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At least 91 records · Page 5

Assessment of binary eutectic Ni alloys for high-temperature applications via laser remelting

It has been recently demonstrated that eutectic alloys processed by additive manufacturing have excellent high-temperature mechanical properties. We suggest that nickel-base eutectic alloys may enable new combinations of structural and functional properties. To this end, we investigate the processability, microstructure, and thermal stability of five, binary near-eutectic Ni-X (X = B, Ce, La, Y, and Zr) alloys processed via surface laser-remelting. The microstructure of all alloys contain a two-phase lamellar eutectic microstructure consisting of γ-Ni and intermetallic phases; this microstructure is significantly finer (100–200 nm lamellar spacing) in the laser-remelted alloys than in the cast substrate (0.5–1.0 µm lamellar spacing). The microhardness of the laser-remelted alloys (550–770 HV) is 35–50% higher than that of the cast alloys (370–570 HV) due to this finer eutectic spacing. An anomalous eutectic microstructure appears at the meltpool boundaries, containing globular and lamellar γ-Ni phases. The alloys contain a high volume fraction (>50 vol%) of intermetallic phase which forms a continuous network, causing brittleness. Following laser-remelting trials, the alloys showed a high density of solid-state cracks, except for the Ni-Zr alloy which processed well. During thermal exposure at 700 and 900°C for up to 500 h, the eutectic microstructure coarsens. Coarsening occurs heterogeneously and initiates at the meltpool boundaries. This process occurs more slowly in the Ni-Zr and Ni-Y alloys, and more rapidly in the remaining alloys, resulting in greater microhardness retention in the Ni-Zr and Ni-Y alloys following thermal exposure at 700°C. Thus, among the five alloys, the Ni-Zr system exhibits a good combination of high-temperature mechanical properties and processability. Here, we conclude with recommendations for future work on designing additively manufactured alloys based on these eutectic Ni systems.

Additive manufacturing↗

Influence of implantation temperature and He implantation-induced defects on morphological evolution of co-deposited Cu-Mo nanocomposites

Here, we investigate the effect of high-temperature helium (He) implantation on microstructural evolution in physical-vapor-co-deposited nanocomposite thin films of copper (Cu) and molybdenum (Mo). The microstructure morphologies of He-implanted and He-free domains are characterized using transmission electron microscopy and statistical analysis. High implantation temperatures (500°C and 750°C) lead to coarsening of Cu and Mo domains and their eventual reorientation. The microstructure evolution in He-implanted and He-free domains is comparable, indicating that implantation-induced defects do not accelerate the coarsening of the nanocomposite as compared to annealing alone. This observation contrasts with previously reported effects of implantation-induced defects on single-phase nanocrystalline metals, which include enhancement of grain growth by increasing self-diffusivity or its inhibition by pinning of grain boundaries.

36 MATERIALS SCIENCE↗

Microstructure-Based Degradation Modeling in Solid Oxide Cells

The presentation is intended for a graduate class in Georgia Southern University taught by Dr. Hayri Sezer on electrochemistry, SOFC and Li ion battery. It summaries NETL's recent works on microstructure-based modeling of degradation in solid oxide cells. It covers the degradation mechanism of Ni coarsening, Ni migration and the build-up of oxygen partial pressure inside the electrolyte. The phase-field models developed for Ni coarsening and migration are reviewed and the results are compared to experiments in literature to examine different diffusion mechanisms (Ni self-diffusion, Ni(OH)2 diffusion in pores and Ni(OH) surface diffusion) and driving forces (Ni(OH)x concentration and Ni-YSZ contact angle change). It also demonstrates the developed model for oxygen partial pressure and shows that the predicted oxygen partial pressure can explain the Ni oxidation in the hydrogen electrode and crack growth on the electrolyte-oxygen electrode interface under certain operating conditions.

nickel coarsening↗

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↗

Hypereutectic Al-Ce-X (X=Mn, Cr, V, Mo, W) alloys fabricated by laser powder-bed fusion

Here, we characterize the microstructures and high-temperature mechanical properties of Al-2Ce and ternary Al-2Ce-1X (at.%) alloys fabricated by laser powder-bed fusion (LPBF), where X = Mn, Cr, V, Mo, and W are slow-diffusing transition metals. All ternary alloys show a hypereutectic microstructure in the as-LPBF state, containing an interconnected network of eutectic Al 11 Ce 3 phases (~10 vol.%) and an additional population of submicron, equiaxed Al 20 CeX 2 primary precipitates (~10 vol.%) which are isomorphous among these five alloys. Similar microstructures are present in arc-melted rods and atomized powders but are coarser due to the slower cooling rates in these processes. The hardness of the as-LPBF ternary Al-Ce-X alloys (1300–1400 MPa) is higher than that of the binary Al-Ce alloy (~1100 MPa) due to the higher volume fraction of strengthening phases. Furthermore, during exposure at 400 °C for up to three months, greater hardness retention is achieved in the ternary Al-Ce-X alloys (65–75%) than in the binary Al-Ce alloy (~55%), which is attributed to the extreme coarsening resistance of the Al 20 CeX 2 precipitates imparted by the very slow-diffusing ternary solute. These coarsening-resistant Al 20 CeX 2 precipitates also substantially improve alloy creep resistance, increasing the threshold stress for dislocation creep at 300°C from ~32 MPa for the binary Al-Ce alloy to ~77–100 MPa for the ternary Al-Ce-X alloys, and at 400°C from <10 MPa for the binary Al-Ce alloy to >40 MPa for the ternary Al-Ce-V alloy.

36 MATERIALS SCIENCE↗

Hardenability and microstructural evolution of a precipitation strengthened Ni 50 Ti 21 Hf 25 Al 4 alloy

NiTi-based quaternary alloys are used in a variety of mechanical components, such as bearings, actuators, and dampers, owing to their good hardenability, wear resistance, and corrosion resistance. Additionally, one of the most notable characteristics of NiTi-based alloys is their shape memory effect and pseudoelastic properties. Connecting the macroscopic processing parameters employed in the design of new intermetallic alloys to the nanoscale structural characteristics dictating their behavior is crucial for improving their mechanical properties and expanding the spectrum of potential applications. Here, in this work, an arc melted Ni 50 Ti 21 Hf 25 Al 4 (at%) alloy was solution treated at 1050 °C followed by quenching and aging at 600 °C to investigate the effect of aging time on the microstructure and mechanical properties. Two types of nano-sized precipitates were observed and determined as face-centered orthorhombic H-phase (TiHf)Ni and L2 1 Heusler precipitates Ni 2 TiAl. The morphology and orientation of the H-phase were investigated using scanning and transmission electron microscopy (SEM and TEM), elucidating the coarsening kinetics and strengthening contribution of that phase to the intermetallic mechanical behavior. Following coarsening, the presence of Heusler nanoprecipitates was detected under overaged conditions through TEM imaging and nanobeam electron diffraction patterns. A peak hardness condition of 756 HV was achieved after 70 h of aging, indicating that the co-precipitation of H-phase and Heusler precipitates through a well-designed aging treatment can lead to optimal mechanical performance, thus elevating the alloy’s potential as a viable material for industrial applications.

36 MATERIALS SCIENCE↗

Characterization of γ′/γ″ compact and sandwich type precipitates during long-term high-temperature exposure in Ni-based superalloys

Here, the formation of γ′/γ″ co-precipitates is investigated in Ni-based superalloys with a varying Ti/Al ratio and Ta content and their stability is studied using long-term high-temperature exposure. Transmission electron microscopy and atom probe tomography analyses demonstrate that both higher Ti/Al ratios and increased Ta promote γ″ phase formation, leading to sandwich and compact structures. The compact co-precipitation significantly reduces γ′ precipitate coarsening during 10,000 h exposure at 700°C by restricting elemental diffusion, particularly of aluminum, from the γ matrix to the γ′ phase. For the alloy without a compact structure, and only γʹ precipitates, at the beginning of the exposure, the coarsening rate over 10,000 h was 3.5 times faster than for the alloy with compact γʹ/γʺ precipitates. Evidence of destabilization of the compact morphology was found to occur between 5,000 and 10,000 h exposure and originated from the extensive formation and growth of δ platelets that extended throughout the grains. Thus, the outer layer of the compact, which consists of γʺ, was subjected to the γ″ to δ phase transformation.

gamma double prime↗

Co-, Ni- and Fe-rich grain-boundary phases enhance creep resistance in θ'-strengthened Al-Cu alloys

Here, microstructural evolution and creep response were investigated in the cast Al-5.0Cu-0.3Mn-0.2Zr (wt.%) alloy with and without addition of slow-diffusing, intermetallic-forming elements Fe, Ni, or Co. Baseline Al-5.0Cu-0.3Mn-0.2Zr alloy exhibits high creep resistance at 300 °C, up to ~75 MPa, which is attributed to high-aspect-ratio, intragranular θ'-Al 2 Cu precipitates that effectively suppress dislocation climb. However, θ'-Al 2 Cu precipitate-free zones form along grain boundaries upon heat treatment, whose extent is amplified during subsequent creep. Such weak regions experience dislocation creep, leading to strain localization and acceleration of grain-boundary sliding. Adding Ni and Co, individually or in combination, leads to the formation of grain-boundary precipitates (Al 9 Co 2 , Al 3 Ni 2 ) which are resistant to coarsening, thus suppressing the formation of θ'-Al 2 Cu precipitate-free zones. This microstructure provides high creep resistance at stresses up to 75–80 MPa, with strain rates much lower than in unmodified Al-5.0Cu-0.3Mn-0.2Zr. Adding Fe, which results in extensive decoration of grain boundaries with coarsening-resistant Al 7 Cu 2 Fe, and then increasing the Cu content to compensate for the Cu loss to this new phase, leads to a new Al-7.4Cu-1.6Fe-0.3Mn-0.2Zr alloy with creep resistance at 300 °C that surpasses known cast aluminum alloys. Adding Fe to improve the creep resistance of Al-Cu alloys is both cost-effective and sustainable. Our findings offer guidelines applicable to various alloy systems on controlling the evolution of precipitate-free zones and its ensuing effects on creep deformation.

36 MATERIALS SCIENCE↗

Why Seeding Works When Nucleation Barriers Vanish

Crystallization is a process governed by the interplay between nucleation and growth. While crystalline seeds are known to reduce nucleation barriers and accelerate crystallization under nucleation-limited conditions, their influence when nucleation is not the limiting step remains poorly understood. This creates a mechanistic puzzle in systems where nucleation barriers are already negligible, yet seeding still accelerates crystallization. Here, the synthesis of zeolites is a quintessential example of growth-limited crystallization in which seeds accelerate the process despite negligible homogeneous nucleation barriers. Using coarse-grained molecular dynamics simulations─validated across two zeolites and the unrelated case of ice crystallization─we establish that growth-limited crystallization produces many small, misoriented crystallites whose slow coarsening into larger domains controls the emergence of X-ray-detectable crystallinity. Local crystalline order, structural coherence, and X-ray detectability are therefore kinetically decoupled milestones: the first can be reached rapidly while the latter two lag significantly. Seeds resolve this lag by imposing a common orientational registry on nascent crystallites, enabling their coherent coalescence into large seed-bound domains. This early coherence-building step produces a crystallite-size asymmetry that accelerates subsequent coarsening, advancing the onset of X-ray-detectable crystallinity without necessarily increasing the nucleated fraction. We conclude that under growth-limited conditions, the apparent induction period observed in powder X-ray diffraction reflects the time required to build long-range coherence, not the time to form crystalline material. Accordingly, seeds function not primarily by reducing nucleation barriers but by enforcing spatial coherence, thereby shortening the time required to develop long-range order detectable by X-ray diffraction.

Growth-Limited Crystallization↗

Machine Learned Empirical Numerical Integrator from Simulated Data

Recently, a number of state-of-the-art surrogate machine learning (ML) models have been designed for global weather and climate prediction, which have been trained using reanalysis data products. Reanalysis data products are constructed using numerical model simulations that combine numerical integration of partial differential equations and parameterization schemes. These products are typically only archived and made available using coarsened spatial and temporal resolutions. This study explores the impact of the numerical generation methods used to produce the training datasets and the temporal resolution of those datasets on machine learning surrogate models. Using the nonlinear vector autoregression (NVAR) machine as an explainable ML technique, simple dynamical systems are emulated with ML models trained on data produced by three classical numerical integration schemes. NVAR is validated as a skillful ML method, capable of producing accurate predictions and, more importantly, reconstructing both the underlying dynamics and the numerical integration scheme used to generate the training data. However, the machine fails to generalize predictions on unseen test data generated by different numerical integration schemes, despite the underlying dynamical system being the same. This result provides a word of caution for the growing field of machine learning emulation of weather and climate dynamics. Furthermore, we illustrate using NVAR that training on temporally coarsened data may increase the required complexity of ML models and potentially introduce new numerical challenges. Finally, we discover that empirical integration schemes with arbitrary time-stepping sizes can be constructed directly from the data, which implies a potential for the development of empirical numerical integration schemes.

54 ENVIRONMENTAL SCIENCES↗

Scalable multilevel Monte Carlo methods exploiting parallel redistribution on coarse levels

Here, we study an element agglomeration coarsening strategy that requires data redistribution at coarse levels when the number of coarse elements becomes smaller than the number of MPI processes used on the finest level. The overall procedure generates coarse elements (general unstructured unions of fine grid elements) within the framework of element-based algebraic multigrid methods (or AMGe) studied previously. The AMGe-generated coarse spaces have the ability to exhibit approximation properties of the same order as the fine-level spaces since by construction they contain the piecewise polynomials of the same order as on the fine level. These approximation properties are key for the successful use of AMGe in multilevel solvers for nonlinear partial differential equations as well as for multilevel Monte Carlo (MLMC) simulations. The ability to coarsen without being constrained by the number of MPI processes, as described in the present paper, allows to improve the scalability of these solvers as well as the overall MLMC method. The paper illustrates this latter fact with detailed scalability study of MLMC simulations applied to model Darcy equations with a stochastic log-normal permeability field.

AMGe↗

Elucidating the mechanical and thermal response of nanotwinned Ni alloys

Transformative advances in nanoscale materials synthesis, characterization and modeling are enabling the synthesis of materials with unprecedent properties and greater understanding of the nanoscale mechanisms that underpin these properties. Nanotwinned Cu alloys have received considerable attention due to their impressive balance of strength and ductility, but they have limited microstructural stability. Recent instantiation of nanotwins in sputter deposited Ni-Mo-W, and several commercial Ni-based superalloys, point to the potential development of a new class of high temperature materials with a very beneficial suite of mechanical and physical properties. The experimental study described in this report was undertaken to elucidate the nanoscale origins of the thermal and mechanical behavior of nanotwinned Ni alloys. Micropillar compression experiments have shown nanotwinned Ni 85 Mo 15-x W x alloys to possess unusually high strengths above 3.5GPa and enhanced microstructural stability. The strength of these nanotwinned alloys is determined by the abrupt formation of shear bands. This study focused on identifying the nanoscale trigger, or triggers, for shear banding in nanotwinned materials using in situ experiments and atomic-scale postmortem analysis. Contrasting and comparing the mechanical response and postmortem nanostructures of “Mo-rich” and “W-rich” nanotwinned specimens elucidated the importance of the lateral motion of easy glide defects that results in erasure of twins and local coarsening of the nanotwinned microstructure. This twin coarsening was then associated with very localized plasticity, strain softening, and shear band formation. The difference between alloys was further studied by considering the role of various material factors: stacking fault energy, coherent twin boundary spacing and flatness, grain size, and the interactions of solute atoms with twin and grain boundaries. The effect of alloy composition and sputtering power and temperature were also investigated and used to control twin spacing and geometry. Combined with atomic-scale simulations, these experiments insights should allow us to identify strategies for achieving concomitant ultrahigh strength and ductility in nanotwinned Ni alloys. In parallel but synergistic studies, our work was buoyed by collaborative state-of-the-art nanoscale orientation and strain mapping at the DOE National Center for Electron Microscopy (NCEM). For example, novel 4D-STEM techniques were used to acquire nanoscale strain maps. The extremely fine twin spacing limited our measurements of atomic-scale thermal expansion within twins, but recent results from NCEM suggest that it will soon be possible to conduct such measurements and to unravel the origins of the novel thermal expansion characteristics of nanotwinned Ni alloys.

36 MATERIALS SCIENCE↗

Interpretation of Ion Irradiation and Neutron Irradiation Damage in Additively Manufactured 316 Stainless Steel using Multiscale Modeling

The accelerated adoption of nuclear energy necessitates advanced manufacturing technologies, such as additive manufacturing, to meet heightened supply chain requirements and support innovative reactor technologies. Due to the unique microstructural characteristics of additively manufactured materials under distinct solidification conditions, comprehensive evaluation of their performance in reactor environments is essential. The Advanced Materials and Manufacturing Technologies program under the Department of Energy's Office of Nuclear Energy focuses on understanding the irradiation performance and damage evolution of laser powder bed fusion 316 stainless steel, with an emphasis on integrating ion and neutron irradiation data to accelerate the development and qualification of materials for advanced nuclear reactor applications. While ion irradiation is a cost- and time-effective method, modeling and simulation are required to interpret the data for the broader range of irradiation conditions encountered in advanced reactors. In fiscal year 2025, integrated multiscale modeling and simulations were conducted to assess irradiation damage in additively manufactured 316 stainless steel. Key outcomes include predictions of chromium enrichment at grain boundaries, nickel enrichment at dislocation cell walls and void surfaces, and heterogeneous void evolution under ion and neutron irradiation conditions. Cluster dynamics simulations revealed the coarsening of voids at high irradiation temperatures and the suppression of void growth by high network dislocation density, while also demonstrating significant growth and coarsening of voids and self-interstitial atom loops at low dose rates. Machine learning-accelerated atomistic simulations highlighted the impact of the local environment and chromium concentration on vacancy diffusivity, providing key insights on the influence of composition on void swelling and radiation-induced segregation. Additionally, molecular dynamics simulations demonstrated the presence of defect production bias and a significant effect of carbon content on defect cluster behavior. These combined efforts aim to predict the performance of additively manufactured materials under various reactor conditions, supporting their qualification for nuclear reactor applications by interpreting ion irradiation data. This report underscores the potential of integrated multiscale modeling to analyze ion irradiation data in the effort to accelerate the qualification of additively manufactured materials for nuclear reactor components.

316 stainless steel↗

Effect of Processing Parameters on Recrystallization During Hot Isostatic Pressing of Stellite-6 Fabricated Using Laser Powder Bed Fusion Technique

Crack-free Stellite-6 alloy was fabricated using the laser powder bed fusion technique equipped with a heating module as the first attempt. Single tracks were printed with a build plate heated to 400 °C to identify the processing window. Based on the melt pool dimensions, two combinations (sample A: 300 W/750 mm/s and sample B: 275 W/1000 mm/s) were identified to print the cubes. The as-printed microstructure comprised FCC-Co dendrites with M7C3 in the interdendritic region. W-rich M6C particles were found in the overlapping regions between the melt pools, matching the Scheil simulations. However, gas pores were observed due to the higher nitrogen and oxygen content of the feedstock requiring hot isostatic pressing (HIP) at 1250 °C and 150 MPa for 2 h. Sample A was partially recrystallized with slightly coarsened M7C3, while sample B underwent complete recrystallization followed by grain growth along with higher coarsening of the M7C3 after HIP. The varying recrystallization behavior can be attributed to the difference in residual stresses and grain aspect ratio in the as-built condition dictated by laser power and scanning speed. The microhardness after HIP was slightly higher than its wrought counterpart, indicating no severe impact of post-processing on the properties of Stellite-6 alloy.

Sridar, Soumya (ORCID:0000000306775408)↗

The effect of alloy composition on the mechanism of stress-corrosion cracking of titanium alloys in aqueous environments

A detailed study was made of the relation between the size distribution of Ti3Al particles in a Ti-8Al alloy and the tensile properties measured in air and in saltwater. The size distribution of Ti3Al was varied by isothermal aging for various times at temperatures in the range 770 to 970 K (930 to 1290 F). The aging kinetics were found to be relatively slow. Quantitative measurements of the particle coarsening rate at 920 K (1200 F) showed good agreement with the predicted behavior for coarsening controlled by matrix diffusion, and suggested that the specific free energy of the Ti3Al alpha interface in negligible small. In all cases, the Ti3Al particles were sheared by the glide dislocations. It was concluded that there is a definite correlation between the presence of deformable Ti3Al particles and an alloy's susceptibility to aqueous stress corrosion cracking. Furthermore, the appearance of the surface slip lines and the dislocation substructure in deformed specimens suggest that the specific effect of the Ti3Al particles is to cause a nonhomogeneous planar slip character and an enhanced chemical potential of the slip bands.

Wood, R. A.↗

Nitridation of silicon

Silicon powders with three levels of impurities, principally Fe, were sintered in He or H2. Non-densifying mechanisms of material transport were dominant in all cases. High purity Si showed coarsening in He while particle growth was suppressed in H2. Lower purity powder coarsened in both He and H2. The same three Si powders and Si /111/ single crystal wafers were nitrided in both N2 and N2/H2 atmospheres. Hydrogen increased the degree of nitridation of all three powders and the alpha/beta ratio of the lower purity powder. Some Si3N4 whiskers and open channels through the surface nitride layer were observed in the presence of Fe, correlating with the nitridation-enhancing effects of Fe. Thermodynamic calculations showed that when SiO2 is present on the Si, addition of H2 to the nitriding atmosphere decreases the amount of SiO2 and increases the partial pressure of Si-containing vapor species, that is, Si and SiO. Large amounts of NH3 and SiH4 were also predicted to form.

Shaw, N. J.↗

Morphological changes of gamma prime precipitates in nickel-base superalloy single crystals

Changes in the morphology of the gamma prime precipitate were examined during tensile creep at temperatures between 927 and 1038 C in 001-oriented single crystals of a Ni-Al-Mo-Ta superalloy. In this alloy, which has a large negative misfit of -0.80%, the gamma prime particles link together during creep to form platelets, or rafts, which are aligned with their broad faces perpendicular to the applied tensile axis. The dimensions of the gamma and gamma prime phases were measured as directional coarsening developed in an attempt to trace the changing morphology under various stress levels. In addition, the effects of initial microstructure, as well as slight compositional variations, were related to raft development and creep properties. The results showed that directional coarsening of gamma prime began during primary creep, and under certain conditions, continued to develop after the onset of steady-state creep. The length of the rafts increased linearly with time up to a plateau region. The thickness of the rafts, however, remained equal to the initial gamma prime size at least up through the onset of tertiary creep; this is a clear indication of the stability of the finely-spaced gamma-gamma prime lamellar structure. It was found that the single crystals with the finest gamma prime size exhibited the longest creep lives, because the resultant rafted structure had a larger number of gamma-gamma prime interfaces per unit volume of material.

Mackay, R. A.↗

Microstructure-property relationships in directionally solidified single crystal nickel-base superalloys

Some of the microstructural features which influence the creep properties of directionally solidified and single crystal nickel-base superalloys are discussed. Gamma precipitate size and morphology, gamma-gamma lattice mismatch, phase instability, alloy composition, and processing variations are among the factors considered. Recent experimental results are reviewed and related to the operative deformation mechanisms and to the corresponding mechanical properties. Special emphasis is placed on the creep behavior of single crystal superalloys at high temperatures, where directional gamma coarsening is prominent, and at lower temperatures, where gamma coarsening rates are significantly reduced. It can be seen that very subtle changes in microstructural features can have profound effects on the subsequent properties of these materials.

Mackay, R. A.↗