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At least 145 records · Page 8

The derivation of CRSS in pure Ti and Ti-Al alloys

The work focuses on the determination of the critical resolved shear stress (CRSS) in titanium (Ti) and titanium-aluminum (Ti-Al) alloys, influenced by an array of factors such as non-symmetric fault energies and minimum energy paths, dislocation core-widths, short-range order (SRO) effects which alter the local atomic environment, and tension-compression (T-C) asymmetry affected by intermittent slip motion. To address these multifaceted complexities, an advanced theory has been developed, offering an in-depth understanding of the mechanisms underlying slip behavior. The active slip systems in these materials are basal, prismatic, and pyramidal planes, with the latter involving both $\langle$a$\rangle$ and $\langle$c + a$\rangle$ dislocations. Each slip system is characterized by distinct Wigner-Seitz cell configurations for misfit energy calculations, varying partial dislocation separation distances, and unique dislocation trajectories—all critical to precise CRSS calculations. The theoretical CRSS results were validated against a comprehensive range of experimental data, demonstrating a strong agreement and underscoring the model's efficacy.

Critical stress↗

Defect formation and transmutation behaviors in irradiated tungsten under thermal-neutron shielded and mixed spectrum conditions

Here, this study investigates the microstructural evolution of pure tungsten irradiated under thermal-neutron shielded and mixed spectrum conditions in the High Flux Isotope Reactor (HFIR). Four samples were irradiated at temperatures from 570 °C to 1130 °C up to 0.73 dpa. Neutron spectrum significantly influenced the accumulation of transmutation products, with Re+Os content estimated at ∼0.3–0.6% under thermal-neutron shielded conditions and ∼5.2% under the mixed spectrum condition. Irradiation temperature strongly influences tungsten’s microstructure, with dislocation loops and fine voids forming at lower temperatures and only larger voids and Re/Os segregation observed at higher temperature. Under thermal-neutron shielded conditions, dislocation loops and voids were observed at 570 °C and 790 °C. At the highest irradiation temperature (1130 °C), dislocation loops were no longer observed, while larger but less dense voids remained. Re and Os segregation to void surfaces was evident at 790 °C and 1130 °C, though no precipitation was observed. In contrast, under the mixed-spectrum condition, both spherical and needle-like Re/Os-rich precipitates were observed, frequently accompanied by large voids. Dislocation loops were not observed, but loop-like contrast within the precipitates suggests they may have nucleated on pre-existing loops. Irradiation-induced hardening was assessed for the shielded samples at 570 °C and 790 °C. Dispersed barrier hardening (DBH) analysis, based on TEM-resolved defects, revealed that voids were the dominant contributors to hardening, consistent with literature results. A schematic model is proposed to describe defect and precipitate evolution in tungsten under fusion-relevant transmutation-to-dpa conditions.

Dislocation loops↗

Strengthening mechanisms for microstructures containing unimodal and bimodal γ' precipitates in ATI 718Plus

Here, the influence of γ' precipitate size distribution on the deformation mechanisms under tensile loading in ATI 718Plus was studied. A set of aging treatments within the temperature range of 720 °C–900 °C was performed on solution-treated samples to obtain various γ' precipitate size distributions. Unimodal and bimodal γ' precipitate size distributions were achieved through single-step and two-step aging sequences, respectively, and such microstructures were tensile tested to failure to assess their yield strength, ultimate tensile strength, and elongation-to-failure. Some of the tensile samples were interrupted after achieving 3–4 % plastic strain, and the deformed microstructures were examined using transmission electron microscopy to investigate the γ' precipitate-dislocation interactions. For the unimodal γ' precipitate size distribution samples with the smaller γ' precipitates (radius ~ 7 nm), dislocations sheared through the precipitates. Both dislocation loops and paired dislocations were observed for the microstructures containing larger γ' precipitates (radius ~ 24 nm). The microstructure containing a bimodal γ' precipitate size distribution, which included average γ' precipitate radii of ~6 nm and ~28 nm, exhibited shearing as the dominant deformation mechanism, and this microstructure exhibited the highest strength values. The experimental observations were rationalized based on the theoretically-calculated critical resolved shear stress values for shearing and looping and a modified model for predicting the yield strength for bimodal microstructures was introduced.

36 MATERIALS SCIENCE↗

Insights into Prismatic Loop Formation in Irradiated Fe–Cr Alloys from Hypothesis-Driven Active Learning and Causal Analysis

Neutron and electron irradiation experimental studies conducted on body-centered cubic Fe and Fe–Cr alloys have established two prismatic dislocation loop populations, which have Burgers vectors of either a/2$\langle$111$\rangle$ or a$\langle$100$\rangle$. Here, the loop formation depends on factors such as dose (D), dose rate (D rt ), temperature (T), chromium content (Cr%), and other alloying elements. Hence, it is important to understand how irradiation-induced dislocation loops evolve conditional upon the loop characteristics, such as loop density (DD), average loop size d̅, and irradiation parameters (D, D rt , T, and irradiation type), which is still an active area of research. To understand these complex structure–property relationships, machine learning (ML) is employed in a three-step approach. This includes imputing missing data with a k-nearest neighbor, generating functionalized features, and assessing feature importance with random forest classification and regression. Physics-based features are incorporated in a hypothesis-driven active learning scheme to overcome data unavailability challenges. Insights obtained from ML models (i) to categorize dislocation loop types, show the highest correlation with d̅; (ii) Log(DD), obtained through mathematical formulations involving D, Cr%, d̅, and T (e.g., Log(DD) ~ D + exp(-Cr%) + 1/d̅ and log(DD) ~ D + exp(-Cr%) + 1/T). Hypothesis-driven active learning is able to predict Log(DD) in which the experimental date is not known. Causal models verify cause–effect relationships for dislocation loop classification and irradiation factors in FeCr alloys.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fundamental Study of Fatigue Crack Initiation at Grain and Twin Boundaries in Austentic Stainless Steel (Final Technical Report)

The overarching goal of this project was to understand the dislocation-based mechanisms driving fatigue crack initiation at grain and twin boundaries. The hypothesis of the work is that dislocation structures equivalent to persistent slip bands (PSBs) form in the boundaries, leading to local stress concentrations and fatigue crack initiation. The sub-goals associated with this work include: • Understanding the evolution of the dynamic stress state and dislocation density surrounding PSB/grain boundary interactions. This will require the development of new techniques that couple high resolution electron backscatter diffraction (HREBSD) with in situ scanning electron microscopy (SEM) deformation. • Uncover the mechanisms by which dislocations are accommodated in grain and twin boundaries during fatigue. The proposed approach here is to conduct in situ transmission electron microscopy (TEM) deformation experiments on fatigued samples. • Establish correlations between microstructure, deformation accommodation, and crack initiation across time and length scales. This work primarily focuses on understanding fatigue crack initiation in austenitic stainless steels, though promising work by an undergraduate researcher extended the work to high purity Al.

42 ENGINEERING↗

Temperature-dependent mechanism on hardening mitigation in thermomechanically processed 800H alloys under neutron irradiation

Irradiation induced hardening is commonly observed in structural materials, and is often associated with the degraded ductility. This study explores the role of thermomechanical processing (TMP) in mitigating irradiation-induced hardening in Incoloy 800H. The radiation response of solution-annealed and TMP-treated samples was systematically investigated to elucidate the underlying mechanisms of hardening reduction. Neutron irradiation was performed on solution-annealed and TMP-treated samples at 359, 431, and 580 °C, revealing consistently lower hardening in TMP samples. Microstructural characterization compared dislocation loops, cavities, clusters, and precipitates to assess their contributions to hardening. The strengthening contributions from individual microstructural features were estimated, and the microstructure-derived yield strength is consistent with the hardness-converted yield strength. The microstructure–properties correlation revealed the temperature-dependent primary hardening mechanism: dislocation loops dominated at lower temperature, whereas Ni3(Al,Ti) γ′ precipitates were predominant at higher temperature. TMP reduced radiation-induced hardening through two mechanisms: (1) increased sink strength from dislocations and Ti(C,N) precipitates limited dislocation loop formation at lower temperatures, and (2) reduced Ti solute within the matrix in TMP samples suppressed γ′ precipitate formation at higher temperatures. These findings identify the mechanisms governing radiation-induced hardening across different temperatures, which lays the foundation for TMP optimization for the development of advanced radiation-tolerant materials.

Zhong, Weicheng [ORNL] (ORCID:0000000231589271)↗

Divergent evolution of slip banding in CrCoNi alloys

Abstract Metallic materials under high stress often exhibit deformation localization, manifesting as slip banding. Over seven decades ago, Frank and Read introduced the well-known model of dislocation multiplication at a source, explaining slip band formation. Here, we reveal two distinct types of slip bands (confined and extended) in compressed CrCoNi alloys through multi-scale testing and modeling from microscopic to atomic scales. The confined slip band, characterized by a thin glide zone, arises from the conventional process of repetitive full dislocation emissions at Frank–Read source. Contrary to the classical model, the extended band stems from slip-induced deactivation of dislocation sources, followed by consequent generation of new sources on adjacent planes, leading to rapid band thickening. Our findings provide insights into atomic-scale collective dislocation motion and microscopic deformation instability in advanced structural materials.

Science & Technology - Other Topics↗

Interband cascade light-emitting diodes grown on silicon substrates using GaSb buffer layer

Interband cascade light-emitting diodes (ICLEDs) offer attractive advantages for infrared applications, which would greatly expand if high-quality growth on silicon substrates could be achieved. Here, this work describes the formation of threading dislocations in ICLEDs grown monolithically on GaSb-on-Silicon wafers. The epitaxial growth is done in two stages: the GaSb-on-Silicon buffer is grown first, followed by the ICLED growth. The buffer growth involves the nucleation of a 10-nm-thick AlSb buffer layer on the silicon surface, followed by the GaSb growth. The AlSb nucleation layer promotes the formation of 90° and 60° interfacial misfit dislocations, resulting in a highly planar morphology for subsequent GaSb growth that is almost 100% relaxed. The resulting GaSb buffer for growth of the ICLED has a threading dislocation density of ~10 7 /cm 2 after ~3 μm of growth. The fabricated LEDs showed variations in device performance, with some devices demonstrating comparable light–current–voltage curves to those for devices grown on GaSb substrates, while other devices showed somewhat reduced relative performance. Cross-sectional transmission electron microscopy observations of the inferior diodes indicated that the multiplication of threading dislocations in the active region had most likely caused the increased leakage current and lower output power. Enhanced defect filter layers on the GaSb/Si substrates should provide more consistent diode performance and a viable future growth approach for antimonide-based ICLEDs and other infrared devices.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The effect of heat treatment on the defect evolution in LPBF 316H stainless steel

This work investigates the effect of processing and heat treatment on defect evolution and irradiation response of laser powder bed fusion (LPBF) 316H stainless steel, with comparisons to LPBF 316L and wrought 316L/316H. Using in-situ and ex-situ ion irradiations across a wide parameter space—temperature (300–675 °C), dose (0.2–25 dpa), dose rate (10 -3 –10 -5 dpa/s), and helium co-implantation (20–2500 appm)—we correlated void swelling, dislocation loop evolution, and segregation behavior with pre-irradiation microstructures (as-built, stress-relieved, solution-annealed, and cold-worked). Results show that swelling is strongly controlled by dislocation density: intermediate densities maximize swelling, while solution annealing or cold working reduce susceptibility to levels comparable to wrought alloys. Low dose rates and helium both promote cavity nucleation and lower the incubation barrier, with helium suppressing the role of dislocation density and driving swelling behavior toward wrought-like response. Loop evolution in SA LPBF 316H resembles wrought 316L but shows localized denuded zones near low-angle grain boundaries. STEM-EDS mapping further revealed Ni segregation at voids and sparse Al-rich oxides, without evidence of Ni–Si precipitates. Collectively, these findings identify dislocation density, helium content, and dose rate as the factors governing swelling in LPBF 316H and provide mechanistic datasets for model validation, supporting LAIN and the qualification of AM austenitic steels for nuclear service.

316 stainless steel↗

In situ irradiation of spent nuclear fuels

To improve the economics of commercial nuclear reactors, nuclear vendors and utilities are seeking approval for increased burnup usage of the existing nuclear fleet. This is especially critical for meeting the clean energy initiative by the United States Government, Department of Energy (DOE). However, one of the key challenges the nuclear industry faces in this regard is that the regions exposed to high burnup and low temperatures exhibit a fine-grained microstructure with large bubbles known as high-burnup structure (HBS) [1]. The formation of HBS has been correlated to the diminished performance of the reactor, as well as fuel fragmentation and pulverization during transient and accidental conditions [2]. Therefore, it is paramount to understand the mechanisms for HBS formation along with its impact on the properties and performance of nuclear fuels. While existing programs, such as Nuclear Energy Advanced Modeling and Simulation (NEAMS) and Advanced Fuel Campaign (AFC) are focusing on evaluating the performance impact of HBS, the physical mechanisms contributing to HBS formation are still not fully understood. In addition, having predictive capabilities and sound understanding of the microstructural evolution of nuclear fuel is essential for accelerated development, qualification, and deployment of new nuclear materials and novel reactor designs for advanced nuclear reactors. There is a lack of consensus among researchers regarding the mechanisms leading to such restructuring observed in HBS. Grain subdivision due to polygonization versus recrystallization, continuous versus discrete recrystallization occurring in tandem or conjunction, etc., have been proposed and debated. In general, it is hypothesized that defect accumulation and dislocation interaction within the grains cause the realignment of dislocations into grain boundaries, leading to the new subgrain formation, which over time transforms into new grains. However, due to the lack of transient data, the importance of fission rate, irradiation, thermal, and stress history of the fuel on the restructuring could not be assessed. In situ microstructural evolution under various irradiation conditions is desired to bridge this gap. Alternatively, phase-field-based models have been developed to capture HBS formation via discrete recrystallization utilizing the classical nucleation approach [3–5]. However, in these models, the grain nucleation criteria are often defined based on empirical relations for burnup and fission gas density leading to dislocation density change. A mechanistic approach to capture the dislocation interaction with the microstructural features leading to grain subdivision is lacking.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A theoretical study of solid solution strengthening in the refractory medium entropy alloy Nb 45 Ta 25 Ti 15 Hf 15

The refractory medium-entropy alloy (RMEA) Nb 45 Ta 25 Ti 15 Hf 15 exhibits exceptional tensile ductility and fracture toughness at ambient temperature, but its engineering applications are limited by a lack of high temperature strength. Using a machine-learning interatomic potential (MLIP) with near-density functional theory (DFT) accuracy, we conducted molecular dynamics (MD) and statics simulations of the behavior of dislocations with both screw and edge characters. We also analyze experimentally measured yield strengths using the Rao-Suzuki model and the Maresca-Curtin model modified to include a temperature-dependent shear modulus and a bulk modulus-dependent misfit volume, thereby uncovering the mechanisms underlying the yielding of this RMEA. Compared with the published experimental yield strength, the models parameterized by the MLIP effectively reproduce the experimental results over a wide temperature range. The models and MD simulations indicate that yielding is governed by screw dislocations, with dipole dragging as the dominant mechanism. In MD simulations, we observed a potential softening mechanism not considered by the Rao-Suzuki screw model: slow migration of interstitial jogs along the dislocation core, which could lead to the annihilation of vacancy and interstitial jog pairs by their combination.

BCC complex concentrated alloys↗

Unlocking Electrostrain in Plastically Deformed Barium Titanate

Achieving substantial electrostrain alongside a large effective piezoelectric strain coefficient (d 33 *) in piezoelectric materials remains a formidable challenge for advanced actuator applications. Here, in this work, a straightforward approach to enhance these properties by strategically designing the domain structure and controlling the domain switching through the introduction of arrays of ordered {100}<100> dislocations is proposed. This dislocation engineering yields an intrinsic lock-in steady–state electrostrain of 0.69% at a low field of 10 kV cm -1 without external stress and an output strain energy density of 5.24 J cm -3 in single-crystal BaTiO 3 , outperforming the benchmark piezoceramics and relaxor ferroelectric single-crystals. Additionally, applying a compression stress of 6 MPa fully unlocks electrostrains exceeding 1%, yielding a remarkable d 33 * value over 10 000 pm V -1 and achieving a record-high strain energy density of 11.67 J cm -3 . Optical and transmission electron microscopy, paired with laboratory and synchrotron X-ray diffraction, is employed to rationalize the observed electrostrain. Phase-field simulations further elucidate the impact of charged dislocations on domain nucleation and domain switching. These findings present an effective and sustainable strategy for developing high-performance, lead-free piezoelectric materials without the need for additional chemical elements, offering immense potential for actuator technologies.

36 MATERIALS SCIENCE↗

In-situ observations of cyclic deformation in an extruded Mg-2Nd-1Y-0.1Zr-0.1Ca alloy

In this study, the evolution of deformation mechanisms during cyclic loading in an extruded, solution-treated Mg–2Nd–1Y–0.1Zr–0.1Ca alloy was investigated using a combination of in-situ loading, scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and focused ion beam (FIB) nanofabrication. The initial microstructure exhibited a random crystallographic texture with no preferred grain orientation. Flat, rectangular dog-bone specimens were subjected to load-controlled, fully reversed fatigue for 50 cycles, during which the same region was sequentially mapped to track microstructural changes. After 10 cycles of loading deformation twins were observed. During tensile reloading detwinning or narrowing of those twinned regions occurred. After 20 cycles, detwinning ceased and residual twins remained in the material. SEM imaging revealed numerous surface slip traces after cyclic loading. EBSD-assisted slip trace analysis identified the activation of prismatic and pyramidal < c+a> slip systems during low-cycle fatigue. Site-specific scanning transmission electron microscopy (STEM) further revealed that deformation was also accommodated by basal < a> slip and the dissociation of < c+a> dislocations. Center-of-symmetry (COS) analysis confirmed that the dissociation of < c+a> dislocations resulted in the formation of I₁ intrinsic stacking faults after cyclic loading. These findings provide new insights into the complex interplay of dislocation mechanisms governing fatigue deformation in rare-earth-containing Mg alloys.

Cyclic deformation↗

Mechanistic nuclear fuel performance modeling of uranium nitride

Uranium mononitride (UN) is a nuclear fuel candidate for advanced reactor designs and an alternative being considered for light water reactors due to its higher thermal conductivity and uranium density than UO 2 . As with any nuclear fuel, swelling and fission gas release are important factors for safety, while also being some of the hardest phenomena to predict with a high degree of confidence. Getting a grasp on the gas swelling behavior and release is crucial to lower the barrier for UN utilization. An accelerated swelling rate at high temperatures observed experimentally, sometimes referred to as “breakaway swelling,” further complicates the prediction of fuel performance of UN. A mechanistic model has been developed using a multiscale approach to describe the intragranular and intergranular fission gas behavior. Lower-length-scale calculations have been employed to inform models of the gas and self-diffusion behavior, resolution rate, and bubble shape. Leveraging previous work on high burnup UO 2 , two populations of intragranular bubbles are considered; small bulk bubbles and larger bubbles located along dislocations. The dislocation bubbles were found to be crucial to the overall swelling behavior, and the breakaway swelling transition was associated with the transition in the gas atom diffusion mechanism from an irradiation-induced athermal diffusion regime at lower temperatures to an intrinsic thermal equilibrium regime at higher temperatures, accelerating the growth of the dislocation bubbles. Similarly, the threshold for fission gas release was associated with the grain boundary vacancy diffusivity surpassing the gas atom diffusivity at sufficiently high temperatures, allowing the over-pressurized grain boundary bubble to grow in size and interconnect. Using thermo-mechanical models with the fission gas model, two integral fuel pin assessment cases were simulated. Finally, this work demonstrates the ability of a multiscale approach to accelerate the understanding of advanced fuel forms when experimental data is limited.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Scanning Transmission Electron Microscopy–Atom Probe Tomography Correlative Analysis for the Characterization of Solute-defect Interactions

Atom probe tomography (APT) and (scanning) transmission electron microscopy ((S)TEM) are complementary techniques that provide spatially resolved chemical and structural information at the atomic scale. Here, in this study, we employ two different STEM/APT correlative analysis methods to investigate Cr segregation at dislocation loops in ultra-high purity Fe–Cr alloys. APT needles for the correlative analysis were extracted either from bulk material or from thinned TEM lamellae. STEM analysis was used to determine the Burgers vectors of ion-irradiation-induced dislocation loops, while APT reconstruction of the same region revealed the Cr segregation to these loops. We extended the g•b = 0 invisibility criterion of dislocation loops from TEM mode in a lamella to STEM mode in a needle-shaped specimen. STEM and APT analysis on the same needle provide straightforward correlative analysis, although it is limited by a small observation volume. In contrast, iterative STEM analysis of TEM lamellae, followed by the selective extraction of specific regions of interest for APT analysis, expands the observation area by up to 100 times but requires additional time-consuming steps for APT needle extraction from the lamellae.

47 OTHER INSTRUMENTATION↗

At Extreme Strain Rates, Pure Metals Thermally Harden while Alloys Thermally Soften

When materials are deformed at extreme strain rates, >10 6 s -1 , a counterintuitive mechanical response is seen where the strength and hardness of pure metals increases with increasing temperature. This anti-thermal hardening is due to dislocations meeting resistance to their motion from phonons in the crystal lattice. However, here, using optically-driven microballistic impact testing to measure dynamic strength and hardness, we show that when the composition is systematically varied away from high purity, the mechanical response of metals transitions from phonon drag of dislocations back to thermally activated pinning of dislocations, even at the highest strain rates. This boundary from “hotter-is-stronger” to “hotter-is-softer” is observed and mapped for nickel, titanium and gold. Furthermore, the ability to tune between deformation mechanisms with very different temperature dependencies speaks to new directions for alloy design in extreme conditions.

Ballistic transport↗

Uncooled GeSn MWIR Photodetectors Using Fully Relaxed Thin Triple‐Step Buffer

GeSn photodetectors monolithically grown on Ge virtual substrates demonstrate mid-wave infrared (MWIR) detection at room temperature. The lattice mismatch between GeSn and Ge causes dislocations and compressive strain, creating leakage pathways and unwanted indirect band transitions. Designed thin Ge 0.91 Sn 0.09 triple-step buffer layers of ≈175 nm total thickness reduce dislocations and enable full relaxation, showing 100% lattice relaxation and smooth surface roughness of 0.83 nm with shorter auto-correlation length in surface morphology compared to single-step buffers. Ge 1-x Sn x photodetectors (x = 0.09, 0.12, and 0.15) on triple-step buffers with n-i-p configurations achieve lattice strain relaxations of 99%, 88%, and 80%, respectively. Ge 0.91 Sn 0.09 and Ge 0.88 Sn 0.12 show gradual variation in auto-correlation amplitude, while Ge 0.85 Sn 0.15 shows an increase due to lattice mismatch. Shockley–Read–Hall recombination current dominates at low reverse bias due to mismatch-induced dislocations, while band-to-band tunneling current dominates at higher reverse bias due to narrowing bandgap under strong electric fields. Here, the photodetectors show extended spectral response with increasing Sn composition of i-GeSn active layer sandwiched by barriers. Ge 0.88 Sn 0.12 and Ge 0.85 Sn 0.15 exhibit extended wavelength cut-offs of 3.12 and 3.27 µm at room temperature, demonstrating significant potential for silicon-based MWIR applications.

GeSn↗

Monte Carlo Simulations of 347H Stainless Steel Aging for the Synthetic Generation of Microstructures Under Creep Conditions

Here, a Monte Carlo simulation method capable of replicating the kinetics of M 23 C 6 precipitation in 347H stainless steels was developed for the purpose of producing synthetic microstructures that approximate its microstructural evolution under aging periods of up to 10,000 hours at temperatures between 600 °C and 750 °C. To accomplish this, experimental data from the literature was used to parameterize simulations and replicate the nucleation and growth kinetics of M 23 C 6 particles within 347H and similar austenitic stainless steel alloys. These simulations were found to have considerable fidelity to previous efforts to study the precipitation of M 23 C 6 in other 300 series stainless steel alloys. Synthetic 347H microstructures were then generated that accounted the effects of aging temperature, duration, dislocation density, and the presence of boron within the microstructure. These simulations predict several key trends, those being that (1) the size of M 23 C 6 precipitates decreased with aging temperature and (2) the growth rate of M 23 C 6 particles decreased with aging temperature. Further, while (3) the addition of dislocation density due to creep conditions resulted in increasing intragranular nucleation of M 23 C 6 precipitates with increasing dislocation density and (4) B additions within the microstructure led to modest increases in precipitate size above 700 °C, which indicates that more complex physics are necessary to account for the presence of B.

36 MATERIALS SCIENCE↗