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NASA NTRS1995

Microstructure of the IMF turbulences at 2.5 AU

A detailed analysis of small period (15-900 sec) magnetohydrodynamic (MHD) turbulences of the interplanetary magnetic field (IMF) has been made using Pioneer-11 high time resolution data (0.75 sec) inside a Corotating Interaction Region (CIR) at a heliocentric distance of 2.5 AU in 1973. The methods used are the hodogram analysis, the minimum variance matrix analysis and the cohenrence analysis. The minimum variance analysis gives evidence of linear polarized wave modes. Coherence analysis has shown that the field fluctuations are dominated by the magnetosonic fast modes with periods 15 sec to 15 min. However, it is also shown that some small amplitude Alfven waves are present in the trailing edge of this region with characteristic periods (15-200 sec). The observed wave modes are locally generated and possibly attributed to the scattering of Alfven waves energy into random magnetosonic waves.

Mavromichalaki, H.↗

DOE OSTI2022

Measuring representative volume elements from high-resolution grain-scale strain fields

Most crystalline materials present a highly heterogeneous response at the microscale, which can be affected by both internal factors (such as microstructural parameters) and external factors (such as loading). Relating microscale inhomogeneities to the macroscale response of a material requires the use of homogenisation techniques, usually based on the concept of a representative volume element (RVE)—the smallest volume of material that represents the global average response. Here, in this work, we present a new and robust experimental method of measuring the size of a strain-based RVE from high-resolution grain-scale strain fields obtained using digital image correlation (DIC). The proposed method is based on the statistical (stereological) nature of the RVE, which has been widely adopted in numerical studies, and involves dividing a strain field into randomly selected regions of varying sizes and statistically analysing the distributions of average strains within them. To validate the new method, we generate a large number of synthetic strain fields from a fractional Gaussian noise algorithm. The proposed stereological method is shown to be capable of producing reliable RVE measurements from a very large range of possible microscale strain fields while at the same time being robust in that it can produce RVE measurement results even in cases where other existing methods may be unable to do so. The proposed method has a low field-of-view requirement, only needing a field-of-view about 1.2 times as large as the RVE to produce reliable measurements. In addition, the stereological method offers significant flexibility since its statistical nature allows for control over how strict the RVE measurement should be in each case.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Establishment of computerized numerical databases on thermophysical and other properties of molten as well as solid materials and data evaluation and validation for generating recommended reliable reference data

The Center for Information and Numerical Data Analysis and Synthesis, (CINDAS), measures and maintains databases on thermophysical, thermoradiative, mechanical, optical, electronic, ablation, and physical properties of materials. Emphasis is on aerospace structural materials especially composites and on infrared detector/sensor materials. Within CINDAS, the Department of Defense sponsors at Purdue several centers: the High Temperature Material Information Analysis Center (HTMIAC), the Ceramics Information Analysis Center (CIAC) and the Metals Information Analysis Center (MIAC). The responsibilities of CINDAS are extremely broad encompassing basic and applied research, measurement of the properties of thin wires and thin foils as well as bulk materials, acquisition and search of world-wide literature, critical evaluation of data, generation of estimated values to fill data voids, investigation of constitutive, structural, processing, environmental, and rapid heating and loading effects, and dissemination of data. Liquids, gases, molten materials and solids are all considered. The responsibility of maintaining widely used databases includes data evaluation, analysis, correlation, and synthesis. Material property data recorded on the literature are often conflicting, diverging, and subject to large uncertainties. It is admittedly difficult to accurately measure materials properties. Systematic and random errors both enter. Some errors result from lack of characterization of the material itself (impurity effects). In some cases assumed boundary conditions corresponding to a theoretical model are not obtained in the experiments. Stray heat flows and losses must be accounted for. Some experimental methods are inappropriate and in other cases appropriate methods are carried out with poor technique. Conflicts in data may be resolved by curve fitting of the data to theoretical or empirical models or correlation in terms of various affecting parameters. Reasons (e.g. phase transitions) must be found for unusual dependence or any anomaly. Such critical evaluation involves knowledge of theory, experience in measurement, familiarity with metallurgy (microstructural behavior) and not inconsiderable judgment. An examination of typical data compiled and analyzed by CINDAS shows that the thermal conductivity of a material reported in the literature may vary by a factor of two of more; the range of reported values increases as temperature increases reflecting the difficulty of high temperature measurements. Often only estimates of melt behavior are available, despite the importance of melt properties in modeling, welding, or other solidification processes. There may be only a few measurements available for properties such as kinematic viscosity, even for widely used materials such as stainless steel. In the face of such a paucity of existing data and in a national environment where too few new data are being generated it is nonetheless the responsibility of CINDAS to select and disseminate recommended values of a wide variety of thermophysical properties.

Ho, C. Y.↗

DOE OSTI2023

Finding simplicity: unsupervised discovery of features, patterns, and order parameters via shift-invariant variational autoencoders *

Abstract Recent advances in scanning tunneling and transmission electron microscopies (STM and STEM) have allowed routine generation of large volumes of imaging data containing information on the structure and functionality of materials. The experimental data sets contain signatures of long-range phenomena such as physical order parameter fields, polarization, and strain gradients in STEM, or standing electronic waves and carrier-mediated exchange interactions in STM, all superimposed onto scanning system distortions and gradual changes of contrast due to drift and/or mis-tilt effects. Correspondingly, while the human eye can readily identify certain patterns in the images such as lattice periodicities, repeating structural elements, or microstructures, their automatic extraction and classification are highly non-trivial and universal pathways to accomplish such analyses are absent. We pose that the most distinctive elements of the patterns observed in STM and (S)TEM images are similarity and (almost-) periodicity, behaviors stemming directly from the parsimony of elementary atomic structures, superimposed on the gradual changes reflective of order parameter distributions. However, the discovery of these elements via global Fourier methods is non-trivial due to variability and lack of ideal discrete translation symmetry. To address this problem, we explore the shift-invariant variational autoencoders (shift-VAEs) that allow disentangling characteristic repeating features in the images, their variations, and shifts that inevitably occur when randomly sampling the image space. Shift-VAEs balance the uncertainty in the position of the object of interest with the uncertainty in shape reconstruction. This approach is illustrated for model 1D data, and further extended to synthetic and experimental STM and STEM 2D data. We further introduce an approach for training shift-VAEs that allows finding the latent variables that comport to known physical behavior. In this specific case, the condition is that the latent variable maps should be smooth on the length scale of the atomic lattice (as expected for physical order parameters), but other conditions can be imposed. The opportunities and limitations of the shift VAE analysis for pattern discovery are elucidated.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Sensitivity of UO 2 fuel performance to microstructural evolutions driven by dilute additives

Use of dilute additives to nuclear fuel is being considered to increase the security of commercial fuel management through traceability of fabricated fuel elements. Taggants, as additives are denoted when included for traceability purposes, may also improve fuel performance, as demonstrated in Cr-containing uranium dioxide as described in the literature, and they may also improve fuel safety. In fact, studies have shown that some additives affect fuel material properties such as grain size and density after sintering. Given the possible range of elements that could be used as additives, the impact of such fuel property variations on the fuel’s thermomechanical behavior becomes relevant. These effects can be evaluated through a sensitivity study of standard fuel models to analyze changes in these properties using a fuel performance code. In this work, the BISON code is being used to investigate these effects through a 2D axisymmetric model of smeared UO 2 fuel pellets and ZIRLO® cladding under realistic pressurized water reactor core irradiation conditions. Here, randomly sampled densities and grain sizes within specified ranges are used as input parameters in the simulations, and several fuel model-related outputs are evaluated. The thermomechanical response of the cladding is also addressed in this study. The simultaneous variation of both input parameters offers a more comprehensive path to identify key sensitivities. Outputs explored include temperature, fission gas release, creep, and radial stress. Results show that although most of these outputs are sensitive to grain size to a certain extent, density mainly affects fuel temperature and elastic strain. Furthermore, sensitivities can vary depending on the radial position within the fuel pellet.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1984

Interlaminar fracture of random short-fiber SMC composite

In the experimental phase of the present study of the interlaminar fracture behavior of a randomly oriented short fiber sheet molding compound (SMC) composite, the double cantilever beam fracture test is used to evaluate the mode I interlaminar fracture toughness of different composite thicknesses. In the analytical phase of this work, a geometrically nonlinear analysis is introduced in order to account for large deflections and nonlinear load deflection curves in the evaluation of interlaminar fracture toughness. For the SMC-R50 material studied, interlaminar toughness is an order of magnitude higher than that of unreinforced neat resin, due to unusual damage mechanisms ahead of the crack tip, together with significant fiber bridging across crack surfaces. Composite thickness effects on interlaminar fracture are noted to be appreciable, and a detailed discussion is given on the influence of SMC microstructure.

Wang, S. S.↗

DOE OSTI2026

Structural Heterogeneity in Medium-Entropy AgMnSbPbTe 4 for Glassy Thermal Transport and High Thermoelectric Performance

Medium-entropy semiconductors represent a unique category of entropy-engineered materials. They possess a considerable level of randomness in atomic mixing, although this is not sufficient to conclusively achieve single-phase structure stabilization, in contrast to high-entropy materials. This introduces strong competition between the formation of different phases, which can potentially lead to structural heterogeneity. Here, in this work, we uncover endotaxial nanoprecipitates in the microscopically identified homogeneous medium-entropy semiconductor AgMnSbPbTe 4 . These nanoprecipitates initially crystallize in a cubic phase $(Fm\bar{3}m)$ within kinetically stabilized AgMnSbPbTe 4 , subsequently evolving into a thermodynamically stable monoclinic phase $(P2_1/c)$ during thermal annealing while maintaining an endotaxial relationship with the matrix lattice. This nanophase segregation and the resultant lattice mismatch at interfaces introduce strain fluctuations up to 5% at intervals of 20 nm across the entire microstructure. Within the matrix phase, atomic displacement of up to 23 pm was observed. This structural heterogeneity results in glass-like thermal transport behavior, achieving an ultralow lattice thermal conductivity κ L = 0.312 Wm –1 K –1 at 800 K, which is in accordance with the amorphous limit predicted by the Cahill model. The synergy of band convergence effect and well-maintained carrier mobility leads to a maximum ZT of 1.72 at 800 K and an average ZT avg of 1.02 over the temperature range of 300–825 K. This study highlights that the underexplored structural heterogeneity in medium-entropy semiconductors can potentially yield beneficial phenomena, such as the phonon-glass electron-crystal transport behavior in this case, which holds promise for advancing thermoelectric applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1987

Crack diffusion coefficient - A candidate fracture toughness parameter for short fiber composites

In brittle matrix composites, crack propagation occurs along random trajectories reflecting the heterogeneous nature of the strength field. Considering the crack trajectory as a diffusive process, the 'crack diffusion coefficient' is introduced. From fatigue crack propagation experiments on a set of identical SEN polyester composite specimens, the variance of the crack tip position along the loading axis is found to be a linear function of the effective 'time'. The latter is taken as the effective crack length. The coefficient of proportionality between variance of the crack trajectory and the effective crack length defines the crack diffusion coefficient D which is found in the present study to be 0.165 mm. This parameter reflects the ability of the composite to deviate the crack from the energetically most efficient path and thus links fracture toughness to the microstructure.

Mull, M. A.↗

DOE OSTI2025

Texture Analysis of Inconel 718 with Different Modes During Single-Track Laser Surface Re-Melting

An in-depth understanding of the texture formation in melt pools allows for the modification of the surface layer microstructure and corresponding material properties, providing an opportunity to integrate laser surface re-melting into metal additive manufacturing. This study investigates crystallographic texture formation at different cooling rates in single melting tracks on the Inconel 718 (IN718) plate produced by laser surface re-melting. The cooling rate varies from 2.31 × 10 5 °C/s to 9.56 × 10 5 °C/s with the increase in scanning rates from 400 mm/s to 1200 mm/s, measured by recently developed real-time temperature monitoring of melt pools. Columnar grains are dominant, with distinct crystallographic textures forming in the melt pools. At a slower scanning speed, the keyhole mode shows three different textures forming at different depths (crystallographically layered structure), while, at a faster scanning speed, the conduction mode shows only random grain orientation. There are no pores/voids detected, and the columnar grain morphology and columnar grain width (8.6 μm to 12.4 μm) follow the analysis framework in terms of thermal gradient and solidification rate analysis. This implies that laser surface re-melting provides the potential to modify the surface structure from a random grain orientation to a crystallographically layered structure.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Characterization of low thermal conductivity PAN-based carbon fibers

The microstructure and surface chemistry of eight low thermal conductivity (LTC) PAN-based carbon fibers were determined and compared with PAN-based fibers heat treated to higher temperatures. Based on wide-angle x ray diffraction, the LTC PAN fibers all appear to have a similar turbostratic structure with large 002 d-spacings, small crystallite sizes, and moderate preferred orientation. Limited small-angle x ray scattering (SAXS) results indicate that, with the exception of LTC fibers made by BASF, the LTC fibers do not have well developed pores. Transmission electron microscopy shows that the texture of the two LTC PAN-based fibers studied (Amoco T350/23X and /25X) consists of multiple sets of parallel, wavy, bent layers that interweave with each other forming a complex three dimensional network oriented randomly around the fiber axis. X ray photoelectron spectroscopy (XPS) analysis finds correlations between heat treated temperatures and the surface composition chemistry of the carbon fiber samples.

Katzman, Howard A.↗

DOE OSTI2023

Understanding the Effect of Electron Beam Melting Scanning Strategies on the Aluminum Content and Materials State of Single Ti-6Al-4V Feedstock

Research on the additive manufacturing of metals often neglects any characterization of the composition of final parts, erroneously assuming a compositional homogeneity that matches the feedstock material. Here, the composition of electron-beam-melted Ti-6Al-4V produced through three distinct scanning strategies (linear raster and two point melting strategies, random fill and Dehoff fill) is characterized both locally and globally through energy-dispersive spectroscopy and quantitative chemical analysis. As a result of the different scanning strategies used, differing levels of preferential vaporization occur across the various parts, leading to distinct final compositions, with extremes of ~5.8 wt.% Al and ~4.8 wt.% Al. In addition, energy-dispersive spectroscopy composition maps reveal specific features in both the XY and XZ planes (with Z being the build direction) as a result of local inhomogeneous preferential vaporization. The subsequent change in composition significantly modifies the materials’ state of parts, wherein parts and local regions with higher aluminum contents lead to higher hardness levels (with a ~50 HV difference) and elastic property values and vice versa. While varying scan strategies and scan parameters are known to modify the microstructure and properties of a part, the effect on composition cannot, and should not, be neglected.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Effect of grain boundary character distribution on weld heat-affected zone liquation cracking behavior of AISI 316Ti austenitic stainless steel

Highlights: • Grain boundary engineered AISI 316 was produced through thermomechanical processing. • Grain boundary engineering resulted in random high angle boundary network disruption. • Liquation cracks are arrested at triple junctions having one or more CSL boundaries. • Grain boundary engineering resulted in improvement in liquation cracking resistance. - Abstract: In this work, the role of grain boundary engineering (GBE) on the weld heat-affected-zone (HAZ) liquation cracking resistance of austenitic stainless steel AISI 316Ti was investigated. Standard wrought-processed alloy 316Ti was cold rolled to 5% strain and subsequently annealed at 1373 K for 30 min to achieve the optimum grain boundary character distribution (GBCD). The GBE samples were found to consist of a significantly higher fraction (72%) of low Ʃ coincident site lattice (CSL) boundaries as compared to the as received (AR) samples (45%). To study the liquation cracking behavior, single-track longitudinal varestraint tests was performed on AR and GBE samples. Microstructural examination revealed that the grain coarsening and the liquation events were less prominent in the GBE samples as compared to the AR samples. It is believed that the reduced segregation of impurities to the special boundaries (coherent Ʃ3 twins, in particular) present in the GBE samples is responsible for the observed improvement in the HAZ liquation cracking resistance.

36 MATERIALS SCIENCE↗

NASA NTRS2004

Brazing SiC/SiC Composites to Metals

Experiments have shown that active brazing alloys (ABAs) can be used to join SiC/SiC composite materials to metals, with bond strengths sufficient for some structural applications. The SiC/SiC composite coupons used in the experiments were made from polymerbased SiC fiber preforms that were chemical-vapor-infiltrated with SiC to form SiC matrices. Some of the metal coupons used in the experiments were made from 304 stainless steel; others were made from oxygen-free, high-conductivity copper. Three ABAs were chosen for the experiments: two were chosen randomly from among a number of ABAs that were on hand at the time; the third ABA was chosen because its titanium content (1.25 percent) is less than those of the other two ABAs (1.75 and 4.5 percent, respectively) and it was desired to evaluate the effect of reducing the titanium content, as described below. The characteristics of ABAs that are considered to be beneficial for the purpose of joining SiC/SiC to metal include wettability, reactivity, and adhesion to SiC-based ceramics. Prior to further development, it was verified that the three chosen ABAs have these characteristics. For each ABA, suitable vacuum brazing process conditions were established empirically by producing a series of (SiC/SiC)/ABA wetting samples. These samples were then sectioned and subjected to scanning electron microscopy (SEM) and energy-dispersive x-ray spectrometry (EDS) for analysis of their microstructures and compositions. Specimens for destructive mechanical tests were fabricated by brazing of lap joints between SiC/SiC coupons 1/8-in. (.3.2- mm) thick and, variously, stainless steel or copper tabs. The results of destructive mechanical tests and the SEM/EDS analysis were used to guide the development of a viable method of brazing the affected materials.

Steffier, Wayne S.↗

DOE OSTI2022

Effects of internal swelling on residual elasticity of a quasi-brittle material through a composite sphere model

This work describes the development of a micromechanical-based constitutive model accounting for the effect of internal expansion on the residual elasticity of a Hashin composite material. This material is made of spherical inclusions that are subjected to gradual swelling within a quasi-brittle matrix. The main focus of this work is to describe and analyze the material mechanical response, with an additional focus on the internal swelling’s effect on the stress–strain response and residual elasticity. Microstructural features and parameters of major importance for the mechanical responses were identified. The innovative characteristics of the proposed approach are summarized as follows: (1) a full determination of the physics of a complete-damage problem throughout the whole process of inclusion swelling with upscaling techniques, which transfers the microcrack-related properties from the lower scale to upper scale; and (2) an evolution of the mechanical fields and the corresponding residual elasticity for various inclusion swelling levels. Concerning the matrix–inclusion composite, it was hypothesized that only the matrix was susceptible to cracking, with varied degrees of damage, whereas the inclusions behave elastically and the elastic modulus of the expanding inclusions remains constant. It is to emphasize that the gradual swelling of inclusions is modeled by an increasing strain in the current micromechanical-based constitutive model, and the microcracks are represented by a set of randomly oriented penny-shaped microcracks with identical radii (namely, closed cracks). The main contribution of the current research is to establish the exact mathematical solutions for the mechanical fields (stress, strain) caused by the swelling of the inclusions (mechanical loading) and derive the effective residual elasticity of a composite (structural response) subject to internal expansion and quasi-brittle damage. Based on the assumption of closed cracks that could be extended to open cracks in the upcoming work, the results proposed by the present paper help to understand the non-linear mechanical behavior of quasi-brittle materials subject to microcracking and provide a theoretical framework to be used as academical benchmark for numerical simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Prediction of defect properties in concentrated solid solutions using a Langmuir-like model

The alleged existence of sluggish diffusion in high-entropy alloys has drawn controversy. In high-entropy alloys and, in general, in all solids, transport properties are controlled by point defect concentration, which must be known before performing atomistic simulations to compute transport coefficients. In this work, we present a general Langmuir-like model for defect concentration in an arbitrarily complex solid solution and apply this model to generate expressions for concentrations of vacancies and small interstitial atoms. We then calculate the vacancy concentration as a function of temperature in the equiatomic CoNiCrFeMn and FeAl alloys with modified embedded-atom-method potentials for various chemical orderings, showing there is no clear correlation between vacancy thermodynamics and chemical ordering in the CoNiCrFeMn alloy, but clear systematic patterns for FeAl. We believe this is due to the high stability of disordered, random, and ordered intermetallic phases, respectively, in the CoNiCrFeMn and FeAl systems. Finally, this work provides future avenues to the prediction of thermal interstitials and vacancies in solid solutions, which is necessary for models of nonequilibrium behavior of solid solutions.

composition↗

DOE OSTI2021

Microstructure evolution of gadolinium doped cerium oxide under large thermal gradients

In this report the effects of large thermal gradient annealing on the microstructure of 10 mol% gadolinium doped ceria (GDC) were investigated. GDC powder was prepared by solvent deficient method and sintered at 1650 °C for 10 h to achieve dense ceramics with ~8 μm grain size. The densified GDC samples were subsequently annealed using a 60 W infrared laser at over 2100 °C for 1 h under a thermal gradient equivalent to ~0.3–0.5 °C/μm. The post-annealed samples at 2150 °C for 1 h exhibit grains with average length and width of 37 and 28 μm, respectively. Electron backscattered diffraction (EBSD) analysis revealed that the post-annealed sample at 2150 °C consists of grains oriented close to five principal directions (<4 3 10>, <0 0 1> and <13 1 14> on [0 0 1], and <7 6 20> and <7 2 7> on [0 1 0]) within a tolerance angle of ±10°, whereas the grains of the pre-annealed sample are randomly oriented. Gadolinium diffuses 20–30 μm away from the irradiated surface, with the measured composition of regions deeper than 30 μm, Ce 0.86 Gd 0.14 O 1.93 , is close to that of the pre-annealed sample, Ce 0.87 Gd 0.13 O 1.94 . Enhancement of total conductivity of the post-annealed GDC (1.1 × 10 -3 S cm -1 at 500 °C, and 2.1 × 10 -2 S cm -1 at 700 °C) is observed when compared to the pre-annealed GDC (3.1 × 10 -5 S cm -1 at 500 °C, and 1.7 × 10 -3 S cm -1 at 700 °C), and points to the decrease in the grain boundary (GB) resistivity. This could be attributed to both the change in GB area and grain alignment.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Microstructure analysis of laser beam weldments performed on neutron-irradiated 304L steel containing 3 and 8 appm helium

We report that AISI 304 L austenitic stainless steel is one of the major structural materials used in light water reactors (LWRs). In the future, 304 L components may require repair, and several welding techniques have been proposed as candidates. In this study, laser beam welding using the low-energy contribution approach was performed in ~2016 on neutron-irradiated AISI 304 L steel with nominal values of 3 and 8 appm helium (He). The goal was to investigate the impact of helium on the irradiated material weldability and evaluate helium-associated damage. The weld and heat-affected zone (HAZ) microstructure was studied using scanning electron microscopy, electron backscatter diffraction, and transmission electron microscopy (TEM). Analysis of the weldment cross-sections did not reveal severe cracking. Still, evidence of incipient helium-associated damage was observed in the HAZ, manifesting as degraded grain boundaries (GBs) “decorated” by pore chains and mostly small (i.e., ≤ 25-30 µm) scattered cracks. The largest observed crack was ~50 µm in length. Helium-associated damage was localized within ~200-300 µm of the weld pool boundary, and the fraction of the compromised GBs, as a rule, was below ~9-11% of the total GB network. TEM analysis showed significant annealing of the radiation-induced defects at distances up to ~300 µm from the weld pool boundary. Inside the HAZ, the cavities (likely, helium bubbles) tended to form at GBs and inclusions, such as manganese sulfide precipitates in the grain interior. Crystallography analysis of the HAZ damage showed that random high-angle boundaries were most susceptible to helium-associated damage. In contrast, low-angle random boundaries and twin boundaries appeared to be strongly resistant to degradation from the combined effects of helium and welding.

36 MATERIALS SCIENCE↗

DOE OSTI2026

One-dimensional neutron diffraction from layered graphite: Reciprocal space structure and grating behavior

In this work we report observations of one-dimensional neutron diffraction from highly oriented pyrolytic graphite (HOPG), where the scattering angle varies continuously with incident angle following classical grating-like behavior. The 2D polycrystalline structure of HOPG—with highly aligned layers along the 𝑐 axis but random in-plane rotations—creates planes of scattering intensity in reciprocal space at 𝑄 𝑐 =𝑛⁢(2⁢𝜋/𝑑) where 𝑑=3.35Å is the interlayer spacing. As the Ewald sphere sweeps through reciprocal space during sample rotation, it continuously intersects these planes, producing the observed angular dispersion. We observe both first-order (𝑛=1) and second-order (𝑛=2) diffraction at conventional scattering angles (25°–70°), with peak positions that remain temperature-independent between 10 K and 294 K and follow quantitative agreement with momentum conservation 𝑄 𝑐 =𝑘⁢[sin⁡𝜓−sin⁡𝜓 𝑓 ]=𝑛⁢(2⁢𝜋/𝑑). X-ray diffraction under similar conditions shows no comparable behavior, confirming that sharp nuclear-vacuum contrast is essential. While diffraction intensities are weak (∼10 −6 of Bragg peaks), the observations demonstrate how the interplay of atomic-scale periodicity, nuclear contrast, and structural disorder enables observation of continuous diffraction curves at thermal neutron wavelengths, illustrating how HOPG's unique microstructure determines its scattering properties beyond conventional Bragg diffraction.

2-dimensional systems↗