Lichtenberg T., Schaefer L.K., Nakajima M., and Fischer R.A. Submitted. “Geophysical evolution during rocky planet formation.” In Protostars and Planets VII.
Dong J., Fischer R.A., Stixrude L.P., Lithgow-Bertelloni C.R., Eriksen Z.T., and Brennan M.C. Submitted. “Water storage capacity of the Martian mantle through time”.
Brennan M.C., Fischer R.A., Nimmo F., and O'Brien D.P. 2022. “Timing of Martian core formation from models of Hf–W evolution coupled with N-body simulations.” Geochimica et Cosmochimica Acta. Publisher's VersionAbstract

Determining how and when Mars formed has been a long-standing challenge for planetary scientists. The size and orbit of Mars are difficult to reproduce in classical simulations of planetary accretion, and this has inspired models of inner solar system evolution that are tuned to produce Mars-like planets. However, such models are not always coupled to geochemical constraints. Analyses of Martian meteorites using the extinct hafnium–tungsten (Hf–W) radioisotopic system, which is sensitive to the timing of core formation, have indicated that the Martian core formed within a few million years of the start of the solar system itself. This has been interpreted to suggest that, unlike Earth's protracted accretion, Mars grew to its modern size very rapidly. These arguments, however, generally rely on simplified growth histories for Mars. Here, we combine likely accretionary histories from a large number of N-body simulations with calculations of metal–silicate partitioning and Hf–W isotopic evolution during core formation to constrain the range of conditions that could have produced Mars.

We find that there is no strong correlation between the final masses or orbits of simulated Martian analogs and their 182W anomalies, and that it is readily possible to produce Mars-like Hf–W isotopic compositions for a variety of accretionary conditions. The Hf–W signature of Mars is very sensitive to the oxygen fugacity (fO2) of accreted material because the metal–silicate partitioning behavior of W is strongly dependent on redox conditions. The average fO2 of Martian building blocks must fall in the range of 1.3–1.6 log units below the iron–wüstite buffer to produce a Martian mantle with the observed Hf/W ratio. Other geochemical properties (such as sulfur content) also influence Martian 182W signatures, but the timing of accretion is a more important control. We find that while Mars must have accreted most of its mass within ~5 million years of solar system formation to reproduce the Hf–W isotopic constraints, it may have continued growing afterwards for over 50 million years. There is a high probability of simultaneously matching the orbit, mass, and Hf–W signature of Mars even in cases of prolonged accretion if giant impactor cores were poorly equilibrated and merged directly with the proto-Martian core.

Dong J., Fischer R.A., Stixrude L.P., and Lithgow-Bertelloni C.R. 2021. “Constraining the volume of Earth’s early oceans with a temperature-dependent mantle water storage capacity model.” AGU Advances, 2, Pp. e2020AV000323. Publisher's VersionAbstract
The water content in Earth's mantle today remains poorly constrained, but the bulk water storage capacity in the solid mantle can be quantified based on experimental data and may amount to a few times the modern surface ocean mass (OM). An appreciation of the mantle water storage capacity is indispensable to our understanding of how water may have cycled between the surface and mantle reservoirs and changed the volume of the oceans through time. In this study, we parameterized high pressure‐temperature experimental data on water storage capacities in major rock‐forming minerals to track the bulk water storage capacity in Earth's solid mantle as a function of temperature. We find that the mantle water storage capacity decreases as mantle potential temperature (Tp) increases, and its estimated value depends on the water storage capacity of bridgmanite in the lower mantle: 1.86–4.41 OM with a median of 2.29 OM for today (Tp = 1600 K), and 0.52–1.69 OM with a median of 0.72 OM for the early Earth's solid mantle (for a Tp that was 300 K higher). An increase in Tp by 200–300 K results in a decrease in the mantle water storage capacity by 1.19 (+0.9, –0.16) – 1.56 (+1.1, –0.22) OM. We explored how the volume of early oceans may have controlled sea level during the early Archean (4–3.2 Ga) with some additional assumptions about early continents. We found that more voluminous surface oceans might have existed if the actual mantle water content today is > 0.3–0.8 OM and the early Archean Tp was ≥1900 K.
Daviau K., Fischer R.A., Brennan M.C., Dong J., Suer T.-A., Couper S., Meng Y., and Prakapenka V.B. 2021. “Equation of state of TiN at high pressures and temperatures: A possible host for nitrogen in planetary mantles.” Journal of Geophysical Research: Solid Earth, 126, Pp. e2020JB020074. Publisher's VersionAbstract

Nitrogen, the most abundant gas in Earth’s atmosphere, is also a primary component of solid nitride minerals found in meteorites and on Earth’s surface. If they remain stable to high pressures and temperatures, these nitrides may also be important reservoirs of nitrogen in planetary interiors. We used synchrotron X-ray diffraction to measure the thermal equation of state and phase stability of titanium nitride (TiN) in a laser-heated diamond anvil cell at pressures up to ~70 GPa and temperatures up to ~2500 K. TiN maintains the cubic B1 (NaCl-type) crystal structure over the entire pressure and temperature range explored. It has K0 = 274(4) GPa, K0' = 3.9(2), and γ0 = 1.39(4) for a fixed V0 = 76.516(30) Å3 (based on experimental measurements), q = 1, and θ0 = 579 K. Additionally, we collected Raman spectra of TiN up to ~60 GPa, where we find that the transverse acoustic (TA), longitudinal acoustic (LA), and transverse optical (TO) phonon modes exhibit mode Grüneisen parameters of 1.66(17), 0.54(15), and 0.93(4), respectively. Based on our equation of state, TiN has a density of ~5.6–6.4 g/cm3 at Earth’s lower mantle conditions, significantly more dense than both the mantle of the Earth and the estimated densities of the mantles of other terrestrial planets, but less dense than planetary cores. We find that TiN remains stable against physical decomposition at the pressures and temperatures found within Earth’s mantle, making it a plausible reservoir for deep planetary nitrogen if chemical conditions allow its formation.

Chidester B.A., Thompson E.C., Fischer R.A., Heinz D.L., Prakapenka V.B., Meng Y., and Campbell A.J. 2021. “An experimental thermal equation of state of B2-KCl.” Physical Review B, 104, Pp. 094107. Publisher's VersionAbstract
The alkali halides are often used as optically-transparent pressure-transmitting media and thermal insulators in laser-heated diamond anvil cell experiments. High P–T equations of state for these materials would allow them to be used simultaneously as sensitive in situ pressure markers, making sample preparation and data analysis simpler. KCl is especially useful for this application because its high melting point, crystallographic simplicity, and low electron density are ideal for use in high-temperature X-ray diffraction experiments. However, the high-temperature static equation of state data for this material is limited in pressure to 8 GPa. As experiments routinely exceed 100 GPa in pressure and thousands of Kelvin, it is necessary for the equation of state of KCl to be determined experimentally at these conditions if it is to be used as an equation of state calibrant in the future. This work combines new high-pressure, high-temperature data of the B2 phase of KCl (up to 167 GPa and 2400 K) with the previously published room-temperature data of Dewaele et al. (2012) to produce a Mie-Grüneisen-Debye thermal equation of state for this material. The room temperature equation of state parameters are similar to those reported previously: V0 = 32.0(3) cm3/mole, K0 = 24(1) GPa and K0' = 4.56(5). The thermal parameters, γ0 and q, are 2.9(4) and 1.0(1), respectively. While a q of 1 is expected, the γ0 is higher than expected from previous calculations, lower pressure experimental data, and the available shockwave data. Thus, previously-reported equations of state underestimate the pressure of KCl at high temperatures.
Brennan M.C., Fischer R.A., Couper S., Miyagi L., Antonangeli D., and Morard G. 2021. “High-pressure deformation of iron–nickel–silicon alloys and implications for Earth's inner core.” Journal of Geophysical Research: Solid Earth, 126, Pp. e2020JB021077. Publisher's VersionAbstract

Earth's inner core exhibits strong seismic anisotropy, often attributed to the alignment of hexagonal close-packed iron (hcp-Fe) alloy crystallites with the Earth's poles. How this alignment developed depends on material properties of the alloy and is important to our understanding of the core’s crystallization history and active geodynamical forcing. Previous studies suggested that hcp-Fe is weak under deep Earth conditions but did not investigate the effects of the lighter elements known to be part of the inner core alloy. Here, we present results from radial X-ray diffraction experiments in a diamond anvil cell that constrain the strength and deformation properties of iron–nickel–silicon (Fe–Ni–Si) alloys up to 60 GPa. We also show the results of laser heating to 1650 K to evaluate the effect of temperature. Observed alloy textures suggest different relative activities of the various hcp deformation mechanisms compared to pure Fe, but these textures could still account for the theorized polar alignment. Fe–Ni–Si alloys are mechanically stronger than Fe and Fe–Ni; extrapolated to inner core conditions, Si-bearing alloys may be more than an order of magnitude stronger. This enhanced strength proportionally reduces the effectivity of dislocation creep as a deformation mechanism, which may suggest that texture developed during crystallization rather than as the result of post-solidification plastic flow.

Fischer R.A., Zube N.G., and Nimmo F. 2021. “The origin of the Moon's Earth-like tungsten isotopic composition from dynamical and geochemical modeling.” Nature Communications, 12, Pp. 35. Publisher's VersionAbstract
The Earth and Moon have identical or very similar isotopic compositions for many elements, including tungsten. However, canonical models of the Moon-forming impact predict that the Moon should be made mostly of material from the impactor, Theia. Here we evaluate the probability of the Moon inheriting its Earth-like tungsten isotopes from Theia in the canonical giant impact scenario, using 242 N-body models of planetary accretion and tracking tungsten isotopic evolution, and find that this probability is <1.6–4.7%. Mixing in up to 30% terrestrial materials increases this probability, but it remains <10%. Achieving similarity in stable isotopes is also a low-probability outcome, and is controlled by different mechanisms than tungsten. The Moon’s stable isotopes and tungsten isotopic composition are anticorrelated due to redox effects, lowering the joint probability to significantly less than 0.08–0.4%. We therefore conclude that alternate explanations for the Moon’s isotopic composition are likely more plausible.
Jackson M.G., Blichert-Toft J., Halldórsson S.A., Mundl-Petermeier A., Bizimis M., Kurz M.D., Price A.A., Harðardóttir S., Willhite L.N., Breddam K., Becker T.W., and Fischer R.A. 2020. “Ancient helium and tungsten isotopic signatures preserved in mantle domains least modified by crustal recycling.” Proceedings of the National Academy of Sciences of the U.S.A., 117, Pp. 30993–31001. Publisher's VersionAbstract
Rare high-3He/4He signatures in ocean island basalts (OIB) erupted at volcanic hotspots derive from deep-seated domains preserved in Earth’s interior. Only high-3He/4He OIB exhibit anomalous 182W—an isotopic signature inherited during the earliest history of Earth—supporting an ancient origin of high 3He/4He. However, it is not understood why some OIB host anomalous 182W while others do not. We provide geochemical data for the highest-3He/4He lavas from Iceland (up to 42.9 times atmospheric) with anomalous 182W and examine how Sr-Nd-Hf-Pb isotopic variations—useful for tracing subducted, recycled crust—relate to high 3He/4He and anomalous 182W. These data, together with data on global OIB, show that the highest-3He/4He and the largest-magnitude 182W anomalies are found only in geochemically depleted mantle domains—with high 143Nd/144Nd and low 206Pb/204Pb—lacking strong signatures of recycled materials. In contrast, OIB with the strongest signatures associated with recycled materials have low 3He/4He and lack anomalous 182W. These observations provide important clues regarding the survival of the ancient He and W signatures in Earth’s mantle. We show that high-3He/4He mantle domains with anomalous 182W have low W and 4He concentrations compared to recycled materials and are therefore highly susceptible to being overprinted with low 3He/4He and normal (not anomalous) 182W characteristic of subducted crust. Thus, high 3He/4He and anomalous 182W are preserved exclusively in mantle domains least modified by recycled crust. This model places the long-term preservation of ancient high 3He/4He and anomalous 182W in the geodynamic context of crustal subduction and recycling and informs on survival of other early-formed heterogeneities in Earth’s interior.
Mundl-Petermeier A., Walker R.J., Fischer R.A., Lekic V., Jackson M.G., and Kurz M.D. 2020. “Anomalous 182W in high 3He/4He ocean island basalts: Fingerprints of Earth's core?” Geochimica et Cosmochimica Acta, 271, Pp. 194–211. Publisher's VersionAbstract
The short-lived 182Hf–182W isotope system (t1/2 = 9 Ma) left evidence in both ancient and modern terrestrial rock record of processes that took place during the earliest stages of Earth’s accretionary and differentiation history. We report µ182W values (the deviation of 182W/184W of a sample from that of laboratory standards, in parts per million) and corresponding 3He/4He ratios for rocks from 15 different hotspots. These rocks are characterized by µ182W values that range from ~0 to as low as –23 ± 4.5. For each volcanic system that includes rocks with negative µ182W values, the values tend to be negatively correlated with 3He/4He. The W–He isotopic characteristics of all samples can be successfully modeled via mixing involving at least three mantle source reservoirs with distinct µ182W–3He/4He characteristics. One reservoir has 3He/4He ≈ 8 R/RA and µ182W ≈ 0, which is indistinguishable from the convecting upper mantle. Based on high 3He/4He, the other two reservoirs are presumed to be relatively un-degassed and likely primordial. One reservoir is characterized by µ182W ≈ 0, while the other is characterized by µ182W ≤ –23. The former reservoir likely formed from a silicate differentiation process more than 60 Myr after the origin of the solar system, but has remained partially or wholly isolated from the rest of the mantle for most of Earth history. The latter reservoir most likely includes a component that formed while 182Hf was extant. Mass balance constraints on the isotopic composition of the core suggest it has a strongly negative µ182W value of ~ –220. Thus, it is a candidate for the origin of the negative µ182W in the plume sources. Mixing models show that the direct addition of outer core metal into a plume rising from the core-mantle boundary would result in collateral geochemical effects, particularly in the abundances of highly siderophile elements, which are not observed in OIB. Instead, the reservoir characterized by negative µ182W most likely formed in the lowermost mantle as a result of core–mantle isotopic equilibration. The envisioned equilibration process would raise the W concentration and lower the µ182W of the resulting silicate reservoir, relative to the rest of the mantle. The small proportion (<0.3%) of this putative core-mantle equilibrated reservoir required to account for the µ182W signatures observed in OIB is insufficient to result in observable effects on most other elemental and/or isotopic compositions. The presumed primordial reservoirs may be linked to seismically distinct regions in the lower mantle. Seismically imaged mantle plumes appear to preferentially ascend from the vicinity of large low-shear velocity provinces (LLSVPs), which have been interpreted as thermochemical piles. We associate the LLSVPs with the primordial reservoir characterized by high 3He/4He and µ182W = 0. Smaller, ultra-low velocity zones (ULVZs) present at the core-mantle boundary have been interpreted to consist of (partially) molten lower mantle material. The negative µ182W signatures observed in some plume-derived lavas may result from small contributions of ULVZ material that has inherited its negative µ182W signature through core–mantle equilibration.
Fischer R.A., Cottrell E., Hauri E., Lee K.K.M., and Le Voyer M. 2020. “The carbon content of Earth and its core.” Proceedings of the National Academy of Sciences of the U.S.A., 117, Pp. 8743–8749. Publisher's VersionAbstract
Earth’s core is likely the largest reservoir of carbon (C) in the planet, but its C abundance has been poorly constrained because measurements of carbon’s preference for core versus mantle materials at the pressures and temperatures of core formation are lacking. Using metal–silicate partitioning experiments in a laser-heated diamond anvil cell, we show that carbon becomes significantly less siderophile as pressures and temperatures increase to those expected in a deep magma ocean during formation of Earth’s core. Based on a multistage model of core formation, the core likely contains a maximum of 0.09(4) to 0.20(10) wt% C, making carbon a negligible contributor to the core’s composition and density. However, this accounts for ∼80 to 90% of Earth’s overall carbon inventory, which totals 370(150) to 740(370) ppm. The bulk Earth’s carbon/sulfur ratio is best explained by the delivery of most of Earth’s volatiles from carbonaceous chondrite-like precursors.
Brennan M.C., Fischer R.A., and Irving J.C.E. 2020. “Core formation and geophysical properties of Mars.” Earth and Planetary Science Letters, 530, Pp. 115923. Publisher's VersionAbstract

The chemical and physical properties of the interiors of terrestrial planets are largely determined during their formation and differentiation. Modeling a planet’s formation provides important insights into the properties of its core and mantle, and conversely, knowledge of those properties may constrain formational narratives. Here, we present a multi-stage model of Martian core formation in which we calculate core–mantle equilibration using parameterizations from high pressure–temperature metal–silicate partitioning experiments. We account for changing core–mantle boundary (CMB) conditions, composition-dependent partitioning, and partial equilibration of metal and silicate, and we evolve oxygen fugacity (fO2) self-consistently. The model successfully reproduces published meteorite-based estimates of most elemental abundances in the bulk silicate Mars, which can be used to estimate core formation conditions and core composition. This composition implies that the primordial material that formed Mars was significantly more oxidized (0.9–1.4 log units below the iron–wüstite buffer) than that of the Earth, and that core–mantle equilibration in Mars occurred at 42–60% of the evolving CMB pressure. On average, at least 84% of accreted metal and at least 40% of the mantle were equilibrated in each impact, a significantly higher degree of metal equilibration than previously reported for the Earth. In agreement with previous studies, the modeled Martian core is rich in sulfur (18–19 wt%), with less than one weight percent O and negligible Si.

We have used these core and mantle compositions to produce physical models of the present-day Martian interior and evaluate the sensitivity of core radius to crustal thickness, mantle temperature, core composition, core temperature, and density of the core alloy. Trade-offs in how these properties affect observable physical parameters like planetary mass, radius, moment of inertia, and tidal Love number k2 define a range of likely core radii: 1620–1870 km. Seismic velocity profiles for several combinations of model parameters have been used to predict seismic body-wave travel times and planetary normal mode frequencies. These results may be compared to forthcoming Martian seismic data to further constrain core formation conditions and geophysical properties.

Zube N.G., Nimmo F., Fischer R.A., and Jacobson S.A. 2019. “Constraints on terrestrial planet formation timescales and equilibration processes in the Grand Tack scenario from Hf-W isotopic evolution.” Earth and Planetary Science Letters, 522, Pp. 210–218. Publisher's VersionAbstract
We examine 141 N-body simulations of terrestrial planet late-stage accretion that use the Grand Tack scenario, coupling the collisional results with a hafnium-tungsten (Hf-W) isotopic evolution model. Accretion in the Grand Tack scenario results in faster planet formation than classical accretion models because of higher planetesimal surface density induced by a migrating Jupiter. Planetary embryos that grow rapidly experience radiogenic ingrowth of mantle 182W that is inconsistent with the measured terrestrial composition, unless much of the tungsten is removed by an impactor core that mixes thoroughly with the target mantle. For physically Earth-like surviving planets, we find that the fraction of equilibrating impactor core kcore 0.6 is required to produce results agreeing with observed terrestrial tungsten anomalies (assuming equilibration with relatively large volumes of target mantle material; smaller equilibrating mantle volumes would require even larger kcore). This requirement of substantial core re-equilibration may be difficult to reconcile with fluid dynamical predictions and hydrocode simulations of mixing during large impacts, and hence this result does not favor the rapid planet building that results from Grand Tack accretion.
Fischer R.A. and Nimmo F. 2018. “Effects of core formation on the Hf–W isotopic composition of the Earth and dating of the Moon-forming impact.” Earth and Planetary Science Letters, 499, Pp. 257–265. Publisher's VersionAbstract
Earth’s core formation set the initial compositions of the core and mantle. Various aspects of core formation, such as the degree of metal–silicate equilibration, oxygen fugacity, and depth of equilibration, have significant consequences for the resulting compositions, yet are poorly constrained. The Hf–W isotopic system can provide unique constraints on these aspects relative to other geochemical or geophysical methods. Here we model the Hf–W isotopic evolution of the Earth, improving over previous studies by combining a large number of N-body simulations of planetary accretion with a core formation model that includes self-consistent evolution of oxygen fugacity and a partition coefficient of tungsten that evolves with changing pressure, temperature, composition, and oxygen fugacity. The effective average fraction of equilibrating metal is constrained to be k > 0.2 for a range of equilibrating silicate masses (for canonical accretion scenarios), and is likely <0.55 if the Moon formed later than 65 Ma. These values of k typically correspond to an effective equilibration depth of ~0.5–0.7x the evolving core–mantle boundary pressure as the planet grows. The average mass of equilibrating silicate was likely at least 3x the impactor’s silicate mass. Equilibration temperature, initial fO2, initial differentiation time, semimajor axis, and planetary mass (above ~0.9 Earth masses) have no systematic effect on the 182W anomaly, or on fHf/W (except for fO2), when applying the constraint that the model must reproduce Earth’s mantle W abundance. There are strong tradeoffs between the effects of k, equilibrating silicate mass, depth of equilibration, and timing of core formation, so the terrestrial Hf–W isotopic system should be interpreted with caution when used as a chronometer of Earth’s core formation. Because of these strong tradeoffs, the Earth’s tungsten anomaly can be reproduced for Moon-forming impact timescales spanning at least 10–175 Ma. Early Moon formation ages require a higher degree of metal–silicate equilibration to produce Earth’s 182W anomaly.
Fischer R.A., Campbell A.J., Chidester B.A., Reaman D.M., Thompson E.C., Pigott J.S., Prakapenka V.B., and Smith J.S. 2018. “Equations of state and phase boundary for stishovite and CaCl2-type SiO2.” American Mineralogist, 103, Pp. 792–802. Publisher's VersionAbstract

Silica is thought to be present in the Earth’s lower mantle in subducting plates, in addition to being a prototypical solid whose physical properties are of broad interest. It is known to undergo a phase transition from stishovite to the CaCl2-type structure at ~50–80 GPa, but the exact location and slope of the phase boundary in pressure-temperature space is unresolved. There have been many previous studies on the equation of state of stishovite, but they span a limited range of pressures and temperatures, and there has been no thermal equation of state of CaCl2-type SiO2 measured under static conditions. We have investigated the phase diagram and equations of state of silica at 21–89 GPa and up to ~3300 K using synchrotron X-ray diffraction in a laser-heated diamond anvil cell. The phase boundary between stishovite and CaCl2-type SiO2 can be approximately described as T = 64.6(49)*P – 2830(350), with temperature T in Kelvin and pressure P in GPa. The stishovite data imply K0' = 5.24(9) and a quasi-anharmonic T2 dependence of –6.0(4) x 10–6 GPa*cm3/mol/K2 for a fixed q = 1, ɣ0 = 1.71, and K0 = 302 GPa, while for the CaCl2-type phase K0 = 341(4) GPa, K0' = 3.20(16), and ɣ0 = 2.14(4) with other parameters equal to their values for stishovite. The behaviors of the a and c axes of stishovite with pressure and temperature were also fit, indicating a much more compressible c axis with a lower thermal expansion as compared to the a axis. The phase transition between stishovite and CaCl2-type silica should occur at pressures of 68–78 GPa in the Earth, depending on the temperature in subducting slabs. Silica is denser than surrounding mantle material up to pressures of 58–68 GPa, with uncertainty due to temperature effects; at higher pressures than this, SiO2 becomes gravitationally buoyant in the lower mantle.

Chidester B.A., Pardo O.S., Fischer R.A., Thompson E.C., Heinz D.L., Prescher C., Prakapenka V.B., and Campbell A.J. 2018. “High-pressure phase behavior and equations of state of ThO2 polymorphs.” American Mineralogist, 103, Pp. 749–756. Publisher's VersionAbstract

ThO2 is an important material for understanding the heat budget of Earth’s mantle, as well as the stability of nuclear fuels at extreme conditions. We measured the in situ high-pressure, high-temperature phase behavior of ThO2 to ~60 GPa and ~2500 K. It undergoes a transition from the cubic fluorite-type structure (thorianite) to the orthorhombic α-PbCl2 cotunnite-type structure between 20 and 30 GPa at room temperature. Prior to the transition at room temperature, an increase in unit cell volume is observed, which we interpret as anion sub-lattice disorder or pre-transformation “melting” (Boulfelfel et al., 2006). The thermal equation of state parameters for both thorianite (V0 = 26.379(7), K0 = 204(2), αKT = 0.0035(3)) and the high-pressure cotunnite-type phase (V0 = 24.75(6), K0 = 190(3), αKT = 0.0037(4)) are reported, holding K0´ fixed at 4. The similarity of these parameters suggests that the two phases behave similarly within the deep Earth. The lattice parameter ratios for the cotunnite-type phase change significantly with pressure, suggesting a different structure is stable at higher pressure.

Fischer R.A., Nimmo F., and O'Brien D.P. 2018. “Radial mixing and Ru–Mo isotope systematics under different accretion scenarios.” Earth and Planetary Science Letters, 482, Pp. 105–114. Publisher's VersionAbstract
The Ru–Mo isotopic compositions of inner Solar System bodies may reflect the provenance of accreted material and how it evolved with time, both of which are controlled by the accretion scenario these bodies experienced. Here we use a total of 116 N-body simulations of terrestrial planet accretion, run in the Eccentric Jupiter and Saturn (EJS), Circular Jupiter and Saturn (CJS), and Grand Tack scenarios, to model the Ru–Mo anomalies of Earth, Mars, and Theia analogues. This model starts by applying an initial step function in Ru–Mo isotopic composition, with compositions reflecting those in meteorites, and traces compositional evolution as planets accrete. The mass-weighted provenance of the resulting planets reveals more radial mixing in Grand Tack simulations than in EJS/CJS simulations, and more efficient mixing among late-accreted material than during the main phase of accretion in EJS/CJS simulations. We find that an extensive homogeneous inner disk region is required to reproduce Earth's observed Ru–Mo composition. EJS/CJS simulations require a homogeneous reservoir in the inner disk extending to ≥3–4 AU (≥74–98% of initial mass) to reproduce Earth's composition, while Grand Tack simulations require a homogeneous reservoir extending to ≥3–10 AU (≥97–99% of initial mass), and likely to ≥6–10 AU. In the Grand Tack model, Jupiter's initial location (the most likely location for a discontinuity in isotopic composition) is ∼3.5 AU; however, this step location has only a 33% likelihood of producing an Earth with the correct Ru–Mo isotopic signature for the most plausible model conditions. Our results give the testable predictions that Mars has zero Ru anomaly and small or zero Mo anomaly, and the Moon has zero Mo anomaly. These predictions are insensitive to wide variations in parameter choices.
Wordsworth R.D., Schaefer L., and Fischer R.A. 2018. “Redox evolution via gravitational differentiation on low mass planets: Implications for biosignatures, water loss, and habitability.” The Astronomical Journal, 155, Pp. 195. Publisher's VersionAbstract

The oxidation of rocky planet surfaces and atmospheres, which arises from the twin forces of stellar nucleosynthesis and gravitational differentiation, is a universal process of key importance to habitability and exoplanet biosignature detection. Here we take a generalized approach to this phenomenon. Using a single parameter to describe redox state, we model the evolution of terrestrial planets around nearby M-stars and the Sun. Our model includes atmospheric photochemistry, diffusion and escape, line-by-line climate calculations and interior thermodynamics and chemistry. In most cases we find abiotic atmospheric O2 buildup around M-stars during the pre-main sequence phase to be much less than calculated previously, because the planet’s magma ocean absorbs most oxygen liberated from H2O photolysis. However, loss of non-condensing atmospheric gases after the mantle solidifies remains a significant potential route to abiotic atmospheric O2 subsequently. In all cases, we predict that exoplanets that receive lower stellar fluxes, such as LHS1140b and TRAPPIST- 1f and g, have the lowest probability of abiotic O2 buildup and hence are the best targets for future biosignature searches. Key remaining uncertainties can be minimized in future by comparing our predictions for the atmospheres of hot, sterile exoplanets such as GJ1132b and TRAPPIST-1b and -c with observations.

Fischer R.A., Campbell A.J., and Ciesla F.J. 2017. “Sensitivities of Earth’s core and mantle compositions to accretion and differentiation processes.” Earth and Planetary Science Letters, 458, Pp. 252–262. Publisher's VersionAbstract
The Earth and other terrestrial planets formed through the accretion of smaller bodies, with their core and mantle compositions primarily set by metal–silicate interactions during accretion. The conditions of these interactions are poorly understood, but could provide insight into the mechanisms of planetary core formation and the composition of Earth's core. Here we present modeling of Earth's core formation, combining results of 100 N-body accretion simulations with high pressure–temperature metal–silicate partitioning experiments. We explored how various aspects of accretion and core formation influence the resulting core and mantle chemistry: depth of equilibration, amounts of metal and silicate that equilibrate, initial distribution of oxidation states in the disk, temperature distribution in the planet, and target:impactor ratio of equilibrating silicate. Virtually all sets of model parameters that are able to reproduce the Earth's mantle composition result in at least several weight percent of both silicon and oxygen in the core, with more silicon than oxygen. This implies that the core's light element budget may be dominated by these elements, and is consistent with ≤1–2 wt% of other light elements. Reproducing geochemical and geophysical constraints requires that Earth formed from reduced materials that equilibrated at temperatures near or slightly above the mantle liquidus during accretion. The results indicate a strong tradeoff between the compositional effects of the depth of equilibration and the amounts of metal and silicate that equilibrate, so these aspects should be targeted in future studies aiming to better understand core formation conditions. Over the range of allowed parameter space, core and mantle compositions are most sensitive to these factors as well as stochastic variations in what the planet accreted as a function of time, so tighter constraints on these parameters will lead to an improved understanding of Earth's core composition.
Deep Earth: Physics and Chemistry of the Lower Mantle and Core
2016. Deep Earth: Physics and Chemistry of the Lower Mantle and Core. American Geophysical Union / John Wiley and Sons. Publisher's VersionAbstract

Deep Earth: Physics and Chemistry of the Lower Mantle and Core highlights recent advances and the latest views of the deep Earth from theoretical, experimental, and observational approaches and offers insight into future research directions on the deep Earth. In recent years, we have just reached a stage where we can perform measurements at the conditions of the center part of the Earth using state-of-the-art techniques, and many reports on the physical and chemical properties of the deep Earth have come out very recently. Novel theoretical models have been complementary to this breakthrough. These new inputs enable us to compare directly with results of precise geophysical and geochemical observations. This volume highlights the recent significant advancements in our understanding of the deep Earth that have occurred as a result, including contributions from mineral/rock physics, geophysics, and geochemistry that relate to the topics of: 

I. Thermal structure of the lower mantle and core

II. Structure, anisotropy, and plasticity of deep Earth materials

III. Physical properties of the deep interior

IV. Chemistry and phase relations in the lower mantle and core

V. Volatiles in the deep Earth 

The volume will be a valuable resource for researchers and students who study the Earth's interior. The topics of this volume are multidisciplinary, and therefore will be useful to students from a wide variety of fields in the Earth Sciences.