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    We expand the scope of HeFESTo by encompassing the rich physics of iron in the mantle, including the existence of multiple valence and spin states. In our previous papers, we considered iron only in its most common state in the mantle: the high-spin divalent (ferrous) cation. We now add ferric iron end-members to six phases, as well as the three phases of native iron. We also add low-spin states of ferrous and ferric iron and capture the behaviour of the high-spin to low-spin transition. Consideration of the multi-state nature of iron, unique among the major elements, leads to developments of our theory, including generalization of the chemical potential to account for the possibility of multiple distinguishable states of iron co-existing on a single crystallographic site, the effect of the high-spin to low-spin transition on seismic wave velocities in multiphase systems, and computation of oxygen fugacity. Consideration of ferric iron also motivates the addition of the chromia component to several phases, so that we now consider the set of components: Ca, Na, Fe, Mg, Al, Si, O and Cr (CNFMASO+Cr). We present the results of a new global inversion of mineral properties and compare our results to experimental observations over the entire pressure–temperature range of the mantle and over a wide range of oxygen fugacity. Applications of our method illustrate how it might be used to better understand the seismic structure, dynamics and oxygen fugacity of the mantle.

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  2. Abstract

    The contrasting internal luminosity of Uranus and Neptune present a challenge to our understanding of the origin and evolution of these bodies, as well as extra-solar ice giants. The thermal evolution of Neptune is known to be nearly consistent with an entirely fluid interior, but this is not a unique solution, and does not account for the tidal dissipation required by the migration of its moons. We examine a model that has been previously shown to explain the thermal and tidal evolution of Uranus: one that features a growing, frozen core. The core traps heat in the interior, affecting the cooling time scale, and provides a source of tidal dissipation. We review the growing, frozen core model, and the computation of thermal and tidal evolution. We then apply this model to Neptune. We find that the growing frozen core model can account for the observed internal luminosity of Neptune and the migration of its moons, in the form of resonances that were either encountered or avoided in the past. We discuss prospects for observational tests of the growing frozen core model and possible implications for understanding the gas giants.

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  3. Abstract

    The upper boundary of the mantle transition zone, known as the “410-km discontinuity”, is attributed to the phase transformation of the mineral olivine (α) to wadsleyite (β olivine). Here we present observations of triplicated P-waves from dense seismic arrays that constrain the structure of the subducting Pacific slab near the 410-km discontinuity beneath the northern Sea of Japan. Our analysis of P-wave travel times and waveforms at periods as short as 2 s indicates the presence of an ultra-low-velocity layer within the cold slab, with a P-wave velocity that is at least ≈20% lower than in the ambient mantle and an apparent thickness of ≈20 km along the wave path. This ultra-low-velocity layer could contain unstable material (e.g., poirierite) with reduced grain size where diffusionless transformations are favored.

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    Phase transitions play an important role for the style of mantle convection. While observations and theory agree that a substantial fraction of subducted slabs and rising plumes can move through the whole mantle at present day conditions, this behaviour may have been different throughout Earth’s history. Higher temperatures, such as in the early Earth, cause different phase transitions to be dominant, and also reduce mantle viscosity, favouring a more layered style of convection induced by phase transitions. A period of layered mantle convection in Earth’s past would have significant implications for the secular evolution of the mantle temperature and the mixing of mantle heterogeneities. The transition from layered to whole mantle convection could lead to a period of mantle avalanches associated with a dramatic increase in magmatic activity. Consequently, it is important to accurately model the influence of phase transitions on mantle convection. However, existing numerical methods generally preclude modelling phase transitions that are only present in a particular range of pressures, temperatures or compositions, and they impose an artificial lower limit on the thickness of phase transitions. To overcome these limitations, we have developed a new numerical method that solves the energy equation for entropy instead of temperature. This technique allows for robust coupling between thermodynamic and geodynamic models and makes it possible to model realistically sharp phase transitions with a wide range of properties and dynamic effects on mantle processes. We demonstrate the utility of our method by applying it in regional and global convection models, investigating the effect of individual phase transitions in the Earth’s mantle with regard to their potential for layering flow. We find that the thickness of the phase transition has a bigger influence on the style of convection than previously thought: with all other parameters being the same, a thin phase transition can induce fully layered convection where a broad phase transition would lead to whole-mantle convection. Our application of the method to convection in the early Earth illustrates that endothermic phase transitions may have induced layering for higher mantle temperatures in the Earth’s past.

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  5. SUMMARY We derive exact expressions for the thermal expansivity, heat capacity and bulk modulus for assemblages with arbitrarily large numbers of components and phases, including the influence of phase transformations and chemical exchange. We illustrate results in simple two-component, two-phase systems, including Mg–Fe olivine-wadsleyite and Ca–Mg clinopyroxene-orthopyroxene and for a multicompontent model of mantle composition in the form of pyrolite. For the latter we show results for the thermal expansivity and heat capacity over the entire mantle pressure–temperature regime to 40 GPa, or a depth of 1000 km. From the thermal expansivity, we derive a new expression for the phase buoyancy parameter that is valid for arbitrarily large numbers of phases and components and which is defined at every point in pressure–temperature space. Results reveal regions of the mantle where the magnitude of the phase buoyancy parameter is larger in magnitude than for those phase transitions that are most commonly included in mantle convection simulations. These regions include the wadsleyite to garnet and ferropericlase transition, which is encountered along hot isentropes (e.g. 2000 K potential temperature) in the transition zone, and the ferropericlase and stishovite to bridgmanite transition, which is encountered along cold isentropes (e.g. 1000 K potential temperature) in the shallow lower mantle. We also show the bulk modulus along a typical mantle isentrope and relate it to the Bullen inhomogeneity parameter. All results are computed with our code HeFESTo, updates and improvements to which we discuss, including the implementation of the exact expressions for the thermal expansivity, heat capacity and bulk modulus, generalization to allow for pressure dependence of non-ideal solution parameters and an improved numerical scheme for minimizing the Gibbs free energy. Finally, we present the results of a new global inversion of parameters updated to incorporate more recent results from experiment and first principles theory, as well as a new phase (nal phase), and new species: Na-majorite and the NaAlO2 end-member of ferropericlase. 
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  6. Abstract

    The origin of the very low luminosity of Uranus is unknown, as is the source of the internal tidal dissipation required by the orbits of the Uranian moons. Models of the interior of Uranus often assume that it is inviscid throughout, but recent experiments show that this assumption may not be justified; most of the interior of Uranus lies below the freezing temperature of H2O. We find that the stable solid phase of H2O, which is superionic, has a large viscosity controlled by the crystalline oxygen sublattice. We examine the consequences of finite viscosity by combining ab initio determinations of the thermal conductivity and other material properties of superionic H2O with a thermal evolution model that accounts for heat trapped in the growing frozen core. The high viscosity provides a means of trapping heat in the deep interior while also providing a source of tidal dissipation. The frozen core grows with time because its outer boundary is governed by the freezing transition rather than compositional layering. We find that the presence of a growing frozen core explains the anomalously low heat flow of Uranus. Our thermal evolution model also predicts time-varying tidal dissipation that matches the requirements of the orbits of Miranda, Ariel, and Umbriel. We make predictions that are testable by future space missions, including the tidal Love number of Uranus and the current recessional rates of its moons.

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