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

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Improved pore network models to simulate single-phase flow in porous media by coupling with lattice Boltzmann method

In this paper, different pore network models to simulate single-phase flow in porous media are built and their accuracy is evaluated. In addition to the conventional pore network model (CPNM) which consists of regular pore bodies and throat bonds, three improved pore network models (IPNMs) are developed allowing to better describing the real pore and throat geometry. The first improved pore network model (IPNM1) replaces the regular throat bond with a throat bond showing the real throat cross section. The second improvement (IPNM2) uses a series of sub-throat bonds with varying cross sections to better describe the real throat geometry, which is firstly proposed in this paper. The third model (IPNM3) extracts the real pore-throat-pore geometry without simplification. The conductance of fluid flow through these more realistic throat bonds is calculated by the lattice Boltzmann method (LBM). The accuracy and computational efficiency of the different pore network models are evaluated taking the LBM simulation over the whole porous medium as reference solution. The global permeability and detailed pressure distributions in the pores for the different pore network models are validated. The results show that the accuracy of the pore network model increases from CPNM to IPNM3, but at the expense of increasing computational cost. This study suggests that IPNM3 can replace a whole-domain LBM simulation with similar accuracy but much lower computational cost. As a first-order approximation the newly proposed IPNM2 is suggested as good compromise between accuracy and computational cost.

42 ENGINEERING↗
DOE OSTI2022

Imposition of local boundary conditions in peridynamics without a fictitious layer and unphysical stress concentrations

Here, this study introduces a general approach for the imposition of local boundary conditions in non- ordinary state-based peridynamics (NOSB PD) to eliminate the displacement kinks near the boundary without a fictitious layer under quasi-static loading conditions. It identifies the underlying reason for the unphysical displacement kinks. Under an imposed linear displacement field, the NOSB PD equilibrium equation is not satisfied near the boundary due to the unsymmetric horizon of material points. However, the equilibrium equation derived by using the PD differential operator is satisfied at such material points. Therefore, the material body is divided into three regions to satisfy the equilibrium equations and to impose displacement and tractions boundary conditions. This approach does not deviate from the original NOSB PD; however, it provides a simple solution to eliminate the displacement kink near the boundary, which leads to unphysical stress concentrations. Its efficacy is demonstrated by considering elastic rectangular and square plates subjected to various types of boundary conditions leading to homogeneous as well as nonhomogeneous deformations. The creep response of a rectangular plate further proves the robustness of the present approach. Also, a quasi-static crack propagation from a pre-existing crack in a square plate under mode-I, mode-II and mixed-mode loading conditions demonstrates its capability for failure prediction based on the critical stretch criteria. Finally, its applicability for 3D analysis is demonstrated by considering a rectangular prism under applied stretch and normal stress.

42 ENGINEERING↗
DOE OSTI2023

Development of an interatomic potential for the W–Ta system

A physics-inspired, data-driven interatomic potential framework for multi-element system is presented. This potential is based on the generalization of the embedded atom method potential and systematically incorporates two-, three- and many-body effects. Different atomic environments are described by atom-centered Gaussian basis sets which provides sufficient flexibility to capture diverse atomic environments and allows for easy optimization of the free parameters. An interatomic potential model for the tungsten–tantalum (W–Ta) system is developed using this framework by training on data from ab initio density functional theory (DFT) calculations. The potential is thoroughly tested at various compositions by comparing bulk and defect properties from experimental and DFT data. It is shown that the potential predicts the elastic constants, defect properties, such as vacancy and interstitial formation energies, core structures of dislocations, and melting points for both pure and tantalum and tungsten with an accuracy comparable to other single element machine learning based potentials. In conclusion, the potential model is used to investigate the formation energies of ordered alloys and vacancy formation energies for chemically random W–Ta alloys.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Quantum mechanics based non-bonded force field functions for use in molecular dynamics simulations of materials and systems: The nitrogen and oxygen columns

Accurate Force Fields (FFs) are essential for Molecular Dynamics (MD) simulations of the dynamics of realistic materials in terms of atomic-level interactions. The FF parameters of short-range valence interactions can be derived through Quantum Mechanical (QM) calculations on model systems practical for QM (<300 atoms). Similarly, the dynamic electrostatic interactions can be described with methods such as QEq or PQEq that allow charges and polarization to adjust dynamically. However, accurately extracting long-range van der Waals (vdW) interactions from QM calculations poses challenges due to the absence of a definitive method to distinguish between the different energetic components of electrostatics, polarization, vdW, hydrogen bonding, and valence interactions. To do this we use the Perdew–Burke–Ernzerhof flavor of Density Functional Theory, including empirical D3 vdW corrections, to predict the Equation of State for each element (keeping any covalent bonds fixed), from which we obtain the two-body vdW nonbond potential. Here, we extend these calculations to include non-bonded parameters for the N and O columns of the periodic table so that we now describe columns 15 (N), 16 (O), 17 (F), and 18 (Ne) of the periodic table. For these 20 elements, we find that the two-body vdW potentials can all be mapped to a single universal two-body curve, with just three scaling parameters: Re, De, and L. We refer to this as the Universal NonBond (UNB) potential. We expect this to be useful for new MD simulations and a helpful starting point to obtain UNB parameters for the remainder of the periodic table.

Chemistry↗
DOE OSTI2025

Dissociation of gas-phase anisole induced by low-energy electron interactions: understanding patterns of aromatic bond cleavage

Abstract In view of elucidating the fragmentation patterns of aromatic systems induced by low-energy electron interactions, dissociative electron attachment (DEA) to gas-phase anisole was performed. Anionic fragments resulting from this DEA process were detected by a quadrupole mass spectrometer, and ion yields of those fragments as a function of incident electron energy were rendered. Our study showed the formation of CH 3 − , HCC − , and OCH 3 − fragments, suggesting that various dissociation channels proceed out of DEA to anisole. We employed density functional theory to compute thermodynamic threshold energies for each potential dissociation channel. Those theoretical calculations supported the prediction that the CH 3 − and OCH 3 − fragments form via mechanisms of single-bond cleavage; the HCC − fragments may form through two-, three-, or four-body dissociation channels that entail hydrogen transfers and the cleavage of multiple aromatic bonds. The experimental resonance energies that form the CH 3 − , HCC − , and OCH 3 − fragments were 6.0 eV, 5.8 and 9.7 eV, and 9.8 eV, respectively. Given the classification of anisole as a monosubstituted aromatic species, our results explain generalizable patterns of electron-mediated dissociation in aromatic systems.

Finley, Jacob (ORCID:0009000606963352)↗
DOE OSTI2025

A comparison of effective field theory models of redshift space galaxy power spectra for DESI 2024 and future surveys

In preparation for the next generation of galaxy redshift surveys, and in particular the year-one data release from the Dark Energy Spectroscopic Instrument (DESI), we investigate the consistency of a variety of effective field theory models that describe the galaxy-galaxy power spectra in redshift space into the quasi-linear regime using 1-loop perturbation theory. These models are employed in the pipelines velocileptors, PyBird, and Folpsν. While these models have been validated independently, a detailed comparison with consistent choices has not been attempted. After briefly discussing the theoretical differences between the models we describe how to provide a more apples-to-apples comparison between them. We present the results of fitting mock spectra from the AbacusSummit suite of N-body simulations provided in three redshift bins to mimic the types of dark time tracers targeted by the DESI survey. We show that the theories behave similarly and give consistent constraints in both the forward-modeling and ShapeFit compressed fitting approaches. We additionally generate (noiseless) synthetic data from each pipeline to be fit by the others, varying the scale cuts in order to show that the models agree within the range of scales for which we expect 1-loop perturbation theory to be applicable. Finally, this work lays the foundation of Full-Shape analysis with DESI Y1 galaxy samples where in the tests we performed, we found no systematic error associated with the modeling of the galaxy redshift space power spectrum for this volume.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N -body mock challenge for the quasar sample

ABSTRACT The growth rate and expansion history of the Universe can be measured from large galaxy redshift surveys using the Alcock–Paczynski effect. We validate the Redshift Space Distortion models used in the final analysis of the Sloan Digital Sky Survey (SDSS) extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 quasar clustering sample, in configuration and Fourier space, using a series of halo occupation distribution mock catalogues generated using the OuterRim N-body simulation. We test three models on a series of non-blind mocks, in the OuterRim cosmology, and blind mocks, which have been rescaled to new cosmologies, and investigate the effects of redshift smearing and catastrophic redshifts. We find that for the non-blind mocks, the models are able to recover fσ8 to within 3 per cent and α∥ and α⊥ to within 1 per cent. The scatter in the measurements is larger for the blind mocks, due to the assumption of an incorrect fiducial cosmology. From this mock challenge, we find that all three models perform well, with similar systematic errors on fσ8, α∥, and α⊥ at the level of $\sigma _{f\sigma _8}=0.013$, $\sigma _{\alpha _\parallel }=0.012$, and $\sigma _{\alpha _\bot }=0.008$. The systematic error on the combined consensus is $\sigma _{f\sigma _8}=0.011$, $\sigma _{\alpha _\parallel }=0.008$, and $\sigma _{\alpha _\bot }=0.005$, which is used in the final DR16 analysis. For baryon acoustic oscillation fits in configuration and Fourier space, we take conservative systematic errors of $\sigma _{\alpha _\parallel }=0.010$ and $\sigma _{\alpha _\bot }=0.007$.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Fast baryonic field painting for Sunyaev-Zel’dovich analyses: Transfer function vs hybrid effective field theory

Here, we present two approaches for “painting” baryonic properties relevant to the Sunyaev-Zel’dovich (SZ) effect—optical depth and Compton-y—onto three-dimensional N-body simulations, using the MillenniumTNG suite as a benchmark. The goal of these methods is to produce fast and accurate reconstruction methods to aid future analyses of baryonic feedback using the SZ effect. The first approach employs a Gaussian process emulator to model the SZ quantities via a transfer function, while the second utilizes hybrid effective field theory (HEFT) to reproduce these quantities within the simulation. Our analysis involves comparing both methods to the true MillenniumTNG optical depth and Compton-y fields using several metrics, including the cross-correlation coefficient, power spectrum, and power spectrum error. Additionally, we assess how well the reconstructed fields correlate with dark matter haloes across various mass thresholds. The results indicate that the transfer function method yields more accurate reconstructions for fields with initially high correlations (r ≈ 1), such as between the optical depth and dark matter fields. Conversely, the HEFT-based approach proves more effective in enhancing correlations for fields with weaker initial correlations (r ∼ 0.5), such as between the Compton-y and dark matter fields. Lastly, we discuss extensions of our methods to improve the reconstruction performance at the field level.

Liu, R. Henry [University of California, Berkeley,↗
DOE OSTI2021

Quantifying multipoint ordering in alloys

A central problem in multicomponent lattice systems is to systematically quantify multipoint ordering. Ordering in such systems is often described in terms of pairs, even though this is not sufficient when three-point and higher-order interactions are included in the Hamiltonian. Current models and parameters for multipoint ordering are often only applicable for very specific cases or require approximating a subset of correlated occupational variables on a lattice as being uncorrelated. In this paper, cluster order parameters are introduced to systematically quantify arbitrary multipoint ordering motifs in substitutional systems through direct calculations of normalized cluster probabilities. These parameters can describe multipoint chemical ordering in crystal systems with multiple sublattices, multiple components, and systems with reduced symmetry. These are defined in this paper and applied to quantify four-point chemical ordering motifs in platinum/palladium alloy nanoparticles that are of practical interest to the synthesis of catalytic nanocages. Impacts of chemical ordering on nanocage stability are discussed. It is demonstrated that approximating four-point probabilities from superpositions of lower-order pair probabilities is not sufficient in cases where three- and four-body terms are included in the energy expression. Furthermore, conclusions about the formation mechanisms of nanocages may change significantly when using common pair approximations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Fully gauge-fixed SU(2) Hamiltonian for quantum simulations

Here, we demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new “sequestered” basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.

Lattice gauge theory↗
DOE OSTI2020

Materials Data on Na2Li5Sn4 by Materials Project

Na2Li5Sn4 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Na sites. In the first Na site, Na is bonded in a 11-coordinate geometry to five Li and six Sn atoms. There are a spread of Na–Li bond distances ranging from 3.01–3.12 Å. There are three shorter (3.34 Å) and three longer (3.56 Å) Na–Sn bond lengths. In the second Na site, Na is bonded in a distorted q6 geometry to three equivalent Li and six Sn atoms. All Na–Li bond lengths are 2.88 Å. There are three shorter (3.18 Å) and three longer (3.23 Å) Na–Sn bond lengths. There are five inequivalent Li sites. In the first Li site, Li is bonded in a 3-coordinate geometry to one Li and three equivalent Sn atoms. The Li–Li bond length is 2.76 Å. All Li–Sn bond lengths are 3.05 Å. In the second Li site, Li is bonded in a 4-coordinate geometry to one Li and four equivalent Sn atoms. The Li–Li bond length is 2.82 Å. There are one shorter (2.86 Å) and three longer (3.15 Å) Li–Sn bond lengths. In the third Li site, Li is bonded in a 4-coordinate geometry to one Na and four Sn atoms. There are one shorter (2.92 Å) and three longer (3.03 Å) Li–Sn bond lengths. In the fourth Li site, Li is bonded in a 11-coordinate geometry to four Na, one Li, and six Sn atoms. There are three shorter (3.15 Å) and three longer (3.25 Å) Li–Sn bond lengths. In the fifth Li site, Li is bonded in a distorted body-centered cubic geometry to three equivalent Na, one Li, and four Sn atoms. There are one shorter (2.94 Å) and three longer (3.00 Å) Li–Sn bond lengths. There are four inequivalent Sn sites. In the first Sn site, Sn is bonded in a 11-coordinate geometry to three equivalent Na, seven Li, and one Sn atom. The Sn–Sn bond length is 2.83 Å. In the second Sn site, Sn is bonded to four Li atoms to form distorted corner-sharing SnLi4 tetrahedra. In the third Sn site, Sn is bonded in a 6-coordinate geometry to three equivalent Na and six Li atoms. In the fourth Sn site, Sn is bonded in a 11-coordinate geometry to six Na, four Li, and one Sn atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Fe3Ge2 by Materials Project

Fe3Ge2 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are two inequivalent Fe sites. In the first Fe site, Fe is bonded in a distorted body-centered cubic geometry to three equivalent Fe and five equivalent Ge atoms. All Fe–Fe bond lengths are 2.45 Å. There are a spread of Fe–Ge bond distances ranging from 2.44–2.46 Å. In the second Fe site, Fe is bonded to six equivalent Fe and six equivalent Ge atoms to form face-sharing FeFe6Ge6 cuboctahedra. All Fe–Ge bond lengths are 2.83 Å. Ge is bonded in a 5-coordinate geometry to eight Fe atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Flashback Measurements in Hydrogen Enriched Low Swirl Flames Using High Speed OH-PLIF

The fundamentals of stabilized flame dynamics and flashback events in a premixed low swirl burner (LSB) configuration are visualized experimentally using nanosecond (ns)-based high-speed hydroxyl radical planar laser-induced fluorescence (OH-PLIF). Swirlers with two different turning angles, 〖26〗^o and 〖33〗^o and three different center-body hole diameters, 1.08, 1.12 and 1.16 mm with measured swirl numbers varying from 0.43 to 0.49 are tested in this study at atmospheric temperature and pressure inlet conditions. An increase in flashback propensity is observed with increasing ϕ, X_(H_2 ) and decreasing V via detailed investigation of flame lift-off length (L) above the burner rim. Flashback ϕ (ϕ_FB) investigations show an expected linearly increasing trend with decreasing X_(H_2 ) and increasing V for each swirler studied and the results agree well with detailed L investigations in a stable flame configuration. ϕ_FB studies for different swirlers show an increase in flashback resistance with the increase in center-body hole diameter and swirl angle. Spatiotemporally resolved kHz-rate OH-PLIF is a promising technique to observe rapidly occurring flashback events and it can be applied for turbulence-chemistry interaction model validation.

Parajuli, Pradeep↗
DOE OSTI2025

Geophysical measurements of a demolition at NRF

On May 31 st , 2025, at approximately 14:40:00 UTC, the former Submarine First Westinghouse (SW1) structure housing a large crane was demolished at the Naval Reactors Facility (NRF) located within the perimeter of the Idaho National Laboratory (INL). Several targeted explosives were used to facilitate this demolition. The INL Seismic Monitoring Program (SMP) installed four temporary seismic instrument suites around the site of the demolition in order to monitor ground motion including measuring peak ground acceleration (PGA), peak ground velocity (PGV), and to calculate peak ground displacement (PGD). The demolition produced three types of waves: body waves, surface waves, and acoustic waves. The acoustic wave represents the largest signal received. The PGA, measured on the eastern component of the instrument located approximately 95m away from the demolition site, was 0.187g. The PGV measured was 0.0004 m/s, and the PGD was approximately 0.000006m. Rayleigh waves incident on an instrument located at the Advanced Test Reactor, about 7.6km away, were used to estimate a magnitude of 0.3 at the ATR, representing a yield of energy equivalent to approximately 3 grams of TNT.

58 - GEOSCIENCES↗
DOE OSTI2024

High-Speed OH-PLIF Diagnostics of Flame Flashback in Low Swirl Hydrogen-Enriched Flames

Hydrogen-enrichment is a potential strategy to reduce carbon emissions for the development of next-generation lean premixed combustors. However, the higher flashback propensity with hydrogen enrichment owing to the faster chemical kinetics is one of the key challenges in existing natural gas turbine combustors. The fundamentals of stabilized flame dynamics and flashback events in a premixed low swirl burner (LSB) configuration are visualized experimentally using nanosecond (ns)-based high-speed hydroxyl radical planar laser-induced fluorescence (OH-PLIF). Swirlers with two different turning angles, 26 and 33 and three different center-body hole diameters, 1.08, 1.12 and 1.16 mm with measured swirl numbers varying from 0.43 to 0.49 are tested in this study at atmospheric temperature and pressure inlet conditions. The inlet conditions are varied systematically with respect to pre-mixer velocities (V), flame equivalence ratio (ϕ) and hydrogen content (X_(H_2 )) for 50%-90% (H2, by mole) H2/ CH4 reactant mixtures and OH-PLIF characterization is performed in a stable flame at 20 kHz repetition rate. An increase in flashback propensity is observed with increasing ϕ, X_(H_2 ) and decreasing V via detailed investigation of flame lift-off length (L) above the burner rim.

Parajuli, Pradeep↗
DOE OSTI2020

Materials Data on Mn4Fe8SiGe3 by Materials Project

Mn4Fe8Ge3Si is Tungsten-derived structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Mn sites. In the first Mn site, Mn is bonded in a distorted body-centered cubic geometry to eight Fe and three equivalent Ge atoms. There are a spread of Mn–Fe bond distances ranging from 2.46–2.51 Å. All Mn–Ge bond lengths are 2.84 Å. In the second Mn site, Mn is bonded in a distorted body-centered cubic geometry to eight Fe, three equivalent Ge, and three equivalent Si atoms. There are a spread of Mn–Fe bond distances ranging from 2.40–2.48 Å. All Mn–Ge bond lengths are 2.84 Å. All Mn–Si bond lengths are 2.84 Å. There are five inequivalent Fe sites. In the first Fe site, Fe is bonded in a body-centered cubic geometry to four Mn and four Ge atoms. There are three shorter (2.46 Å) and one longer (2.47 Å) Fe–Ge bond lengths. In the second Fe site, Fe is bonded in a body-centered cubic geometry to four equivalent Mn and four Ge atoms. There are three shorter (2.46 Å) and one longer (2.49 Å) Fe–Ge bond lengths. In the third Fe site, Fe is bonded in a distorted body-centered cubic geometry to four equivalent Mn, one Ge, and three equivalent Si atoms. The Fe–Ge bond length is 2.50 Å. All Fe–Si bond lengths are 2.44 Å. In the fourth Fe site, Fe is bonded in a body-centered cubic geometry to four Mn, three equivalent Ge, and one Si atom. All Fe–Ge bond lengths are 2.48 Å. The Fe–Si bond length is 2.40 Å. In the fifth Fe site, Fe is bonded in a distorted body-centered cubic geometry to four equivalent Mn, one Ge, and three equivalent Si atoms. There are one shorter (2.40 Å) and three longer (2.48 Å) Fe–Mn bond lengths. The Fe–Ge bond length is 2.50 Å. All Fe–Si bond lengths are 2.44 Å. There are two inequivalent Ge sites. In the first Ge site, Ge is bonded in a distorted body-centered cubic geometry to six Mn and eight Fe atoms. In the second Ge site, Ge is bonded in a distorted body-centered cubic geometry to eight Fe atoms. Si is bonded in a distorted body-centered cubic geometry to six equivalent Mn and eight Fe atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on ZrSc(NiSn)2 by Materials Project

ScZr(NiSn)2 is half-Heusler-derived structured and crystallizes in the trigonal R3m space group. The structure is three-dimensional. Sc is bonded in a 4-coordinate geometry to four Ni and six Sn atoms. All Sc–Ni bond lengths are 2.68 Å. There are three shorter (3.08 Å) and three longer (3.09 Å) Sc–Sn bond lengths. Zr is bonded in a 4-coordinate geometry to four Ni and six Sn atoms. There are three shorter (2.66 Å) and one longer (2.68 Å) Zr–Ni bond lengths. There are three shorter (3.08 Å) and three longer (3.10 Å) Zr–Sn bond lengths. There are two inequivalent Ni sites. In the first Ni site, Ni is bonded in a body-centered cubic geometry to one Sc, three equivalent Zr, and four Sn atoms. There are one shorter (2.67 Å) and three longer (2.68 Å) Ni–Sn bond lengths. In the second Ni site, Ni is bonded in a body-centered cubic geometry to three equivalent Sc, one Zr, and four Sn atoms. There are three shorter (2.66 Å) and one longer (2.69 Å) Ni–Sn bond lengths. There are two inequivalent Sn sites. In the first Sn site, Sn is bonded in a distorted q6 geometry to three equivalent Sc, three equivalent Zr, and four Ni atoms. In the second Sn site, Sn is bonded in a distorted q6 geometry to three equivalent Sc, three equivalent Zr, and four Ni atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on ScTi(NiSn)2 by Materials Project

ScTi(NiSn)2 is half-Heusler-derived structured and crystallizes in the trigonal R3m space group. The structure is three-dimensional. Sc is bonded in a 4-coordinate geometry to four Ni and six Sn atoms. There are three shorter (2.64 Å) and one longer (2.67 Å) Sc–Ni bond lengths. There are three shorter (3.04 Å) and three longer (3.06 Å) Sc–Sn bond lengths. Ti is bonded in a 4-coordinate geometry to four Ni and six Sn atoms. All Ti–Ni bond lengths are 2.59 Å. There are three shorter (2.98 Å) and three longer (3.01 Å) Ti–Sn bond lengths. There are two inequivalent Ni sites. In the first Ni site, Ni is bonded in a body-centered cubic geometry to one Sc, three equivalent Ti, and four Sn atoms. There are one shorter (2.53 Å) and three longer (2.61 Å) Ni–Sn bond lengths. In the second Ni site, Ni is bonded in a body-centered cubic geometry to three equivalent Sc, one Ti, and four Sn atoms. There are three shorter (2.60 Å) and one longer (2.76 Å) Ni–Sn bond lengths. There are two inequivalent Sn sites. In the first Sn site, Sn is bonded in a 10-coordinate geometry to three equivalent Sc, three equivalent Ti, and four Ni atoms. In the second Sn site, Sn is bonded in a distorted q6 geometry to three equivalent Sc, three equivalent Ti, and four Ni atoms.

36 MATERIALS SCIENCE↗