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DOE OSTI2021

4D-STEM of Beam-Sensitive Materials

We report that a scanning electron nanobeam diffraction, or 4D-STEM (four-dimensional scanning transmission electron microscopy), is a flexible and powerful approach to elucidate structure from "soft" materials that are challenging to image in the transmission electron microscope because their structure is easily damaged by the electron beam. In a 4D-STEM experiment, a converged electron beam is scanned across the sample, and a pixelated camera records a diffraction pattern at each scan position. This four-dimensional data set can be mined for various analyses, producing maps of local crystal orientation, structural distortions, crystallinity, or different structural classes. Holding the sample at cryogenic temperatures minimizes diffusion of radicals and the resulting damage and disorder caused by the electron beam. The total fluence of incident electrons can easily be controlled during 4D-STEM experiments by careful use of the beam blanker, steering of the localized electron dose, and by minimizing the fluence in the convergent beam thus minimizing beam damage. This technique can be applied to both organic and inorganic materials that are known to be beam-sensitive; they can be highly crystalline, semicrystalline, mixed phase, or amorphous. One common example is the case for many organic materials that have a π-π stacking of polymer chains or rings on the order of 3.4-4.2 Å separation. If these chains or rings are aligned in some regions, they will produce distinct diffraction spots (as would other crystalline spacings in this range), though they may be weak or diffuse for disordered or weakly scattering materials. We can reconstruct the orientation of the π-π stacking, the degree of π-π stacking in the sample, and the domain size of the aligned regions. This Account summarizes illumination conditions and experimental parameters for 4D-STEM experiments with the goal of producing images of structural features for materials that are beam-sensitive. We will discuss experimental parameters including sample cooling, probe size and shape, fluence, and cameras. 4D-STEM has been applied to a variety of materials, not only as an advanced technique for model systems, but as a technique for the beginning microscopist to answer materials science questions. It is noteworthy that the experimental data acquisition does not require an aberration-corrected TEM but can be produced on a variety of instruments with the right attention to experimental parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Spin Dynamics of Triple-𝐐 Magnetic Orderings in a Triangular Lattice: Implications for Multi-𝐐 Orderings in General Two-Dimensional Lattices

Multi-𝐐 magnetic structures on two-dimensional (2D) lattices provide a key route to realizing topological physics in 2D magnetism. A major experimental challenge is to unambiguously confirm their formation by excluding the possibility of topologically trivial multidomain single- or double-𝐐 magnetic orders, which cannot be distinguished using conventional diffraction techniques. Here, we propose that long-wavelength spin dynamics offers a universal diagnostic for triangular lattices: Triple-𝐐 orders that preserve rotational symmetry and single- or double-𝐐 orders that break it exhibit qualitatively distinct anisotropies in their Goldstone-mode velocities, stemming from fundamental differences in their underlying spin configurations. We validate this concept using the metallic triangular-lattice antiferromagnet Co 0.325 ⁢TaS 2 , which hosts both a stripe-type single-𝐐 state and a triple-𝐐 tetrahedral ordering at different temperatures. Using inelastic neutron-scattering and spin dynamics simulations, we first refine the spin Hamiltonian by fitting the paramagnetic excitation spectra, allowing us to develop an unbiased model independent of magnetic ordering. We then show that the observed velocity profiles of the Goldstone modes agree with the high-temperature model’s predictions: markedly anisotropic for the single-𝐐 phase and near isotropic for the triple-𝐐 phase. Importantly, this contrast persists across various exchange parameters, highlighting its model-independent nature and suggesting potential applicability to other 2D lattice systems. Beyond the long-wavelength regime, we present a substantial discrepancy between the measured and simulated magnon spectra exclusively in the triple-𝐐 phase. We attribute this discrepancy to magnon energy renormalization arising from order-of-magnitude-enhanced magnon-magnon interactions in the triple-𝐐 phase, due to its noncollinear configuration. This work provides universal insight into the dynamical properties of topological multi-𝐐 magnetic orderings in 2D lattice structures, offering a broadly applicable diagnostic to distinguishing them from topologically trivial single- or double-𝐐 counterparts. The unequivocal confirmation of the triple-𝐐 structure in Co 0.325 ⁢TaS 2 further establishes it as a prominent material platform for exploring topological spin textures in the genuine 2D limit.

Park, Pyeongjae [Oak Ridge National Laboratory (OR↗

DOE OSTI2021

Null geodesics and thermodynamic phase transition of four-dimensional Gauss–Bonnet AdS black hole

Highlights: • Modified gravity theories. • Null geodesics and the thermodynamic phase transition. • Four-dimensional Gauss–Bonnet AdS black hole. • Correlation between gravity and thermodynamics. Modified gravity theories are of great interest in both observational and theoretical studies. In this article, we study the correlation between the null geodesics and the thermodynamic phase transition of a four-dimensional Gauss–Bonnet AdS black hole. Firstly, we study the phase structure of the black hole, using the coexistence and spinodal curves, to understand the phase transition in an extended phase space. The imprints of these phase transition features can be clearly observed from the functional dependence of photon orbit radius and minimum impact parameter with respect to the Hawking temperature and pressure. The change in these two quantities during the phase transition serve as order parameters which characterise the critical behaviour. The correlation shows that thermodynamic phase transition can be studied by observing the effects of strong gravitational field on the photon orbit and vice versa.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Computational design of thermoelectric alloys through optimization of transport and dopability

Alloying is a common technique to optimize the functional properties of materials for thermoelectrics, photovoltaics, energy storage etc. Designing thermoelectric (TE) alloys is especially challenging because it is a multi-property optimization problem, where the properties that contribute to high TE performance are interdependent. In this work, we develop a computational framework that combines first-principles calculations with alloy and point defect modeling to identify alloy compositions that optimize the electronic, thermal, and defect properties. We apply this framework to design n-type Ba 2(1–x) Sr 2x CdP 2 Zintl thermoelectric alloys. Our predictions of the crystallographic properties such as lattice parameters and site disorder are validated with experiments. To optimize the conduction band electronic structure, we perform band unfolding to sketch the effective band structures of alloys and find a range of compositions that facilitate band convergence and minimize alloy scattering of electrons. Here, we assess the n-type dopability of the alloys by extending the standard approach for computing point defect energetics in ordered structures. Through the application of this framework, we identify an optimal alloy composition range with the desired electronic and thermal transport properties, and n-type dopability. Such a computational framework can also be used to design alloys for other functional applications beyond TE.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Quantifying Quantum Chaos through Microcanonical Distributions of Entanglement

A characteristic feature of “quantum chaotic” systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this feature, we introduce a framework that allows us to compare the properties of eigenstates in local systems with those of pure random states. In particular, our framework defines a notion of distance between quantum state ensembles that utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). This notion gives rise to a quantitative metric for quantum chaos that not only accounts for averages of the distributions but also higher moments. The differences in moments are compared on a highly resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. As a result, the metric can distinguish between chaotic and integrable behaviors and, in addition, quantify and compare the of chaos (in terms of proximity to RMT behavior) between two systems that are assumed to be chaotic. We implement our framework in local, minimally structured, Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed-field Ising model (MFIM). Importantly, for Hamiltonian systems, we find that the reference random distribution must be appropriately constrained to incorporate the effect of energy conservation in order to describe the ensemble properties of midspectrum eigenstates. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that “maximally chaotic” Hamiltonians may exist in fine-tuned pockets of parameter space. Published by the American Physical Society 2024

Physics↗

DOE OSTI2025

Appraising constrained second-order power corrections in HQET with Λ b →Λ c Ι⁢ν

We derive the Λ b →Λ c form factors for the Standard Model and beyond at second order in heavy quark effective theory, applying the recently proposed residual chiral expansion to reduce the set of unknown subsubleading hadronic functions to a single, highly constrained function, that is fully determined by hadron mass parameters at zero recoil. We fit a form factor parametrization based on these results to all available lattice QCD predictions and experimental data. We find that the constrained and predictive structure of the form factors under the residual chiral expansion is in excellent agreement with lattice QCD predictions and experimental data, as well as prior heavy-quark-effective-theory-based fits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Boron Nitride Solid-State Neutron Detectors

The goal of this project is to build upon the work performed under the Texas Tech IDEAS project (DE-AR0000964 monitored by Dr. Isik Kizilyalli) to bring the developed B-10 enriched hexagonal boron nitride (h- 10 BN or 10 BN or BN) semiconductor neutron detector technology to the next level of maturity. In comparison to He-3 ( 3 He) gas detectors, BN neutron detectors possess all the intrinsic advantages of semiconductor devices: light weight, compact size, fast response speed, high spatial resolution, high temperature and low voltage operation capability, ease of mass production via existing semiconductor infrastructures, low cost of operation and maintenance, flexible form factors, and durability. The project will develop a prototype h- 10 BN neutron detector as a potential replacement for the 3 He gas neutron detectors (LND 25185 or equivalent) used in various neutron survey meters currently produced and commercialized by Ludlum Measurements, Inc. (LMI). To increase the overall detection efficiency, it is essential to maximize the collection efficiency of charge carriers (electrons and holes) generated by the nuclear reaction, which demands a further push to achieve 10 BN epilayers with improved material quality. The material growth processes will be guided by characterization of structural, optical, and electrical properties of h-BN. Selective devices will be calibrated at LMI. During ARPA-E supporting period, the key material parameters of h-BN produced by metal organic chemical vapor deposition (MOCVD), including the layer thickness, mobility-lifetime product, surface recombination field and detector size for maintaining a high charge collection efficiency all have been improved by several orders of magnitude. These improvements have enabled the realization of high-performance h 10BN semiconductor thermal neutron detectors. Presently, h- 10 BN thermal neutron detectors developed under ARPA-E’s support hold the record high detection efficiency among all solid-state detectors at 59%. With further development in manufacturing, there is no question that h-BN detectors will replace the traditional He-3 gas detectors in certain application areas by offering obvious advantages of semiconductor technologies over gas detectors and opportunities for users to dedicate the scarce and expensive supply of He-3 gas to other application areas where substitutes of He-3 gas are not possible.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Establishing Self-Dopant Design Principles from Structure–Function Relationships in Self-n-Doped Perylene Diimide Organic Semiconductors

Self-doping is a particular doping method that has been applied to a wide range of organic semiconductors. However, there is a lack of understanding regarding the relationship between dopant structure and function. A structurally diverse series of self-n-doped perylene diimides (PDIs) is investigated to study the impact of steric encumbrance, counterion selection, and dopant/PDI tether distance on functional parameters such as doping, stability, morphology, and charge-carrier mobility. The studies show that self-n-doping is best enabled by the use of sterically encumbered ammoniums with short tethers and Lewis basic counterions. Additionally, water is found to inhibit doping, which concludes that thermal degradation is merely a phenomenological feature of certain dopants, and that residual solvent evaporation is the primary driver of thermally activated doping. In situ grazing-incidence wide-angle X-ray scattering studies show that sample annealing increases the π–π stacking distance and shrinks grain boundaries for improved long-range ordering. These features are then correlated to contactless carrier-mobility measurements with time-resolved microwave conductivity before and after thermal annealing. In conclusion, the collective relationships between structural features and functionality are finally used to establish explicit self-n-dopant design principles for the future design of materials with improved functionality.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Charge transport and antiferromagnetic ordering in nitroxide radical crystals

Nonconjugated radical polymers and small molecules are employed as functional materials in organic electronic devices. Furthermore, the unpaired electrons on these materials have permanent magnetic moments, making these materials promising candidates for organic magnets. Through molecular design, strong antiferromagnetic and ferromagnetic ordering have been achieved in conjugated materials. However, the magnetic properties of nonconjugated radical polymers have only shown weak magnetic interactions among the open-shell sites due to the large mean separation between radicals in typical materials. Here, we have designed, synthesized, and crystalized two open-shell molecules that used molecular engineering to control the assembly of the open-shell sites into a strong antiferromagnetically ordered network. The strong antiferromagnetic interaction is evidenced by a high paramagnetic-to-antiferromagnetic transition temperature of ~40 K. This high transition temperature was a result of a high spin exchange coupling constant J of about –20 cm –1 , which was suggested by both experimental and computed coupling parameters given by the energy difference between high-spin and low-spin broken-symmetry structures. In addition, a single-crystal electrical conductivity of ~10 –3 S m –1 was achieved, which indicated the potential of this material in electronic applications. As a result, this work provides an insight into a design strategy for radical-based electronic and magnetic materials through proper molecular structure modifications.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Map-level baryonification: unified treatment of weak lensing two-point and higher-order statistics

Precision cosmology benefits from extracting maximal information from cosmic structures, motivating the use of higher-order statistics (HOS) at small spatial scales. However, predicting how baryonic processes modify matter statistics at these scales has been challenging. The baryonic correction model (BCM) addresses this by modifying dark-matter-only simulations to mimic baryonic effects, providing a flexible, simulation-based framework for predicting both two-point and HOS. We show that a 3-parameter version of the BCM can jointly fit weak lensing maps' two-point statistics, wavelet phase harmonics coefficients, scattering coefficients, and the third and fourth moments to within 2% accuracy across all scales ℓ < 2000 and tomographic bins for a DES-Y3-like redshift distribution ( z ≲ 2), using the FLAMINGO simulations. These results demonstrate the viability of BCM-assisted, simulation-based weak lensing inference of two-point and HOS, paving the way for robust cosmological constraints that fully exploit non-Gaussian information on small spatial scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Enhancement of charge density wave correlations in a Holstein model with an anharmonic phonon potential

The Holstein Hamiltonian describes itinerant electrons whose site density couples to local phonon degrees of freedom. In the single-site limit, at half filling, the electron-phonon coupling results in a double-well structure for the lattice displacement, favoring empty or doubly occupied sites. In two dimensions and on a bipartite lattice in d ≥ 2, intersite hopping causes these doubly occupied and empty sites to alternate in a charge density wave (CDW) pattern when the temperature is lowered. Because a discrete symmetry is broken, this occurs in a conventional second-order transition at finite T cdw . In this paper, we investigate the effect of changing the phonon potential energy to one with an intrinsic double-well structure even in the absence of electron-phonon coupling. While this aids in the initial process of pair formation, the implications for subsequent CDW order are nontrivial. One expects that, when the electron-phonon coupling is too strong, the double wells become deep and the polaron mass gets large, an effect which reduces T cdw . Here, we show here the existence of regions of parameter space where the double-well potential, while aiding local pair formation, does so in a way which also substantially enhances long-range CDW order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Gifts from anomalies: Exact results for Landau phase transitions in metals

Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in “Hertz-Millis” theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, \mathbf{q}=0 𝐪 = 0 , is a constant independent of frequency, and the real part of the optical conductivity, \sigma(\omega) σ ( ω ) , is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Design and Synthesis of Cubic K 3−2 x Ba x SbSe 4 Solid Electrolytes for K–O 2 Batteries

Developing K-ion conducting solid-state electrolytes (SSEs) plays a critical role in the safe implementation of potassium batteries. In this work, a chalcogenide-based potassium ion SSE is reported, K 3 SbSe 4 , which adopts a trigonal structure at room temperature. Single-crystal structural analysis reveals a trigonal-to-cubic phase transition at the low temperature of 50 °C, which is the lowest among similar compounds and thus provides easy access to the cubic phase. The substitution of barium for potassium in K 3 SbSe 4 leads to the creation of potassium vacancies, expansion of lattice parameters, and a transformation from a trigonal phase to a cubic phase. As a result, the maximum conductivity of K 3−2x Ba x SbSe 4 reaches around 0.1 mS cm −1 at 40 °C for K 2.2 Ba 0.4 SbSe 4 , which is over two orders of magnitude higher than that of undoped K 3 SbSe 4 . This novel SSE is successfully employed in a K–O 2 battery operating at room temperature where a polymer-laminated K 2.2 Ba 0.4 SbSe 4 pellet serves as a separator between the oxygen cathode and the potassium metal anode. Effective protection of the K metal anode against corrosion caused by O 2 is demonstrated.

25 ENERGY STORAGE↗

DOE OSTI2023

New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies

Here we report a new test of modified gravity theories using the large-scale structure of the Universe. This paper is the first attempt to (1) apply a joint analysis of the anisotropic components of galaxy two- and three-point correlation functions (2 and 3PCFs) to actual galaxy data and (2) constrain the non-linear effects of degenerate higher-order scalar-tensor (DHOST) theories on cosmological scales. Applying this analysis to the Baryon Oscillation Spectroscopic Survey (BOSS) data release 12, we obtain the lower bounds of –1.655 < ξ t and –0.504 < ξ s at the $95{{\ \rm per\ cent}}$ confidence level on the parameters characterizing the time evolution of the tidal and shift terms of the second-order velocity field. These constraints are consistent with GR predictions of ξ t = 15/1144 and ξs = 0. Moreover, they represent a 35-fold and 20-fold improvement, respectively, over the joint analysis with only the isotropic 3PCF. We ensure the validity of our results by investigating various quantities, including theoretical models of the 3PCF, window function corrections, cumulative S/N, Fisher matrices, and statistical scattering effects of mock simulation data. We also find statistically significant discrepancies between the BOSS data and the Patchy mocks for the 3PCF measurement. Finally, we package all of our 3PCF analysis codes under the name hitomi and make them publicly available so that readers can reproduce all the results of this paper and easily apply them to ongoing future galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Effect of Methyl Groups on Formation of Ordered or Layered Graphitic Materials from Aromatic Molecules

Abstract Developing functionally complex carbon materials from small aromatic molecules requires an understanding of how the chemistry and structure of its constituent molecules evolve and crosslink, to achieve a tailorable set of functional properties. Here, molecular dynamics (MD) simulations are used to isolate the effect of methyl groups on condensation reactions during the oxidative process and evaluate the impact on elastic modulus by considering three monodisperse pyrene‐based systems with increasing methyl group fraction. A parameter to quantify the reaction progression is designed by computing the number of new covalent bonds formed. Utilizing the previously developed MD framework, it is found that increasing methylation leads to an almost doubling of bond formation, a larger fraction of the new bonds oriented in the direction of tensile stress, and a higher basal plane alignment of the precursor molecules along the direction of tensile stress, resulting in enhanced tensile modulus. Additionally, via experiments, it is demonstrated that precursors with a higher fraction of methyl groups result in a higher alignment of molecules. Moreover, increased methylation results in the lower spread of single molecule alignment which may lead to smaller variations in tensile modulus and more consistent properties in carbon materials derived from methyl‐rich precursors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Effect of Thermodynamic and Environmental Factors on Crystallization of DNA‐Origami Superlattices

The directed self‐assembly of nanoscale materials into ordered superlattices presents a powerful strategy for creating next‐generation materials with programmable mechanical, optical, and photonic properties. Deoxyribonucleic acid (DNA) origami has emerged as a versatile scaffold for encoding nanoscale geometry and guiding the crystallization of complex 3D architectures. However, a systematic understanding of the parameters that govern the efficiency and quality of superlattice formation remains limited. In this study, we utilize octahedral DNA nanoscale frames as a model system to investigate the relative influence of key factors, including buffer composition, ionic strength, frame concentration, and thermal annealing protocols, on the size, order, and reproducibility of the resulting superlattices. Our findings provide a quantitative framework to rationally optimize DNA‐based assembly pathways. Structural characterization via small‐angle x‐ray scattering (SAXS), scanning electron microscopy (SEM), and optical microscopy validates the quality and fidelity of the assembled lattices. Moreover, by templating these DNA frameworks into inorganic replicas, we establish general design principles that extend beyond biomolecular systems, providing a foundation for the synthesis of programmable materials in broader nanofabrication contexts.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Sharp front tracking with geometric interface reconstruction

Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.

42 ENGINEERING↗

DOE OSTI2024

Nuclear magnetic resonance investigation of superconducting and normal state Nb 3 Sn

The superconductor Nb3Sn has important applications for construction of very high-field superconducting magnets. In this work we investigate its microscopic electronic structure with 93 Nb nuclear magnetic resonance (NMR). The high-quality Nb 3 Sn powder sample was studied in both 3.2 T and 7 T magnetic fields in the temperature range from 4 K to 300 K. From measurement of the spectrum and its theoretical analysis, we find evidence for anisotropy despite its cubic crystal structure. Magnetic alignment of the powder grains in the superconducting state was also observed. The Knight shift and spin-lattice relaxation rate, T 1 -1 , were measured and the latter compared with BCS theory for the energy gap Δ(0) = 2.7 ± 0.3k B T c at 3.2 T and Δ(0) = 2.33 ± 0.07 k B T c at 7 T, indicating suppression of the order parameter by magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗