W-WO joins the deep Earth electrochemical series

The core/mantle boundary is the major interface governing mechanical and thermal mixing of the entire planet. The equilibrium position of this boundary, and the associated equilibrium compositions of the overlying oxide mantle and underlying metal core are determined by planetary-scale redox thermodynamics. The observed and inferred abundances of transition metals in the Earth’s mantle can be interpreted in terms of core formation and core/mantle evolution processes if armed with the relevant thermodynamics: such as an analog of the familiar table of aqueous standard reduction potentials, but for geologically relevant metals, oxides, and silicates at conditions of planetary interiors. This “deep Earth electrochemical series” defines the relative thermodynamic stability of end-member metal-metal oxide equilibria (buffers¹) and maps them as a function of pressure and temperature. The current library of relative energetics of metal-metal oxide systems extended to conditions of the Earth’s deep mantle includes Fe-FeO (Fischer et al. 2011), Ni-NiO (Campbell et al. 2009), and Co-CoO (Armentrout et al. 2013). With the publication of Shofner et al. (2016), the W-WO system can be added as well. Thus the entire electrochemical series for transition metals throughout the pressure and temperature conditions of planetary interiors can begin to be assembled.

Shofner et al. use both multi-anvil press and laser-heated diamond-anvil cell techniques in conjunction with synchrotron-based X-ray diffraction to determine the phase diagram of WO₂, discovering an additional high-pressure polymorph. In addition, the bulk thermoelastic properties of the WO₂ polymorphs up to ~55 GPa and 2500 K were determined. Three parameters determine the pressure-volume relationship at a reference temperature (usually 300 K), and an additional three parameters determine the thermal pressure as a function of temperature at each volume, using a Mie-Gruneisen-Debye formalism. Together, the six parameters determine the density of each tungsten dioxide phase as a function of pressure and temperature—thus providing the total information of density, bulk modulus, and thermal expansion as a function of pressure and temperature, including cross derivatives. Because W was used as a reference material in these experiments, the relative P-V energetics of the W-WO buffer system can be calculated to pressures and temperatures of ~70 GPa and ~2250 K.

The energetics of metal-metal oxide systems can be equivalently determined in terms of the (Helmholtz) free energy difference, the oxygen fugacity, f_O2, or as a standard reduction potential (e.g., Kavner et al. 2007). All of these conventions have an implicit reference state, which may be fictive, as in the case of f_O2 at deep Earth conditions. Figure 1 plots the energetics of four M-MO systems as a function of pressure and temperature down an Earthlike-adiabat. This plot shows that for all systems, the combination of pressure and temperature increases the free energy difference between the oxide and the metal—to first approximation, these four transition metals become increasingly siderophile in the Earth (a higher f_O2 is required to oxidize the metals). However, the curves on Figure 1 are not perfectly parallel, indicating that the buffer system energetics have different dependencies on pressure and temperature.

Figure 2 plots these different dependencies, showing the energetics of the buffer systems relative to iron-wustite as a function of depth. At lower pressures, the W, Ni, and Co equilibria all are above the I-W buffer, indicating their siderophile nature, and approach the Fe-FeO equilibrium with increasing pressure along a present-day Earth-interior adiabat, though with different behaviors. At pressures below 35 GPa, the W-WO system parallels the iron-wustite system, indicating little change in relative oxygen fugacity between the two systems in that pressure range, consistent with the conclusions from partitioning measurements between the Mo and W and iron systems by Wade et al. (2011). However, at lower mantle conditions, Shofner et al. show that W becomes less siderophile—predicting a crossover with the Fe-FeO at conditions close to the core-mantle boundary. To calculate the partition coefficients of W between core and mantle phases, Shofner et al. combine the W-WO equilibrium energetics with estimates of the mixing energetics of multicomponent phases and determine a nonlinear pressure dependence of W partitioning between peridotite liquidus and core.

The real Earth is a multicomponent mixture, and end-member thermodynamics play only a partial role in determining partitioning behavior in a system that must include multiple phases, mixing energetics, and possibly non-ideal and/or non-stoichiometric behavior. This requires experimental tests targeting the systems of interest. One of the powers of Figure 2 is that it suggests optimal pressure and temperature ranges where more detailed petrological partitioning experiments can be performed. For example, the Ni-CoO = Co-NiO exchange reaction is predicted around 58 GPa and 2200 K, corresponding to a depth of 1400 km in the mantle. These crossover predictions are subject to solution effects and should thus be tested by a series of targeted high-pressure and temperature partitioning experiments to investigate the effects of speciation and solubility.