Nuclear Resonant Inelastic X-ray Research Articles

Fractionation of iron and titanium isotopes by ilmenite and the isotopic compositions of lunar magma ocean cumulates

Basaltic volcanism on the Moon produced low- and high-Ti mare basalt suites that are also distinct with respect to their iron, titanium, and magnesium isotopic compositions. Here, the equilibrium fractionation of Fe and Ti isotopes between ilmenite and melt was experimentally investigated in order to evaluate the role of ilmenite in generating the isotopic compositional variability among the lunar mare basalts. Ilmenite crystallization experiments were conducted using two bulk compositions: an ilmenite-saturated basaltic andesite and an ilmenite-saturated Apollo 14 black glass, and the Fe and Ti isotopic compositions of the experimental ilmenites and glass (quenched melt) were analyzed using solution MC-ICPMS after hand-picking. Additionally, Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements on synthetic ilmenite were conducted and compared to previous NRIXS measurements on synthetic lunar glasses in order to derive temperature-dependent equilibrium ilmenite-melt Fe isotopic fractionations. Experimentally determined ilmenite-melt fractionations were then incorporated into a lunar magma ocean crystallization model that tracks the major element and isotopic compositional evolution of lunar magma ocean cumulates and residual liquid. There is good agreement between the Fe equilibrium isotopic fractionation measured by NRIXS and the laboratory equilibration experiments, and we find that the isotopic fractionation is sensitive to ilmenite compositional differences (0 vs. 10% Fe3+). Further, the light Ti isotopic composition of ilmenite relative to the melt (Δ49Ti=ilmenite-melt−0.09±0.03‰ at 1100∘C) is consistent with the higher coordination of Ti in ilmenite relative to melts and results of previous studies. The modeled Ti isotopic compositions for lunar magma ocean cumulates display Ti isotopic variability sufficient to explain the low- and high-Ti mare basalt sources. However, the difference in Fe isotopic composition between the low- and high-Ti mare basalts cannot be attributed solely to ilmenite fractionation. Instead, Fe isotopic fractionation by additional products of lunar magma ocean crystallization, such as clinopyroxene, is required to generate the inferred Fe and Mg isotopic variability in the lunar mantle. Alternatively, the Fe and Mg isotopic compositions of the lunar mare basalts may indicate Fe-Mg interdiffusion has occurred in the Ti-rich component of the mare basalt source regions via reaction between ilmenite cumulates and the olivine- and pyroxene-rich lunar mantle.

Paramagnon excitations' theory for nuclear magnetic resonance and resonant inelastic X-ray scattering studies in doped plane copper oxide superconductors

Paramagnon excitations' theory for nuclear magnetic resonance and resonant inelastic X-ray scattering studies in doped plane copper oxide superconductors

A novel integrated time-resolved array avalanche photodiode detection system for nuclear resonant scattering measurements.

The nuclear resonant scattering (NRS) experiment requires photon-counting detectors with high time resolution, short dead time, large dynamic range, low noise, and large detection area. An 8-channel avalanche photodiode (APD) array detector system with high integrity, flexibility, and reliability has been developed to adapt to the demands of NRS experiments. The detector system mainly consists of four key parts: (i) an array-APD sensor, (ii) 8-channel integrated fast preamplifiers, (iii) the time-to-digital converter readout electronics, and (iv) a data acquisition system and EPICS support software. Remarkably, the system exhibits a time resolution of better than 500ps and has a sufficiently low noise level, allowing for the lowest detection energy threshold of 4keV. The performance of the new array-APD system as well as its real application in nuclear forward scattering (NFS) and nuclear resonant inelastic x-ray scattering (NRIXS) experiments was tested in two synchrotron facilities. With the new system, the NFS signal very close to the prompt electronic scattering signal can be extracted. Thanks to the customized EPICS-areaDetector-based control software, NRIXS spectra can be readily measured with time and energy information of the NRIXS signal stored in the raw data, which is promising for developing NRIXS data analysis in the time domain. The array-APD detector can be deployed for nuclear resonant scattering experiments at various synchrotron radiation facilities.

Isotopic Constraints on the Nature of Primary Precipitates in Archean–Early Paleoproterozoic Iron Formations from Determinations of the Iron Phonon Density of States of Greenalite and 2L- and 6L-Ferrihydrite

Iron formations (IFs) are chemical sedimentary rocks that were widely deposited before the Great Oxidation Event (GOE) around 2.4–2.2 Ga. It is generally thought that IFs precipitated as hydrated Fe3+ oxides (HFOs) such as ferrihydrite following surface oxidation of Fe2+-rich, anoxic deep waters. This model often implicates biological oxidation and underpins reconstructions of marine nutrient concentrations. However, nanoscale petrography indicates that an Fe2+ silicate, greenalite, is a common primary mineral in well-preserved IFs, motivating an alternative depositional model of anoxic ferrous silicate precipitation. It is unclear, however, if Fe2+-rich silicates can produce the Fe isotopic variations in IFs that are well explained by Fe2+ oxidation. To address this question, we constrain the equilibrium Fe isotopic (56Fe/54Fe) fractionation of greenalite and ferrihydrite by determining the iron phonon densities of states for those minerals. We use ab initio density functional theory (DFT + U) calculations and nuclear resonant inelastic X-ray scattering spectroscopy to show that ferrous greenalite should be isotopically lighter than ferrihydrite by ∼1–1.2‰ at equilibrium, and fractionation should scale linearly with increasing Fe3+ content in greenalite. By anchoring ferrihydrite–greenalite mineral pair fractionations to published experimental Fe isotopic fractionations between HFOs and aqueous Fe2+, we show that ferrous greenalite may produce all but the heaviest pre-GOE Fe isotopic compositions and mixed valence greenalites can produce the entire record. Our results suggest that heavy Fe isotope enrichments alone are not diagnostic of primary IF mineralogies, and ferrihydrite and partially oxidized or even purely ferrous greenalite are all viable primary IF mineralogies.

Equilibrium fractionation of REE isotopes in nature: Insights from NRIXS and DFT+U studies of Eu and Dy phonon density of states

Rare Earth Elements (REEs) are commonly utilized in Earth and environmental sciences to study a variety of geological processes due to their distinct patterns and radioactive-radiogenic decay systems (147Sm-143Nd, 146Sm-142Nd, 138La-138Ce). Advances in analytical techniques now enable the use of REE stable isotopic fractionations to clarify lingering ambiguities in REE systematics. In this study, we employed Nuclear Resonant Inelastic X-ray Scattering (NRIXS) to study the phonon density of states of 151Eu and 161Dy in several pure compounds, as well as in synthetic basalt and andesite glasses, and rhyolite glasses produced under various redox conditions, to determine equilibrium isotopic fractionation factors for the REEs. We additionally utilized Density Functional Theory with a Hubbard U correction (DFT+U) to calculate these factors. Our findings indicate that the directionally averaged mean force constant of Dy3+ is ∼270 N/m across various compounds, while those of Eu2+ and Eu3+ are ∼83 and 214 N/m, respectively, in geologically relevant glasses and other pure compounds. These force constants were then used to estimate those of all REEs using scaling arguments. The results suggest that equilibrium isotopic fractionation should be limited for REEs in igneous rocks, allowing for the interpretation of REE isotopic fractionation in these rocks and minerals as a result of kinetic effects. This could facilitate understanding the role of diffusion in igneous rocks and ore formation. Additionally, our results imply that significant Eu isotopic fractionation could exist in hydrothermal fluids, which could aid in understanding the formation of ore deposits and REE cycling in the oceans.

Impact of magnetic and antisite disorder on the vibrational densities of states in Ni2MnSn Heusler alloys

We have performed a combined experimental and theoretical investigation of the vibrational properties of ${\mathrm{Ni}}_{2}\mathrm{Mn}\mathrm{Sn}$ Heusler alloys. Sn-partial vibrational density of states (VDOS) of $^{119}\mathrm{Sn}$ was measured by nuclear resonant inelastic x-ray scattering at temperatures of 15 and 300 K, while magnetism and local environment of Sn was resolved by $^{119}\mathrm{Sn}$ M\"ossbauer spectroscopy. Using density functional theory, we associate the peaks in the VDOS with particular features in the element-resolved phonon dispersion of $\mathrm{L}{2}_{1}$ ordered ${\mathrm{Ni}}_{2}\mathrm{Mn}\mathrm{Sn}$. The good agreement between theory and experiment in the low-energy region provides the evidence that the inversion of optical modes at $\mathrm{\ensuremath{\Gamma}}$ involving the displacement of Ni and the heavier main group element atoms, which was predicted previously for other Ni-Mn-based Heusler compounds, is also a characteristic property of ${\mathrm{Ni}}_{2}\mathrm{Mn}\mathrm{Sn}$. Introducing different types of magnetic and antisite disorder in our calculations results in a distinctive redistribution and broadening of the Sn-VDOS, suggesting that considering partial disorder further improves the agreement with the experiment in particular at the highest phonon energies.

Structural, redox and isotopic behaviors of iron in geological silicate glasses: A NRIXS study of Lamb-Mössbauer factors and force constants

We report a combined conventional Mössbauer and synchrotron Nuclear Resonant Inelastic X-ray Scattering (NRIXS) study of a series of basalt, andesite, dacite, and rhyolite glasses at temperatures ranging from 5 to 1223 K. These glasses were synthesized under controlled oxygen fugacities and span a wide range of Fe3+/Fetot ratios. As expected from theory, we find that in these glasses, the inverse of the Lamb-Mössbauer factor (the recoil-free fraction) correlates linearly with the fraction of the conventional Mössbauer spectrum that can be ascribed to Fe3+. Extrapolating the linear relationships to pure Fe3+ and Fe2+ endmembers yields a ratio for the Lamb-Mössbauer factors C of Fe3+ and Fe2+ of 1.203 ± 0.017 (1σ), with no clear dependence on the chemical composition of the glass. We show that the materials studied follow the harmonic approximation up to 1223 K for olivine and 773 K for basaltic glass, allowing us to extrapolate C in temperature. The temperature-dependence of C is well approximated by the formula C=1.203±0.033T/300 over the temperature range 50–750 K. This calibration is used to correct previous redox ratio determinations. We investigate how chemical composition and iron redox state influence the mean force constant of iron in glasses, a key driver of Fe isotopic fractionation during magma generation and differentiation. As previously documented by Dauphas et al. (2014), we find clear correlation between bond strength and iron redox ratio that is secondarily modulated by coordination effects in more alkali-rich felsic magmas. New data on simplified glass compositions reveal that network modifiers, notably K and Na, seem to exert an important control on Fe2+ bond strengths. The refined ratio of Mössbauer factors for Fe2+ and Fe3+ is used to improve on calibrations of iron redox state in geological glasses using XANES spectroscopy. We reevaluate the Fe3+/Fetot ratio of MORBs based on previously published XANES and Mössbauer data. 0.087±0.005

Onset of anharmonicity and thermal conductivity in SnSe

The anharmonicity in SnSe is investigated through the analysis of moments of $^{119}\mathrm{Sn}$ nuclear resonant inelastic x-ray scattering and ab initio molecular dynamics calculations. Experimental evidences show that the anharmonic behavior started around 300 K, substantially lower than the usually suggested structural transition at 800 K. Both theory and experiments reveal substantial lifetime broadening and frequency renormalization of the optical phonons. Thermal conductivities calculated from the temporal energy moment using the Einstein diffusion equation are in good agreement with previous experiments. The abrupt increase of the thermal power near 800 K is driven by an electronic factor and not by the enhanced anharmonicity due to structural change.

Vibrational anisotropy of <i>δ</i>-(Al,Fe)OOH single crystals as probed by nuclear resonant inelastic X-ray scattering

Abstract. The formation of high-pressure oxyhydroxide phases spanned by the components AlOOH–FeOOH–MgSiO2(OH)2 in experiments suggests their capability to retain hydrogen in Earth's lower mantle. Understanding the vibrational properties of high-pressure phases provides the basis for assessing their thermal properties, which are required to compute phase diagrams and physical properties. Vibrational properties can be highly anisotropic, in particular for materials with crystal structures of low symmetry that contain directed structural groups or components. We used nuclear resonant inelastic X-ray scattering (NRIXS) to probe lattice vibrations that involve motions of 57Fe atoms in δ-(Al0.87Fe0.13)OOH single crystals. From the recorded single-crystal NRIXS spectra, we calculated projections of the partial phonon density of states along different crystallographic directions. To describe the anisotropy of central vibrational properties, we define and derive tensors for the partial phonon density of states, the Lamb–Mössbauer factor, the mean kinetic energy per vibrational mode, and the mean force constant of 57Fe atoms. We further show how the anisotropy of the Lamb–Mössbauer factor can be translated into anisotropic displacement parameters for 57Fe atoms and relate our findings on vibrational anisotropy to the crystal structure of δ-(Al,Fe)OOH. As a potential application of single-crystal NRIXS at high pressures, we discuss the evaluation of anisotropic thermal stresses in the context of elastic geobarometry for mineral inclusions. Our results on single crystals of δ-(Al,Fe)OOH demonstrate the sensitivity of NRIXS to vibrational anisotropy and provide an in-depth description of the vibrational behavior of Fe3+ cations in a crystal structure that may motivate future applications of NRIXS to study anisotropic vibrational properties of minerals.

The influence of \u03b4-(Al,Fe)OOH on seismic heterogeneities in Earth\u2019s lower mantle

The high-pressure phases of oxyhydroxides (δ-AlOOH, ε-FeOOH, and their solid solution), candidate components of subducted slabs, have wide stability fields, thus potentially influencing volatile circulation and dynamics in the Earth’s lower mantle. Here, we report the elastic wave velocities of δ-(Al,Fe)OOH (Fe/(Al + Fe) = 0.13, δ-Fe13) to 79 GPa, determined by nuclear resonant inelastic X-ray scattering. At pressures below 20 GPa, a softening of the phonon spectra is observed. With increasing pressure up to the Fe3+ spin crossover (~ 45 GPa), the Debye sound velocity (vD) increases. At higher pressures, the low spin δ-Fe13 is characterized by a pressure-invariant vD. Using the equation of state for the same sample, the shear-, compressional-, and bulk-velocities (vS, vP, and vΦ) are calculated and extrapolated to deep mantle conditions. The obtained velocity data show that δ-(Al,Fe)OOH may cause low-vΦ and low-vP anomalies in the shallow lower mantle. At deeper depths, we find that this hydrous phase reproduces the anti-correlation between vS and vΦ reported for the large low seismic velocity provinces, thus serving as a potential seismic signature of hydrous circulation in the lower mantle.

Sign of lattice and spin entropy change during phase transition in giant magnetocaloric materials

<p indent=0mm>Solid-state refrigeration based on the magnetocaloric effect (MCE) has garnered worldwide attention because of its superior energy conservation and environment friendliness. A common feature of giant magnetocaloric materials is the simultaneous magnetic and lattice transitions, while some of them undergo negative expansion, i.e., lattice contraction, during the transition from the ferromagnetic (FM) to the paramagnetic (PM) phase. Generally, a larger lattice volume indicates softer phonons and therefore a larger phonon entropy. However, experimental and theoretical studies have shown that there are great differences in the mechanism of phonon modes for different materials. In particular, the strengthening or softening of the phonon vibration mode during magnetic phase transition determines the magnitude and sign of lattice entropy change. Therefore, for the giant MCE materials with negative thermal expansion, whether the sign of lattice and spin entropy change is the same or the opposite has always been controversial. Combined with previous studies of nuclear resonance inelastic X-ray scattering (NRIXS), and by means of heat flow measurements and Debye theory calculations, we have clarified the sign of lattice and spin entropy change of giant magnetocaloric La(Fe, Si)₁₃-based compounds and MM<italic></italic>X alloys with negative thermal expansion. Results show that the lattice and spin entropy changes retain the same sign for La(Fe, Si)₁₃-based compounds and MM′X (M, M′ = transition element, X = main element) alloys, which conforms to the principle of entropy increase. This work is helpful in fully understanding the intrinsic mechanism of giant magnetocaloric effect and its multi-field regulation for magnetostructural/magnetoelastic materials with negative thermal expansion during phase transition.

Measurements of the Lamb-Mössbauer factor at simultaneous high-pressure-temperature conditions and estimates of the equilibrium isotopic fractionation of iron

Abstract Isotopic fractionation has been linked to the lattice vibrations of materials through their phonon spectra. The Lamb-Mössbauer factor (fLM) has the potential to provide information about the lattice vibrations in materials. We constrain the temperature evolution of the fLM of γ- and ε-Fe at in situ high-P-T conditions between 1650 K and the melting point. We find that the vibrations of γ- and ε-Fe can be described using a quasiharmonic model with a pressure- and temperature-dependent Debye temperature computed from the measured fLM. From the Debye temperature, we derive the equilibrium isotopic fractionation β-factor of iron. Our results show that the quasiharmonic behavior of metallic iron would lower the value of lnβFe57/54 by 0.1‰ at 1600–2800 K and 50 GPa when compared to the extrapolation of room temperature nuclear resonant inelastic X-ray scattering data. Our study suggests that anharmonicity may be more prevalent in Fe metal than in lower mantle minerals at 2800 K and 50 GPa, a relevant condition for the core formation, and the silicate mantle may be isotopically heavy in iron.

Iron force constants of bridgmanite at high pressure: Implications for iron isotope fractionation in the deep mantle

The isotopic compositions of iron in major mantle minerals may record chemical exchange between deep-Earth reservoirs as a result of early differentiation and ongoing plate tectonics processes. Bridgmanite (Bdg), the most abundant mineral in the Earth’s lower mantle, can incorporate not only Al but also Fe with different oxidation states and spin states, which in turn can influence the distribution of Fe isotopes between Bdg and ferropericlase (Fp) and between the lower mantle and the core. In this study, we combined first-principles calculations with high-pressure nuclear resonant inelastic X-ray scattering measurements to evaluate the effects of Fe site occupancy, valence, and spin states at lower-mantle conditions on the reduced Fe partition function ratio (β-factor) of Bdg. Our results show that the spin transition of octahedral-site (B-site) Fe3+ in Bdg under mid-lower-mantle conditions generates a +0.09‰ increase in its β-factor, which is the most significant effect compared to Fe site occupancy and valence. Fe2+-bearing Bdg varieties have smaller β-factors relative to Fe3+-bearing varieties, especially those containing B-site Fe3+. Our models suggest that Fe isotopic fractionation between Bdg and Fp is only significant in the lowermost mantle due to the occurrence of low-spin Fe2+ in Fp. Assuming early segregation of an iron core from a deep magma ocean, we find that neither core formation nor magma ocean crystallization would have resulted in resolvable Fe isotope fractionation. In contrast, Fe isotopic fractionation between low-spin Fe3+-bearing Bdg/Fe2+-bearing Fp and metallic iron at the core-mantle boundary may have enriched the lowermost mantle in heavy Fe isotopes by up to +0.20‰.

Reconciling elasticity tensor constraints from mineral physics and seismological observations: applications to the Earth’s inner core

SUMMARY This study establishes the proper framework in which to compare seismic observations with mineral physics constraints for studies of the inner core by determining how the elements of the elasticity tensor are sampled by the normal modes of the Earth. The obtained mapping between the elements of the elasticity tensor and the seismic wave speeds shows that the choice of averaging scheme used to calculate isotropic properties is crucial to understand the composition of the inner core, especially for comparison with the shear wave speed such as that provided in PREM. For example, the appropriate shear wave speed calculated for an Fe-Ni-Si hcp alloy at inner-core conditions differs from the shear wave speed obtained by taking a Reuss average by as much as $27\, {\rm per\, cent}$. It is also shown for the first time that by combining the isotropic observations based upon normal-mode characteristic frequencies and anisotropic parameters from their splitting, the five independent elastic parameters (A, C, F, L and N) that fully describe a transversely isotropic inner core can be uniquely constrained. The elastic values based upon a variety of mode-splitting studies are reported, and the differences between models from various research groups are shown to be relatively small ($\lt 10\, {\rm per\, cent}$). Additionally, an analogous body-wave methodology is developed to approximately estimate the five independent elastic constants from observations of compressional wave traveltime anomalies. The body-wave observations are utilized to consider the depth dependence of inner-core anisotropy, in particular, the structure of the innermost inner core. Finally, we demonstrate that substantial errors may result when attempting to relate seismically observed P and S wave speeds from Debye velocities obtained through nuclear resonant inelastic X-ray scattering. The results of these experiments should be compared directly with the Debye velocity calculated from seismically constrained elastic constants. This manuscript provides a new set of formulae and values of seismic observations of the inner core that can be easily compared against mineral physics constraints for better understanding of the inner-core composition.

Seismic Wave Speeds Derived from Nuclear Resonant Inelastic X-ray Scattering for Comparison with Seismological Observations

Nuclear resonant inelastic X-ray scattering (NRIXS) experiments have been applied to Earth materials, and the Debye speed is often related to the material’s seismic wave speeds. However, for anisotropic samples, the Debye speed extracted from NRIXS measurements is not equal to the Debye speed obtained using the material’s isotropic seismic wave speeds. The latter provides an upper bound for the Debye speed of the material. Consequently, the acoustic wave speeds estimated from the Debye speed extracted from NRIXS (Nuclear Resonant Inelastic X-ray Scattering) measurements are underestimated compared to the material’s true seismic wave speeds. To illustrate the differences, the effects of various assumptions used to estimate the Debye speed, as well as seismic wave speeds, are examined with iron alloys at Earth’s inner core conditions. For the case of pure iron, the variation of the crystal orientation relative to the incoming X-ray beam causes a 40 % variation in the measured Debye speed, and leads to 3% and 31% underestimation in the compressional and shear wave speeds, respectively. Based upon various iron alloys, the error in the inferred seismic shear wave speed strongly depends upon the strength of anisotropy that can be quantified. We can also derive Debye speeds based upon seismological observations such as the PREM (Preliminary Reference Earth Model) and inner core anisotropy model. We show that these seismically derived Debye speeds are upper bounds for Debye speeds obtained from NRIXS experiments and that interpretation of the Debye speeds from the NRIXS measurements in terms of seismic wave speeds should be done with utmost caution.

Interface-related magnetic and vibrational properties in Fe/MgO heterostructures from nuclear resonant spectroscopy and first-principles calculations

We combine $^{57}$Fe M\"ossbauer spectroscopy and $^{57}$Fe nuclear resonant inelastic x-ray scattering (NRIXS) in nanoscale polycrystalline [bcc-$^{57}$Fe/MgO] multilayers with various Fe layer thicknesses and layer-resolved density-functional-theory (DFT) based first-principles calculations of a (001)-oriented [Fe(8 ML)/MgO(8 ML)](001) heterostructure to unravel the interface-related atomic vibrational properties of a multilayer system. In theory and experiment, we observe consistently enhanced hyperfine magnetic fields compared to bulk which are associated with the Fe/MgO interface layers. NRIXS and DFT both reveal a strong reduction of the longitudinal acoustic (LA) phonon peak in combination with an enhancement of the low-energy vibrational density of states (VDOS) suggesting that the presence of interfaces and the associated increase in the layer-resolved magnetic moments results in drastic changes in the Fe-partial VDOS. From the experimental and calculated VDOS, vibrational thermodynamic properties have been determined as a function of Fe thickness and are found to be in excellent agreement.

The influence of phonon softening on the superconducting critical temperature of Sn nanostructures

The increase in superconducting transition temperature (TC) of Sn nanostructures in comparison to bulk, was studied. Changes in the phonon density of states (PDOS) of the weakly coupled superconductor Sn were analyzed and correlated with the increase in TC measured by magnetometry. The PDOS of all nanostructured samples shows a slightly increased number of low-energy phonon modes and a strong decrease in the number of high-energy phonon modes in comparison to the bulk Sn PDOS. The phonon densities of states, which were determined previously using nuclear resonant inelastic X-ray scattering, were used to calculate the superconducting transition temperature using the Allen-Dynes-McMillan (ADMM) formalism. Both the calculated as well as the experimentally determined values of TC show an increase compared to the bulk superconducting transition temperature. The good agreement between these values indicates that phonon softening has a major influence on the superconducting transition temperature of Sn nanostructures. The influence of electron confinement effects appears to be minor in these systems.

Influence of hydrogenation on the vibrational density of states of magnetocaloric LaFe11.4Si1.6H1.6

We report on the impact of magnetoelastic coupling on the magnetocaloric properties of LaFe$_{11.4}$Si$_{1.6}$H$_{1.6}$ in terms of the vibrational density of states, which we determined with $^{57}$Fe nuclear resonant inelastic X-ray scattering measurements and with density-functional-theory based first-principles calculations in the ferromagnetic low-temperature and paramagnetic high-temperature phase. In experiments and calculations, we observe pronounced differences in the shape of the Fe-partial VDOS between non-hydrogenated and hydrogenated samples. This shows that hydrogen does not only shift the temperature of the first-order phase transition, but also affects the elastic response of the Fe-subsystem significantly. In turn, the anomalous redshift of the Fe VDOS, observed by going to the low-volume PM phase, survives hydrogenation. As a consequence, the change in the Fe specific vibrational entropy $\Delta S_\mathrm{lat}$ across the phase transition has the same sign as the magnetic and electronic contribution. DFT calculations show that the same mechanism, which is a consequence of the itinerant electron metamagnetism associated with the Fe subsystem, is effective in both the hydrogenated and he hydrogen-free compounds. Although reduced by 50 % as compared to the hydrogen-free system, the measured change $\Delta S_\mathrm{lat}$ of 3.2\pm1.9 J/kgK across the FM to PM transition contributes with 35 % significantly and cooperatively to the total isothermal entropy change $\Delta S_\mathrm{iso}$. Hydrogenation is observed to induce an overall blueshift of the Fe-VDOS with respect to the H-free compound; this effect, together with the enhanced Debye temperature observed, is a fingerprint of the hardening of the Fe sublattice by hydrogen incorporation. In addition, the mean Debye velocity of sound of LaFe$_{11.4}$Si$_{1.6}$H$_{1.6}$ was determined from the NRIXS and the DFT data.

Elastic and magnetic properties of Fe3P up to core pressures: Phosphorus in the Earth's core

Phosphorus (P) is considered a possible light element alloying with iron (Fe) in the Earth's core due to its siderophile nature and the ubiquity of P-bearing iron alloys in iron meteorites. The sequestration of P by liquid metals during the core formation possibly results in the relatively low concentration of P in the bulk silicate Earth. In this study, we performed single-crystal and powder X-ray diffraction, synchrotron Mössbauer spectroscopy and nuclear resonant inelastic X-ray scattering measurements in diamond anvil cells to investigate the elastic and magnetic properties of Fe3P under high pressures. Our X-ray diffraction results suggest that there is no structural phase transition up to 111 GPa. However, a volume collapse was observed at 21.5 GPa in Fe3P, ascribed to a magnetic transition as evidenced by synchrotron Mössbauer spectroscopy results. Fitting the volume-pressure data by the Birch-Murnaghan equation of state gives bulk modulus KT0=162.4(7) GPa, its first pressure derivative KT0′=4.0 (fixed) and zero-pressure volume V0=370.38(6) Å3 for the magnetic phase and KT0=220(7) GPa, KT0′=4.0 (fixed) and V0=357(1) Å3 for the non-magnetic phase. Sound velocities of Fe3P were determined up to 152 GPa by nuclear resonant inelastic X-ray scattering, demonstrating that Fe3P bears a low shear velocity and high Poisson's ratio at core pressures compared to Fe and Fe3S. When forming a solid solution Fe3(S,P) with Fe3S at core pressures, Fe3P may favorably influence the elastic properties of Fe3(S,P) to match the seismic observations of the inner core.

Redox and structural controls on tin isotopic fractionations among magmas

Recent analytical developments have made possible the determination of the isotopic composition of tin in igneous rocks. In order to establish a framework to interpret the mass-dependent tin isotopic signatures of planetary materials, seven geologically-relevant silicate glasses (basalt, rhyolite, enstatite and anorthite glasses) were synthesized with moderate amounts of 119Sn (on the order of a weight percent). Redox conditions were controlled during sample synthesis to set the redox ratio (Sn2+/Sntot) from stannous (Sn2+) to stannic (Sn4+) glasses. The mean force constants of tin bonds in these glasses were determined by synchrotron nuclear resonant inelastic X-ray scattering (NRIXS) in order to determine the reduced isotopic partition function ratios (β-factors) of these glasses. Clues on the coordination chemistry and the valence state of tin in these glasses were also derived from synchrotron Mossbauer spectroscopy (SMS). The force constants of tin drastically increases from Sn2+-bearing to Sn4+-bearing glasses and varies significantly with the glass composition at a given redox state. The average coordination number of tin likely controls these variations with glass composition as suggested by SMS results. It is concluded that large isotope fractionation is expected between materials containing Sn2+ and Sn4+ respectively even at magmatic temperatures and that the coordination chemistry of tin in silicates strongly affect its isotope partitioning behavior. Our experimental data are finally used to interpret available Sn isotope data collected in terrestrial rocks. The incompatible behavior of Sn4+ in mantle minerals leads to a enrichment in heavy isotopes in mantle melts and to the depletion in heavy isotopes in solid residues of melting with a magnitude consistent with the isotope fractionation between Sn2+ and Sn4+ predicted by NRIXS data. Finally, we show that during fractional crystallization of basalt and considering the effect of tin coordination number in minerals and melts, the partitioning of Sn4+ into ilmenite leads to an enrichment in light isotopes in the residual melt.