Abstract– Low-iron, manganese-enriched (LIME) olivine grains are found in cometary samples returned by the Stardust mission from comet 81P/Wild 2. Similar grains are found in primitive meteoritic clasts and unequilibrated meteorite matrix. LIME olivine is thermodynamically stable in a vapor of solar composition at high temperature at total pressures of a millibar to a microbar, but enrichment of solar composition vapor in a dust of chondritic composition causes the FeO/MnO ratio of olivine to increase. The compositions of LIME olivines in primitive materials indicate oxygen fugacities close to those of a very reducing vapor of solar composition. The compositional zoning of LIME olivines in amoeboid olivine aggregates is consistent with equilibration with nebular vapor in the stability field of olivine, without re-equilibration at lower temperatures. A similar history is likely for LIME olivines found in comet samples and in interplanetary dust particles. LIME olivine is not likely to persist in nebular conditions in which silicate liquids are stable.
The compositions of LIME olivines and pyroxenes are significantly different from the compositions typical of ferromagnesian silicates from undifferentiated meteoritic material. For the latter, MnO contents of olivine and pyroxene are almost always below 0.5 wt%, or XTep < 0.005, where XTep is the mole fraction tephroite (Mn2SiO4) in olivine, with no significant correlation between FeO and MnO contents (Klöck et al. 1989; their Fig. 1b). MnO contents of olivine in FeO-poor chondrules of CR chondrites do increase slightly with increasing FeO content, but most of the wt% FeO/MnO ratios in olivine remain above 5 (Fig. 1; Weisberg et al. 1995).
Here, we explore the effect of oxygen fugacity on the relative stabilities of olivine components in this composition range. We present the results of thermochemical calculations, which suggest that LIME silicates are the natural outcomes of high-temperature equilibration between solids and vapors expected in protoplanetary disks and other astrophysical environments for a restricted suite of bulk chemical compositions. Thus, the existence of LIME silicates places important constraints on environments of formation, and silicate crystallization in these environments. We note that, although these calculations may apply to other astrophysical environments (e.g., atmospheres of AGB stars), the focus here is on nebular environments of olivine formation.
Methods I: Condensation Calculations
A straightforward approach to understanding LIME olivine stability is to incorporate a complete olivine solid solution model directly into the VAPORS code of Ebel and Grossman (2000; cf. Ebel et al. 2000; Ebel 2006), and to then explore olivine stability at fixed total pressure, Ptot, and total composition as a function of temperature. In a condensation calculation, the free energy of the system is minimized to determine the stable phase assemblage and the composition of each phase at equilibrium. Ebel and Grossman (2000) only allowed for (Mg, Fe, Ca)2SiO4 olivine solid solutions. A more recent thermodynamic model that is now embedded in the MELTS thermodynamic crystallization package (Ghiorso and Sack 1995) accounts for the solution of additional divalent transition elements in olivine, including Mn (M. Hirschmann, personal communication; Sack and Ghiorso 1989; Hirschmann 1991; Hirschmann and Ghiorso 1994). We have incorporated this model into the VAPORS code so that the stability and compositions of olivines with the general formula (Mg,Fe,Ca,Mn,Co,Ni)2SiO4 can be evaluated. As VAPORS is based on MELTS, internal consistency with the implementation of this olivine model is assured. Sugiura et al. (2009) presented calculations of wt% MnO in olivine in equilibrium with a vapor of solar composition at Ptot = 10−4 bar. They allowed Mn condensation only into olivine (cf. Petaev and Wood 2005). For comparison, we also calculate compositions of olivine solid solution in equilibrium with a cooling vapor of solar composition at Ptot = 10−4 bar.
In the VAPORS code, H2-rich vapor, silicate liquid, olivine, MnS, the tephroite (MnTiO3) component of rhombohedral oxide (Ghiorso 1990), Mn° (metal), MnSi (brownleeite), and MnO are the only phases allowed to contain Mn. A variety of Mn-bearing gaseous species are considered, but, for all conditions investigated here, Mn in the vapor phase speciates overwhelmingly as monatomic Mn(g). Mn solubility in pyroxenes is not included in our calculations, even though LIME pyroxenes exist in primitive meteorites. Robust equations of state for Mn-bearing multicomponent pyroxenes, consistent with the MELTS database, do not yet exist, as noted by Petaev and Wood (2005). However, we do provide a zeroth order assessment based on the known similarity in partitioning for Mn among olivine and pyroxenes (Kennedy et al. 1993; http://earthref.org/KDD/e:25/). Furthermore, the calibration of (Mg, Fe, Ca, Mn, Co, Ni)2SiO4 olivine solid solution properties must be extrapolated beyond their ranges of calibration for some of the calculations reported here. Nominal maximum temperatures of calibration are 1370 K for fayalite, 1500 K for tephroite, and 1807 K for forsterite. Finally, we note that grains of low-iron, chromium-enriched olivine (LICE-ol) are also observed in some samples from comet 81P/Wild 2 (Zolensky et al. 2006), and in some primitive meteorites and IDPs (Klöck et al. 1989). Sugiura et al. (2009) did calculate the stability of the Cr component in forsteritic olivine, using a model by Li et al. (1997). Our analysis does not extend to Cr-bearing olivine compositions, for lack of an activity model for Cr-olivine that is consistent with the model of Hirschmann and Ghiorso (1994).
Methods II: Ellingham Diagrams
An alternative springboard for exploration of the Mn, Cr, and Fe content of silicates is the Ellingham diagram (Ellingham 1944). These diagrams, familiar in the metallurgical literature, describe the relative oxidation/reduction or sulfidation/reduction tendencies of pure metals and compounds at smelting temperatures T by plotting the Gibbs free energies of oxidation (or sulfidation) reactions, where . Richardson and Jeffes (1948) developed this concept into a graphical representation of metal-oxide equilibrium relations in space from which CO/CO2, H2/H2O, and could be read. This “nomogram” allowing analog interpolation for a myriad of buffer curves from a single diagram is a classic example of compact, interpretable presentation of information (Tufte 2001). Examples of this nomogram are given by Darken and Gurry (1953, their Fig. 14-4), and by Larimer (1967, his Fig. 4) in illustrating the effect of oxidation potential on oxides in ordinary and enstatite chondrites. We will use this diagram to explore the relative stabilities of olivine components.
Figure 2 follows the diagram of Darken and Gurry (1953). Plotted are reaction equilibria for oxides of selected metals (Mn, Cr, Fe, Co, and Ni) calculated with VAPORS (Ebel and Grossman 2000). The oxide is stable above each curve. Also shown are trajectories for equilibrium condensation of solids from a vapor of solar composition (Anders and Grevesse 1989) at Ptot = 10−3 and 10−6 bar, calculated for the temperature range 2400–1150 K (Ebel 2006). These curves are labeled “1” to indicate the bulk composition of the system has 1 times CI abundances of the condensable elements. At lower temperatures, both of these curves converge to ≈ 103. At high temperatures and low Ptot, the of these chemical systems is not dominated by the reaction 2H2 + O2 = 2H2O, so that the Ptot = 10−6 trajectory dips below ≈ 103.
In addition to the solar condensation trajectories shown in Fig. 2, condensation paths for vapors that have been enriched in dust of CI chondrite composition relative to solar by factors of 100 and 1000 (Ebel and Grossman 2000) are shown. It is reasonable to expect enrichment of the solar nebula in previously condensed dust in the disk midplane, in the region of terrestrial planet formation. A major effect of enrichment in a carbonaceous chondrite-like (CI) dust is to decrease the H2/H2O ratio of the system, because dust brings substantial oxygen in the form of condensed silicates, and little hydrogen. Note that for a given enrichment in dust, trajectories for Ptot = 10−6 and 10−3 bar diverge at high temperatures, as they do for the solar case, and converge at low temperatures to a specific dictated by the degree of dust enrichment.
Relative positions of oxidation equilibria in Fig. 2 give a general idea of the propensity for a given element for oxidized or reduced forms. Thus, we would expect Ni and Co, under the relatively reducing conditions considered here, to be generally in the metallic phase, Cr and Mn to be oxidized, and Fe to vary depending on specific conditions. In detail, however, it is the solution of an element into major silicates like olivine and pyroxene that dictates the distribution. For Mn, it is the stability of the Mn-endmember (tephroite) in olivine that is of interest. At any particular temperature and Ptot, the reaction
may be described by a Gibbs free energy of reaction (ΔGrxn):
where R is the gas constant (J mol−1 K−1), T is temperature (Kelvin), is the activity of endmember x (e.g., tephroite) in olivine, are the standard state Gibbs free energies of species s, and py is the partial pressure of gas species y in the vapor. Equation 2 is valid at low pressures for which fugacities are equivalent to partial pressures of gaseous species.
For equation 2, and its analog for fayalite, ΔGrxn = 0 at equilibrium. Upon rearranging the equation, can be obtained for fixed mole fractions of olivine endmembers, over a range of temperatures:
This requires calculation of , partial pressures of gaseous species, and the , at each particular temperature. Here, we use this calculation as a basis for exploring the relative stabilities of olivine with fixed mole fractions of tephroite or fayalite in solid solution, by reference to the Ellingham diagram (Fig. 2). The activities and in olivine are calculated for fixed mole fractions of 0.001, 0.01, and 0.025 at each temperature using the models described by Sack and Ghiorso (1989) and Hirschmann and Ghiorso (1994), a set of compositions that spans most of the observed range of LIME olivines (Fig. 1a). Values for the partial pressures of SiO(g), Mn(g), and Fe(g) in equation 3, and in the analogous equation for fayalite, are taken directly from condensation calculations at the appropriate total composition, temperature, and Ptot (Ebel and Grossman 2000). An implicit assumption in this approach is that small degrees of solid solution of tephroite or fayalite in olivine do not affect the activity of the other endmember in the same solid solution. Values for are calculated using equations of state for olivine endmembers and gaseous species (Hirschmann and Ghiorso 1994; Ebel and Grossman 2000). In essence, the calculations establish the redox conditions under which olivine of a particular composition can be in equilibrium with a particular gas.
We focus below on condensation trajectories of a vapor of solar composition (Anders and Grevesse 1989) at Ptot in the range 10−3 to 10−6 bar, and several dust enriched compositions, over the temperature range 2400–1150 K taken at 10 degree steps. These calculated trajectories yield partial pressures of SiO (pSiO) and other gaseous species at each step. Because equation 3, and also the condensation calculations, describes chemical equilibrium conditions, the gas species used in equation 3 are inconsequential. For example, although SiO(g) is the dominant Si-bearing species in solar and more oxidizing vapors, equations equivalent to equation 3 could be written that incorporate alternative species and this would have no effect on the calculated Mn concentrations in olivine.
Figure 3 illustrates the result of a direct condensation calculation (Method I) for the solids, including multicomponent olivine, from a vapor of solar composition at Ptot = 10−4 bar (10 Pa). Results for Ptot from 10−2 to 10−6 bar are qualitatively similar, because, although changes in Ptot shift the temperatures of solid stability fields, the relative shifts are similar for each crystalline phase. In these calculations, mole fractions of the Mn endmember (tephroite, Tep) in olivine peak at 0.025, when ∼100% of the Mn has condensed. Since a vapor of canonical solar composition has considerably more Mg and Fe than Mn (atomic ratios of Mn/Mg = 0.009, and molar Mn/Fe = 0.011; Anders and Grevesse 1989), the condensation of MnO into olivine has a negligible effect on condensate modes or appearance temperatures.
A weakness of the current VAPORS code is that partitioning of Mn among coexisting olivine, Ca-rich pyroxene (clinopyroxene, Cpx), and Ca-free pyroxene (orthopyroxene, Opx) is not considered. We address this by assuming an Mn2Si2O6 endmember for both pyroxenes, and Mn partition coefficients among olivine and the two pyroxenes of unity (equipartition). We assume that the affinity of the Mn endmember in the pyroxenes is the same as in olivine, and, therefore, assume that the calculated olivine Mn-component abundance represents the total condensable Mn at each temperature. Results of this calculation are shown in Fig. 3. The mole fraction of the Mn endmember in all three silicates reaches a maximum of 0.0085 (i.e., 1/3 of the maximum for olivine computed using the VAPORS code) or ∼0.85 wt% MnO. Most of the LIME olivines plotted in Fig. 1a fall below this value.
Direct condensation calculations account for the depletion of Mn in the vapor at temperatures below the appearance of olivine. Equation 3 can be used to calculate for fixed XTep under the assumptions that pMn and pSiO are constant. The first assumption becomes less tenable as the vapor becomes more depleted in Mn, a factor not accounted for in the source calculations for the vapor pressures used in equation 3. Thus, the temperature at which XTep = 0.001 according to Method II and equation 3 is essentially equivalent to that obtained from a full-scale condensation calculation, but the temperatures at which XTep = 0.01 and 0.025 are reached are higher by 15 and 90 K, respectively, at Ptot = 10−4 bar.
In addition to showing XTep as a function of temperature, Fig. 3 illustrates the variation of XFa and the influence of condensate metal on Fe in coexisting silicates. Forsteritic olivine condenses at 1370 K from a vapor of solar composition at Ptot = 10−4 bar, and metal alloy condenses at 1360 K, significantly lowering pFe in the vapor. Mn is unaffected because of a negligible solubility in the alloy. Condensate olivines quenched at high temperature have XFa > XTep, but both are extremely low. As temperature decreases, Mn in olivine increases more rapidly than Fe and, below 1240 K, XTep > XFe. However, little new olivine or pyroxene condenses under these conditions (Fig. 3). Overall, these calculations imply that a condensate olivine exposed to a vapor of solar composition over a range of temperatures during cooling, that is not re-equilibrated, will be normally zoned (i.e., Mn will increase from core to rim).
A strength of Method II is that it allows a simple assessment of the influence of changing redox conditions on the compositions of phases. Figure 4 illustrates the result of applying equation 3 (Method II) to a portion of Fig. 2, for a single condensation scenario. Calculated isopleths are plotted for fixed mole fractions of tephroite and fayalite components dissolved in olivine solid solutions condensing from a vapor of solar composition at 10−3 bar, calculated using values for pSiO, pMn, and pFe from condensation calculations (Ebel and Grossman 2000), at those chemical and pressure conditions, at each temperature. For modest perturbations from the solar condensation curve, values of pSiO, pMn, and pFe change much more slowly than , and we can therefore use Fig. 4 to deduce relative changes in the olivine composition caused by changes in the redox conditions. Note that the intersection of a tephroite isopleth with the solar condensation trajectory occurs at a higher temperature than the intersection for a fayalite isopleth of the same mole fraction. Thus, at 1300 K, olivine containing XTep = 0.001 and XFa∼0.001 is stable, but XTep increases to 0.025 at 1200 K whereas XFa remains ∼0.001.
In more oxidizing systems, for example, systems enriched in ices, the trajectories must shift to higher in the Ellingham diagram. Thus, the addition of water ice to a system of solar composition will stabilize fayalite relative to tephroite, at the temperatures considered here. The addition of chondritic dust to a vapor of solar composition would cause a similar shift in oxidation potential of the system, and preferentially stabilize the fayalitic component of olivine. For example, Fig. 4 illustrates the trajectory of a vapor 1000× enriched in CI chondrite dust. Below 1600 K, the corresponding trajectory for a vapor 50× enriched in CI chondritic dust would plot subparallel to the XFa = 0.01 curve. Perturbations in gas composition that lead to conditions more reducing than those of a solar gas (e.g., removal of ices, or C enrichment) would have the opposite effect and destabilize fayalite relative to tephroite.
Figure 5 illustrates the effects of varying Ptot and dust enrichment on olivine composition. Stability curves for 0.001, 0.01, and 0.025 mole fraction tephroite and fayalite in olivine are shown. Values for the partial pressures of SiO(g), Mn(g), and Fe(g) in equation 3 used to calculate these curves were taken directly from condensation calculations at the appropriate total composition, T, and Ptot. For all 10−6 ≤ Ptot ≤ 10−2 bar, Mn-enriched olivine is more thermodynamically stable than Fe-enriched olivine in a cooling gas of solar composition at temperatures within the olivine stability field. Figure 5 also illustrates the effect of 100× enrichment of the system in a dust of CI composition, relative to solar, at constant Ptot = 10−3 bar. Ebel and Grossman (2000; cf. Ebel 2006) demonstrated that silicate liquids similar to those quenched in chondrules become stable at dust enrichments between ∼15 × CI and 1000 × CI at Ptot = 10−3 bar. At 100 × CI dust enrichment, olivine incorporates the fayalite component of a given mole fraction at higher temperature than it does the tephroite component. When XTep reaches 0.001, olivine already contains XFa >0.01. At 100× enrichment, a nearly constant ∼0.025 mole fraction fayalite is stabilized, and primary olivine ceases to condense below ∼1620 K (cf. Ebel and Grossman 2000; their Fig. 8a). Were olivine to continue to equilibrate with vapor to lower temperatures, mole fractions of tephroite would increase, reaching XTep ∼ XFa ∼ 0.025 at 1500 K. At 1000 × CI dust enrichment, olivine condensation ceases at ∼1680 K, and the fayalite component is much more stable than the tephroite component in olivine at all temperatures. Therefore, XTep > XFa only at dust enrichments well below 100 × CI. From Fig. 5, it is clear that decreasing H2/H2O will decrease the Mn/Fe ratio in olivine for any particular Ptot or dust enrichment condition.
From Fig. 3 and the analysis of Figs. 4 and 5 above, Mn concentrations in forsteritic olivine condensed from solar compositions, and from solar compositions enriched by CI dust, are expected to increase with decreasing temperature. This is qualitatively consistent with olivine in AOAs, which are Mn-poor in AOA interiors and Mn-enriched in their rims (Weisberg et al. 2004; Sugiura et al. 2009). Although Ca, Ti, and Al can also substitute into the olivine crystal structure at high temperatures (Steele 1990; Spandler and O’Neill 2010), they condense more readily into other oxide and silicate solids at these conditions, and their affinity for olivine is low at the temperatures where Mn concentrations in olivine reach their maxima. For the conditions explored here, Mn (and Cr) are only incorporated into pyroxenes coexisting with olivine. Nakamura-Messenger et al. (2010) reported brownleeite (MnSi) epitaxially intergrown with LIME olivine in an anhydrous chondritic-porous IDP, probably from comet 26P/Grigg-Skjellerup. Here, brownleeite was found to be unstable in a solar composition vapor at Ptot = 10−4 bar at any temperature, suggesting that even more reducing conditions are required to stabilize this phase. Although we are not able to effectively model Cr condensation into olivine or pyroxene, consideration of Fig. 2 suggests that Cr should enter silicates less readily than Mn under the same redox conditions (e.g., H2/H2O ratio). Sugiura et al. (2009), however, found that the CrO (wt%) content of olivine exceeded MnO above ∼1200 K. However, they suppressed formation of Cr-rich spinel, which is not found in association with AOAs, and would become stable at 1200 K in their calculation. In the present calculation, Cr spinel (∼Mg1.03Al0.77Cr1.16Ti0.04O4) becomes stable at 1220 K. The elements Ni and Co, which readily enter the olivine structure under favorable conditions, require much more oxidizing conditions than Mn to do so; for the astrophysically plausible redox conditions explored here, these elements will be strongly reduced and concentrated in coexisting metal alloy.
The condensation behavior of Mn has previously been reported in detail only by Sugiura et al. (2009), with markedly different results from the present calculations. Larimer (1967) calculated the condensation temperature of pure tephroite (Mn2SiO4) as 1470 K in a vapor with solar oxygen fugacity at Ptot = 6.6 × 10−3 bar at ∼1100 K. Larimer (1973, his Fig. 2b) calculated a 50% condensation temperature (Tc) for Mn as MnSiO3 of ∼1250 K at Ptot=10−4 bar. Wai and Wasson (1977, their Table 1) calculated Tc as 1190 K for the same conditions, with activity coefficients of Mn2SiO4 in olivine of unity. Palme and Fegley (1990) predicted FeO/MnO ratios in olivine for high H2O/H2 ratios, neglecting the details of gas depletion in Fe and Mn and their incorporation into other phases. Ebel and Grossman (2000), and Petaev et al. (2003) did not include Mn in silicate solid solutions. Lodders (2003) calculated the Tc for Mn as 1158 K in a vapor of solar composition at Ptot=10−4 bar, with Mn entering both olivine and orthopyroxene solid solutions, using methods described by Kornacki and Fegley (1986).
The preservation of LIME olivines in a wide range of primitive nebular materials (Fig. 1) indicates that these objects did not undergo re-equilibration with Fe-bearing vapor or condensed material under oxidizing conditions. Such re-equilibration would have dramatically enriched the olivine in Fe. The coexistence of LIME olivine with LIME pyroxene (e.g., in cometary grains, Nakamura et al. 2008) suggests that these phases formed co-genetically. However, the data of Nakamura et al. (2008) allow calculation of apparent distribution coefficients (wt% MnO in olivine/wt% MnO in pyroxene) ranging from 0.95 to 4.0, so a variety of local environments may have been sampled. In a cooling vapor of solar composition, enstatite forms by the reaction of forsteritic olivine with Si from vapor (Grossman 1972; Ebel and Grossman 2000).
The formation of LIME olivine is highly sensitive to redox conditions. In the chemical systems investigated here, LIME olivine is only stable in reduced vapors, with CI dust enrichments well below 100×. There is, therefore, a very limited range of CI dust enrichments, below ∼50×, in which both silicate melts and LIME olivines may be stable under the same Ptot and temperature conditions. For similar reasons, the objects in which LIME silicates are found cannot have formed in regions enriched in water ice. LIME olivine is primarily found in unmelted objects such as IDPs, AOAs, and primitive chondrite matrices. These objects show little evidence for pervasive melting under conditions where silicate melt is stable against evaporation (Ebel 2006). Mn-enrichment should be observed at the outer edges of primitive (i.e., highly magnesian), unequilibrated olivine and pyroxene grains formed under low conditions. The chondrule-like objects recovered from comet Wild 2 (Nakamura et al. 2008) are not particularly Mn-enriched (Fig. 1b), consistent with the fact that conditions that stabilize silicate liquids do not stabilize LIME olivine.
Acknowledgments–– The authors thank two anonymous reviewers. This work was supported by NASA-COS-NNX10AI42G (DSE), NASA-COS-NNG09AG94G (MKW), NASA-DDAP-NNX08AG23G (MKW), and NASA-COS-NNX09AG40G (E. Stolper, PI). This research has made use of NASA’s Astrophysics Data System.