should be used instead of the erroneous equation of Holloway et al. (1992) for FMQ based on the same data. Many of the formulations do not explicitly account for pressure effects, and often the buffers are not experimentally calibrated for high pressures; additional buffer equations that include pressure terms are provided by Ballhaus et al. (1991). The use of different buffer formulations can result in small discrepancies; for example, the use of the NNO formulation according to Schwab and Küstner (1981) for log fO2 = −9.3 and T = 1200 °C yields NNO − 1.8, whereas use of the regression of the O’Neill and Pownceby (1993) data (Table 1⇓) yields NNO − 1.6. Although the discrepancies tend to be small, typically less than the uncertainty on an oxybarometer estimate, an explicit statement of the formulation used to calculate and express oxygen fugacity provides the reader with the ability to compare oxygen fugacity estimates without introducing added uncertainties.
THE OXIDATION STATE OF THE EARTH’S MANTLE
The differences between oxygen fugacity, oxidation state and oxygen content, as outlined above, are fundamentally important for understanding the Earth’s mantle. Iron is the most abundant element that exists in more than one oxidation state in planetary interiors; for this reason the oxidation state of the Earth’s mantle is expressed in terms of iron oxidation state, i.e., the relative proportions of the different valence states of iron (Fe0, Fe2+ and Fe3+; commonly given as Fe3+/∑Fe, where ∑Fe = Fe2+ + Fe3+). Oxygen fugacity is related to iron oxidation state through equilibria between Fe-bearing minerals. The valence state of iron in minerals in a natural system, such as the Earth’s mantle, however, is the result of the complex interplay of mineral crystal chemistry and the oxidation state of the system. The oxidation state of iron may thus change as a result of crystal chemical effects, without a correlative change in oxygen fugacity.
The relationship of oxygen fugacity to iron oxidation state through mineral equilibria can only be determined under the assumption of equilibrium. The quantification of this relationship is dependent on our knowledge of the stability of mineral assemblages at pressures and temperatures appropriate for the Earth’s mantle. This knowledge is derived from studies of mantle xenoliths and complementary experimental data, as well as high-pressure experiments for deeper parts of the mantle, from which no direct samples exist. A brief overview of the oxidation state and oxygen fugacity of the lower and upper parts of the Earth’s mantle is provided here; for a more complete review, see McCammon (2005).
The lower mantle
High-pressure experiments indicate that the lower mantle is dominated by (Mg,Fe) (Si,Al)O3 perovskite, with minor ferropericlase (Mg,Fe)O and CaSiO3 perovskite (e.g., Kesson et al. 1998). Recent experimental work on (Mg,Fe2+)SiO3 perovskite has demonstrated that the substitution of Al in the structure has significant effects on the iron oxidation state in perovskite (McCammon 1997). The coupled substitution Mg2+ + Si4+ = Fe3+ + Al3+ is energetically favorable, and causes an increase in the Fe3+ content of perovskite while maintaining charge balance in the structure. The Al content is correlated with Fe0/∑Fe, even at low oxygen fugacity (Lauterbach et al. 2000). Thus, the Al-Fe3+ substitution in Mg perovskite is an example of a crystal-chemical control on the iron oxidation state recorded by a mineral, independent of oxygen fugacity.
The implication of these observations is that the lower mantle has a higher Fe3+ content than previously assumed. Frost et al. (2004) calculate that the Fe3+/∑Fe of the lower mantle is 0.60, on the basis of their experimental results in conjunction with a bulk silicate earth composition in which the lower mantle contains 70 wt% perovskite containing approximately 5 wt% Al2O3. This implies that the lower mantle is enriched in Fe3+ relative to the upper mantle, or that the formation of Al-substituted perovskite is accompanied by a complementary reaction to maintain the same overall oxidation state as the upper mantle. The latter could involve the reduction of volatile (C-H-O) species, or the disproportionation of iron through the reaction:
In experiments on Al-substituted perovskite, reaction (1) is manifested in the presence of discrete blebs of iron metal (Lauterbach et al. 2000; Frost et al. 2004). The volatile budget of the mantle (Wood et al. 1996) is inadequate to account for the amount of reduction required (Frost et al. 2004). Evidence for whole-mantle convection (e.g., van der Hilst et al. 1997) precludes a scenario in which the lower mantle has a higher oxidation state than the upper mantle.
The disproportionation reaction has other implications for the redox evolution of the Earth’s mantle. If the experimental results are representative, they imply that the lower mantle contains metal blebs, which are dispersed throughout the silicate assemblage; the recombination of iron metal and ferric iron would occur as material moves out of the perovskite stability field, resulting in no net change in bulk oxygen content (Frost et al. 2004). In the lower mantle of the early Earth, however, the metal formed by disproportionation may have been transported to the core during core formation, resulting in a net increase in O relative to Fe in the mantle (Wood and Halliday 2005). Assuming whole-mantle convection, this process may explain why the upper mantle is apparently out of equilibrium with an iron-rich core. Furthermore, the formation of iron blebs in the lower mantle would likely have implications for the abundances of siderophile elements in the Earth’s mantle (Frost et al. 2004).
Although ferric iron may be the dominant form of iron in the lower mantle, its bulk abundance does not constrain the oxygen fugacity of the lower mantle. Ultimately, the problem with determining the oxygen fugacity of the lower mantle is the lack of appropriate mineral equilibria. Unlike the upper mantle, the temperature dependency of the lower mantle mineral assemblage is poorly known. At relevant pressures and temperatures, experimental studies show that Ca-perovskite can contain Fe3+, although natural samples are chemically very pure (Harte et al. 1999; Stachel et al. 2000). Ferropericlase is the only phase in the mantle in which Fe3+/∑Fe reflects oxygen fugacity (McCammon et al. 1998; Frost et al. 2001). McCammon et al. (2004) used the composition and Fe3+/∑Fe of ferropericlase in diamond inclusions to estimate an oxygen fugacity for the lower mantle between the IW and Re-ReO2 (e.g., Pownceby and O’Neill 1994) buffers. However, the estimate is largely qualitative and poorly constrained. Other, indirect approaches show promise, such as geophysical measurements of the lower mantle calibrated using experimental results (e.g., Wood and Nell 1991).
The upper mantle
The upper mantle is dominated by olivine, orthopyroxene, clinopyroxene, and spinel or garnet. All of these phases are iron-bearing; mineral equilibria involving them can be used to calculate oxygen fugacity in the spinel (lower pressure) and garnet (higher pressure) facies of the upper mantle. In the spinel facies, at depths less than ~60 km (~2 GPa), the dominant mineral equilibrium is
which is commonly referred to as the spinel peridotite reaction. Calculation of oxygen fugacity in spinel peridotites, as outlined in a later section, shows a range of over 4 orders of magnitude, and a relationship to tectonic environment, metasomatism, and partial melting (e.g., Mattioli et al. 1989; Ballhaus et al. 1990; Bryndzia and Wood 1990; Wood et al. 1990; Ballhaus 1993; Kadik 1997; Parkinson and Arculus 1999; McCammon et al. 2001). Generally, the more reduced samples have oxygen fugacities between 2 log units below the fayalite-magnetite-quartz buffer and the buffer (FMQ − 2 to FMQ), and are derived from suboceanic abyssal peridotites and undepleted, fertile subcontinental mantle xenoliths, whereas the more oxidized samples, up to ~ FMQ + 2, are peridotites that have been influenced by the effects of subduction and metasomatism. Summaries are provided by Wood et al. (1990), Wood (1991), Ballhaus et al. (1990), Ballhaus (1993), Ionov and Wood (1992), Woodland et al. (1992) and Amundsen and Neumann (1992).
The effect of pressure on equilibrium (2) is to drive the reaction to the right, favoring smaller-volume phases and resulting in lower oxygen fugacity. The volume change for the solids in equilibrium (2) is about half that of the solids in the FMQ buffer (8.6 cm3 vs. 17.95 cm3; Wood et al. 1996). Therefore, all else being equal, the oxygen fugacity will decrease by about 0.25 log units per GPa pressure increase relative to the FMQ buffer (Ballhaus 1995; Wood et al. 1996).
At greater depths, garnet becomes stable and the mineral equilibrium that dominates is
Calibration of this equilibrium for calculation of oxygen fugacity is provided by Gudmundsson and Wood (1995). Woodland and Koch (2003) point out that an erroneous expression for skiagite (Fe2+3Fe3+2Si3O12) activity was given by Gudmundsson and Wood (1995), and refer to Woodland and Peltonen (1999) for the correct expression. Application to garnet peridotite xenoliths from the Kaapvaal (Southern Africa) and Slave (Canada) Cratons yields oxygen fugacities of FMQ − 3 or lower, decreasing to below FMQ − 4 at about 6 GPa (Gudmundsson and Wood 1995; Woodland and Koch 2003; McCammon and Kopylova 2004).
The decrease in oxygen fugacity with depth observed in garnet peridotite xenoliths is consistent with thermodynamic arguments, specifically volume effects. The volume change of reaction (3) is greater than that for reaction (2), and increasing pressure favors the incorporation of Fe3+ into garnet. The expected decrease in oxygen fugacity is 0.9 log units/GPa (Wood et al. 1996).
The volume effects on the oxygen fugacity-depth relationships within the garnet and spinel facies are examples of crystal chemical controls on iron oxidation state. The lower oxygen fugacity of the garnet facies relative to the spinel facies is attributable to the effect of the relative modal abundances of Fe3+-bearing mineral phases—whereas the Fe3+ content (and therefore the O content) of the upper mantle is quite low, Fe3+/∑Fe ~ 0.023±0.010 (O’Neill et al. 1993), the relative oxygen fugacity of the spinel facies is quite high (near FMQ) because the Fe3+ is concentrated into spinel, the least abundant phase, and virtually excluded from all other phases. In fact, the oxygen fugacity of the spinel facies would be 4 log units lower if Fe3+ were concentrated equally in all mineral phases (O’Neill et al. 1993). Assuming the same bulk chemistry for the garnet, including Fe3+/∑Fe (O’Neill et al. 1993), the higher modal abundance of garnet at these pressures will dilute the concentration of Fe3+ in the garnet, lowering the activity of the skiagite component and resulting in a lower relative oxygen fugacity. Furthermore, the increase in the modal abundance of garnet with depth contributes to a further decrease in relative oxygen fugacity with increasing pressure (Wood et al. 1990; Ballhaus 1995).
Deeper into the upper mantle, the modal abundances of garnet and clinopyroxene increase at the expense of orthopyroxene. Oxygen fugacity may therefore be controlled by
where FeSiO3 is the clinoferrosilite component in clinopyroxene (McCammon 2005). The breakdown of pyroxene to majorite garnet dilutes the Fe3+ in garnet, further lowering the relative oxygen fugacity (Wood et al. 1996). This may be offset by the difference in volume change in equilibrium (4) relative to equilibrium (3). The decrease in oxygen fugacity relative to FMQ may therefore be muted at these depths (McCammon 2005). Uncertainties in the thermodynamic properties of the components currently prevent an accurate assessment. Oxybarometry of the lower part of the upper mantle is important for mapping the overall redox stratigraphy of the mantle, however, and for addressing specific redox-dependent questions, such as where the oxygen fugacity of the bottom of the upper mantle lies relative to the Ni precipitation curve (e.g., Ballhaus 1995).
Carbon is considered to be another important element in the Earth’s interior that is involved in redox-dependent equilibria. Fluids in the Earth’s mantle are dominated by species involving C, H and O in oxidized (e.g., CO2, H2O) and reduced (e.g., CH4, CO) forms, in equilibrium with C (as graphite in the upper mantle). The fluid species may also be dissolved in a melt. Two such equilibria are
As written, reaction (5) involves the oxidation of methane and reaction (6) the oxidation of C; reaction (6) is often referred to as the CCO buffer. Because these equilibria involve fluids and/or melt and graphite instead of mostly solid phases, the effect of pressure is different than that for equilibria (2), (3) and (4). This is simply due to volume effects—solid phases have smaller volumes than fluid phases. As a result, equilibria (5) and (6) have opposite slopes on plots of oxygen fugacity (relative to FMQ) as a function of increasing pressure. The implication is that mantle material that is buffered by Fe-bearing equilibria will have associated fluids that gradually shift with depth from H2O–CO2 to H2O–CH4, without any change in the activity of the ferric iron components.
Opinions diverge as to the relative importance of Fe-bearing mineral equilibria and C-H-O equilibria in controlling the oxygen fugacity of the upper mantle. Wood et al. (1996) argue that volatile speciation in the upper mantle depends on the oxygen fugacity determined by Fe-bearing mineral equilibria, because the concentration of C (80 ppm) is much less than that of iron (FeO ~ 8 wt%, Fe2O3 ~ 0.2 wt%). Ballhaus (1995) estimates the extent of relative oxidation with depth, taking into account all the factors that would influence this property, including those that would force a decrease, such as: volume effects (−0.3 to −0.4 log units/GPa, mainly for equilibrium (2)); solid solution (−0.1 log units/GPa); and the spinel-to-garnet transition (−1.5 to −2 log units/GPa). However, he further argues that volatile equilibria (C-HO and S) are a moderating influence on the oxygen fugacity-depth gradient, providing enough oxygen for one-third to one-half of the Fe2O3 in the upper mantle. The average gradient would therefore be about −0.6 log units/GPa. Thus, this perspective has volatiles playing a more important role, relative to ferrous-ferric equilibria, in influencing the oxygen fugacity of the upper mantle.
OXYBAROMETERS APPLICABLE TO BASALTIC ROCKS
Basaltic volcanism is a fundamental process on differentiated planetary bodies; samples from the Moon, Mars, and differentiated asteroids (e.g., 4 Vesta) are dominated by basaltic samples. Like other physical and chemical factors involved in its petrogenesis, the oxygen fugacity of a basalt is the result of the complex history of partial melting, extraction, ascension, eruption and emplacement. Basalts can be used as probes of planetary interiors, provided that the effects of post-extraction processes can be adequately assessed. The effort is worthwhile—ultimately, insights into fundamental differences in the origin and evolution of the terrestrial planets can be gained, as exemplified by the comparative studies of the Basaltic Volcanism Study Project (BVSP 1981). The suite of planetary samples has expanded significantly since the completion of the BVSP, resulting in further insights (e.g., Wadhwa 2008).
Igneous petrologists, it often seems, would be happy if magmas never crystallized, and instead quenched to glasses that are representative of the parent magmas from which the physical and chemical factors involved in their petrogeneses can be directly determined. The relationship between redox state and the concentrations of FeO and Fe2O3 in a multicomponent silicate liquid, i.e.,
has been calibrated experimentally over a wide range of oxygen fugacity and bulk composition (Sack et al. 1980; Kilinc et al. 1983; Kress and Carmichael 1988, 1991) and is given by the empirical equation
where a, b, c and di are constants determined by regression of experimental data; details are provided by Carmichael and Ghiorso (1990). Equation (8) allows calculation of oxygen fugacity from determinations of FeO and Fe2O3 in glassy lavas. More importantly, it has been demonstrated that the change in oxygen fugacity with temperature of a silicate liquid is parallel to the change in oxygen fugacity of a solid oxygen buffer such as NNO or FMQ. Otherwise said, the relative oxygen fugacity of a silicate liquid is independent of temperature. The implication is that in the absence of crystallization, determination of the redox state of a magma is straightforward. Furthermore, the redox states of different magmas can be easily compared by calculating the oxygen fugacity relative to a solid oxygen buffer at an arbitrary temperature. This has been done for glassy basic lavas from a range of tectonic environments on the Earth, demonstrating that oxygen fugacity varies more widely than any other variable in petrology, by over 7 orders of magnitude (Carmichael and Ghiorso 1990; Carmichael 1991).
With a couple of rare exceptions, glassy lavas are absent from the planetary sample suite and we must rely on oxybarometers to see through the effects of crystallization. The ultimate goal of an oxybarometer is to employ a redox-sensitive element, or suite of elements, to provide a record of oxygen fugacity at a particular stage in a sample’s petrogenesis. Given that the stage of interest is typically prior to crystallization, in order to assess the redox conditions of the parent magma and infer the nature of its source, a couple of caveats are worth noting.
Oxybarometers are thermodynamic models, and as such, the inherent assumptions outlined by Ghiorso (1997) regarding the application of thermodynamic models to igneous systems are relevant: that the igneous system is in equilibrium everywhere along its evolutionary path; and that the processes being modeled are reversible. The example given by Ghiorso (1997) is one in which a magmatic system evolves from melting in the source region (state A) to final solidification in a shallow reservoir (state B); as noted, there is an infinite number of reversible paths that will take the system from state A to state B. We could equally imagine the evolution of the redox state of a magma where state X is pooling in a shallow magma body, and state Y is 20% crystallization of an assemblage of olivine, pyroxene and chromite phenocrysts. In the application of an oxybarometer, one would do well to remember the following:
“Utilizing thermodynamic models of igneous processes, one cannot ever hope to attain a unique inversion to provide the unique history of magma evolution. That history is lost in the assumption of the applicability of the method.” (Ghiorso 1997)
Instead of trying to uniquely determine the history of a magma, thermodynamic models ought to be used in forward modeling of magmatic evolution in order to assist in discrimination between competing hypotheses (Ghiorso 1997).
Another potential pitfall worth noting is that the oxygen fugacity recorded by an oxybarometer depends on how readily the redox-sensitive elements can be reset by subsequent processes. Using ferrous-ferric iron equilibria as an example, it does not require much oxygen to affect the ferric iron in a system with initial Fe3+/∑Fe = 0.10. The effects of subsolidus re-equilibration are a concern for any oxybarometer, as eloquently summarized by the following poem by Cin-Ty A. Lee (loosely in the haiku style):
Fugacity has no memory
It has no past
Only what it sees last
The memory of an oxybarometer has been compared to those of elephants and goldfish by John Delano: whereas elephants remember paths for yearly migration and the locations of burial grounds, goldfish cannot remember what happened in the previous few seconds such that every trip around the fishbowl is a new one.
Whether a particular oxybarometer is an “elephant” or a “goldfish” will depend equally on the geochemical behavior of the redox-sensitive element involved and on the petrogenesis of the rock to which it is applied. Textural or compositional evidence for equilibrium among mineral phases will bolster application of the oxybarometer, and results need to be assessed in the context of petrologic studies of the sample.
Forward modeling of changes in oxygen fugacity with crystallization are useful in assessing, for example, the effect of crystallization on the redox state of the melt. Ghiorso (1997) models the equilibrium and fractional crystallization of primitive MORB under closed system conditions using the MELTS program (Ghiorso and Sack 1995). In contrast to experiments in which oxygen fugacity is fixed relative to a buffer, MELTS allows modeling of a system in which the total oxygen content of the system (liquid + solids) is constant. The results show the expected trend of increasing ferric iron in the melt resulting in an increase in the relative oxygen fugacity of the melt due to crystallization of Fe2+-bearing olivine and pyroxene; in this example, the increase is a maximum (under equilibrium crystallization) of 0.7 log units. Subsequent crystallization of (Fe3+-bearing) spinel results in a decrease in relative oxygen fugacity of 1 log unit; the total excursion throughout the crystallization history is a maximum of 0.8 log units (Ghiorso 1997). This is consistent with Carmichael and Ghiorso (1990), who argue that in a closed system, the iron redox state of the liquid during crystallization will be regulated such that it may resemble a buffered path; specifically, that the increase in ferric iron in the melt as a result of crystallization of an early, Fe3+-poor phase will stabilize a later, Fe3+-rich phase such as spinel, and an immiscible (Fe-S-O) sulfide liquid, both of which will counteract the increase in relative oxygen fugacity of the melt. In a crystallizing liquid under open-system conditions, any addition or subtraction of oxygen should result (initially) in a change in the proportion of the solids; any change in oxygen fugacity should result in a change in the iron redox ratio in the solids and liquid (Carmichael and Ghiorso 1990).
These insights represent a framework in which oxybarometry results can be interpreted; for example, although Fe-Ti oxides (titanomagnetite and ilmenite) typically appear later in the crystallization of a basalt, the oxygen fugacity that they record may be reflective (i.e., within a log unit) of magmatic redox conditions, if the system was closed with respect to oxygen.
One approach to determination of the redox state of a basaltic sample is to apply an oxybarometer, or multiple oxybarometers, to a range of assemblages in the rock, to determine the fO2-T path of the rock as best as possible. The advantage of this approach is twofold: changes in oxygen fugacity during crystallization can be assessed, resulting in insights into the petrogenesis of the rock (e.g., open- vs. closed-system); and the results from the highest-temperature, presumably near-liquidus assemblages can be more confidently interpreted as representing the redox conditions of the magma.
Several methods (oxybarometers) currently exist to determine oxygen fugacity in basalts, based on ferrous-ferric mineral equilibria, or multivalent trace elements (e.g., Eu, V). The user faces two challenges: choosing the appropriate method; and assessing the relevance of the results within the petrologic context. To assist the reader in determining the best method for his or her particular needs and applying it in an informed manner, a description of each method is provided below, and their respective strengths, assumptions and limitations are outlined.
Oxygen fugacity from mineral equilibria
The Fe-Ti oxide oxybarometer owes its existence to A.F. Buddington, who suggested that the TiO2 content of magnetite was largely a function of temperature, on the basis of over 200 analyses of magnetite compiled from a range of igneous rock types (Buddington et al. 1955; Buddington 1956), and to J. Verhoogen, who demonstrated, on theoretical grounds, that the compositions of Fe-Ti oxides are significantly affected by the partial pressure of oxygen (Verhoogen 1962). Buddington and Lindsley (1964) overcame the lack of experimental data on the compositions of oxides as a function of T and oxygen fugacity, and extrapolated their data to experimentally inaccessible but petrologically important conditions, enabling the first practical application of the oxybarometer, albeit limited to the Fe-Ti binary system (i.e., oxide pairs containing exclusively the Fe and Ti cations). More information on the development of this oxybarometer can be found in Ghiorso and Sack (1991a), Lindsley and Frost (1992), and Lattard et al. (2005).
The strength of the Fe-Ti oxide oxybarometer rests in the nature of the two oxides involved; the cubic oxide in the magnetite (Fe2+Fe3+2O4) - ulvöspinel (Fe2+2TiO4) series and the rhombohedral oxide in the hematite (Fe3+2O3) - ilmenite (Fe2+TiO3) series are each solid solutions of end-members with different oxidation states. As such, the activities of magnetite in the cubic oxide and hematite in the rhombohedral oxide are used as the oxybarometer according to the reaction
Note that this is equivalent to the Magnetite-Hematite (MH) solid oxygen buffer. Exchange of Fe and Ti between the oxide pairs is strongly dependent on temperature and only weakly pressure-dependent. This exchange is expressed in the following equilibrium
The main weakness of this oxybarometer is that Fe and Ti exchange between pairs continues during cooling. As such, the oxides do not retain their high-temperature compositions and are prone to resetting. Furthermore, in many basaltic rocks, they are among the last phases to crystallize. Thus, the oxides may record temperatures and oxygen fugacities that differ from those of the original magma. Fortunately, subsolidus equilibration between the oxides behaves in a somewhat predictable manner, and may be accounted for in many cases, as outlined by Lindsley and Frost (1992).
Currently there exist two commonly-used formulations of the Fe-Ti oxide oxybarometer. Ghiorso and Sack (1991a) noted that the application of Buddington and Lindsley’s formulation to multicomponent oxides required algorithms to project the compositions found in nature into the relevant binary systems. Citing a need for a more robust thermodynamic treatment of the Fe-Ti oxides that includes the main substituting cations, Ghiorso and Sack (1991a) presented a thermodynamic model that accounts simultaneously for all of the complex peculiarities of the Fe-Ti oxides (i.e., phase equilibrium constraints, cation order-disorder, and mixing and end-member properties), while minimizing projection schemes. This is the strength of the formulation, because proportions of some substituting cations, such as Al and Cr in cubic oxides, can be significant. The formulation is available as a software package from the MSA website (Supplemental Material at http://www.minsocam.org), and is simple to use, requiring standard wt %-oxide compositional data for the two oxides. A new version of the oxybarometer, which is much improved for conditions of fO2 = NNO to NNO + 3 and T = 700 to 900 °C is expected in 2008 (Ghiorso, pers.comm.).
The formulation is based on the quinary model for cubic oxides, using solution theory adopted from Sack and Ghiorso (1991a, 1991b) for cubic oxides in the system (Mg,Fe2+)(Al,Cr,Fe3+)2O4 – (Mg,Fe2+)2TiO4. Minor elements, specifically V, Mn, Ca, Zn and Ni, are included in the formulation; however, their inclusion is based on several assumptions. For example Mn, Zn and Ni are modeled as MnAl2O4, ZnAl2O4 and NiAl2O4 components, respectively, and are proxied by an equivalent amount of FeAl2O4. Non-zero concentrations of V2O3, MnO, CaO and ZnO are not rigorously accounted for in the calculation of equilibration temperatures; the authors note that the concentrations of these components in their sample dataset are less than 0.5 wt%, with the exception of MnO (up to 2.8 wt%). Therefore the user should be wary of using this oxybarometer when the concentrations of these components exceed the concentrations used in the oxybarometer formulation. The energetics of rhombohedral oxides are modeled in the quaternary system Fe2O3 – FeTiO3 – MgTiO3 – MnTiO3. Minor elements include Al, V, Cr, Ca, Zn and Ni. Non-zero concentrations of Al2O3, V2O3, Cr2O3, CaO and ZnO are not rigorously accounted for, but Al2O3 and V2O3 are proxied as hematite, and the concentrations of each of these components in the authors’ dataset is less than 0.2 wt%. Once again, the utility of the oxybarometer may be limited if the concentrations of these components exceed those used in the formulation. Since the calibration of the model does not account for the energetics of magnetic ordering in either oxide, it cannot be used for assemblages that equilibrated below 600 °C. Non-stoichiometry effects, which would be most significant above 1100 °C and at oxygen fugacity near the limits of cubic oxide stability, are excluded from the model; caution should be used in applying the formulation to assemblages suspected of equilibration under such conditions.
The Buddington and Lindsley work enabled the estimation of oxygen fugacity in various oxide-bearing igneous rocks. Consequently, it was recognized that the oxygen fugacity was not only reflected in the compositions of Fe-Ti oxides, but also in the compositions of coexisting ferromagnesian silicates (Frost et al. 1988) and that much of the common subsolidus re-equilibration of the Fe-Ti oxides could be circumvented through the use of equilibria such as
commonly referred to as QUIlF (Frost et al. 1998).
Lindsley and Frost (1992) and Andersen et al. (1993) presented an updated thermodynamic model for the Mg- and Ca-bearing system, referred to as Ca-QUIlF. This formulation includes equilibria between augite, pigeonite, orthopyroxene, olivine and quartz in addition to the Fe-Ti oxides. The main advantage of this formulation is that it can reduce the uncertainty in using the Fe-Ti oxide oxybarometer alone. For example, the four-component subsystem FeO-MgO-Fe2O3-TiO2, with two phases (the Fe-Ti oxides) has a formal variance of four, but because the partitioning of Fe and Ti are coupled, and the effect of Mg on temperature and oxygen fugacity is minor, two intensive parameters (T and fO2) are tightly constrained. Furthermore, the equilibria can be used to assess equilibrium among phases. For example, if the temperature calculated from Fe-Ti oxides is consistent with a temperature calculated from the same oxides with co-existing olivine and pyroxene, then it supports equilibrium amongst all of these phases. By the same token, the model can be used to “see through” subsolidus re-equilibration of oxides, including oxyexsolution of the cubic oxide (i.e., titanomagnetite). For example, if pyroxene temperatures and oxide temperatures do not agree (assuming these phases were initially in equilibrium) then the original oxygen fugacity can be estimated, given the relative abundances of the oxides and assuming a closed system during cooling. In fact, the rhombohedral oxide is expected to gain FeTiO3 and the cubic oxide is expected to gain Fe3O4 upon equilibrium cooling in a closed system (Lindsley and Frost 1992). Thus, magmatic (or at least super-solidus) oxygen fugacity estimates can be made, even when the Fe-Ti oxides have undergone re-equilibration.
Ca-QUIlF is available as a software package (QUIlF95) from the MSA website (Supplemental Material at http://www.minsocam.org). Mineral compositions must be expressed in terms of mole fractions of end-members (e.g., XHematite, XFayalite, XWollastonite) with the exception of the cubic oxide phase, for which the user must calculate the numbers of Ti, Mg and Mn cations per formula unit (NTi, NMg, NMn; cations per four oxygen). The program can be used to calculate temperature, pressure, oxygen fugacity, equilibrium mineral compositions, and activities of SiO2, Fe and TiO2.
As in the previous case, some limitations are useful to note. The calibration of the oxide models was done below FMQ + 2, and therefore may not be applicable to highly oxidized assemblages. With regard to cubic oxide compositions, Fe, Ti and Mg are the only cations accounted for, and the assumptions of the model provide for only two independent compositional parameters, NTi and NMg. Therefore the model is not appropriate for cubic oxides with significant Al2O3 and Cr2O3 contents. The formulation assumes that silicates have negligible Fe2O3 and TiO2 contents and that CaO is unimportant in the oxides; therefore, caution should be used where, for example, pyroxene contains significant TiO2. Lastly, the model cannot be used quantitatively for MgFe3+2O4-rich cubic oxides because of the limits of the solution models and because such oxides will tend to be nonstoichiometric; as with the Ghiorso-Sack model, nonstoichiometry is not included in the model.
The reader is referred to Ghiorso and Sack (1991a,b), for comparisons of the Ghiorso-Sack formulation with Ca-QUIlF. It should be noted that the Ghiorso-Sack model uses thermodynamic data that are internally consistent with olivine and orthopyroxene solution theory from Sack and Ghiorso (1989) as well as the fayalite, ferrosilite, O2 (gas), and quartz data after Berman (1988); these data could be assembled in a separate formulation of QUIlF. The most obvious difference between the Ca-QUIlF and Ghiorso-Sack formulations of the Fe-Ti oxide oxybarometer is the treatment of minor substituting cations, especially in the cubic oxides. In cases where the concentrations of minor cations are low, the two models agree well (e.g., Herd et al. 2001).
Citing the lack of experimental calibration of the Fe-Ti oxide oxybarometer at high temperatures and over a wide range of oxygen fugacity, Lattard et al. (2005) carried out a series of experiments in the Fe-Ti-O system at temperatures of 1000 to 1300 °C and oxygen fugacity ranging from NNO − 5 to NNO + 5 (~IW to FMQ + 6). The results should lead to an improved thermodynamic model for rhombohedral oxide, thereby reducing the discrepancies between experimental results and those calculated using either the Ca-QUIlF or Ghiorso-Sack models, as well as enabling more accurate calculation of oxygen fugacity, especially under oxidizing conditions (> FMQ + 2). The data of Lattard et al. (2005) also include compositions of ilmenite and pseudobrookite ((Fe3+,Fe2+)2(Ti,Fe3+)O5), which is an additional oxybarometer applicable to some terrestrial and lunar igneous rocks.
In deciding which oxybarometer to apply, the user should exercise caution in applying a particular formulation to oxide compositions that deviate significantly from the Fe-Ti end-members upon which the thermodynamic model is based. The best application of any formulation is informed by detailed petrography and an assessment of the degree of equilibrium.
The olivine-pyroxene-spinel oxybarometer, also referred to as the spinel peridotite oxybarometer, was developed for application to mantle xenoliths from the spinel facies. It is governed by equilibrium (2), repeated here:
This equilibrium has also been referred to as the fayalite-ferrosilite-magnetite (FFM) buffer (e.g., King et al. 2000). Oxygen fugacity is calculated using
involving the activities (a) of the respective iron end-members.
In principle, this equilibrium is applicable to low-pressure assemblages in basaltic samples, assuming equilibrium between olivine, spinel, and low-Ca pyroxene. Spinel in this case is typically chromian spinel. Because the mineral phases in Equation (2) are near the liquidi of many basaltic rocks, the results from this oxybarometer are presumably good indicators of magmatic temperatures and oxygen fugacities. Subsolidus re-equilibration is limited to Fe-Mg exchange. The involvement of three phases requires determination of whether all three are cogenetic and remained in equilibrium. Detailed petrography can assist in overcoming this obstacle.
An overview of the development of the olivine-pyroxene-spinel oxybarometer is given by Wood (1991), where he presents the equation for oxygen fugacity relative to the FMQ buffer, as originally derived by Wood (1990):
where T is the temperature in K and P is the pressure in bars. Each part of this equation can be understood in terms of Equation (2a). The activity of Fe2SiO4 in olivine is modeled assuming random mixing over the two cation sites, and is represented by the term, “−12 log XolFe − (2620/T)(XolMg)2”, in which XolFe and XolMg represent the mole fractions of fayalite and forsterite end-members, respectively, in olivine. The activity of FeSiO3 in orthopyroxene is treated as an ideal two-site solution, represented by the term, “3 log (XM1Fe ·XM2Fe)opx”, in which XM1Fe and XM2Fe represent the atomic fractions of Fe on M1 and M2, respectively. These are calculated as described by Wood (1990): “Al was added to Si to fix tetrahedral occupancy at 2.0 per 6 oxygens. The remaining Al (VI), Cr and Ti were placed in M1, while Ca and Mn were placed in M2. Fe and Mg were then evenly distributed between M1 and M2 positions and atomic fraction of Fe on M1 (XM1Fe) and M2 calculated.” The last term involves the activity of the magnetite component in spinel (aspFe3O4); markedly, no expression is incorporated into the equation. The largest uncertainty in determining oxygen fugacity with this method derives from the uncertainty in aspFe3O4. For this reason there exist several equations for calculating aspFe3O4, outlined below.
The remaining terms in Equation (12) refiect the FMQ buffer to which the results of the calculation are related. The term, “log fO2 (FMQ)P,T” is the oxygen fugacity of the FMQ buffer at the P and T of interest. Numerous formulations of the FMQ buffer exist (Table 1⇑); therefore, it is especially important to note that the Myers and Eugster (1983) formulation was used in the derivation of Equation (12), which is:
The term, “220/T + 0.35 − 0.0369P/T” represents the pressure and temperature dependency of the difference between the FMQ buffer (Eqn. 13; Myers and Eugster 1983) and “FFM” (Eqn. 2), after Mattioli and Wood (1988; their Eqn. 32). The derivation of the pressure term in Equation (12) is not explicit in Wood (1990) or Wood (1991). Significantly, oxygen fugacity calculated using Equation (12) is de facto relative to the FMQ buffer of Myers and Eugster (1983). Absolute log (fO2) can be calculated by also calculating log fO2 (FMQ) according to Equation (13).
Temperature and pressure are required for the calculation. Pressures for planetary basalts are typically close to atmospheric (~1 bar). Temperature can be calculated using any of several formulations of the chromite-spinel geothermometer (e.g., Fabries 1979; Sack and Ghiorso 1991a).
Wood (1991) estimates that oxygen fugacity can be calculated to within ± 0.5 log units using the olivine-pyroxene-spinel oxybarometer, assuming good analyses of all three phases are available. The largest contributor to the uncertainty is in the determination of aspFe3O4. Mattioli and Wood (1988) determined aspFe3O4 across the MgAl2O4-Fe3O4 join, between 900 and 1000 °C at 1 atm (1 bar) pressure. They did not, however, account for the effects of the chromite (FeCr2O4) component. Insights into order-disorder in spinel from models and electrochemical measurements by O’Neill and Wall (1987) and Nell and Wood (1991) provided updates of the model to account for Cr. The Nell-Wood equation for aspFe3O4 (see also Wood 1991) is applicable to XFe3O4 = 0.008 to 0.06 and T = 800 to 1400 °C.
The quinary model for cubic oxides of Sack and Ghiorso (1991a,b) provides an alternative method of calculating aspFe3O4. This is accessible using the MELTS Supplemental Calculator (http://melts.ofm-research.org/CalcForms/index.html), and requires that the user first calculate mole fractions of chromite, hercynite, magnetite, spinel and ulvöspinel, which are then used to calculate thermodynamic properties at a chosen T and P. The Sack and Ghiorso (1991a,b) models are applicable to a range of spinel compositions, which is more desirable when using the olivine-pyroxene-spinel oxybarometer for the compositions typical of basaltic rocks.
Ballhaus et al. (1991) provide an empirical calibration of the O’Neill and Wall (1987) olivine-pyroxene-spinel oxybarometer, using synthetic spinel harzburgite and lherzolite assemblages between 1040 and 1300 °C and 0.3 to 2.7 GPa. The advantage of the formulation is that it obviates the need for an explicit calculation of the activity of the magnetite component in spinel. However, the formulation is simplified by canceling orthopyroxene against the ideal part of the fayalite activity in olivine. This simplification cannot be expected to be valid at XFeol > 0.15. As such, its application is limited to Mg-rich upper mantle-derived rocks.
Wood (1990) ran experiments equilibrating olivine, orthopyroxene and spinel at known oxygen fugacity (between FMQ and FMQ − 2) and temperature (1188 to 1205 °C), in order to test the Mattioli-Wood, O’Neill-Wall and Nell-Wood expressions for aspFe3O4 in the calculation of fO2 using Equation (12). He demonstrated that the Mattioli-Wood model was slightly dependent on Cr content, and that the Nell-Wood version more accurately reproduced the known fO2 compared to the O’Neill-Wall version. For comparison, the calculation was reproduced for this work by using the MELTS calculator for magnetite activity. It more closely reproduced the known fO2 than did the Nell-Wood version, as shown in Figure 1a⇓. Whereas the Nell-Wood version underestimated the fO2 by 0.3 log units, the present calculation underestimates fO2 by only 0.07 log units, on average. The calculation was repeated using the Ballhaus et al. (1991) formulation (Fig. 1b⇓); this model underestimates fO2 by an average of 0.45 log units.
Therefore, the use of the MELTS Supplemental Calculator to calculate the activity of magnetite in spinel, in combination with Equation (12), is as good as other formulations for spinel peridotite compositions. The diversity of solid solutions used in the MELTS Supplemental Calculator allows for wider applicability. As an example, this method has been applied to olivine-phyric martian basalts (Herd et al. 2002; Goodrich et al. 2003; Herd 2003, 2006). In many cases, the results agree with other oxybarometers applied to the same rock (e.g., Goodrich et al. 2003; Herd 2006).
The olivine-pyroxene-spinel oxybarometer has seen little use for low-pressure assemblages in terrestrial basaltic samples. Ballhaus et al. (1991) used their model to calculate fO2 for mid-ocean ridge basalts (MORB), island arc basalts (IAB) and ocean island basalts (OIB), but due to the inherent assumptions, the model is limited to mantle-derived primitive melts, and is not appropriate for more evolved basalts. The Wood – MELTS version of the oxybarometer is readily applicable to olivine-phyric terrestrial basalts.
O’Neill and Wall (1987) used a slightly different approach to calculation of oxygen fugacity from olivine, pyroxene and spinel in mantle assemblages. Instead of “FFM”, they used FMQ, i.e.,
Oxygen fugacity is then given by
The activity of SiO2 is calculated based on the equilibrium
and given by
This method has not been tested for use with basaltic samples from planetary surfaces, although it is potentially applicable, with use of the MELTS Supplemental Calculator (or some other method) to calculate the activities of fayalite, forsterite, magnetite and enstatite.
Multivalent trace elements
The previous oxybarometers are based on the equilibria between iron-bearing minerals in planetary basalts. In essence, they depend on the partitioning of ferrous and ferric iron among phases. Similarly, there exist a number of other multivalent elements whose valence states can be used to determine oxygen fugacity. Those that have a range of valence states under the redox conditions of planetary basalts include some of the transition elements (Ti, V, and Cr) and Eu, a particularly useful rare earth element (REE). The main difference between these elements and iron is that they are present in trace concentrations in major minerals. Their concentrations are such that they can be analyzed by in situ microbeam methods, including Electron Microprobe (EMP) and Secondary Ion Mass Spectrometry (SIMS). Determining their valence states, however, is a challenge, and methods have been developed, or are presently in development, to overcome this hurdle.
The multivalent trace elements of interest for planetary basalts include Eu2+,3+, V2+, 3+, 4+, 5+, Cr2+, 3+, and Ti3+, 4+. These are shown schematically (along with iron) in Figure 2⇓, after Papike et al. (2005). This diagram shows the range of valence states of the multivalent trace elements, for comparison with the range of fO2 of planetary basalts. Each point represents the oxygen fugacity at which the oxidized and reduced species are present in approximately equal proportions in a basaltic melt. The diagram is a useful “roadmap” for selecting appropriate oxybarometers—it is readily seen that mineral equilibria oxybarometers involving Fe2+ and Fe3+ are most applicable to the range of fO2 experienced by terrestrial and martian basalts. Of these elements, only vanadium exists in 4 valence states, covering the range of redox conditions of planetary basalts. For this reason, much recent effort has focused on the development of vanadium oxybarometers.
Oxygen fugacity from multivalent trace elements
Europium is the only REE whose geochemical behavior is significantly different from the rest of the REE in planetary magmas, due to its stability as Eu2+ or Eu3+ at fO2 ≤ FMQ. The “Eu anomaly” that is often observed in chondrite-normalized REE patterns in minerals and bulk rocks is due to this effect, coupled with crystal chemistry. The valence state of Eu in a silicate melt is related to oxygen fugacity by
which is analogous to the relationship between ferrous and ferric iron and fO2. However, europium’s status as a trace element requires a different approach to for determination of the relationship of Eu behavior to oxygen fugacity, which involves the partitioning of Eu between minerals or between mineral and melt.
Equilibrium (18) can be rearranged to solve for oxygen fugacity as
which demonstrates that at constant T and P, the ratio of the activities of Eu2+ and Eu3+ is a function of oxygen fugacity. As soon as minerals become involved, crystal chemical effects, especially crystal/liquid partitioning, must be taken into account. Thus, it is expected that the Eu3+/Eu2+ ratio in a given mineral will be a function of the composition of the melt, the crystal chemistry of the mineral, and the oxygen fugacity at the time of crystallization.
Recognizing the potential of Eu as an oxybarometer, J. A. Philpotts developed a method for calculating Eu2+ and Eu3+ concentrations in igneous phases (Philpotts 1970). His formulation addresses the fact that Eu2+ and Eu3+ cannot be directly measured. Instead, it uses partition coefficients, i.e.,
where EuX+y is the concentration of Eu of some valence X in phase y. In each phase, the concentration of Eu can be expressed as
Assuming two phases in equilibrium, for example, where α is the matrix (as a proxy for the melt) and β is a plagioclase phenocryst, Equations (20), (21a) and (21b) can be combined to solve for the concentration of one of the valence states of Eu in the matrix (α), i.e.,
with the concentration of Eu2+ in the matrix determined by
The same could be repeated if other phenocrysts are in equilibrium with the matrix, to check for internal consistency (Philpotts 1970). Note that, in order to apply Equation (22a), the concentrations of Eu in the matrix and phenocryst (Euα and Euβ, respectively), and the partition coefficients for Eu2+ and Eu3+ for the phenocryst mineral must be known. Philpotts (1970) used analyses determined by mineral separation and stable isotope dilution mass spectrometry for the former (e.g., Schnetzler and Philpotts 1970); today, in situ microbeam techniques (e.g., SIMS, LA-ICPMS) would be used. The partition coefficients were estimated by Philpotts (1970), with DSr2+β/α used as a proxy for DEu2+β/α, and DEu3+β/α interpolated from a plot of DREE3+ β/α for the same phases. Since that time, experimental studies have addressed the partitioning of Eu in different phases under different redox conditions (e.g., Grutzeck et al. 1974; Sun et al. 1974; Drake 1975; Weill and McKay 1975; McCanta et al. 2004), and parameterized it using DEu/DGd or DEu/DSm, as described below.
Philpotts (1970) applied Equations (22a) and (22b) to a suite of terrestrial and lunar samples, and to the eucrite meteorites Moore County and Juvinas (thought to be from the differentiated asteroid 4 Vesta; Drake 1979). He employed the Eu2+/Eu3+ ratios of the sample matrices to calculate oxygen fugacity according to Equation (19). In spite of certain variations in temperature, pressure and bulk composition among the samples, he determined that lunar basalt crystallized under redox conditions 4 to 5 log units below that of terrestrial basalts, and that the Juvinas eucrite oxygen fugacity is an additional 2 or 3 log units more reduced than lunar basalts. Drake (1975) applied his experimental Eu partitioning data for plagioclase to the Philpotts (1970) Eu2+/Eu3+ ratios and obtained fO2 results consistent with those of Philpotts (1970). These results are broadly consistent with observations of lunar basalts, which are essentially at metal saturation; however, similarities in mineral compositions and experimental petrology results for lunar and eucrite basalts suggest virtually identical oxygen fugacities (e.g., Kesson and Lindsley 1976; Stolper 1977; Longhi 1992). Regardless, subsequent studies of planetary basalts (e.g., BVSP 1981; Wadhwa 2008) have corroborated this range of oxygen fugacity among the terrestrial planets.
The approach of McKay (1989) and McKay et al. (1994) is worth highlighting, since it uses the Eu oxybarometer to constrain the oxygen fugacity of a planetary basalt, specifically the LEW 86010 angrite meteorite, to within one log unit. Using appropriate experimental partitioning data for Eu among Al-, Ti-rich (fassaitic) pyroxene, anorthite and melt at 1175 to 1210 °C and atmospheric pressure, McKay (1989) determined the relationship between DEu/DGd and oxygen fugacity for plagioclase and pyroxene. At high oxygen fugacity (~ FMQ), Eu3+ is the dominant species and, having a smaller ionic radius ([VI]Eu3+ radius = 1.09 Å; Shannon 1976) than the divalent cation ([VI]Eu2+ radius = 1.31 Å; Shannon, 1976), it is more readily incorporated into the pyroxene M sites. Presumably the substitution of Eu3+ occurs via a coupled substitution with Na+ in the M2 site or Al3+ in the tetrahedral (T) site. At low fO2 (~ IW), Eu2+ is favored in the large feldspar site, as a substitution for Ca2+ or Na+ ([VIII]Eu2+ radius = 1.39 Å; [VIII]Eu3+ radius = 1.21 Å; Shannon 1976).
The predicted relationship of DEu as a function of fO2 is an S-shaped curve that asymptotically approaches the values of DEu2+ at low fO2 and DEu3+ at high fO2. The observations follow the predicted relationship between DEu and fO2 on the basis of theory, as outlined by McKay et al. (1994). The advantage of the application of Eu in pyroxene and plagioclase for planetary basalts is that the greatest variation in DEu in each of these phases occurs over the range of fO2 between IW-2 and FMQ, which covers the majority of the range of oxygen fugacity of planetary basalts. The contrasting behavior of DEupl and DEupx, with the former increasing and the latter decreasing with fO2, provides an additional advantage: assuming that the concentrations of Eu and Gd in pyroxene and plagioclase are known, the two phases are in equilibrium, and the experimental phase compositions and temperatures are similar to those of the rock, then the two curves can be combined to give a calibration curve for the Eu oxybarometer. This is done by determining the ratio of (DEupl/DGdpl)/(DEupx/DGdpx); because these are mineral-melt partition coefficients, the melt concentrations cancel out, and only the Eu and Gd concentrations in the two phases are required. Thus, a plot of log (Eu/Gd)pl/(Eu/Gd)px vs. log fO2 will yield a linear relationship from which oxygen fugacity can be calculated (McKay et al. 1994). In the application of McKay et al. (1994), the Eu oxybarometer was used to determine that the LEW 86010 meteorite crystallized at an oxygen fugacity between IW and IW + 1.
The primary advantage of the Eu oxybarometer is that the REE are relatively immobile elements (e.g., Van Orman et al. 2001) that are taken up by igneous phases and are present in concentrations that are measurable by available in situ methods. Thus, the magmatic Eu/Gd (or Eu/Sm) ratio is likely to be preserved through subsolidus re-equilibration; assuming an appropriate calibration, the magmatic oxygen fugacity can be determined. As with other oxybarometers, the user should be aware of potential pitfalls. Ideally, the Eu oxybarometer is applied to samples in which pyroxene and plagioclase are in equilibrium on the liquidus. In reality, this does not often occur. The crystal chemistry of the REE in pyroxene and plagioclase is such that compositional effects on Eu partitioning may be significant. For example, the SiO2/Al2O3 activity ratio in the melt may influence Eu partitioning in plagioclase (Morris and Haskin 1974; Drake 1975). Likewise, the uptake of Eu3+ into pyroxene M sites requires a coupled substitution, and so is presumably influenced by the content of univalent cations (especially Na+); hence the need for calibration curves using appropriate melt compositions.
Recently, a variation on the Eu oxybarometer has been developed for martian meteorites involving Eu in pyroxene (Wadhwa 2001; Musselwhite and Jones 2003; McCanta et al. 2004). Pyroxene, especially low-Ca pyroxene, is a liquidus phase in these basalts, with plagioclase crystallizing later. This work has provided an important means of estimating the magmatic oxygen fugacity in martian basalts (Wadhwa 2008). The fractionation of Eu into pyroxene becomes small at higher oxygen fugacity, however, where Eu3+ becomes dominant, resulting in greater uncertainty, up to ± 1 log unit at FMQ (McCanta et al. 2004). Therefore, this version of the oxybarometer has the greatest resolution at lower oxygen fugacity (< IW + 1).
As shown in Figure 2⇑, vanadium exists in four valence states. In theory, if the relative proportions of V species can be calibrated for oxygen fugacity, then it would provide an oxybarometer appropriate for all planetary basalts. This step has been accomplished for V in glass by Sutton et al. (2005) using vanadium K-edge X-ray Absorption Near-Edge Structure (XANES) spectroscopy, done with synchrotron light at the Advanced Photon Source (APS), Argonne National Laboratory in Argonne, IL. Vanadium K edge XANES spectra have a pronounced pre-edge feature whose intensity and energy increase systematically with valence state. Sutton et al. (2005) used a suite of synthetic basalt (forsterite-anorthite-silica and forsterite-anorthite-diopside) glasses in which vanadium valence state had been determined by titration. They then determined the relationship between the pre-edge peak intensity, I, and the effective vanadium valence, V*,
where V* is given by
and f is the fractional content of each species. It is assumed that V2+ has zero pre-edge peak intensity. Equation (23) was used to determine V* for 5 other suites of synthetic glasses; observations were consistent with predictions of the dominant species at different oxygen fugacity. The effects of temperature and melt structure are accounted for, but introduce little additional uncertainty (± 0.2 and 0.5 log units, respectively). A calibration curve of vanadium pre-edge peak intensity vs. log fO2 was constructed from the data from all synthetic glasses. Due to uncertainties at very low fO2, and the dominance of V5+ at the highest fO2 (and a concomitant reduction in resolution) the oxybarometer can be effectively used for glasses between IW − 2 to IW + 6 (corrected to a temperature of 1400 °C); a range that is unparalleled in oxybarometry.
Application of the V XANES oxybarometer to natural glasses from the Earth, Moon and Mars yields results that are broadly consistent with previous studies, over a range from IW − 2 (lunar) to IW + 4 (terrestrial) with an uncertainty of ± 0.2 log units (Karner et al. 2006). The method is non-destructive and can be used on traditional polished thin sections at micron-scale resolution; furthermore, it is sensitive to V concentrations at the ~100 ppm level (Sutton et al. 2005). The main disadvantage is the lack of preserved glasses in natural basaltic samples. For this reason, the application of K edge XANES spectrometry to V in minerals is under development. This application faces the dual challenges of orientation effects and crystal chemical controls on V species partitioning.
Papike et al. (2005) developed a semi-quantitative oxybarometer for V in chromite. The basis of this oxybarometer is the crystal chemistry of spinel, which has an affinity for V3+ over V4+. Canil (2002) recognized the dependence of DVsp on oxygen fugacity, noting that DVsp in high Cr/Al spinels (chromite) decreases by about an order of magnitude (from 32 to 5) between IW − 1 and IW + 4. Papike et al. (2005) note that V behaves differently in spinel from different planetary basalts, as evidenced by core-to-rim traverses across grains using the EMP. As illustrated in Figure 2⇑, V4+ dominates under terrestrial redox conditions, V3+ dominates under lunar redox conditions, and martian basalts have subequal proportions of both. This is reflected in the core-to-rim patterns in spinel, which show compositional zonation from chromite cores to ulvöspinel rims: in lunar basalts, V as predominantly V3+ follows Cr (as Cr3+), decreasing from core to rim; in terrestrial basalts, V as predominantly V4+ follows Ti (as Ti4+), increasing from core to rim; in martian basalts, the trends vary, consistent with differences in oxygen fugacity between different samples (Papike et al. 2005).
A comparison of the V contents of chromite cores among planetary basalts also reflects differences in oxygen fugacity; a plot of 100V/(Cr+Al) atomic with distance in chromite cores from lunar, martian and terrestrial basalts qualitatively differentiates the ranges of oxygen fugacity for the Moon, Mars and Earth (Papike et al. 2005). The method can be made quantitative if the V content of the parental melt is known, assuming equilibrium between the melt and chromite cores, by calculating oxygen fugacity from the relationship of DVsp to fO2 of Canil (2002),
Where d, b and c are fit parameters dependent on melt composition and temperature. Papike et al. (2005) use the fit parameters for komatiite from Canil (1999), which are d = 32.8, b = 0.41, and c = 0.77. Other fit parameters for different compositions, including spinel with low Cr/Al, are provided in the Background Data Set that accompanies Canil (2002), http://www.elsevier.com/locate/epsl. In the absence of parental melt data, Papike et al. (2005) used whole-rock V concentrations to approximate the V contents of parental melts, and obtained results that are broadly consistent with those of other studies.
As it currently stands, application of the V-in-chromite oxybarometer is limited to fO2’s between IW − 1 and IW + 4, which is the range over which DVsp for chromite has been determined (Canil 2002). In addition, V4+ becomes dominant at ~ FMQ (IW + 3.5), and the oxybarometer loses resolution due to the limits of the crystal chemistry of spinel. The relationship of DVsp to fO2 is dependent on melt composition, P and T, and the user should take care to choose appropriate fit parameters. Furthermore, application of the oxybarometer to spinels in which Cr and Al vary significantly, or to ulvöspinel-rich compositions, could yield spurious results. Regardless, this oxybarometer relies only on EMP data, and so is widely accessible.
Perhaps the most powerful use of vanadium to determine oxygen fugacity relies on its geochemical behavior in combination with its existence in multiple valence states. The V/Sc ratio in terrestrial basalts and mantle xenoliths has been used to infer the oxygen fugacity of the primary magma or mantle source (Lee et al. 2003, 2005; Li and Lee 2004). Vanadium and scandium behave so similarly in magmatic systems that the V/Sc ratio will remain largely unaffected by olivine fractionation, cryptic metasomatism, crustal contamination, or degassing (Canil 2004; Lee et al. 2005). Oxygen fugacity will have the most significant effect on V/Sc; whereas V has variable valence, Sc exists only as Sc3+. Therefore, the V/Sc ratio will “see through” post-extraction processes and reflect the oxygen fugacity of magmagenesis.
Lee et al. (2005) implemented the V/Sc oxybarometer by modeling the dependence of V/Sc on oxygen fugacity, under assumptions of isothermal (1410 °C) and isobaric (1.5 GPa) partial melting within the spinel stability field, and a fertile convecting mantle with a constant V/Sc ratio. Analyses of whole-rock V and Sc concentrations are all that are required; these values are compared to the modeled values to determine the primary oxygen fugacity. The results of Lee et al. (2005) have significant implications for the question of whether basalt oxygen fugacity reflects that of its mantle source.
THE BASALT-MANTLE SOURCE REDOX RELATIONSHIP
Is basalt oxygen fugacity reflective of the redox state of its mantle source?
Whether the oxygen fugacity of a planetary basalt reflects the redox state of the mantle source from which it was derived is of fundamental importance in determining the redox states and histories of planetary interiors. In the absence of mantle samples from the other terrestrial planets, insights into the basalt-mantle source relationship can be gained from attempts to explain the diversity of basalt oxygen fugacity on the Earth.
The relationship between oxygen fugacity and FeO and Fe2O3 in silicate liquids (Eqn. 8) is extended by Kress and Carmichael (1991) to quantify the effect of pressure. The Fe3+/∑Fe ratio of a melt closed to oxygen during its ascent will change such that the oxygen fugacity will be broadly parallel to FMQ; i.e., the relative oxygen fugacity is nearly independent of pressure. Pressure affects the solid oxygen buffers differently, with the FMQ buffer changing by −0.17 log units/GPa and the NNO buffer by −0.51 log units/GPa (Kress and Carmichael 1991). The implication is that a silicate liquid that is closed to oxygen during ascent will retain a record of its oxygen fugacity relative to FMQ to within a fraction of a log unit; therefore, glassy lavas can be used as probes of planetary interior redox state. Given that there is a 7-log unit range in oxygen fugacity in basic lavas on the Earth, it follows that there must exist mantle sources with an equivalent range of oxygen fugacity (Carmichael 1991).
Other workers hold a different view, in which the C-H-O volatile species play a more significant role in buffering basalt mantle sources, or ascending magmas, and in determining the oxygen fugacity of the erupted basalt (Mathez 1984; Blundy et al. 1991; Ballhaus and Frost 1994). In the Ballhaus and Frost (1994) model, the range of oxygen fugacity of basalts is explained by variation in mantle source redox state combined with pressure effects, and the redox states of mantle sources are constrained to a much narrower range than proposed by Carmichael (1991). Ballhaus and Frost (1994) envision decompression melting, along an adiabatic ascent path, and assume that the melt remains in major element equilibrium with the crystalline phases of the mantle material until fairly low pressure. They choose an arbitrary initial oxygen fugacity of FMQ − 4 at a depth of 4 – 5 GPa; at these conditions, the system is buffered by ferrous-ferric equilibria. Although this is within graphite-water-methane stability, the oxygen fugacity, and hence CO2 activity, are too low to be controlled by C-H-O equilibria. Given that the relative change in oxygen fugacity with increasing pressure is approximately −0.6 log units/GPa (Ballhaus 1995), upwelling asthenosphere will experience oxidation (relative to FMQ, for example) with decreasing pressure. This results in oxidation of graphite, an increase in the activity of CO2, and a shift in buffering from ferrous-ferric to C-H-O; that is, buffering by the presence of graphite and the activity of CO2. At some point, the adiabatic ascent path intersects the dry solidus of the asthenosphere, causing a rapid advance in the degree of partial melting. Eventually, the melt reaches a critical pressure and oxygen fugacity interval where the solubility of carbon in the melt as CO2 exceeds the amount of elemental carbon present in the residue; graphite is eliminated as a phase, and the buffering switches to ferrous-ferric equilibria, with an increase in relative oxygen fugacity with further decompression. Mathez (1984) outlines a model in which degassing of C-rich vapor species play a significant role in buffering fO2. An example is provided in which a C-supersaturated, reduced magma degasses in a shallow magma chamber (depths of < 0.3 GPa), exsolving a CO-rich gas and liberating O2, which oxidizes iron in the melt according to equation (7). Assuming slow, continuous and infinitesimal exsolution of the vapor, an initially reduced (~IW) magma can be oxidized such that the erupted melt approaches FMQ (Mathez 1984). However, this model assumes a magma that is C-supersaturated and reduced; contrast this with the Ballhaus and Frost (1994) model, in which the magma is no longer buffered by graphite by the time it has reached shallow depths.
The Ballhaus and Frost (1994) model requires much less variation of redox state among basalt mantle sources. Instead of an intrinsic variation in redox state of mantle sources, the oxygen fugacity of the basalt at the surface will depend on the depth at which buffering switches from C-H-O to ferrous-ferric: the greater the depth at which graphite becomes eliminated in the residue, the more oxidized the melt will be at the surface. The model is used to explain the higher oxygen fugacity of OIB relative to MORB; because MORBs are typically derived from shallow mantle sources, their recorded oxygen fugacity is only slightly higher than that at which major melting (and separation from graphite buffering) occurred. Ocean island basalts, on the other hand, are more oxidized because melting occurs at greater depths and the melt experiences more relative oxidation during ascent. The much higher oxygen fugacity of island arc basalt relative to MORB and OIB can be explained by a source that is intrinsically more oxidized than graphite stability, due to the oxidation of the mantle wedge by slab-derived fluids. As such, the IAB source may be around FMQ, and these basalts have high oxygen fugacities as a result of relatively deep major melting. In contrast to Carmichael (1991), this model implies that the oxygen fugacities of MORB and OIB can be produced from the same mantle, by simply changing the depth of first major melting; the Mathez (1984) model implies that oxidation can occur by stalling and degassing the magma in a crustal reservoir. Such models highlight a potential incongruity between the oxygen fugacity of the basalt collected at the surface, and the redox state of the mantle from which the basaltic melt was derived.
Insight into which of these models is more accurate may be derived from the use of V/Sc ratios to infer the oxygen fugacity of melting for terrestrial basalts and mantle xenoliths (Lee et al. 2005). Using new V and Sc measurements, and data from the literature, Lee et al. (2005) obtain oxygen fugacity results of FMQ − 2 to FMQ for peridotites. This is in good agreement with the results from ferrous-ferric mineral equilibria (e.g., olivine-pyroxene spinel oxybarometry) for suboceanic abyssal peridotites and undepleted, fertile subcontinental mantle xenoliths. V/Sc results for MORB are self-consistent with the results for peridotites, falling within FMQ − 1.25 and FMQ + 0.25 (Lee et al. 2005), which agree with previous studies of MORB oxygen fugacity (Christie et al. 1986; Wood et al. 1990). Remarkably, V/Sc ratios for IAB overlap those from MORB, implying that the IAB and MORB mantle sources have the same oxygen fugacity, between FMQ − 1.25 and FMQ + 0.25. This is in contrast to results from the application of equation (8) to glassy arc lavas, which yield FMQ to FMQ + 6 (Carmichael 1991). The implication of the V/Sc results is that the oxygen fugacity of the Earth’s asthenosphere is buffered, perhaps in a manner suggested by Blundy et al. (1991) or Ballhaus and Frost (1994). It is notable that in the range of 1 to 3 GPa, the CCO buffer curve falls between FMQ − 2 and FMQ − 1 (Ballhaus and Frost 1994). Studies of V and Cr in basalts and mantle xenoliths with ages ranging from Archean to the present demonstrate that the oxygen fugacity of the Earth’s asthenosphere has remained buffered to within a log unit of FMQ throughout its history (Delano 2001; Canil 2002; Lee et al. 2003; Li and Lee 2004).
The implications of the V/Sc results for the interpretation of oxygen fugacity results from planetary basalts are profound. The observation that the oxygen fugacity of IAB (as derived from mineral equilibria and ferrous-ferric ratios in glass) is several log units higher than that of its source implies that post-extraction processes, such as fractional crystallization, dissociation of volatiles and degassing, auto-oxidation (e.g., Holloway 2004), and hydrothermal alteration may significantly affect the oxygen fugacities recorded by most oxybarometers. Furthermore, it calls into question whether models of basaltic magma evolution in which the system is closed to oxygen (e.g., Kress and Carmichael 1991; Ghiorso 1997) are applicable to most natural systems.
Implications for understanding the redox states of planetary interiors
There are several methods now available for determining the oxygen fugacities of planetary basalts; many of these methods have been applied to samples from the Moon, Mars and asteroids, as summarized by Wadhwa (2008). The debate and uncertainty regarding the cause of the variation in oxygen fugacity of terrestrial basaltic samples is instructive – in the absence of mantle xenoliths, what can be said about the redox state of the interiors of the other terrestrial planets? The observation from V/Sc ratios that the mantle source of arc basalts is reduced, while the corresponding eruptives are up to several log units more oxidized, indicates that basalts from arc environments are open systems whose oxygen fugacity reflects post-extraction processes such as differentiation, degassing and assimilation; the same might be true for basalts from other tectonic environments. Although plate tectonics is removed as a complicating factor when discussing other terrestrial planets, the question of whether planetary basalts are open to oxygen during ascension and eruption is equivocal. Variations in oxygen fugacity, such as those observed for Mars (Wadhwa 2001; Herd 2003), need to be interpreted in the context of other indicators of mantle source characteristics.
In spite of the lack of mantle xenoliths among our sample suites from the other terrestrial planets, insights into redox states of planetary interiors can be gained through the consideration of the relative roles of volatiles and Fe-bearing mineral equilibria, by analogy with the Earth. High-pressure experiments on mantle or primitive basalt compositions can assist in elucidating the relative change in oxygen fugacity with depth, and determine whether processes such as iron disproportionation have influenced the redox states of the lower mantles of the larger bodies (e.g., Venus, Mars). Comparative studies are particularly relevant and lead to new avenues of research. For example, given the large differences in the C-H-O budgets of the Earth, Moon, Mars and asteroids, what factors in the formation and geologic evolution of the planetary body have the greatest influence on whether mantle source redox state is dominated by volatiles or Fe-bearing mineral equilibria? Given the similarities in C-H-O budgets of the Earth and Mars, what is the role of volatiles in controlling basalt oxygen fugacity on Mars? How can the observation of methane in the martian atmosphere (Formisano et al. 2004) be interpreted in this context?
The relatively high (~FMQ) and constant redox state of the Earth’s asthenosphere since the Archean has implications for the speciation of volatiles that were available during the development of life (Delano 2001; Canil 2002). Likewise, insights into the redox evolution of Mars will influence our understanding of the conditions on early Mars and contribute to the assessment of whether the environment of early Mars was conducive to life.
The author thanks all of the participants of the Oxygen in the Terrestrial Planets Workshop for contributing to the discussion of redox conditions in planetary samples. This paper benefited from discussion with Bob Luth, Karlis Muehlenbachs, Tom Chacko and Thomas Stachel. Thanks to Cin-Ty Lee for the fugacity poetry. A thorough review by John Longhi and the editorship of Steve Simon are gratefully acknowledged.