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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

High Pressure Melting Curve of Fe‐Si: Implication for the Thermal Properties in Mercury's Core

The motion of liquid iron (Fe) alloy materials in the outer core drives the dynamo, which generates Mercury's magnetic field. The assessment of core models requires laboratory measurements of the melting temperature of Fe alloys at high pressure. Here, we experimentally determined the melting curve of Fe9wt%Si and Fe17wt%Si up to 17 GPa using in situ and ex situ measurements of intermetallic fast diffusion that serves as the melting criterion in a large-volume press. Our determined melting slopes are comparable with previous studies up to about 17 GPa. However, when extrapolated, our melting slopes significantly deviate from previous studies at higher pressures. For Mercury's core with a model composition of Fe9wt%Si, the melting temperature-depth profile determined in our study is lower by ∼150–250 K when compared with theoretical calculations. Using the new melting curve of Fe9wt%Si and the electrical resistivity values from a previous study of Fe8.5wt%Si, we estimate that the electronic thermal conductivity of liquid Fe9wt%Si is 30 Wm −1 K −1 at the Mercury's CMB pressure of 5 GPa and 37 Wm −1 K −1 at an assumed ICB of 21 GPa, corresponding to heat flux values of 23 mWm −2 and 32 mWm −2 , respectively. These values provide new constraints on the core models.

58 GEOSCIENCES↗
DOE OSTI2024

Barium stars as tracers of s -process nucleosynthesis in AGB stars

Barium (Ba) stars help to verify asymptotic giant branch (AGB) star nucleosynthesis models since they experienced pollution from an AGB binary companion and thus their spectra carry the signatures of the slow neutron capture process (s process). For a large number (180) of Ba stars, we searched for AGB stellar models that match the observed abundance patterns. We aim to uncover any systematic deviations of the sample abundances from the predictions of the nucleosynthesis models. We employed three machine learning algorithms as classifiers: a Random Forest method, developed for this work, and the two classifiers used in our previous study. Compared to that work, we also expanded our observational sample with 11 Ba stars available in the supersolar metallicity range. We studied the statistical behaviour of the different s-process elements in the observational sample to investigate if the AGB models systematically under- or overpredict the abundances observed in the Ba stars and show the results in the form of violin plots of the residuals between spectroscopic abundances and model predictions. We inspected the correlations between the observed [Fe/H], the s-process elemental abundances, and the residuals. We employed the [Zr/Fe] and [Nb/Fe] abundances as a thermometer to constrain the operational temperature that rules the production of these elements in the sample stars, assuming a steady-state s process. We also investigated the mass distribution of the identified polluter AGB stars and the behaviour of the δ parameter, which describes the fraction of accreted AGB material relative to the Ba star envelope. We find a significant trend in the residuals that implies an underproduction of the elements just after the first s-process peak (Nb, Mo, and Ru) in the models relative to the observations. This may originate from a neutron-capture process (e.g. the intermediate neutron-capture process, i process) not yet included in the AGB models of metallicity from solar to roughly 1/5 solar, corresponding to the range of the Ba stars. Correlations are found between the residuals of these peculiar elements, suggesting a common origin for the deviations from the models. In addition, there is a weak metallicity dependence of the residuals of these elements. The s-process temperatures derived with the [Zr/Fe] – [Nb/Fe] thermometer have an unrealistic value for the majority of our stars. The most likely explanation is that at least a fraction of these elements are not produced in a steady-state s process, and instead may be due to processes not included in the AGB models. The mass distribution of the identified models confirms that our sample of Ba stars was polluted by low-mass AGB stars (< 4 M ⊙ ). Most of the matching AGB models require low accreted mass, but a few systems with high accreted mass are needed to explain the observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A new accurate ground-state potential energy surface of ethylene and predictions for rotational and vibrational energy levels

In this paper we report a new ground state potential energy surface for ethylene (ethene) C{sub 2}H{sub 4} obtained from extended ab initio calculations. The coupled-cluster approach with the perturbative inclusion of the connected triple excitations CCSD(T) and correlation consistent polarized valence basis set cc-pVQZ was employed for computations of electronic ground state energies. The fit of the surface included 82 542 nuclear configurations using sixth order expansion in curvilinear symmetry-adapted coordinates involving 2236 parameters. A good convergence for variationally computed vibrational levels of the C{sub 2}H{sub 4} molecule was obtained with a RMS(Obs.–Calc.) deviation of 2.7 cm{sup −1} for fundamental bands centers and 5.9 cm{sup −1} for vibrational bands up to 7800 cm{sup −1}. Large scale vibrational and rotational calculations for {sup 12}C{sub 2}H{sub 4}, {sup 13}C{sub 2}H{sub 4}, and {sup 12}C{sub 2}D{sub 4} isotopologues were performed using this new surface. Energy levels for J = 20 up to 6000 cm{sup −1} are in a good agreement with observations. This represents a considerable improvement with respect to available global predictions of vibrational levels of {sup 13}C{sub 2}H{sub 4} and {sup 12}C{sub 2}D{sub 4} and rovibrational levels of {sup 12}C{sub 2}H{sub 4}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

High spatial uniformity of photoluminescence spectra in semipolar (202{sup ¯}1) plane InGaN/GaN quantum wells

Scanning near-field optical spectroscopy was applied to study spatial variations of emission spectra at room temperature in semipolar (202{sup ¯}1) In{sub x}Ga{sub 1−x}N/GaN single quantum wells (QWs) for 0.11≤x≤0.36. Photoluminescence (PL) was found to be highly uniform, with peak wavelength deviations and peak intensity deviations divided by average values in the range of 6–12 meV and 0.03–0.07, respectively. Near-field maps of PL parameters showed large, ∼5 to 10 μm size areas of similar values, as opposed to 100 nm scale variations, often reported for InGaN QWs. The near-field PL spectra were found to broaden with increasing InN molar fraction. In the low In content QWs, the broadening is primarily determined by the random cation distribution, while for larger InN molar fractions 10 nm scale localization sites with increasingly deeper band potentials are suggested as the linewidth broadening cause.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

Excitation energy dependence of prompt fission γ-ray emission from 241 Pu*

Prompt fission γ rays (PFGs) resulting from the 240 Pu(d,pf) reaction have been measured as a function of fissioning nucleus excitation energy E x at the Oslo Cyclotron Laboratory. We study the average total PFG multiplicity per fission, the average total PFG energy released per fission, and the average PFG energy. No significant changes in these characteristics are observed over the range 5.75 < E x < 8.25 MeV. The physical implications of this result are discussed. The experimental results are compared to simulations conducted using the computational fission model FREYA. We find that FREYA reproduces the experimental PFG characteristics within 8% deviation across the E x range studied. Furthermore, previous excitation energy-dependent PFG measurements conducted below the second-chance fission threshold have large uncertainties, but are generally in agreement with our results within a 2σ confidence interval. However, both a published parametrization of the PFG energy dependence and the most recent PFG evaluation included in ENDF/B-VIII.0 were found to poorly describe the PFG excitation-energy dependence observed in this and previous experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

SU-E-T-577: Commissioning of a Deterministic Algorithm for External Photon Beams

Purpose: We report commissioning results for a deterministic algorithm for external photon beam treatment planning. A deterministic algorithm solves the radiation transport equations directly using a finite difference method, thus improve the accuracy of dose calculation, particularly under heterogeneous conditions with results similar to that of Monte Carlo (MC) simulation. Methods: Commissioning data for photon energies 6 – 15 MV includes the percentage depth dose (PDD) measured at SSD = 90 cm and output ratio in water (Spc), both normalized to 10 cm depth, for field sizes between 2 and 40 cm and depths between 0 and 40 cm. Off-axis ratio (OAR) for the same set of field sizes was used at 5 depths (dmax, 5, 10, 20, 30 cm). The final model was compared with the commissioning data as well as additional benchmark data. The benchmark data includes dose per MU determined for 17 points for SSD between 80 and 110 cm, depth between 5 and 20 cm, and lateral offset of up to 16.5 cm. Relative comparisons were made in a heterogeneous phantom made of cork and solid water. Results: Compared to the commissioning beam data, the agreement are generally better than 2% with large errors (up to 13%) observed in the buildup regions of the FDD and penumbra regions of the OAR profiles. The overall mean standard deviation is 0.04% when all data are taken into account. Compared to the benchmark data, the agreements are generally better than 2%. Relative comparison in heterogeneous phantom is in general better than 4%. Conclusion: A commercial deterministic algorithm was commissioned for megavoltage photon beams. In a homogeneous medium, the agreement between the algorithm and measurement at the benchmark points is generally better than 2%. The dose accuracy for a deterministic algorithm is better than a convolution algorithm in heterogeneous medium.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2026

Search for resonances decaying to an anomalous jet and a Higgs boson in proton–proton collisions at $\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V}$

This paper presents a search for new physics through the process where a massive particle, X, decays into a Higgs boson and a second particle, Y. The Higgs boson subsequently decays into a bottom quark–antiquark pair, which is reconstructed as a single large-radius jet. The decay products of Yare also assumed to produce a single large-radius jet. The identification of the Yparticle is enhanced by computing the anomaly score of its candidate jet using an autoencoder, which measures deviations from typical quark- or gluon-induced jets. This allows a simultaneous search for multiple Ydecay scenarios within a single analysis. In the main benchmark process, Yis a scalar particle that decays into a Wboson pair. Two other scalar Ydecay processes are also considered as benchmarks: decays to a light quark–antiquark pair, and decays to a top quark–antiquark pair. A fourth benchmark process considers Yas a hadronically decaying top quark, arising from the decay of a vector-like quark into a top quark and a Higgs boson. Data recorded by the CMS experiment at a center-of-mass energy of 13 TeV in 2016–2018, corresponding to an integrated luminosity of 138 fb -1 , are analyzed. The search covers Xmasses between 1.4 and 3.0 TeV and Ymasses between 90 and 400 TeV, with all simulated signals produced in the narrow-width approximation. No significant excess above the standard model background expectation is observed. The most stringent upper limits to date are placed on benchmark signal cross sections for various masses of X and Y particles

Hayrapetyan, A. [Yerevan Physics Institute]↗
DOE OSTI2017

One Law to Rule Them All: The Radial Acceleration Relation of Galaxies

We study the link between baryons and dark matter (DM) in 240 galaxies with spatially resolved kinematic data. Our sample spans 9 dex in stellar mass and includes all morphological types. We consider (1) 153 late-type galaxies (LTGs; spirals and irregulars) with gas rotation curves from the SPARC database, (2) 25 early-type galaxies (ETGs; ellipticals and lenticulars) with stellar and H i data from ATLAS{sup 3D} or X-ray data from Chandra, and (3) 62 dwarf spheroidals (dSphs) with individual-star spectroscopy. We find that LTGs, ETGs, and “classical” dSphs follow the same radial acceleration relation: the observed acceleration (g{sub obs}) correlates with that expected from the distribution of baryons (g{sub bar}) over 4 dex. The relation coincides with the 1:1 line (no DM) at high accelerations but systematically deviates from unity below a critical scale of ∼10{sup −10} m s{sup −2}. The observed scatter is remarkably small (≲0.13 dex) and largely driven by observational uncertainties. The residuals do not correlate with any global or local galaxy property (e.g., baryonic mass, gas fraction, and radius). The radial acceleration relation is tantamount to a natural law: when the baryonic contribution is measured, the rotation curve follows, and vice versa. Including ultrafaint dSphs, the relation may extend by another 2 dex and possibly flatten at g{sub bar}≲10{sup −12} m s{sup −2}, but these data are significantly more uncertain. The radial acceleration relation subsumes and generalizes several well-known dynamical properties of galaxies, like the Tully–Fisher and Faber–Jackson relations, the “baryon-halo” conspiracies, and Renzo’s rule.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The Power Curve Working Group's assessment of wind turbine power performance prediction methods

Wind turbine power production deviates from the reference power curve in real-world atmospheric conditions. Correctly predicting turbine power performance requires models to be validated for a wide range of wind turbines using inflow in different locations. The Share-3 exercise is the most recent intelligence-sharing exercise of the Power Curve Working Group, which aims to advance the modeling of turbine performance. The goal of the exercise is to search for modeling methods that reduce error and uncertainty in power prediction when wind shear and turbulence digress from design conditions. Herein, we analyze data from 55 wind turbine power performance tests from nine contributing organizations with statistical tests to quantify the skills of the prediction-correction methods. We assess the accuracy and precision of four proposed trial methods against the baseline method, which uses the conventional definition of a power curve with wind speed and air density at hub height. The trial methods reduce power-production prediction errors compared to the baseline method at high wind speeds, which contribute heavily to power production; however, the trial methods fail to significantly reduce prediction uncertainty in most meteorological conditions. For the meteorological conditions when a wind turbine produces less than the power its reference power curve suggests, using power deviation matrices leads to more accurate power prediction. We also determine that for more than half of the submissions, the data set has a large influence on the effectiveness of a trial method. Overall, this work affirms the value of data-sharing efforts in advancing power curve modeling and establishes the groundwork for future collaborations.

17 WIND ENERGY↗
DOE OSTI2014

WE-E-18A-09: Application of a Channelized Hotelling Observer Model to Evaluate Angiographic Imaging Equipment

Purpose: To develop and apply an observer model to objectively evaluate and compare the performance of different angiographic imaging equipment and acquisition variables. Methods: Image Acquisition— Iodine-based phantoms were created with target diameters: 0.5, 1, 2, and 4 mm. The phantoms were imaged using both planes of a bi-plane angiography system with detector pixel dimensions 0.1542 mm{sup 2} and 0.1842 mm{sup 2}, respectively. All four phantoms were imaged with magnification factors 1.5, 1.25 and 1 and with the large and small focal spots. Phantom position and the dose per frame (0.12– 0.24 μ Gy/frame) were varied for a single phantom size, magnification and focal spot. Observer Model— For each experimental condition, 1200 signal-present and signal-absent images were acquired and a detectability index (d') was calculated with a Gabor-channelized Hotelling observer (CHO) model. Detectability indices were evaluated as a function of dose, phantom size, and magnification. The model was then applied to compare d' of the two imaging planes and focal spots. Uncertainty in d' was estimated by bootstrapping the data and by examining the shift-variance of systems. Results: Detectability indices varied linearly with magnification and the square root of dose. For the 2 and 4 mm phantoms, d' varied linearly with diameter. For the 0.5 and 1 mm phantoms, d' expectedly deviated from this linear relationship due to substantial detector and focal spot blurring of the phantoms. The small focal spot yielded up to 50% greater d' values than the large focal spot. For the two detectors, differences in d' did not exceed the estimated ∼7% error. Conclusions: The detectability indices predictably scaled with dose, diameter, magnification, and focal spot size and serve to validate the model. Results demonstrate statistically similar target detectability for both investigated detectors, despite differences in pixel dimensions. This CHO model provides a framework to evaluate angiographic system performance.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

A strategy for a general search for new phenomena using data-derived signal regions and its application within the ATLAS experiment

This paper describes a strategy for a general search used by the ATLAS Collaboration to find potential indications of new physics. Events are classified according to their final state into many event classes. For each event class an automated search algorithm tests whether the data are compatible with the Monte Carlo simulated expectation in several distributions sensitive to the effects of new physics. The significance of a deviation is quantified using pseudo-experiments. A data selection with a significant deviation defines a signal region for a dedicated follow-up analysis with an improved background expectation. The analysis of the data-derived signal regions on a new dataset allows a statistical interpretation without the large look-elsewhere effect. The sensitivity of the approach is discussed using Standard Model processes and benchmark signals of new physics. As an example, results are shown for 3.2 fb –1 of proton–proton collision data at a centre-of-mass energy of 13 TeV collected with the ATLAS detector at the LHC in 2015, in which more than 700 event classes and more than 10 5 regions have been analysed. Furthermore, no significant deviations are found and consequently no data-derived signal regions for a follow-up analysis have been defined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Validation and uncertainty quantification of detector response functions for a $1"×2"$ NaI collimated detector intended for inverse radioisotope source mapping applications

Detector response functions (DRFs) are often used for inverse analysis. We compute the DRF of a sodium iodide (NaI) nuclear material holdup field detector using the code named g03 developed by the Center for Engineering Applications of Radioisotopes (CEAR) at NC State University. Three measurement campaigns were performed in order to validate the DRF’s constructed by g03: on-axis detection of calibration sources, off-axis measurements of a highly enriched uranium (HEU) disk, and on-axis measurements of the HEU disk with steel plates inserted between the source and the detector to provide attenuation. Furthermore, this work quantifies the uncertainty of the Monte Carlo simulations used in and with g03, as well as the uncertainties associated with each semi-empirical model employed in the full DRF representation. Overall, for the calibration source measurements, the response computed by the DRF for the prediction of the full-energy peak region of responses was good, i.e. within two standard deviations of the experimental response. In contrast, the DRF tended to overestimate the Compton continuum by about 45–65% due to inadequate tuning of the electron range multiplier fit variable that empirically represents physics associated with electron transport that is not modeled explicitly in g03. For the HEU disk measurements, computed DRF responses tended to significantly underestimate (more than 20%) the secondary full-energy peaks (any peak of lower energy than the highest-energy peak computed) due to scattering in the detector collimator and aluminum can, which is not included in the g03 model. We ran a sufficiently large number of histories to ensure for all of the Monte Carlo simulations that the statistical uncertainties were lower than their experimental counterpart’s Poisson uncertainties. The uncertainties associated with least-squares fits to the experimental data tended to have parameter relative standard deviations lower than the peak channel relative standard deviation in most cases and good reduced chi-square values. The highest sources of uncertainty were identified as the energy calibration polynomial factor (due to limited source availability and NaI resolution) and the Ba-133 peak fit (only a very weak source was available), which were 20% and 10%, respectively.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Quantifying replication through repeated analysis of UVM-A, a liquid reference material for cosmogenic 10 Be and 26 Al studies

In this study, in-situ produced cosmogenic nuclide sample preparation and analysis is a complicated, multi-step process with numerous possible sources of error, many of which have not been robustly quantified. Here, we use a liquid reference material (UVM-A) to test whether the analytic precision associated with individual isotopic ratios (n = 96) measured at two Accelerator Mass Spectrometry facilities (Lawrence Livermore National Laboratory and Purdue Rare Isotope Measurement Laboratory) accurately represents the range of values determined for aliquots prepared in a single laboratory over a period of five years. We find that 10 Be/ 9 Be ratios measured at the different accelerator facilities (n = 26 and n = 70) have statistically indistinguishable central tendencies, matching to within 0.1 %. Based on this large dataset, we suggest preliminary consensus values for UVM-A of 1.45 ± 0.06 x 10 -13 for 10 Be/ 9 Be (mean, one standard deviation, n = 96) and 4.47 ± 0.22 x 10 -13 for 26 Al/ 27 Al (mean, one standard deviation, n = 27). For both 10 Be/ 9 Be and 26 Al/ 27 Al, the relative standard deviations of the measured ratios are similar to the reported analytic uncertainties of sample measurement, suggesting that sample preparation introduced little if any additional scatter beyond the uncertainty of isotopic analysis. This dataset demonstrates that robust sample preparation and measurement can generate isotope ratio data reproducible at the level of counting statistics.

58 GEOSCIENCES↗
DOE OSTI2015

Imperfect Dark Matter

We consider cosmology of the recently introduced mimetic matter with higher derivatives (HD). Without HD this system describes irrotational dust—Dark Matter (DM) as we see it on cosmologically large scales. DM particles correspond to the shift-charges—Noether charges of the shifts in the field space. Higher derivative corrections usually describe a deviation from the thermodynamical equilibrium in the relativistic hydrodynamics. Thus we show that mimetic matter with HD corresponds to an imperfect DM which: i) renormalises the Newton's constant in the Friedmann equations, ii) has zero pressure when there is no extra matter in the universe, iii) survives the inflationary expansion which puts the system on a dynamical attractor with a vanishing shift-charge, iv) perfectly tracks any external matter on this attractor, v) can become the main (and possibly the only) source of DM, provided the shift-symmetry in the HD terms is broken during some small time interval in the radiation domination époque. In the second part of the paper we present a hydrodynamical description of general anisotropic and inhomogeneous configurations of the system. This imperfect mimetic fluid has an energy flow in the field's rest frame. We find that in the Eckart and in the Landau-Lifshitz frames the mimetic fluid possesses nonvanishing vorticity appearing already at the first order in the HD. Thus, the structure formation and gravitational collapse should proceed in a rather different fashion from the simple irrotational DM models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Small scatter and nearly isothermal mass profiles to four half-light radii from two-dimensional stellar dynamics of early-type galaxies

We study the total mass–density profile for a sample of 14 fast-rotator early-type galaxies (stellar masses 10.2≲logM{sub ∗}/M{sub ⊙}≲11.7). We combine observations from the SLUGGS and ATLAS{sup 3D} surveys to map out the stellar kinematics in two dimensions, out to a median radius for the sample of four half-light radii R{sub e} (or 10 kpc) and a maximum radius of 2.0–6.2 R{sub e} (or 4–21 kpc). We use axisymmetric dynamical models based on the Jeans equations, which allow for a spatially varying anisotropy; employ quite general profiles for the dark halos; and, in particular, do not place any restrictions on the profile slope. This is made possible by the availability of spatially extended two-dimensional kinematics. We find that our relatively simple models provide a remarkably good description of the observed kinematics. The resulting total density profiles are well described by a nearly isothermal power law ρ{sub tot}(r)∝r{sup −γ} from R{sub e}/10 to at least 4R{sub e}, the largest average deviation being 11%. The average logarithmic slope is 〈γ〉=2.19±0.03 with observed rms scatter of just σ{sub γ}=0.11. This scatter out to large radii, where dark matter dominates, is as small as previously reported by lensing studies around r ≈ R{sub e}/2, where the stars dominate. Our bulge–halo conspiracy places much tighter constraints on galaxy formation models. It illustrates the power of two-dimensional stellar kinematics observations at large radii. It is now important to test the generality of our results for different galaxy types and larger samples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Four direct measurements of the fine-structure constant 13 billion years ago

Observations of the redshift z = 7.085 quasar J1120+0641 are used to search for variations of the fine structure constant, a, over the redshift range 5:5 to 7:1. Observations at z = 7:1 probe the physics of the universe at only 0.8 billion years old. These are the most distant direct measurements of a to date and the first measurements using a near-IR spectrograph. A new AI analysis method is employed. Four measurements from the x - shooter spectrograph on the Very Large Telescope (VLT) constrain changes in a relative to the terrestrial value (α 0 ). The weighted mean electromagnetic force in this location in the universe deviates from the terrestrial value by Δα/α = (α z - α 0 )/α 0 = (-2:18 ± 7:27) × 10 -5 , consistent with no temporal change. Combining these measurements with existing data, we find a spatial variation is preferred over a no-variation model at the 3:9σ level.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Cation and Vacancy Disorder in U 1-y Nd y O 2.00-X Alloys

In this study, the intermixing and clustering of U/Nd, O, and vacancies were studied by both laboratory and synchrotron-based x-ray diffraction in U 1-y Nd y O 2-X alloys. It was found that an increased holding time at the high experimental temperature during initial alloy preparation results in a lower disorder of the Nd distribution in the alloys. Adjustment of the oxygen concentration in the U 1-y Nd y O 2-X alloys with different Nd concentrations was accompanied by the formation of vacancies on the oxygen sublattice and a nanocrystalline component. The lattice parameters in the U 1-y Nd y O 2-X alloys were also found to deviate significantly from Vegard's law when the Nd concentration was high (53%) and decreased with increasing oxygen concentration. Such changes indicate the formation of large vacancy concentrations during oxygen adjustment at these high temperatures. Finally, the change in the vacancy concentration after the oxygen adjustment was estimated relative to Nd concentration and oxygen stoichiometry.

36 MATERIALS SCIENCE↗