Abstract Decades of study have documented several orders of magnitude variation in the oxygen fugacity $\left( {{f}_{{{\text{O}}_{2}}}} \right)$of terrestrial magmas and of mantle peridotites. This variability has commonly been attributed either to differences in the redox state of multivalent elements (e.g., Fe3+/Fe2+) in mantle sources or to processes acting on melts after segregation from their sources (e.g., crystallization or degassing). We show here that the phase equilibria of plagioclase, spinel, and garnet lherzolites of constant bulk composition (including whole-rock Fe3+/Fe2+) can also lead to systematic variations in fO2 ${{f}_{{{\text{O}}_{2}}}}$in the shallowest ~100 km of the mantle. Two different thermodynamic models were used to calculate fO2 ${{f}_{{{\text{O}}_{2}}}}$vs. pressure and temperature for a representative, slightly depleted peridotite of constant composition (including total oxygen). Under subsolidus conditions, increasing pressure in the plagioclase-lherzolite facies from 1 bar up to the disappearance of plagioclase at the lower pressure limit of the spinel-lherzolite facies leads to an fO2 ${{f}_{{{\text{O}}_{2}}}}$decrease (normalized to a metastable plagioclase-free peridotite of the same composition at the same pressure and temperature) of ~1.25 orders of magnitude. The spinel-lherzolite facies defines a minimum in fO2 ${{f}_{{{\text{O}}_{2}}}}$and increasing pressure in this facies has little influence on fO2 ${{f}_{{{\text{O}}_{2}}}}$(normalized to a metastable spinel-free peridotite of the same composition at the same pressure and temperature) up to the appearance of garnet in the stable assemblage. Increasing pressure across the garnet-lherzolite facies leads to increases in fO2 ${{f}_{{{\text{O}}_{2}}}}$(normalized to a metastable garnet-free peridotite of the same composition at the same pressure and temperature) of ~1 order of magnitude from the low values of the spinel-lherzolite facies. These changes in normalized fO2 ${{f}_{{{\text{O}}_{2}}}}$reflect primarily the indirect effects of reactions involving aluminous phases in the peridotite that either produce or consume pyroxene with increasing pressure: Reactions that produce pyroxene with increasing pressure (e.g., forsterite + anorthite ⇆ Mg-Tschermak + diopside in plagioclase lherzolite) lead to dilution of Fe3+-bearing components in pyroxene and therefore to decreases in normalized fO2 ${{f}_{{{\text{O}}_{2}}}}$whereas pyroxene-consuming reactions (e.g., in the garnet stability field) lead initially to enrichment of Fe3+-bearing components in pyroxene and to increases in normalized fO2 ${{f}_{{{\text{O}}_{2}}}}$(although this is counteracted to some degree by progressive partitioning of Fe3+ from the pyroxene into the garnet with increasing pressure). Thus, the variations in normalized fO2 ${{f}_{{{\text{O}}_{2}}}}$inferred from thermodynamic modeling of upper mantle peridotite of constant composition are primarily passive consequences of the same phase changes that produce the transitions from plagioclase → spinel → garnet lherzolite and the variations in Al content in pyroxenes within each of these facies. Because these variations are largely driven by phase changes among Al-rich phases, they are predicted to diminish with the decrease in bulk Al content that results from melt extraction from peridotite, and this is consistent with our calculations. Observed variations in FMQ-normalized fO2 ${{f}_{{{\text{O}}_{2}}}}$of primitive mantle-derived basalts and peridotites within and across different tectonic environments probably mostly reflect variations in the chemical compositions (e.g., Fe3+/Fe2+or bulk O2 content) of their sources (e.g., produced by subduction of oxidizing fluids, sediments, and altered oceanic crust or of reducing organic material; by equilibration with graphite- or diamond-saturated fluids; or by the effects of partial melting). However, we conclude that in nature the predicted effects of pressure- and temperature-dependent phase equilibria on the fO2 ${{f}_{{{\text{O}}_{2}}}}$of peridotites of constant composition are likely to be superimposed on variations in fO2 ${{f}_{{{\text{O}}_{2}}}}$that reflect differences in the whole-rock Fe3+/Fe2+ ratios of peridotites and therefore that the effects of phase equilibria should also be considered in efforts to understand observed variations in the oxygen fugacities of magmas and their mantle sources.

中文翻译：

---

固-固相平衡对上地幔氧逸度的影响

摘要 数十年的研究记录了地球岩浆和地幔的氧逸度 $\left( {{f}_{{{\text{O}}_{2}}}} \right)$ 的几个数量级变化橄榄岩。这种可变性通常归因于地幔源中多价元素（例如，Fe3+/Fe2+）的氧化还原状态的差异，或者归因于从其来源分离后作用于熔体的过程（例如，结晶或脱气）。我们在这里表明，恒定体积成分（包括全岩 Fe3+/Fe2+）的斜长石、尖晶石和石榴石二辉石的相平衡也会导致 fO2 ${{f}_{{{\text{O} }_{2}}}}$在地幔最浅的~100公里处。两种不同的热力学模型用于计算 fO2 ${{f}_{{{\text{O}}_{2}}}}$vs。代表的压力和温度，成分不变的轻度贫化橄榄岩（包括总氧）。在亚固相条件下，斜长石-二辉石相的压力从 1 bar 增加到尖晶石-二辉石相压力下限处斜长石消失，导致 fO2 ${{f}_{{{\text{O} }_{2}}}}$减少（标准化为在相同压力和温度下具有相同成分的亚稳态无斜长石橄榄岩）约 1.25 个数量级。尖晶石-二辉石相定义了 fO2 ${{f}_{{{\text{O}}_{2}}}}$ 的最小值，并且该相中增加的压力对 fO2 ${{f}_ 几乎没有影响{{{\text{O}}_{2}}}}$（标准化为在相同压力和温度下具有相同成分的亚稳态无尖晶石橄榄岩）直到稳定组合中石榴石的出现。石榴石-二锆石相的压力增加导致 fO2 ${{f}_{{{\text{O}}_{2}}}}$（归一化为相同成分的亚稳态无石榴石橄榄岩）相同的压力和温度）与尖晶石-二辉石相的低值相差约 1 个数量级。归一化 fO2 ${{f}_{{{\text{O}}_{2}}}}$ 的这些变化主要反映了橄榄岩中铝相反应的间接影响，这些反应在压力增加时产生或消耗辉石：随着压力的增加产生辉石的反应（例如镁橄榄石 + 钙长石 ⇆ Mg-Tschermak + 斜长石锂辉石中的透​​辉石）导致辉石中含 Fe3+ 的组分被稀释，因此导致归一化 fO2 ${{f}_{{{ \text{O}}_{2}}}}$ 而消耗辉石的反应（例如，在石榴石稳定性领域）最初导致辉石中含 Fe3+ 组分的富集和归一化 fO2 ${{f}_{{{\text{O}}_{2}}}}$（尽管这是随着压力的增加，Fe3+ 从辉石逐渐分配到石榴石中而在一定程度上抵消了这种影响）。因此，从具有恒定成分的上地幔橄榄岩的热力学模型推断出的归一化 fO2 ${{f}_{{{\text{O}}_{2}}}}$ 的变化主要是相同相变的被动结果产生从斜长石→尖晶石→石榴石二辉石的转变以及这些相中辉石中铝含量的变化。因为这些变化主要是由富铝相之间的相变驱动的，预计它们会随着从橄榄岩中熔体提取而导致的体积铝含量减少而减少，这与我们的计算一致。观察到的 FMQ 归一化 fO2 ${{f}_{{{\text{O}}_{2}}}}$ 在不同构造环境内和跨不同构造环境中的原始地幔衍生玄武岩和橄榄岩的变化可能主要反映了其来源的化学成分（例如 Fe3+/Fe2+ 或整体 O2 含量）（例如，由氧化性流体、沉积物和改变的洋壳或还原性有机材料的俯冲产生；通过与石墨或金刚石饱和流体平衡；或部分熔化的影响）。然而，