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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Thermal conductivity of CaSiO 3 perovskite at lower mantle conditions

Thermal conductivity (κ) of mantle minerals is key to understanding dynamics in the deep Earth. It controls the style of mantle convection and the timescale of cooling both the mantle and the core. Cubic CaSiO 3 perovskite (CaPv) is the third most abundant mineral in the lower mantle (7 vol %). Despite its importance, no theoretical or experimental estimate of CaPv's κ is available. Theoretical investigations of its properties are challenging because of its strong anharmonicity. Experimental measurements at relevant pressures and temperatures are equally challenging. Here we present ab initio results for CaPv's κ obtained using the phonon quasiparticle approach to address its strong anharmonicity. We also offer experimental measurements of κ up to 67 GPa and 1950 K. Predictions and measurements are in good agreement and reveal a surprisingly large κ for cubic CaPv that can be explained on the basis of its high crystal structure symmetry. Despite its relatively low abundance, CaPv's κ increases the lower mantle κ by ~10 %, if accounted for. κ of mantle regions enriched in subducted crustal materials will be more strongly impacted.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Single-crystal elasticity of (Al,Fe)-bearing bridgmanite up to 82 GPa

Abstract Thermoelastic properties of mantle candidate minerals are essential to our understanding of geophysical phenomena, geochemistry, and geodynamic evolutions of the silicate Earth. However, the lower-mantle mineralogy remains much debated due to the lack of single-crystal elastic moduli (Cij) and aggregate sound velocities of (Al,Fe)-bearing bridgmanite, the most abundant mineral of the planet, at the lower mantle pressure-temperature (P-T) conditions. Here we report single-crystal Cij of (Al,Fe)-bearing bridgmanite, Mg0.88Fe0.1Al0.14Si0.90O3 (Fe10-Al14-Bgm) with Fe3+/ΣFe = ~0.65, up to ~82 GPa using X-ray diffraction (XRD), Brillouin light scattering (BLS), and impulsive stimulated light scattering (ISLS) measurements in diamond-anvil cells (DACs). Two crystal platelets with orientations of (–0.50, 0.05, –0.86) and (0.65, –0.59, 0.48), that are sensitive to deriving all nine Cij, are used for compressional and shear wave velocity (νP and νS) measurements as a function of azimuthal angles over 200° at each experimental pressure. Our results show that all Cij of singe-crystal Fe10-Al14-Bgm increase monotonically with pressure with small uncertainties of 1–2% (±1σ), except C55 and C23, which have uncertainties of 3–4%. Using the third-order Eulerian finite-strain equations to model the elasticity data yields the aggregate adiabatic bulk and shear moduli and respective pressure derivatives at the reference pressure of 25 GPa: KS = 326 ± 4 GPa, µ = 211 ± 2 GPa, KS′ = 3.32 ± 0.04, and µ′ = 1.66 ± 0.02 GPa. The high-pressure aggregate νS and νP of Fe10-Al14-Bgm are 2.6–3.5% and 3.1–4.7% lower than those of MgSiO3 bridgmanite end-member, respectively. These data are used with literature reports on bridgmanite with different Fe and Al contents to quantitatively evaluate pressure and compositional effects on their elastic properties. Comparing with one-dimensional seismic profiles, our modeled velocity profiles of major lower-mantle mineral assemblages at relevant P-T suggest that the lower mantle could likely consist of about 89 vol% (Al,Fe)-bearing bridgmanite. After considering uncertainties, our best-fit model is still indistinguishable from pyrolitic or chondritic models.

Geochemistry & Geophysics↗
DOE OSTI2024

Effect of Pressure on Crystal Structure and Phonon Density of States of FeSi

The strongly correlated material FeSi displays several unusual thermal, magnetic, and structural properties under varying pressure-temperature (P-T) conditions. It is a potential thermoelectric alloy and a material with several geochemical implications as a possible constituent at the Earth's core-mantle boundary (CMB). Previous theoretical studies predicted a pressure-induced B20-B2 transition at ambient temperature below 40 GPa; however, experimentally, the structural transition is observed only at high P-T conditions. In this study, we have performed high-pressure powder X-ray diffraction (XRD) up to 90 GPa and Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements up to 120 GPa to understand the phase stability and lattice dynamics. Our study provides evidence for a non-hydrostatic stress-induced B20-B2 transition in FeSi at around 36 GPa. We deduced the Fe partial phonon density of states (PDOS) and thermal parameters from NRIXS measurements up to 120 GPa and compared them with density functional theory (DFT) calculations. Furthermore, the computations show pressure-induced metallization and the band gap closing around 12 GPa.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Implications of the iron oxide phase transition on the interiors of rocky exoplanets

The discovery of an extraordinary number of extrasolar planets, characterized by an unexpected variety of sizes, masses and orbits, challenges our understanding of the formation and evolution of the planets in the Solar System and the perception of the Earth as the prototypical habitable world. Many exoplanets appear to be rocky and yet more massive than the Earth, with expected pressures and temperatures of hundreds of gigapascal and thousands of Kelvin in their deep interiors. At these conditions, the properties of bridgmanite and ferropericlase, expected to dominate their mantles, are largely unconstrained, limiting our knowledge of their interior structure. Here we used nano-second X-ray diffraction and dynamic compression to experimentally investigate the atomic structure and density of iron oxide (FeO), one of the end-members of the (Mg,Fe)O ferropericlase solid solution, up to 700 GPa, a pressure exceeding the core–mantle boundary of a 5 Earth masses planet. Our data document the stability of the high-pressure cesium-chloride B2 structure above 300 GPa, well below the pressure required for magnesium oxide (MgO) to adopt the same phase. These observations, complemented by the calculation of the binary MgO–FeO phase diagram, reveal complex stratification and rheology inside large terrestrial exoplanets.

58 GEOSCIENCES↗
DOE OSTI2022

Constraining composition and temperature variations in the mantle transition zone

The mantle transition zone connects two major layers of Earth’s interior that may be compositionally distinct: the upper mantle and the lower mantle. Wadsleyite is a major mineral in the upper mantle transition zone. Here, we measure the single-crystal elastic properties of hydrous Fe-bearing wadsleyite at high pressure-temperature conditions by Brillouin spectroscopy. Our results are then used to model the global distribution of wadsleyite proportion, temperature, and water content in the upper mantle transition zone by integrating mineral physics data with global seismic observations. Our models show that the upper mantle transition zone near subducted slabs is relatively cold, enriched in wadsleyite, and slightly more hydrated compared to regions where plumes are expected. This study provides direct evidence for the thermochemical heterogeneities in the upper mantle transition zone which is important for understanding the material exchange processes between the upper and lower mantle.

58 GEOSCIENCES↗
DOE OSTI2021

Locating Seismic Events with Local-Distance Data

As the seismic monitoring community advances toward detecting, identifying, and locating ever-smaller natural and anthropogenic events, the need is constantly increasing for higher resolution, higher fidelity data, models, and methods for accurately characterizing events. Local-distance seismic data provide robust constraints on event locations, but also introduce complexity due to the significant geologic heterogeneity of the Earth’s crust and upper mantle, and the relative sparsity of data that often occurs with small events recorded on regional seismic networks. Identifying the critical characteristics for improving local-scale event locations and the factors that impact location accuracy and reliability is an ongoing challenge for the seismic community. Using Utah as a test case, we examine three data sets of varying duration, finesse, and magnitude to investigate the effects of local earth structure and modeling parameters on local-distance event location precision and accuracy. We observe that the most critical elements controlling relocation precision are azimuthal coverage and local-scale velocity structure, with tradeoffs based on event depth, type, location, and range.

42 ENGINEERING↗
DOE OSTI2020

Structure and Stability of Iron Fluoride at High Pressure–Temperature and Implication for a New Reservoir of Fluorine in the Deep Earth

Fluorine (F) is the most abundant halogen in the bulk silicate Earth. F plays an important role in geochemical and biological systems, but its abundance and distribution in the terrestrial mantle are still unclear. Recent studies suggested that F reservoirs in the deep mantle are potentially hosted in terrestrial oxide minerals, especially in aluminous bridgmanite. However, the knowledge about the formation and stability field of fluoride in the Earth’s interior is rare. In this study, we combine in situ laser-heated diamond anvil cell, synchrotron X-ray diffraction, and first-principles structure search to show that a new tetragonal structure of FeF 3 is stable at pressures of 78–130 GPa and temperatures up to ~1900 K. Simulation predicted the tetragonal phase takes a much denser structure due to the rotation of FeF 6 octahedral units. The equations of states of tetragonal FeF3 are determined by experiment and verified by simulation. Our results indicate that FeF 3 can be a potential key phase for storing F in the Earth’s lower mantle and may explain some mantle-derived magma with high F concentration.

58 GEOSCIENCES↗
DOE OSTI2021

Room temperature facile synthesis of olivine-Co 2 SiO 4 nanoparticles utilizing a mechanochemical method

Co 2 SiO 4 is a ceramic pigment and promising battery material of significant technological interest, as well as a model end-member of one of the most important mineral families in the Earth's crust and upper mantle. All previously developed methods for synthesis of Co 2 SiO 4 require high-temperature processing, which promotes grain growth, while the nanocrystalline form is required for some important technological applications. Here, we report a successful method for synthesizing nanocrystalline Co 2 SiO 4 via a simple and inexpensive high-energy ball milling mechanochemical process. Products of the synthesis were characterized by a combination of XRD and TEM, and their crystal structures and elemental compositions are reported.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Graphite resistive heated diamond anvil cell for simultaneous high-pressure and high-temperature diffraction experiments

High-pressure and high-temperature experiments using a resistively heated diamond anvil cell have the advantage of heating samples homogeneously with precise temperature control. Here, we present the design and performance of a graphite resistive heated diamond anvil cell (GRHDAC) setup for powder and single-crystal x-ray diffraction experiments developed at the Extreme Conditions Beamline (P02.2) at PETRA III, Hamburg, Germany. In the GRHDAC, temperatures up to 2000 K can be generated at high pressures by placing it in a water-cooled vacuum chamber. Temperature estimates from thermocouple measurements are within +/–35 K at the sample position up to 800 K and within +90 K between 800 and 1400 K when using a standard seat combination of cBN and WC. Isothermal compression at high temperatures can be achieved by employing a remote membrane control system. Importantly, the advantage of the GRHDAC is demonstrated through the study of geophysical processes in the Earth’s crust and upper mantle region.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

A new hydrous iron oxide phase stable at mid-mantle pressures

The amount of hydrogen stored in the Earth's interior is important for a range of issues, including the volatile incorporation during the Earth formation and the co-evolution of the atmosphere, the hydrosphere, and the interior. Recent experiments found titanium bearing ε-FeOOH in a hydrous basaltic system at 12–19 GPa and 1300 K. Pyrite-type FeOOH was found to be stable at pressures higher than 80 GPa. These discoveries suggest possible hydrogen storage in the mantle transition zone and in the mantle below 1800 km depths, respectively. However, it remains uncertain how the potential deep hydrogen storage can be connected to the shallower storage. Here, we report a new hydrous iron oxide (η-Fe 12 O 18+x / 2 H x , x ≈ 2) stable at pressures between the stability fields of the ε- and the pyrite-type FeOOH. Our experiment also shows that the new η phase can exist together with the major lower mantle minerals including bridgmanite and periclase, making it an important hydrogen-bearing phase in the Earth's deep interior. Because of its limited H 2 O storage capacity, which is less than 1/6 of the storage capacity of the pyrite-type phase and the ε phase, the stability of the η phase would result in H 2 O loss during water transport in the mid mantle and therefore limit the amount of H 2 O potentially stored in the Fe–O–H system of the lower mantle. As a result, the large channel in the crystal structure of the η phase could provide potential storage sites for other volatile elements in the deep mantle.

58 GEOSCIENCES↗
DOE OSTI2020

In situ X-ray diffraction of silicate liquids and glasses under dynamic and static compression to megabar pressures

Properties of liquid silicates under high-pressure and high-temperature conditions are critical for modeling the dynamics and solidification mechanisms of the magma ocean in the early Earth, as well as for constraining entrainment of melts in the mantle and in the present-day core–mantle boundary. In this paper, we present in situ structural measurements by X-ray diffraction of selected amorphous silicates compressed statically in diamond anvil cells (up to 157 GPa at room temperature) or dynamically by laser-generated shock compression (up to 130 GPa and 6,000 K along the MgSiO 3 glass Hugoniot). The X-ray diffraction patterns of silicate glasses and liquids reveal similar characteristics over a wide pressure and temperature range. Beyond the increase in Si coordination observed at 20 GPa, we find no evidence for major structural changes occurring in the silicate melts studied up to pressures and temperatures exceeding Earth’s core mantle boundary conditions. This result is supported by molecular dynamics calculations. Our findings reinforce the widely used assumption that the silicate glasses studies are appropriate structural analogs for understanding the atomic arrangement of silicate liquids at these high pressures.

58 GEOSCIENCES↗
DOE OSTI2020

Structural Modifications of Single-Crystal Aragonite CaCO 3 Beginning at ~15 GPa: In Situ Vibrational Spectroscopy and X-Ray Diffraction Evidence

The structural chemistry of carbonates under mantle conditions facilitates our understanding of carbon recycling pathways in the earth’s interior. It also has impacts on the dynamics of mantle–slab interactions. Aragonite is a common calcium carbonate mineral in pelagic marine sediments. The structural chemistry of single-crystal aragonite during successive compression and the behavior of a structural H+ have been investigated by micro-vibrational spectroscopy and synchrotron X-ray diffraction techniques in diamond anvil cells. We describe a reduction of the b-axial compressibility beginning at ~15 GPa, and the related discontinuities in the first-order derivatives of the vibrational modes. The structural modifications of aragonite are manifested by mutations occurring in the pressure relations of the wavenumbers of the O-C-O bending modes, and of the bandwidth and band intensities of the measured internal and external modes. These anomalies are indicative of changes occurring in the force constant of the C-O bonds, and possibly a second-order phase transition. Besides, the [CaO 9 ] polyhedra begin to deform, possibly with some Ca-O bonds becoming elongated and the others shortening. An increase in the co-ordination number for the Ca 2+ sites could be expected under higher pressures. Additionally, the weakening of the OH modes may imply H + -loss from the aragonite lattice above 11.5 GPa.

58 GEOSCIENCES↗
DOE OSTI2024

Incipient carbonate melting drives metal and sulfur mobilization in the mantle

We present results from high-pressure, high-temperature experiments that generate incipient carbonate melts at mantle conditions (~90 kilometers depth and temperatures between 750° and 1050°C). We show that these primitive carbonate melts can sequester sulfur in its oxidized form of sulfate, as well as base and precious metals from mantle lithologies of peridotite and pyroxenite. It is proposed that these carbonate sulfur–rich melts may be more widespread than previously thought and that they may play a first-order role in the metallogenic enhancement of localized lithospheric domains. They act as effective agents to dissolve, redistribute, and concentrate metals within discrete domains of the mantle and into shallower regions within Earth, where dynamic physicochemical processes can lead to ore genesis at various crustal depths.

58 GEOSCIENCES↗
DOE OSTI2024

The Collaborative Seismic Earth Model: Generation 2

Geological interpretations, earthquake source inversions and ground motion modeling, among other applications, require models that jointly resolve crustal and mantle structure. With the second generation of the Collaborative Seismic Earth Model (CSEM2), we present a global multi-resolution tomographic Earth model that serves this purpose. The model evolves through successive regional- and global-scale refinements. While the first generation aggregated regional models, with this study, we ensure consistency between all individual submodels, resulting in a model that accurately explains wave propagation across scales. Recent regional tomographic models were incorporated, comprising continental-scale inversions for Asia and Africa, as well as regional inversions for the Western US, Central Andes, Iran, and Southeast Asia. Across all regional refinements, over 793,000 source-receiver pairs contributed. Moreover, the long-wavelength Earth model (LOWE) introduces large-scale structures outside of pre-existing local refinements. A full-waveform inversion for global anisotropic P-and S-wave speed structure over a total of 194 iterations with a minimum period of 50 s on a large data set of 1 hr of waveform data from 2,423 earthquakes and over 6 million source-receiver pairs ensures that regional updates in the crust and uppermost mantle translate into updates of deeper, global-scale structure. To test the performance of CSEM2, we evaluate waveform fits between observed and synthetic seismograms at 50 s for an independent data set on the global scale, and on the regional scale for lower periods. We accurately simulate waveforms within and across regional refinements, maintaining the original resolution of the submodels embedded in the global framework.

58 GEOSCIENCES↗
DOE OSTI2020

Mineralogy of the deep lower mantle in the presence of H 2 O

Understanding the mineralogy of the Earth's interior is a prerequisite for unravelling the evolution and dynamics of our planet. Here, we conducted high pressure-temperature experiments mimicking the conditions of the deep lower mantle (DLM, 1800–2890 km in depth) and observed surprising mineralogical transformations in the presence of water. Ferropericlase, (Mg, Fe)O, which is the most abundant oxide mineral in Earth, reacts with H 2 O to form a previously unknown (Mg, Fe)O 2 H x (x ≤ 1) phase. The (Mg, Fe)O 2 H x has a pyrite structure and it coexists with the dominant silicate phases, bridgmanite and post-perovskite. Depending on Mg content and geotherm temperatures, the transformation may occur at 1800 km for (Mg 0.6 Fe 0.4 )O or beyond 2300 km for (Mg 0.7 Fe 0.3 )O. The (Mg, Fe)O 2 H x is an oxygen excess phase that stores an excessive amount of oxygen beyond the charge balance of maximum cation valences (Mg 2+ , Fe 3+ and H + ). This important phase has a number of far-reaching implications including extreme redox inhomogeneity, deep-oxygen reservoirs in the DLM and an internal source for modulating oxygen in the atmosphere.

58 GEOSCIENCES↗
DOE OSTI2023

Activity model for 36 elements in Fe-Ni-Si-S-C liquids with application to terrestrial planet accretion and mantle geochemistry: New data for Ru, Re, Pt, Os, Ti, Nb, and Ta

Understanding siderophile element partitioning between metal and silicate melts under diverse conditions can be used to place important constraints on the materials and conditions of planetary accretion and core formation, as well as post core formation processes. However, the effects of Si on the partitioning and activity coefficients for these elements are not well known, despite Si likely being one of the dominant light elements in Earth’s core. To address this gap in understanding, we have undertaken a systematic study of the highly siderophile elements Re, Pt, Os, and Ru, and the refractory lithophile elements Nb, Ta and Ti at 1600 °C and 1 GPa, to derive epsilon interaction parameters for these elements in FeSi metallic liquids. Positive epsilon interaction parameters were measured for Nb, Ta, Ti, Ru, Re, Pt, and Os, indicating that dissolved Si in Fe liquids causes a decrease in their metal/silicate partition coefficients (or ‘silicophobic’ behavior). Furthermore, ε$_{Re, Os, or Ru}^{Si}$ > ε$_{Re, Os, or Ru}^{S}$ which means Si causes a larger decrease in D(metal/silicate) than S, and the chalcophile behavior expected from some elements will be completely masked by the presence of Si in a metallic liquid. The new parameters are used to update an activity model that now includes 36 siderophile elements in Fe-Ni-Si-S-C liquids (27 trace elements considered here). Systematic assessment of these 27 elements shows which have the strongest affinity for Si, C, and S, and also how activity coefficients for these elements would vary during accretion and core formation in Earth, Mars, and Mercury of widely differing fO 2 and core compositional conditions. The activity model is combined with new partitioning expressions for Mo, W, Cr, Re Ru, Pt, and Os and applied to aspects of post core formation mantle geochemistry of Earth, Mars, and Mercury. Our updated expressions show that the BSE Mo/W ratio can easily be achieved with metal/silicate partitioning during growth of the Earth, whereas Re, Os and Ru become lower than and highly fractionated compared with BSE values during core formation and accretion, and thus nearly 99% of their BSE abundances are likely contributed by late accretion. Ru isotopes should be a very good indicator of the source material for the late accretion. The high Pt/Os and Re/Os developed in a deepening magma ocean during the growth of the Earth, indicates 186 Os and 187 Os isotopes could be coupled if this ancient material remained isolated and subsequently became entrained in mantle plumes and measured in surficial lavas. The extent to which this occurred will be limited by the low Os content of this ancient material, thus requiring mixing as a major component in plume sources. Martian mantle Hf/W ratio stays low during accretion and core formation modelling, suggesting that W isotope anomalies are more likely due to solid/liquid silicate fractionation than to core formation. Finally, Ti contents measured by MESSENGER at Mercury’s surface can be explained by segregation of either a metallic core (IW-6 to -8) or metallic core + sulfide (IW-4 to -7.5) followed by mantle melting.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Neutrino tomography of the Earth with ORCA detector

Abstract Using PREM as a reference model for the Earth density distribution we investigate the sensitivity of ORCA detector to deviations of the Earth (i) outer core (OC) density, (ii) inner core (IC) density, (iii) total core density, and (iv) mantle density, from their respective PREM densities. The analysis is performed by studying the effects of the Earth matter on the oscillations of atmospheric $$\nu _{\mu }$$ ν μ , $$\nu _e$$ ν e , $${\bar{\nu }}_\mu $$ ν ¯ μ and $${\bar{\nu }}_e$$ ν ¯ e . We present results which illustrate the dependence of the ORCA sensitivity to the OC, IC, core and mantle densities on the type of systematic uncertainties used in the analysis, on the value of the atmospheric neutrino mixing angle $$\theta _{23}$$ θ 23 , on whether the Earth mass constraint is implemented or not, and on the way it is implemented, and on the type – with normal ordering (NO) or inverted ordering (IO) – of the light neutrino mass spectrum. We show, in particular, that in the “most favorable” NO case of implemented Earth mass constraint, “minimal” systematic errors and $$\sin ^2\theta _{23}=0.58$$ sin 2 θ 23 = 0.58 , ORCA can determine, e.g., the OC (mantle) density at $$3\sigma $$ 3 σ C.L. after 10 years of operation with an uncertainty of (− 18%)/+ 15% (of (− 6%)/+ 8%). In the “most disfavorable” NO case of “conservative” systematic errors and $$\sin ^2\theta _{23}=0.42$$ sin 2 θ 23 = 0.42 , the uncertainty on OC (mantle) density reads (− 43%)/+ 39% ((− 17%/+ 20%), while for for $$\sin ^2\theta _{23} = 0.50$$ sin 2 θ 23 = 0.50 and 0.58 it is noticeably smaller: (− 37)%/+ 30% and (− 30%)/+ 24% ((− 13%)/+ 16% and (− 11%/+ 14%)). We find also that the sensitivity of ORCA to the OC, core and mantle densities is significantly worse for IO neutrino mass spectrum.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

DUNE atmospheric neutrinos: Earth tomography

In this paper we show that the DUNE experiment can measure the Earth’s density profile by analyzing atmospheric neutrino oscillations. The crucial feature that enables such measurement is the detailed event reconstruction capability of liquid argon time projection chambers. This allows for studying the sub-GeV atmospheric neutrino component, which bears a rich oscillation phenomenology, strongly dependent on the matter potential sourced by the Earth. We provide a pedagogical discussion of the MSW and parametric resonances and their role in measuring the core and mantle densities. By performing a detailed simulation, accounting for particle reconstruction at DUNE, nuclear physics effects relevant to neutrino-argon interactions and several uncertainties on the atmospheric neutrino flux, we manage to obtain a robust estimate of DUNE’s sensitivity to the Earth matter profile. We find that DUNE can measure the total mass of the Earth at 9.3% precision with an exposure of 400 kton-year. By accounting for previous measurements of the total mass and moment of inertia of the Earth, the core, lower mantle and upper mantle densities can be determined with 9%, 14% and 22% precision, respectively, for the same exposure. Finally, for a low exposure run of 60 kton-year, which would correspond to two far detectors running for three years, we have found that the core density could be measured by DUNE at ∼ 30% precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗