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NASA NTRS2018

Improving the Spatial Resolution of Imaging Instruments Using Software

In order to overcome spatial resolution limitations associated with physical sensor limitations when using smallsats and cubesats, we utilize an image processing technology referred to as Super-Resolution (SR). In general, software approaches are increasingly considered in connection with smaller satellites for which size, mass and power constraints limit the sensor capabilities. Being able to perform hardware vs. software trades might enable more capabilities for a lower cost. This paper describes recent experiments conducted to optimize the spatial enhancement of acquired observations using multiple sub-pixel shifted low resolution image.

Image Processing↗

DOE OSTI2023

MnEdgeNet for accurate decomposition of mixed oxidation states for Mn XAS and EELS L2,3 edges without reference and calibration

Accurate decomposition of the mixed Mn oxidation states is highly important for characterizing the electronic structures, charge transfer and redox centers for electronic, and electrocatalytic and energy storage materials that contain Mn. Electron energy loss spectroscopy (EELS) and soft X-ray absorption spectroscopy (XAS) measurements of the Mn L2,3 edges are widely used for this purpose. To date, although the measurements of the Mn L2,3 edges are straightforward given the sample is prepared properly, an accurate decomposition of the mix valence states of Mn remains non-trivial. For both EELS and XAS, 2+, 3+, and 4+ reference spectra need to be taken on the same instrument/beamline and preferably in the same experimental session because the instrumental resolution and the energy axis offset could vary from one session to another. To circumvent this hurdle, in this study, we adopted a deep learning approach and developed a calibration-free and reference-free method to decompose the oxidation state of Mn L2,3 edges for both EELS and XAS. A deep learning regression model is trained to accurately predict the composition of the mix valence state of Mn. To synthesize physics-informed and ground-truth labeled training datasets, we created a forward model that takes into account plural scattering, instrumentation broadening, noise, and energy axis offset. With that, we created a 1.2 million-spectrum database with 1-by-3 oxidation state composition ground truth vectors. The library includes a sufficient variety of data including both EELS and XAS spectra. By training on this large database, our convolutional neural network achieves 85% accuracy on the validation dataset. We tested the model and found it is robust against noise (down to PSNR of 10) and plural scattering (up to t/λ = 1). We further validated the model against spectral data that were not used in training. In particular, the model shows high accuracy and high sensitivity for the decomposition of Mn 3 O 4 , MnO, Mn 2 O 3 , and MnO 2 . The accurate decomposition of Mn 3 O 4 experimental data shows the model is quantitatively correct and can be deployed for real experimental data. Our model will not only be a valuable tool to researchers and material scientists but also can assist experienced electron microscopists and synchrotron scientists in the automated analysis of Mn L edge data.

25 ENERGY STORAGE↗

DOE OSTI2021

Error-controlled, progressive, and adaptable retrieval of scientific data with multilevel decomposition

Extreme-scale simulations and high-resolution instruments have been generating an increasing amount of data, which poses significant challenges to not only data storage during the run, but also post-processing where data will be repeatedly retrieved and analyzed for a long period of time. The challenges in satisfying a wide range of post-hoc analysis needs while minimizing the I/O overhead caused by inappropriate and/or excessive data retrieval should never be left unmanaged. In this paper, we propose a data refactoring, compressing, and retrieval framework capable of 1) fine-grained data refactoring with regard to precision; 2) incrementally retrieving and recomposing the data in terms of various error bounds; and 3) adaptively retrieving data in multi-precision and multi-resolution with respect to different analysis. With the progressive data re-composition and the adaptable retrieval algorithms, our framework significantly reduces the amount of data retrieved when multiple incremental precision are requested and/or the downstream analysis time when coarse resolution is used. Experiments show that the amount of data retrieved under the same progressively requested error bound using our framework is 64% less than that using state-of-the-art single-error-bounded approaches. Parallel experiments with up to 1, 024 cores and ~ 600 GB data in total show that our approach yields 1.36× and 2.52× performance over existing approaches in writing to and reading from persistent storage systems, respectively.

Liang, Xin↗

DOE OSTI2026

Constrained variational optimization of counting-time allocation in sequential scattering measurements: Application to Bonse–Hart USANS

Sequential scattering measurements are often performed under a fixed experimental-time budget, even though the expected count rate varies strongly across the measured coordinate. When the dwell time at each measurement position can be controlled independently, this variation creates a general resource-allocation problem: how should the available time be distributed to minimize the uncertainty of the reconstructed profile? We formulate this problem as a constrained variational optimization for measurements governed by Poisson counting statistics. When each measurement is treated independently, minimizing the averaged squared relative uncertainty yields an inverse-square-root intensity allocation. The formulation is then generalized to include correlations between neighboring measurements and an instrumental resolution operator, leading to an allocation criterion that equalizes the marginal reduction in posterior uncertainty per unit measurement time. Bonse–Hart ultra-small-angle neutron scattering (USANS), in which reciprocal space is sampled sequentially through analyzer-angle stepping, provides an experimentally grounded application. Computational benchmarking shows that the optimized allocation outperforms uniform-time and constant-relative-error strategies, while application to an experimentally measured graphite USANS profile from the Spallation Neutron Source, using Poisson resampling under alternative schedules, demonstrates how counting time should be redistributed toward weak-intensity regions under an identical total duration. The resulting framework applies to sequential scattering and related scanning measurements whenever local dwell times are adjustable and directly determine the measurement uncertainties, and when the relevant correlation and instrumental-response models are available.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗

DOE OSTI2020

Isotopic analysis of plutonium measured with very thick absorbers and high-granularity spectra

FRAM is LANL-designed software designed to extract plutonium and uranium isotopic information from gamma ray spectra. This is an important capability for NEST and STAB; however, FRAM performance has been poor when applied to field data collected in these programs. FRAM Version 5 (commercially available) was fine-tuned and validated for laboratory quality measurements but not for measurements of the high-mass and heavily shielded SNM items encountered in NEST. FRAM is untested for spectra collected with high-granularity lower resolution instruments such as the new 8-MeV Detective-X favored by STAB or the new custom electrocooled systems coming into use for NEST. FRAM Version 6.1 (unreleased) has improvements in physics capabilities, and parameter sets may be adapted that are more specific to NEST and STAB, which is what we have attempted for this assignment. Thick shielding attenuates gamma rays profoundly, especially those at low energy, making them too weak to be measured. The missing low-energy peaks force the analysis to employ only the highest-energy peaks. We adapted FRAM 6.1 for analysis of plutonium spectra obtained with very thick Pb filters (a surrogate for NEST-type configurations). New parameter sets employing only very high energy peaks were created for the analysis. High granularity and low resolution make deconvolution of the 600-keV region particularly challenging, and we have worked to optimally extract information from this region. The results shown in this paper give high confidence that we are on the right track. We used a combination of real and synthetically-modified data. Remaining work includes testing the new software and parameters against genuine data collected with Detective-X and new NEST systems, but such datasets at the moment are unavailable. It also remains to develop and test parameter sets specific to uranium and the new detectors.

07 ISOTOPE AND RADIATION SOURCES↗

NASA NTRS1993

High-resolution absorption cross section measurements of carbon monoxide at 20 K between 96.7 and 98.8 nanometers

Photoabsorption cross sections for five CO bands, at wavelengths between 96.7 and 98.8 nm, have been measured at high-resolution in a supersonic jet-cooled source at the Photon Factory synchrotron facility. New integrated cross sections are reported for the K-X, L(prime)-X, and L-X bands. Low-temperature spectra of the J-X and W-X bands, which were used in the determination of the absorbing CO column densities, are also presented. The rotational structures of the K-X, L(prime)-X, and L-X bands do not overlap in the low-temperature spectra, allowing for the first unambiguous determination of these band oscillator strengths. We also report revised room temperature measurements of integrated cross sections for the K-X, L(prime)-X, and L-X bands, in which distortions in the measured spectra due to insufficient instrumental resolution have been minimized; the revised room temperature integrated cross sections are consistent with the low-temperature results.

Stark, G.↗

DOE OSTI2020

KMT-2019-BLG-1339L: An M Dwarf with a Giant Planet or a Companion near the Planet/Brown Dwarf Boundary

We analyze KMT-2019-BLG-1339, a microlensing event with an obvious but incompletely resolved brief anomaly feature around the peak of the light curve. Although the origin of the anomaly is identified to be a companion to the lens with a low mass ratio q, the interpretation is subject to two different degeneracy types. The first type is the ambiguity in ρ, representing the angular source radius scaled to the angular radius of the Einstein ring, θ {sub E}, and the other is the s ↔ s {sup -1} degeneracy. The former type, “finite-source degeneracy,” causes ambiguities in both s and q, while the latter induces an ambiguity only in s. Here, s denotes the separation (in units of θ {sub E}) in projection between the lens components. We estimate that the lens components have masses (M{sub 1},M{sub 2})-(0.27{sub -0.15}{sup +0.36} M{sub ⊙},11{sub -7}{sup +16} M{sub J}) and -(0.48{sub -0.28}{sup +0.40} M{sub ⊙},1.3{sub -0.7}{sup +1.1} M{sub J}) according to the two solutions subject to the finite-source degeneracy, indicating that the lens comprises an M dwarf and a companion with a mass around the planet/brown dwarf boundary or a Jovian-mass planet. It is possible to lift the finite-source degeneracy by conducting future observations utilizing a high-resolution instrument because the relative lens–source proper motion predicted by the solutions is widely different.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Probing Diffuse Polymer Brush Interfaces Using Resonant Soft X-ray Scattering

The success of a neutron or x-ray scattering experiment relies on sufficient signal from the system being studied. The intensity of scattered radiation depends on instrument resolution, the structure of the scattering elements, and the interaction between the incident radiation and the sample—so-called ‘scattering contrast’. The contrast depends on the square of the difference in the scattering length densities (SLDs) for each component, and each SLD depends on the atoms and radiation involved (eq. 1). For neutrons, the scattering lengths bi are specific to the type of nuclei involved. For conventional x-ray scattering, b i depends on the electron density and thus the atomic number Z.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Resonant x-ray emission across the L 3 edge of uranium compounds

A narrow bandwidth x-ray beamline and a multi-crystal von Hamos spectrometer were used to record x-ray absorption and x-ray emission (XES) across the uranium L 3 edge of UO 2 , UO 3 , Cs 2 UO 2 Cl 4 , and Cs 2 UCl 6 . Measurements were made over 17150–17250 eV with an instrumental resolution of ∼2 eV. This resolution allowed the use of Lorentzian peak fits to the L 3 N 4 and L 3 N 5 characteristic x-ray fluorescence lines that have ∼12–13 eV lifetime widths. The fluorescence yields of the four compounds display strong white lines near threshold and multiple scattering features at higher energies. The XES spectra were fit with three Lorentzians, two for the L 3 N 4 and L 3 N 5 lines and one for inelastic scattering by 2p–6d excitations and 4d–6d final states. The intensities of the white lines were largely due to the inelastic scattering component. To support the measurements, relativistic equation-of-motion coupled-cluster and restricted active space configuration interaction calculations were performed for uranium core-excitation energies in Cs 2 UO 2 Cl 4 and Cs 2 UCl 6 . These calculations with rigorous treatments of relativistic effects are shown to provide accurate uranium L 3 -edge binding energies, L 3 N 5 emission energies, as well as the energy losses in the inelastic scattering process. The measured and calculated results show variations between compounds with U(IV) oxidation states that contain 6d 0 5f 2 electrons in their ground configurations (UO 2 and Cs 2 UCl 6 ) compared with U(VI) compounds (UO 3 and Cs 2 UO 2 Cl 4 ) with empty 5f and 6d configurations.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

Two methods to study inelastic neutron-scattering measurements based on ω n (q) versus S(q, ω) applied to the magnetic open honeycomb lattice Tb 2 Ir 3 Ga 9

This work describes two methods to fit the inelastic neutron-scattering spectrum S(q, ω) with wavevector q and frequency ω. The common and well-established method extracts the experimental spin-wave branches ω n (q) from the measured spectra S(q, ω) and then minimizes the difference between the observed and predicted frequencies. When n branches of frequencies are predicted but the measured frequencies overlap to produce only m < n branches, the weighted average of the predicted frequencies must be compared to the observed frequencies. A penalty is then exacted when the width of the predicted frequencies exceeds the width of the observed frequencies. The second method directly compares the measured and predicted intensities S(q, ω) over a grid {q i , ω j } in wavevector and frequency space. After subtracting background noise from the observed intensities, the theoretical intensities are scaled by a simple wavevector-dependent function that reflects the instrumental resolution. Furthermore, the advantages and disadvantages of each approach are demonstrated by studying the open honeycomb material Tb 2 Ir 3 Ga 9 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Robust long-range magnetic correlation across antiphase domain boundaries in Sr 2 CrReO 6

Here, we report a resonant elastic x-ray scattering study of a thin-film sample of Sr 2 CrReO 6 , which has one of the highest ferrimagnetic transition temperatures among ordered double perovskites.We found resonantly enhanced magnetic Bragg peaks at Q = (odd, odd, odd) at both the rhenium L 2 and L 3 edges, which coincide with the structural Bragg peaks of Sr 2 CrReO 6 . By analyzing the widths of these Bragg peaks, we extracted very different structural and magnetic correlation lengths. The former is about 15 nm, while the latter is constrained by the instrumental resolution to be at least 90 nm. We argue that a finite structural correlation length is consistent with the existence of antiphase nanodomains in our sample. On the other hand, a much larger magnetic correlation length indicates that the magnetic correlation extends far beyond the boundaries of individual domains and is consistent with strong antiferromagnetic coupling between different antiphase domains. Last, from the azimuthal dependence of the magnetic intensity, we show that the magnetic moments lie perpendicular to the c axis, which explains the earlier bulk magnetization data.

36 MATERIALS SCIENCE↗

DOE OSTI2024

First-Principles Treatment of Vibrational Broadening in X-Ray Excited Valence Band Spectra for n-SrTiO 3 (001)

The valence band maximum (VBM) is an important quantity for semiconductors as it locates the Fermi level relative to the band edge. Accurate measurement of this quantity in near-surface regions of semiconductors by photoemission is a first step toward determining the electronic properties of heterostructures involving these materials. While extrapolating the leading edge of the valence band to the energy axis in photoemission spectra is a widely used way to find the VBM, this method can be ambiguous if the leading edge exhibits multiple slopes. Another way to determine the VBM is to fit the leading edge to an appropriately broadened, cross-section modulated theoretical density of states (DOS). Three kinds of broadening that should be included for maximum accuracy are those due to: (1) finite instrumental resolution, (2) valence hole lifetime, and (3) vibrational excitations. While steps (1) and (2) are straightforward to implement, (3) is more difficult because the appropriate amount of broadening is not known a priori. Here, we demonstrate that explicit inclusion of vibrational broadening using ab initio molecular dynamics facilitates accurate VBM determination for n-SrTiO 3 (001). The total DOS is constructed by summing time-averaged projections at elevated temperature onto s - , p - , and d orbitals for the constituent atoms and modulating with the associated photoemission cross sections. Subsequent convolutions of the total DOS, first with a Gaussian of width equal to the experimental energy resolution and second with a Lorentzian to simulate valence hole lifetime effects, yield line shapes that reproduce the experimental leading edges rather well. The VBM is then given by the energy at which the vibrationally broadened total DOS (prior to the convolutions) goes to zero. The VBMs generated by this method quantitatively agree with those resulting from extrapolating from the middle of the measured leading edge for SrTiO 3 .

36 MATERIALS SCIENCE↗

DOE OSTI2024

Spinon continuum in the Heisenberg quantum chain compound Sr 2 ⁢V 3 ⁢O 9

Magnetic excitations in the spin chain candidate Sr 2 ⁢V 3 ⁢O 9 have been investigated by inelastic neutron scattering on a single crystal sample. A spinon continuum with a bandwidth of ~22 meV is observed along the chain formed by alternating magnetic V 4+ and nonmagnetic V 5+ ions, which reveals the importance of the orbital degree of freedom in determining the chain axis as identified by prior electronic structure calculations. Incipient magnetic Bragg peaks due to weak ferromagnetic interchain couplings emerge when approaching the magnetic transition at T N ~ 5.3 K, while the excitations remain gapless within the instrumental resolution. Comparisons to the Bethe ansatz, density matrix renormalization group calculations, and effective field theories confirm Sr 2 ⁢V 3 ⁢O 9 as a host of weakly coupled S = 1/2 chains dominated by antiferromagnetic intrachain interactions of ~7.1(1) meV.

1-dimensional spin chains↗

DOE OSTI2026

Quenched disorder in the triangular lattice antiferromagnet YbZn 2⁢ GaO 5

We investigate the crystal electric field (CEF) excitations of Yb 3+ ions in powder samples of the triangular-lattice rare-earth-based antiferromagnet YbZn 2⁢ GaO 5 using inelastic neutron scattering (INS). Three CEF excitations from the ground-state Kramers doublet were observed, each exhibiting significant broadening beyond instrumental resolution. Combining temperature-dependent INS and neutron powder diffraction, we identify a significant static contribution to this broadening and attribute it to heterogeneous coordination of Yb 3+ ions due to Ga 3+ /Zn 2+ site mixing. Rietveld refinement of neutron powder diffraction indicates that 35% of Ga occupies the Zn site and 60% of Zn occupies the Ga site. We show with a point charge model for the CEF Hamiltonian that heterogeneous coordination of Yb3+ ions leads to broadened CEF peaks. First-principles calculations demonstrate that the random Ga 3+ /Zn 2+ distribution can produce the distortions of the YbO 6 octahedra observed from neutron diffraction. Because the documented heterogeneity will extend to exchange interactions, our results suggest that disorder is a significant factor in the unusual magnetism previously reported in YbZn 2 ⁢GaO 5 , including broad low-energy magnetic excitations and the absence of magnetic ordering down to 0.3 K.

Crystal field excitations↗

DOE OSTI2020

Exact and fast calculation of the X-ray pair distribution function

A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.

36 MATERIALS SCIENCE↗

DOE OSTI2023

POWTEX visits POWGEN

The high-intensity time-of-flight (TOF) neutron diffractometer POWTEX for powder and texture analysis is currently being built prior to operation in the eastern guide hall of the research reactor FRM II at Garching close to Munich, Germany. Because of the world-wide 3 He crisis in 2009, the authors promptly initiated the development of 3 He-free detector alternatives that are tailor-made for the requirements of large-area diffractometers. Herein is reported the 2017 enterprise to operate one mounting unit of the final POWTEX detector on the neutron powder diffractometer POWGEN at the Spallation Neutron Source located at Oak Ridge National Laboratory, USA. As a result, presented here are the first angular- and wavelength-dependent data from the POWTEX detector, unfortunately damaged by a 50 g shock but still operating, as well as the efforts made both to characterize the transport damage and to successfully recalibrate the voxel positions in order to yield nonetheless reliable measurements. Also described is the current data reduction process using the PowderReduceP2D algorithm implemented in Mantid [Arnold et al. (2014). Nucl. Instrum. Methods Phys. Res. A , 764 , 156–166]. The final part of the data treatment chain, namely a novel multi-dimensional refinement using a modified version of the GSAS-II software suite [Toby & Von Dreele (2013). J. Appl. Cryst. 46 , 544–549], is compared with a standard data treatment of the same event data conventionally reduced as TOF diffraction patterns and refined with the unmodified version of GSAS-II . This involves both determining the instrumental resolution parameters using POWGEN's powdered diamond standard sample and the refinement of a friendly-user sample, BaZn(NCN) 2 . Although each structural parameter on its own looks similar upon comparing the conventional (1D) and multi-dimensional (2D) treatments, also in terms of precision, a closer view shows small but possibly significant differences. For example, the somewhat suspicious proximity of the a and b lattice parameters of BaZn(NCN) 2 crystallizing in Pbca as resulting from the 1D refinement (0.008 Å) is five times less pronounced in the 2D refinement (0.038 Å). Similar features are found when comparing bond lengths and bond angles, e.g. the two N—C—N units are less differently bent in the 1D results (173 and 175°) than in the 2D results (167 and 173°). The results are of importance not only for POWTEX but also for other neutron TOF diffractometers with large-area detectors, like POWGEN at the SNS or the future DREAM beamline at the European Spallation Source.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

FY24 Report on Water NSTF Testing: Lower Tank Inlet Piping Configuration

The following report serves as a summary of the accomplishments and testing results by the Natural convection Shutdown heat removal Test Facility (NSTF) experimental program over the past 12-month period. A major activity included reconfiguration of the chimney piping geometry which altered the discharge position into the tank from the original 50% tank height to a new lower position at a 10.9% tank height. This modification increases the volume of available coolant thus extending long-term operating capacity, however also results in a decreased liquid driving head which has the potential to reduce the natural circulation efficiency and decrease overall performance. Examination of the tradeoffs for these two configurations is an area of interest for RCCS designers and drove planned test activities this year. Ten matrix tests were performed in FY24, totaling 195 hours of heated operations and 12.9 MWh of electrical heating throughout the year, with eight classified as Accepted per NQA-1 and two classified as Trending. Testing prior to the facility reconfiguration examined the facility response to throttling at the tank inlet, demonstrating increased sensitivity of flow instabilities to throttling within the two-phase region when compared to throttling at the lower sensitivity single-phase inlet region. Testing after the chimney reconfiguration began with a baseline test at conditions of 80% inventory fill and prototypic thermal power input of 2.1 MW t . In addition to establishing a reference for nominal system behavior and performance, repeat testing with multiple subsequent runs demonstrated strong repeatability between tests performed at the same conditions in this new configuration. These tests also examined if influences would occur to system behavior with installation of new higher-resolution instrumentation within the upper chimney. In this critical region where boiling and flashing phenomena dominate, the test results provided confidence that the new instrumentation does not uncharacteristically influence the observed behaviors. An inventory parametric series was then initiated to examine system behavior with the new chimney configuration at six varying initial inventory levels, ranging from high 80% to low 20% fill. Two-phase oscillations with similar peak and mean flow rates were observed when comparing to the previous mid tank configuration. Generally, similar system response trends with inventory were also observed, such as two phase oscillations suppressing as inventories were lowered. However, in one absolute inventory comparison at the highest fill of 80%, flow oscillations saw a gradual growth over the 4 hours of two-phase operation in the new lower tank inlet configuration, opposite of the gradual dampening observed in the mid tank inlet configuration. This can be attributed to, in part, a greater hydrostatic head pressure above the two-phase discharge region where the boiling front is developed. Furthermore, the change resulted in greater sensitivity to liquid degassing phenomena during single-phase heating, causing loop instabilities to form which trigged moderate flow degradation during the period approaching saturation and boiling conditions. This behavior had been observed previously under some conditions but was a common occurrence in recent testing with the newer lower tank inlet configuration. Initial observations from these first data sets suggest an overall larger window of stability for the mid tank inlet configuration compared to the lower tank inlet. Lastly, the lowest inventory fill test was repeated over an extended testing window to examine depletion behavior. Natural circulation flow and effective heat removal performance were observed during most of the testing period; only after the tank became fully drained (0% fill) did flow stagnate and violent geysering events occur. This early observation confirms one relative advantage over the mid tank inlet configuration, which stagnated under comparable conditions at ~20% inventory remaining in the tank.

42 ENGINEERING↗

DOE OSTI2021

Study of Anharmonicity in Zirconium Hydrides Using Inelastic Neutron Scattering and Ab-Initio Computer Modeling

The anharmonic phonon behavior in zirconium hydrides and deuterides, including ϵ-ZrH 2 , γ-ZrH, and γ-ZrD, has been investigated from aspects of inelastic neutron scattering (INS) and lattice dynamics calculations within the framework of density functional theory (DFT). The harmonic model failed to reproduce the spectral features observed in the experimental data, indicating the existence of anharmonicity in those materials and the necessity of further explanations. Here, we present a detailed study on the anharmonicity in zirconium hydrides/deuterides by exploring the 2D potential energy surface of hydrogen/deuterium atoms and solving the corresponding 2D single-particle Schrödinger equation to obtain the eigenfrequencies, which are then convoluted with the instrument resolution. The convoluted INS spectra qualitatively describe the anharmonic peaks in the experimental INS spectra and demonstrate that the anharmonicity originates from the deviations of hydrogen potentials from quadratic behavior in certain directions; the effects are apparent for the higher-order excited vibrational states, but small for the ground and first excited states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗