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Design of novel refractory equiatomic multi-principal elemental alloys based on Mo-Nb-Ti system for Gen IV reactor applications

Excellent irradiation damage resistance demonstrated by multi-principal elemental alloys (MPEAs) has sparked significant interest among researchers, prompting exploration into their vast compositional space, to validate their suitability for nuclear applications. A combined approach of thermodynamic and empirical parameters calculations alongside CALPHAD (CALculation of PHAse Diagrams) for phase formation predictions enable high-throughput material selection for sophisticated applications like nuclear, overcoming laborious and time-consuming experiments. Key thermodynamic and empirical parameters for eight novel equiatomic MPEAs, based on seven low thermal neutron cross section refractory elements, for predicting phase formation were calculated, and equilibrium and non-equilibrium simulations in CALPHAD were employed to comprehensively model the systems. Pseudo binary phase diagram simulations showed that Zr, V or equiatomic CrV additions to the base MoNbTi alloy (MoNbTi-Zr, MoNbTi-V and MoNbTi-CrV alloys) favor the formation of isomorphous body-centered cubic (BCC) phase at high temperatures, while Cr, Al, equiatomic ZrV, or equiatomic CrAl additions (MoNbTi-Cr, MoNbTi-Al, MoNbTi-ZrV or MoNbTi-CrAl alloys) limit the solubility of them. Equilibrium CALPHAD simulations at 750 oC were consistent with XRD results on MoNbTi, MoNbTiZr and MoNbTiCr alloys, and partially for others. Notably, elemental segregation observed in the backscattered electron (BSE) scanning electron microscopy (SEM) images of the alloys was accurately simulated through non-equilibrium Scheil solidification calculations in CALPHAD, further verified by experiments. The precipitation of TiCr2 Laves phase in Cr containing MoNbTiCr and MoNbTiCrAl was accurately predicted while discrepancies were noted in MoNbTiCrV. The equilibrium simulations also provided insights into phase compositions at specific temperatures offering a pathway for tailoring the desired microstructure and properties of these systems. Empirical parameters calculations successfully predicted random solid solution in the base MoNbTi alloy, and with an exception in MoNbTiV and MoNbTiAl, predicted intermetallic precipitation in the rest, especially, Laves phase precipitation in Cr containing alloys.

36 - MATERIALS SCIENCE

ThO 2 and Th 1– x U x O 2 Nanoscale Materials and Thin Films for Nuclear Science Applications

This study investigates the dynamics and mechanisms of solution combustion synthesis (SCS) for the preparation of nanoscale ThO 2 and Th 1–x U x O 2 materials, utilizing metal nitrates (Th(NO 3 ) 4 and UO 2 (NO 3 ) 2 ) and acetylacetone (C 5 H 8 O 2 ) as reactants dissolved in a 2-methoxyethanol (C 3 H 8 O 2 ) solvent. By combining thermodynamic calculations, dynamic time–temperature profile measurements with differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA), this research reveals how variations in acetylacetone concentration and uranium content influence the structural parameters of the synthesized oxides. The time–temperature measurements show that the heating rate and maximum combustion temperatures are sensitive to acetylacetone concentration. DSC-TGA results indicate shifts in exothermic peak temperatures as the uranium content changes. The complexation between thorium and acetylacetone emerges as a critical factor, impacting combustion parameters and the structural characteristics of the final products. The uniform distribution of Th and U in the Th 1–x U x O 2 solid solution and the formation of nanoscale particles with strained crystallites are considered essential for the low-temperature densification of these materials for nuclear fuel pellet applications. Additionally, high-quality ThO 2 and Th 1–x U x O 2 thin (100–150 nm) films are successfully synthesized via electrospray deposition of combustible solutions followed by a brief period of heat treatment. Furthermore, these films exhibit excellent structural and morphological uniformity, making them ideal candidates for nuclear measurements, irradiation damage studies, and investigations into the physical properties of both pure and mixed oxides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Reducing experimental uncertainty in the calculation of cavity swelling in a transmission electron microscope through crystallographically aided void volume tracking

Accurate measurement of cavity swelling in a transmission electron microscope is essential to define material performance under irradiation, and the conventionally applied spherical assumption for the calculation of cavity volumes in irradiated materials can result in errors ranging between a 25% underestimation and 72% overestimation of volume purely based on the assumption of shape. This assumption is undeniably expedient for calculation but does not sufficiently account for the 3D nature of polyhedral cavities and their shape projection in the transmission electron microscope, and therefore presents too large of an associated uncertainty in swelling determination for faceted cavities. This uncertainty has been defined for many common cavity shapes in FCC and BCC crystal systems, and has been tabulated across the cubic fundamental region. A revised methodology for crystallographically aided void volume tracking, or CAVV-T, is presented and demonstrated on a specimen of neutron irradiated Ni. In-depth discussion on the application of this technique is provided along with resources to allow for conversion between the spherical assumption and this revised method. This work seeks to increase experimental confidence in the characterization and quantification of critical aspects of irradiation damage in materials by applying a crystallographically-resolved approach for cavity swelling calculation.

Haag IV, James V. [Pacific Northwest National Labo

Local aging effects in PuB 4 : Growing inhomogeneity and slow dynamics of local field fluctuations probed by 239 Pu NMR

Plutonium-based correlated electron materials host exotic physical phenomena ranging from unconventional heavy-fermion superconductivity to topological Kondo insulating states. Self-irradiation damage can influence many properties of such radioactive materials. Structural disorder effects due to α radiation have been frequently studied using techniques such as transport, thermodynamics, and x-ray diffraction. Here, in this study, we use 239 Pu nuclear magnetic resonance (NMR) to study the long-term influence of self-damage on the lattice and local electronic structures in a single crystal of the candidate topological insulator plutonium tetraboride (PuB 4 ). We first characterize the anisotropy of the 239 Pu resonance and confirm the local axial-site symmetry inferred from previous polycrystalline measurements. Aging effects are then evaluated over the time frame of six years. We find that, though the static 239 Pu NMR spectra show a slight modulation in their shape, their field-rotation pattern reveals no change in 239 Pu local site symmetry over time, suggesting that aging has a surprisingly small impact on the spatial distribution of the static hyperfine field. Further, ligand-site 11 B NMR finds little time-dependent change in the size of electric field gradient around 11 B sites. By contrast, aging has a prominent impact on the 239 Pu NMR relaxation processes and signal intensity. Specifically, aging-induced damage manifests itself as an increase in the spin-lattice relaxation time 𝑇 1 , an increased distribution of 𝑇 1 , and a signal intensity that decreases linearly by 20% per year. An effective spin-spin relaxation time 𝑇 2,eff in the aged sample shortens drastically towards lower temperature, suggesting growth of slow fluctuations of the hyperfine field that are linked to radiation-damage-induced inhomogeneity. Our NMR study sheds light on the interplay of radiation damage and local magnetic interactions in correlated insulators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Synthesis, Characterization, and Testing of High-Lithium-Density Composite Breeders

Solid tritium breeder materials must first and foremost have sufficiently high concentrations of lithium to enable a plant-scale tritium breeding ratio greater than 1:1. However, in addition to lithium content, such breeder materials must also meet other performance metrics including high tritium release rates, thermal conductivities, and irradiation damage tolerance. Perhaps most importantly, tritium breeders must maintain their mechanical integrity during reactor operation so as to avoid degradation which can jeopardize the functionality of the tritium breeder blanket module, which in most designs takes the form of a pebble bed geometry. Unfortunately, the mechanical robustness of most lithium-bearing ceramics under investigation for fusion applications is often inversely related to the lithium atom density. For example, a material such as lithium oxide (Li2O), which has one of the highest lithium atom densities, has a much lower mechanical splitting strength than lithium metatitanate (Li2TiO3), though Li2TiO3 has less than half the lithium atom density of Li2O. This work seeks to provide an alternative to monolithic ceramic tritium breeders, in the form of metal-reinforced composite tritium breeders. Specifically, composite tritium breeders have been synthesized combining Li2O with various ferrous metal reinforcements via electric field assisted sintering (EFAS), also known as spark plasma sintering (SPS). As the metal reinforcement content is increased, metallic networks are observed, via electron microscopy and X-ray computed tomography, to form throughout the composite material. Through destructive mechanical testing, even dilute metal reinforcement loading enables drastic mechanical strength improvements over pure Li2O while higher loadings give rise to quasi-ductile behavior and higher ultimate strengths than Li2TiO3 – while still maintaining a higher density of lithium atoms than Li2TiO3 and many other breeder candidates. In addition to microstructural characterization and mechanical testing, thermal property measurements and hydrogen permeability testing are underway to further assess the suitability of such composites for fusion reactor applications.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

MX precipitate behavior in an irradiated advanced Fe-9Cr steel: Helium effects on phase stability

As part of an ongoing series aimed at optimizing Fe-9Cr reduced activation ferritic/martensitic (RAFM) alloys for fusion energy systems, this study explores MX precipitate behavior under dual-ion irradiations, specifically examining correlations between helium transmutation and irradiation-induced damage. Utilizing single and dual-beam ion irradiation, the research explores the combined effects of helium (10–25 appm He/dpa), temperature (400–600 °C), and damage levels (15–100 dpa) on the microstructural evolution of CNA9 steel, a variant of Castable Nanostructured Alloys (CNAs). The study demonstrates that helium co-implantation hinders radiation-enhanced coarsening of MX-TiC precipitates at 500 and 600 °C, maintaining MX-TiC precipitate stability at moderate damage levels (15 dpa) but failing to prevent complete precipitate dissolution at higher damage levels (≥50 dpa) when irradiated at 500 °C. Here, a generalized precipitate stability model suggests that helium-induced suppression of diffusion alters the balance between recoil resolution and back diffusion for MX-TiC precipitates, enhancing the current understanding of precipitate behavior under damage and transmutation simulated dual-ion irradiation conditions.

Characterization

AGR-5/6/7 Irradiation Experiment Fission Product Mass Balance

This report presents the fission product mass balance for the AGR-5/6/7 TRISO fuel irradiation experiment. The fission product inventories deposited on capsule components outside of the fuel (e.g., stainless-steel shells, graphite holders, Grafoil disks, and associated hardware) were quantified as part of the post-irradiation examination (PIE) to assess the performance of this fuel. Comparisons were made between these inventories and depletion calculations, non-destructive measurements of fuel fission product inventories in the intact fuel compacts, prior AGR experiments, and results from among each of the five distinct AGR-5/6/7 capsules. The data served as estimates of the condensable fission products released from the fuel during irradiation. Excluding Capsule 1 (which experienced accidental damage during irradiation) and Capsule 3 (which was tested at very high irradiation temperatures of >1300°C), the results indicate that the AGR-5/6/7 fuel performed comparably to fuel from earlier AGR experiments. The mass balance results were also used to estimate the number of particles with in-pile SiC failures. Subject to the assumptions made in these estimates, and excluding Capsules 1 and 3, the in-pile SiC failure rates for AGR-5/6/7 are comparable to those observed in AGR-2.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Nanosecond dual-wavelength irradiation effects on laser-induced damage in hafnia coatings

Nanosecond dual-wavelength laser-induced damage was investigated at 1064 nm (1ω) and 355 nm (3ω) on ion-beam-sputtered hafnia single-layer coatings. Single-wavelength 1-on-1 tests were first conducted to establish reference onset fluences. Dual-wavelength tests combined a primary beam with variable fluence at one wavelength and a background, secondary wavelength beam with fixed fluences set to several percentages of the corresponding onset fluence. When 1ω was used as the background irradiation, the perceived damage resistance at 3ω decreased gradually. Here, in contrast, 3ω background irradiation at as little as 10% of the onset fluence led to an ≈ 50% abrupt reduction in the perceived 1ω damage resistance, followed by modest changes upon further increases in 3ω background fluences. Scanning electron microscopy and conversion ratios indicate that 3ω light is the primary driver of damage onset in the case of dual wavelength irradiation. A two-step precursor generation and activation model reproduces the 3ω behavior (1ω as background), but not the strong initial 1ω reduction (3ω as background), suggesting additional 3ω-induced precursors that saturate at low fluence.

Optics and optical instruments

In situ TEM annealing of neutron-irradiated Ti reveals a two-stage mechanism for elevated temperature radiation damage recovery

Understanding how irradiation-induced defects evolve at elevated temperatures is of critical importance to predicting materials' behavior under steady-state and accident scenarios. However, such mechanistic insight into microstructural evolution is limited by the nature of ex situ annealing and subsequent imaging. Here we show direct observation and quantification of defect recovery in neutron-irradiated Ti using in situ transmission electron microscopy (TEM) annealing experiments. In agreement with our prior work, and at temperatures below the irradiation temperature (T irr = 300 °C), dislocation loops are observed to glide. At elevated temperatures (>500 °C), dislocation lines become mobile and promote significant recovery of the microstructure. These mechanisms challenge the established electron irradiation-based model for radiation damage recovery, which originally suggests dissolution of static defect clusters, and demonstrates the importance of in situ characterization in understanding defect evolution in irradiated materials.

Hirst, Charles A. [Univ. of Michigan, Ann Arbor, M

MX precipitate behavior in an irradiated advanced Fe-9Cr steel: Self-ion irradiation effects on phase stability

In an effort to optimize Fe-9Cr reduced activation ferritic/martensitic (RAFM) steels and to inform the design and operation of fusion reactors, this work represents the first in a series of cohesive studies dedicated to the evolution of MX-TiC precipitates under accelerated single and dual ion irradiations. This study investigates CNA9, a simplified Fe-9Cr RAFM steel featuring initial MX-TiC precipitate densities of (2.3±0.3)×10²¹ m⁻³. This material was subjected to single self-ion irradiation at damage levels ranging from 1 to 100 displacements per atom (dpa) over a temperature range of 300 to 600°C, with a nominal dose rate of 7×10⁻⁴ dpa/s. Irradiation-induced coarsening was observed, as evidenced by statistically significant increases in mean diameter sizes, at 15 dpa at both 500°C and 600°C, whereas no coarsening was noted at 300°C or 400°C. Further, complete dissolution of precipitates occurred at damage levels of 50 and 100 dpa across the two temperatures tested (300°C and 500°C) while no significant changes were observed at any doses below 15 dpa at 500°C. Experimentally parameterized recoil resolution modeling suggests that the observed radiation stability of MX-TiC precipitates is intricately linked to diffusional changes of solutes resulting from the co-evolution of microstructural features within the experiments. The findings align with current theoretical perspectives on radiation-induced precipitate stability in complex alloys.

36 MATERIALS SCIENCE

Understanding spectral dependance of laser-induced damage precursors in dielectric materials (Abbreviated report_23-ERD-006)

High peak and average power laser systems are typically limited by the handling fluence of the optical components. In particular, the multilayer dielectric coatings are known to be much lower operational fluence than the more ideal bulk materials. In this project we proposed and succeeded in probing different established classes of damage prone precursors at different wavelengths to understand their fundamental laser damage response as a function of wavelength. This study helped to shed light on the fundamental physics of the non-linear precursors that govern laser damage phenomena for ns-regime pulsed laser damage. In this study, we utilized the onsite coating capabilities (VPL, IBS coating lab) to purposefully generate laser damage-prone precursors in hafnia-based coatings (both single and multi-layer coatings). Specifically, we engineered coatings with craze lines initiated by nodules, generated coatings with our xenon-based coating process to suppress nanobubble formation and generated hafnia coatings under controlled oxygen flow conditions to study hafnia sub-oxides and oxygen flow dependance. In these studies we found that craze lines are rife with precursors that are sensitive to ultra-violet light but not to infrared light; we found that the removal of nanobubbles helps with all wavelengths tested, but is most impactful for ultra-violet light; we also found that ultra-violet laser damage performance of hafnia is closely matched to oxygen flow rate, while the infrared performance may be slightly better at lower flow rates. During this LDRD we also successfully stood up a new laser damage testing capability, namely a wavelength agile damage test station to study the spectral response of known laser-induced damage precursors. This is a unique and important capability for Lawrence Livermore National Lab, allowing us to understand the spectral response of materials under high intensity irradiation and damage. This is a vital tool to understand non-linear optical response at wavelengths that we have previously been unable to test at.

36 MATERIALS SCIENCE

Laser damage of crazed electron-beam high-reflectors following infrared and ultraviolet irradiation in the nanosecond pulse regime

Laser damage of optical components can be a limiting factor in scaling the energetics of high-peak and average power laser systems. Specifically for optical coatings, damage under nanosecond pulsed irradiation is initiated by pre-existing defects in the coating layers, including those that cause discontinuities in the structure, like craze lines. Crazing or cracking in a multilayer dielectric optical coating is induced when the overall coating stress is sufficiently tensile, and is an occasionally observed issue when employing more porous deposition techniques like electron-beam evaporation. Here, in this study, electron-beam high-reflectors were fabricated utilizing process parameters that are known to induce crazing based on prior processing history to systematically evaluate the impact of crazing on reflector damage performance for 1064 and 355 nm lasers. The crazing that was observed was apparently nucleated at nodular defects. When the cross-section of these nodules was investigated, it was observed that there were cracks into the fused silica substrate of approximately 5 µm in depth. The craze lines were irradiated with 1064 and 355 nm light at fluences slightly above the onset of damage initiation fluence of the coating. The 1064 nm irradiated sub-apertures exhibit laser damage but with no spatial correlation with the craze line, whereas the 355 nm irradiated area exhibited many damage sites along the craze line. Finite-difference time-domain electric-field simulations were conducted, and ∼2× field amplification in hafnia was observed for the 355 nm wavelength case. The laser damage can be attributed to a slight electric-field intensification coincidental with an area where UV damage-prone precursors are known to occur. The 355 nm laser damage in uncoated fused silica substrates has been previously correlated to initiate through localized UV absorption at the broken silica bonds in the tips of fractures.

Harthcock, Colin [Lawrence Livermore National Labo

Thermoreflectance Detection of Point Defects Resulting from Focused Ion Beam Milling

Focused ion beam (FIB) milling is a commonly used tool for nanoscale material processing, such as for transmission electron microscopy (TEM) sample preparation, or the creation of fiducial markers prior to other processes and measurements. During milling, a high energy ion beam is used to remove material via sputtering. The expelled target material may return to the sample surface however, affecting subsequent measurements. Beam spreading or irradiation due to neutral gallium may also irradiate a larger area than intended. Extensive research has explored the effects of FIB milling on the prepared TEM sample, but few have looked at the effects of milling on the properties of the sample surrounding the milled region. We use multiple pump-probe laser-based techniques (time domain thermoreflectance and steady-state thermoreflectance) to measure the spatial extent of FIB-induced surface/subsurface changes on a series of silicon wafers milled at multiple currents and doses. We supplement these measurements with high-resolution scanning transmission electron microscopy, energy dispersive X-ray spectroscopy, stylus profilometry, and time-of-flight secondary ion mass spectroscopy. We find a sample surface affected by the FIB up to 1 mm from where milling occurred, with a notable dependence on the ion beam current. We also note remarkably high sensitivity to surface defects using the thermoreflectance metrologies, including detection where other measurements failed.

defects

Distinctive features of structural evolution and thermodynamic response in wide-bandgap semiconductors driven by intense electronic excitation

Radiation-tolerant material selection requires balancing lattice rigidity, defect dynamics, and electronic stability, as shown by covalent SiC outperforming ionic Ga 2 O 3 and GaN under extreme environments. Responding to intense electronic excitation, irradiation-driven phase segregation (β → δ/κ in Ga 2 O 3 ) and core–shell track (disordered structure in GaN), accompanied by elemental redistribution, contrastingly, exceptional radiation tolerance manifested by comparatively minimal lattice distortion (0.17 % strain variation) was demonstrated in SiC. These differential responses are primarily attributed to two fundamental mechanisms: (i) thermodynamic driving forces governing defect migration and phase separation, and (ii) the synergistic effects of robust covalent bonding composition coupled with efficient defect recombination processes. Here, the stronger electron–phonon (e-ph) coupling in Ga 2 O 3 (4.34 × 1018 W m −3 K −1 ) and GaN (3.55 × 10 18 W m −3 K −1 ) enhances lattice energy deposition, triggering thermal spikes (ΔT ≫ T m ) and structural transition behaviors, whereas weaker e-ph coupling in SiC (3.69 × 10 18 W m −3 K −1 ), relatively high thermodynamic parameters and efficient energy dissipation suppress thermal spikes to maintaining lattice integrity. The photoresponse degradation driven by enhanced radiative recombination is dominant in N-doped SiC, while V-doped systems achieve defect-mediated photoconduction optimization characterized by abrupt current transitions, matching fluorescence yield evolutions, and directly connecting defect engineering to optoelectronic performance.

Intense electronic excitation

High energy X-ray characterization of the microstructure of PuGa alloy samples at macroscopic depths and non-ambient conditions

High energy (95 keV) X-rays were utilized to characterize the microstructure of eight PuGa alloy samples at room temperature and during cooling to ∼10 K. The samples had different Ga content (nominally 0-3.4 at.%), age, and history. A ninth sample, similarly characterized with neutron diffraction, was included to extend the Ga range to 7 at.%. The samples span the range from single phase α (monoclinic) to δ (face-centered cubic) PuGa, as well as a two-phase α′/δ sample. The crystallographic textures, phase fractions, lattice parameters and dislocation densities of each sample were evaluated through distinct analysis techniques. The textures of the samples were modest. In each case, the dislocation densities were relatively high, comparable to cold worked metals and metals exposed to similar radiation dose. At room temperature, the lattice parameters determined in the predominantly single-phase samples were larger than expected based on the nominal Ga concentration. The observed lattice thermal expansions of the single-phase δ samples to 10 K are self-consistent across the samples and consistent with previous measurements reported in the literature. Significantly larger thermal lattice strain is observed in the δ phase of the two-phase material due to mechanical constraint from the α′ phase, which has a three times larger thermal expansion and is much harder than the δ phase. In conclusion, the results demonstrate the unique value of high-energy X-rays for relatively routine microstructural characterization of Pu alloy samples.

36 MATERIALS SCIENCE

Review of SiC material development for nuclear fusion applications: Cross-cutting research and emerging opportunities

The SiC-based materials, particularly SiC-fiber-reinforced SiC matrix (SiC/SiC) composites, show strong potential for structural and functional applications in future fusion power plants because they can operate at high temperatures with a range of coolants and breeders, thereby enabling higher energy conversion efficiency. Here, this paper presents recent advancements in the development of SiC-based materials, focusing on processing techniques and material performance and resistance under fusion-relevant environments. The processing activities have emphasized near-net-shape fabrication and the joining of SiC subcomponents, with processing methods and material compositions informed by previous irradiation experiments on various grades of SiC. Research on irradiation effects has remained focused on degradation mechanisms and the microstructural optimization of SiC/SiC composites irradiated to high neutron damage levels. Analysis of irradiation defects in SiC has advanced via the application of cutting-edge characterization methods, among which Raman spectroscopy is becoming a common tool to assess atomic-scale chemical disorder. Fusion–fission crosscutting irradiation research has explored combined effects in SiC/SiC composites with application-relevant geometries, including bowing of SiC/SiC composite channels under neutron flux gradients, stress evolution in SiC/SiC composite tubes under through-thickness temperature gradients, and irradiation-enhanced corrosion in SiC. Finally, research opportunities for component testing and assessment under fusion-relevant conditions, in support of emerging concepts from the private fusion sector, are discussed.

Advanced manufacturing

Correlated transmission electron microscopy and atom probe tomography characterization of ion irradiated Ni-based alloy Hastelloy N

Ion irradiation of Hastelloy N was conducted to better characterize the effects of irradiation on Hastelloy N using modern tools compared to studies done in the 1950s. The 2 MeV Ni + ion irradiation at 600 °C of Hastelloy N has been investigated using atom probe tomography, transmission electron microscopy and energy dispersive spectroscopy. Irradiation is found to promote formation of nanoscale M 2 C carbides over the thermodynamically favored M 6 C. Segregation of Si to dislocation loops and grain boundaries was also evident and may have assisted in formation of M 2 C. These microstructural changes result in a 20 % hardness increase caused by irradiation alone. These observations are useful in the design of new materials better suited for the harsh environment of a molten salt reactor.

Atom probe tomography

Integral X-ray diffuse scattering for studying irradiation-induced dislocation loops in single crystals

Numerical diffuse scattering cross-section calculations are used to establish a rigorous basis for determining the concentration and size distribution of dis­location loops in irradiated single crystals from integral X-ray diffuse scattering (XRDS) measurements. Differential XRDS intensities for prismatic {111} type dislocation loops are numerically calculated as a function of loop radius R and wavevectors q relative to Bragg reflections in tungsten. The results show the well known 1/q 2 Huang scattering form at small q that transitions to a ∼1/q 4 dependence associated with the Stokes–Wilson approximation for q ≳ 1/R. More importantly, they show further that the 1/q 4 falloff is not the asymptotic large-q form of the diffuse scattering for small loops (R < 200 Å) as has often been assumed. Rather, for loop sizes as small as R ≃ 5 Å with strong curvature, the calculations show definitively that the scattering transitions to a robust 1/q 5 falloff at larger q that arises due to the local strains near the dislocation core defining the circumference of the dislocation loops. The presence of this 1/q 5 asymptotic form for both small and large loops is experimentally confirmed using an integral XRDS measurement around the 110 reflection on self-ion-irradiated tungsten combined with numerically calculated integral XRDS cross-sections. Accordingly, the historical two-region theoretical treatment of the cross-sections for integral XRDS is extended to a three-region model that has direct sensitivity to the (first-moment) dislocation line lengths of dislocation loops. In conclusion, these developments enable the use of both numerical and analytically modeled cross-sections to make accurate integral XRDS determinations of dislocation loop sizes and concentrations using modest-intensity laboratory X-ray sources.

42 ENGINEERING