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At least 163 records · Page 9

Development, validation, and verification of multi-pass thermo-mechanical welding simulations using the open-source MOOSE framework: NeT TG4 benchmark weldment

This study develops and validates a sequentially coupled thermo-mechanical welding simulation for the three-pass 316L stainless steel NeT TG4 benchmark weldment using the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) and the Nuclear Engineering Material model Library (NEML). A diffused ellipsoidal heat source was calibrated against thermocouple data and weld macrographs to accurately model the fusion zone geometry and transient thermal fields. Material hardening is represented using the Lemaitre-Chaboche mixed isotropic-kinematic hardening model, while four annealing models - no annealing, single-stage at 1050 °C and 1300 °C, and two-stage at 800 °C/1300 °C - were implemented to assess the impact of annealing models on the accuracy of the predicted welding-induced plasticity, distortions, and residual stresses. The predictions were validated against experimental measurements and benchmarked against results from commercial software, demonstrating that thermo-mechanical MOOSE welding simulations achieve comparable accuracy with enhanced computational efficiency. This work highlights the potential of using open-source finite element frameworks like MOOSE for advanced manufacturing simulations.

Ji, Wendy [Australian Nuclear Science and Technolo↗

Precipitate growth kinetics under inhomogeneous concentration fields using a phase-field model

We investigate precipitation dynamics in the presence of a local solute gradient using phase-field simulations. During the homogenization heat treatment of the solidified Inconel 718 alloy, high Nb concentration within the Laves phases or at the core of the secondary arms results in Nb diffusion into the γ matrix. The volume fraction and spatial distribution of precipitation during subsequent annealing can be controlled by tailoring the Nb concentration gradient in the matrix during homogenization. We use a surrogate Ni-Fe-Nb alloy for Inconel 718 to explore the growth dynamics of δ precipitates related to the local Nb concentration levels. The simulations indicate that in the presence of a Nb concentration gradient the growth rate of δ precipitates is higher than in a matrix of uniform average Nb concentration. The higher growth rate is a result of the higher local thermodynamic driving force at the interface between the solute-rich matrix and the δ interface. Here, we propose a phenomenological model to describe the diffusion-controlled growth kinetics of the δ phase under a solute concentration gradient.

36 MATERIALS SCIENCE↗

Characterization of Fe-6Si Soft Magnetic Alloy Produced by Laser-Directed Energy Deposition Additive Manufacturing

Abstract Commercial electrical steels, Fe-Si alloys with < 4 wt.% Si, are inexpensive and efficient materials for electrical power conversion. Further efficiency improvements require increasing the silicon concentration to 6 wt.%, at which point the material becomes brittle and difficult to form by conventional rolling and sheet fabrication methods. Additive manufacturing stands to overcome challenges with commercial manufacturing techniques by leveraging near-net-shape fabrication. The wide array of process conditions provides additive manufacturing with increased flexibility, enabling control over the microstructure and mechanical properties. This work explores the microstructures and magnetic properties of ring-shaped Fe-Si alloys produced using concentric and cross-hatch tool paths on a laser-directed energy deposition additive manufacturing system. Concentric-built samples exhibit elongated grain structures while cross-hatch-built samples comprise lower aspect ratio grain structures. Thermal finite element analysis simulations model the stress conditions produced by the different scan path geometries. Microhardness measurements probe the mechanical properties as a function of anneal temperature, providing a qualitative understanding of the intergranular defect density. Soft magnetic properties measured under quasistatic and AC conditions show frequency- and microstructure-dependent coercivity and permeability. Finally, analysis of the core loss quantifies how the build strategies and thermal treatments influence efficiency in electrical power conversion applications. Understanding the influences of scan path geometry and thermal treatment provides a pathway towards application of additively manufactured soft magnetic materials.

Adamczyk, Jesse M.↗

Hierarchical microstructures: a potential route to enhanced stability in structural materials for advanced nuclear reactors

The drive to increase efficiency in nuclear energy systems is leading to the need for materials that operate at higher temperatures and stress levels for extended periods, while maintaining stable microstructures to ensure their performance is not compromised. A novel route to producing materials that can perform well in such environments is the creation of hierarchical microstructures. A hierarchical microstructure is a microstructure in which features are present at multiple length scales simultaneously. In this work, a hierarchical microstructure is fabricated in a nickel-base superalloy, featuring nanometer-size gamma precipitates inside larger gamma-prime particles, which are in turn embedded in the gamma matrix phase. The hierarchical features of the microstructure lead to enhanced stability of the gamma-prime precipitates during annealing; the particle size does not follow the expected t^(1/3) growth law predicted by the classic LSW theory. Phase-field simulations are used to understand the unexpected stability of the gamma-prime precipitates.

36 MATERIALS SCIENCE↗

Hierarchical microstructures: a potential route to enhanced stability in structural materials for advanced nuclear reactors

The drive to increase efficiency in nuclear energy systems is leading to the need for materials that operate at higher temperatures and stress levels for extended periods, while maintaining stable microstructures to ensure their performance is not compromised. A novel route to producing materials that can perform well in such environments is the creation of hierarchical microstructures. A hierarchical microstructure is a microstructure in which features are present at multiple length scales simultaneously. In this work, a hierarchical microstructure is fabricated in a nickel-base superalloy, featuring nanometer-size gamma precipitates inside larger gamma-prime particles, which are in turn embedded in the gamma matrix phase. The hierarchical features of the microstructure lead to enhanced stability of the gamma-prime precipitates during annealing; the particle size does not follow the expected t^(1/3) growth law predicted by the classic LSW theory. Phase-field simulations are used to understand the unexpected stability of the gamma-prime precipitates.

36 - MATERIALS SCIENCE↗

Efficient BiVO 4 /CoFeO x H y photoanodes using controlled annealing and conformal linear-sweep electrocatalyst photodeposition

Although monoclinic bismuth vanadate (BiVO 4 ) is a promising photoanode for solar water splitting, its practical use is hindered by imperfect photocurrent generation/collection, low photovoltage compared to the bandgap, and corrosion side reactions that limit durability. Here, we introduce a controlled-annealing sol–gel process for BiVO 4 thin-film photoanodes along with an optimized linear-sweep-voltammetry photodeposition of CoFeO x H y cocatalysts. The resulting BiVO 4 films annealed at 550 °C exhibited a photocurrent density of 4.1 mA/cm 2 at 1.23 V RHE under 1 sun AM 1.5G solar simulation and a low onset potential of 0.26 V RHE due to high majority carrier conductivity, a crystalline bulk with reduced defects as evidenced by x-ray photoelectron spectroscopy and photoluminescence lifetime analysis, and thus enhanced photocarrier collection. However, significant degradation in performance was found due to interfacial photocorrosion. To protect the surface and speed the oxygen-evolution reaction CoFeO x H y cocatalyst layers were deposited. By varying the number of consecutive sweeps and adjusting the applied bias range, an ultra-thin (~15 nm) CoFeO x H y cocatalyst layer was uniformly grown deposited over 30 cycles on the BiVO 4 surface. The resulting BiVO 4 /CoFeO x H y yielded 4.03 mA/cm 2 at 1.23 V RHE and onset potential of 0.24 V RHE , with stable operation (~15 % loss in photocurrent at 1.23 V RHE relative to ~60 % loss in the uncatalyzed control sample). These conformal CoFeO x H y catalytic layers function simultaneously to selectively collect photoexcited holes from the BiVO 4 , catalyze the water-oxidation reaction, and protect the BiVO 4 from photodegradation.

42 ENGINEERING↗

Computationally guided experimental validation of divacancy defect formation in 4H-SiC

Recent research into solid-state qubits for quantum information science has focused on optically addressable spin defects such as the negatively charged nitrogen-vacancy center in diamond and the neutrally charged divacancy (VV) in 4H-SiC as scalable quantum sensors and networking qubits. Within this context, direct investigations of the structural origin and defect formation dynamics of a sub-set of the VV center in 4H-SiC remain lacking. Here, we take a systematic experimental approach guided by predictions from first-principles simulations to gain a thorough mechanistic understanding of the VV defect formation and control in 4H-SiC. We study the effect of annealing time and temperature on VV formation in high-purity semi-insulating 4H-SiC samples following electron irradiation. Three different temperatures (1123, 1273, and 1473 K) and annealing duration (from 0.5 to 72 h) are chosen to explore VV formation in different regions. We find that samples annealed at 1273 K give the highest VV-related photoluminescence (PL) intensities, in agreement with the prediction from first-principles calculations. Furthermore, the logarithmic dependence of VV-related PL intensities on the annealing duration at 1273 K indicates that 1273 K provides sufficient thermal energy for silicon vacancy migration but not for VV migration. Together, these results suggest that efficient VV formation occurs above the V Si migration temperature and below the VV migration threshold.

74 ATOMIC AND MOLECULAR PHYSICS↗

Experimental characterization and atomistic simulation of grain boundary segregation in Mg-Y alloys

As a rare earth solute element in Mg alloys, Y has the beneficial effects of increasing both the strength and the ductility as well as weakening the crystallographic texture. To achieve a more fundamental understanding on how Y addition affects the microstructural evolution and mechanical properties, the Y segregation behavior at grain boundaries was investigated in Mg-1wt.%Y and Mg-7wt.%Y alloys at different conditions. The segregation intensity and its dependence on the grain boundary misorientation angle were experimentally characterized and computationally predicted. Strong segregation at grain boundaries was observed in both low and high Y-containing alloys. Y segregation was found to remain in alloy Mg-7Y after high-temperature annealing heat treatment at 540 °C. No direct correlation between the Y segregation intensity and the grain boundary misorientation angle could be established based on either the experimental characterization or the atomistic simulation with a spectral model. We thus conclude that grain boundary segregation of Y is independent of grain boundary misorientation angle.

Grain boundary↗

Strength models for stainless steel 304L alloys

This report provides nominal, weak and strong calibrations of Preston- Tonks-Wallace (PTW) plasticity model [1] parameters for stainless steel 304L alloys. The data sets shown indicate that for these alloys, the material’s prove- nance plays an important role in accurate characterization. First we provide a parameter set fit to compression-tested annealed samples, both quasistatic (QS) and split Hopkinson pressure bar (SHPB), from the MST-8 group at LANL within the last year. Then we compare simulations using the FLAG hydrocode [2], with this and other parameter sets, to data from a Taylor cylinder impact test performed within the same group around 2013.

36 MATERIALS SCIENCE↗

New Approaches to Low-Cost Scalable Doping of Interdigitated back Contact Silicon Solar Cells (Final Report)

The goal of this project was to develop novel approaches to patterning of dopants in the rear fingers of interdigitated back contact (IBC) Si solar cells to reduce the cost of manufacturing this high-efficiency-potential cell architecture. The work throughout this project can be divided into four categories: (a) development of dopant patterning technique using laser scribed Si contacts masks that are mechanically aligned with ~10 μm resolution to the underlying Si substrate; (b) measuring dopant spreading profiles in the isolation region between n- and p-type dopant fingers during plasma-enhanced chemical vapor deposition (PECVD) of doped hydrogenated amorphous silicon (a-Si:H) via shadow masks, and dopant desorption and re-adsorption during high-temperature annealing; (c) understanding the role of dopant compensation on the shunt resistance in contaminated isolation regions through analysis of defect-enhanced compensation; and (d) simulation and fabrication of passivated two-sided grid and back-contact solar cells to demonstrate the use of direct dopant patterning in cell fabrication. For the passivated two-sided grid solar cells, masked deposition was used to demonstrate an improvement in the blue response of the cell by creating a shallow front emitter. During development of the masked PECVD patterning process, we measured 3-D dopant profiles using secondary ion mass spectrometry. After deposition, in the masked region, the phosphorus dopant tail was >100 µm at concentrations >10 19 cm -3 while the boron dopant tail was shorter. During high-temperature crystallization of doped a-Si:H films to polycrystalline Si (poly-Si), phosphorus atoms spread by desorbing from the poly-Si surface and re-adsorbing onto intrinsic poly-Si on adjacent wafers that were separated by several millimeters. These contamination mechanisms resulted in a decrease in resistivity from ~10 5 Ω·cm for intrinsic poly-Si to ~10 -1 Ω·cm for contaminated poly-Si. Mitigation strategies for each contamination mechanism were developed to maintain a resistivity of ~10 5 Ω·cm between doped fingers. During fabrication of the 209 cells created during this project, it was found that despite contamination of the IBC gap through the abovementioned mechanisms, high shunt resistances and FF ~75% were still reached. Investigation into this led to the discovery of defect-enhanced compensation which exists within highly defective poly-Si when net doping concentrations reach the value of defect density (~10 18 cm -3 for many poly-Si films). Simulations guided us in the fabrication of IBCs and the cells fabricated were able to meet the year-end goals for BP 2 and 3 of 15% and 17% IBC cell efficiency, as well as the BP 4 goal of a 1% absolute increase in efficiency for PERC-like devices. However, the most efficient cell created during this project of 18.6% fell short of the 21% final project target. While the champion device fell short in V oc and J sc , many devices fabricated were able to reach the necessary goals of ~40 mA/cm 2 , ~700 mV, and ~75% FF required for a 21% device. The results generated from this project were disseminated through 11 conference presentations and proceedings. Presentations included oral talks at 2019 IEEE PVSC, 2019 MRS Fall Meeting, 2020 PVSEC-30 and 2021 IEEE PVSC, as well as poster presentations at 2020 IEEE PVSC and 2021 SiPV. The project resulted in 2 peer reviewed publications – one published in IEEE Journal of Photovoltaics and one in ACS Applied Energy Materials. The information gained in this project will aid in development of improved processes for fabrication of high-efficiency solar cells and other areas of the semiconductor device industry as well. The IBC cells will also pave the way for higher efficiency tandem devices. Through further manufacturing of high-efficiency solar cells, more of the world’s energy demands can be met through renewable sources, helping to stave off the worst effects that may come about from global climate change.

14 SOLAR ENERGY↗

Coupling Microstructural Evolution Simulations to Material Property Degradation Predictions for Plasma-Facing Materials

Reliable material performance is required for plasma-facing material (PFM) candidates. Previous research has shown that plasma and neutron radiation exposure induces microstructural changes in PFMs; changes in thermal and electrical conductivities and in material hardening and embrittlement were also observed after neutron irradiation. These material property changes will negatively impact the performance of the PFMs in a fusion reactor. Despite the well-known connection between material microstructure, properties, and performance, there is a need for validated modeling capabilities connecting PFM property degradation with microstructural evolution under fusion-relevant conditions. We are developing a simulation capability to couple plasma-induced microstructural evolution to material property degradation. Our approach relies on deliberate mapping between individual simulation models and experimental characterization for validation. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) software was used for this simulation capability development. A MOOSE phase-field model was coupled with the cluster dynamics code, Xolotl, to predict microstructural evolution. Microstructure characterization techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser scanning confocal microscopy (LSCM) are used to validate these microstructural evolution simulations. Calculation of thermal and electrical conductivities with first principles simulations was performed for bulk material and for grain boundaries; these results are used within MOOSE models to calculate effective thermal and electrical conductivities as a function of grain characteristics. Thermoreflectance and four-probe techniques were employed to measure the thermal and electrical conductivities, respectively. A MOOSE crystal plasticity model was adapted to predict microstructure-sensitive deformation behavior, and X-ray diffraction (XRD) was used to collect bulk dislocation density data for validation. After individual simulation validation, these models are coupled to predict material property changes resulting from plasma exposure. We focused here on an experimental design to emphasize the separate effects of moderate thermal loads and plasma exposure using tungsten. Annealing of tungsten was performed under a protective environment for temperatures ranging from 500 C to 1500 C. The plasma exposure was completed in the Tritium Plasma Experiment at Idaho National Laboratory under a deuterium flux of 1e22 D/m^2-s. This incremental approach is employed to build confidence in the modeling capability: separate-effects tests ensure that the models capture key mechanisms from single environmental conditions before predicting PFM property degradation under combined loads. We will show our early results from coupling these simulation models to predict PFM property changes from microstructural evolution. Comparisons of the simulation results with preliminary validation data will be discussed.

36 - MATERIALS SCIENCE↗

Connect microstructure evolution to property degradation with validated simulation

Reliable material performance is required for plasma-facing material (PFM) candidates. Previous research has shown that plasma and neutron radiation exposure induces microstructural changes in PFMs; changes in thermal and electrical conductivities and in material hardening and embrittlement were also observed after neutron irradiation. These material property changes will negatively impact the performance of the PFMs in a fusion reactor. Despite the well-known connection between material microstructure, properties, and performance, there is a need for validated modeling capabilities connecting PFM property degradation with microstructural evolution under fusion-relevant conditions. We are developing a simulation capability to couple plasma-induced microstructural evolution to material property degradation. Our approach relies on deliberate mapping between individual simulation models and experimental characterization for validation. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) software was used for this simulation capability development. A MOOSE phase-field model was coupled with the cluster dynamics code, Xolotl, to predict microstructural evolution. Microstructure characterization techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser scanning confocal microscopy (LSCM) are used to validate these microstructural evolution simulations. Calculation of thermal and electrical conductivities with first principles simulations was performed for bulk material and for grain boundaries; these results are used within MOOSE models to calculate effective thermal and electrical conductivities as a function of grain characteristics. Thermoreflectance and four-probe techniques were employed to measure the thermal and electrical conductivities, respectively. A MOOSE crystal plasticity model was adapted to predict microstructure-sensitive deformation behavior, and X-ray diffraction (XRD) was used to collect bulk dislocation density data for validation. After individual simulation validation, these models are coupled to predict material property changes resulting from plasma exposure. We focused here on an experimental design to emphasize the separate effects of moderate thermal loads and plasma exposure using tungsten. Annealing of tungsten was performed under a protective environment for temperatures ranging from 500$^o$C to 1500$^o$C. The plasma exposure was completed in the Tritium Plasma Experiment at Idaho National Laboratory under a deuterium flux of 1e22 $\frac{D}{m^2s}$. This incremental approach is employed to build confidence in the modeling capability: separate-effects tests ensure that the models capture key mechanisms from single environmental conditions before predicting PFM property degradation under combined loads. We will show our early results from coupling these simulation models to predict PFM property changes from microstructural evolution. Comparisons of the simulation results with preliminary validation data will be discussed.

36 - MATERIALS SCIENCE↗

High-pressure annealing driven nanocrystal formation in Zr 50 Cu 40 Al 10 metallic glass and strength increase

Pressure-induced structural changes in metallic glasses have been of great interest as they are expected to open new ways to synthesize novel materials with unexpected properties. Here, we investigated the effect of simultaneous high-pressure and high-temperature treatment on the structure and properties of a Zr 50 Cu 40 Al 10 metallic glass by in situ X-ray structure measurement and property analysis of the final material. We found the unusual formation of Cu-rich nanocrystals at high pressure and temperature, accompanied by significant strength and hardness enhancement. Based on reverse Monte Carlo modeling and molecular dynamics simulations, the structure of the metallic glass changed to a densely packed, chemically uniform configuration with high short-range and medium-range ordering at high pressure and temperature. These results show that high-pressure annealing processes provide a new way to improve and control properties without changing their composition.

36 MATERIALS SCIENCE↗

Au-free low-temperature ohmic contacts for AlGaN/AlN/GaN heterostructures

We report Au-free, Ti/Al/Ta ohmic contact on the AlGaN/AlN/GaN heterostructure using low annealing temperature is studied in this paper. With SiCl 4 plasma treatment at the recess-etched contact region, a low contact resistance of 0.52 Ω mm and a low sheet resistance of 373 Ω/sq are achieved after annealing at 550 °C for 30 s. The low annealing temperature also leads to better surface morphology. Furthermore, AlGaN/AlN/GaN high-electron-mobility transistors (HEMTs) are fabricated with the 550 °C, 30 s annealed Ti/Al/Ta ohmic contacts, and a maximum transconductance of 123 mS/mm and a maximum drain current of 510 mA/mm are obtained for a gate length of 4 μm. Based on Silvaco's Atlas device simulation framework, a scaled-down device with a short gate length of 1 μm would produce a maximum drain current density of 815 mA/mm. It indicates that the direct current performance of the HEMTs with the ohmic metal proposed in this work is considerably better than that with Au-based ohmic contact.

42 ENGINEERING↗

Material flow behavior and microstructural refinement of AA6061 alloy during friction extrusion

In this work we used friction extrusion (FE), a solid phase processing technique, to produce dense, fully consolidated 5?mm rods of aluminum alloy 6061 (AA6061). The combination of large shear stresses and high temperatures at the tool-billet interface during extrusion produced equiaxed, dynamically recrystallized grains and finely distributed precipitates. Texture and microstructure evolution during extrusion was investigated in detail using scanning electron microscopy, electron backscatter diffraction, and transmission electron microscopy. Smoothed particle hydrodynamics simulation was performed to study complex material flow during extrusion. Simulation results suggest spiral material flow during extrusion which corroborated experimental results. Advantages of friction extruded microstructure over conventionally extruded counterparts are also explored using flash annealing for solution treatment followed by artificial aging. Mechanical properties of the as-friction extruded, and the artificially aged specimens were evaluated using tensile testing and compared with conventional extruded material properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Doping of CdTe Using CuCl2 Solution for Highly Efficient Photovoltaic Devices

Here, we report doping of cadmium telluride (CdTe) thin film solar cells using copper (II) chloride (CuCl 2 ) solution in deionized water. The CdTe thin films were immersed in 0.1 mmol CuCl 2 solution in water and annealed in the temperature range of 180-240 degrees C for various time durations. The devices were completed using thermally evaporated gold (Au) and measured under simulated AM1.5G spectrum. The average device efficiency of CuCl 2 treated CdTe devices increased to 13.7 % (best cell reaching 14.0%) with significant improvement on open-circuit voltage (VOC ) as compared with 12.4% (best cell 12.7%) for thermally evaporated Cu doped CdTe devices. For CuCl 2 treated CdTe devices, we found higher photoluminescence (PL) intensity and longer carrier life time at room temperature indicating solution based doping offers better control of Cu doping density as compared with evaporated Cu.

14 SOLAR ENERGY↗

Beyond-classical computation in quantum simulation

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

King, Andrew D. [D-Wave Quantum Inc., Burnaby, BC ↗

A Gaussian process autoregressive model capturing microstructure evolution paths in a Ni–Mo–Nb alloy

Additive manufacturing is increasingly being employed to produce components of complex geometries in structural alloys because of the expected energy savings associated with the near-net-shape capability and the ability to build in novel internal features that are not possible with many conventional manufacturing approaches. However, because of the extreme thermal conditions encountered, the non-equilibrium microstructures produced during powder bed-based additive manufacturing processes must be subjected to custom post-heat treatment processes to recover the target mechanical properties. Phase-field models and simulation techniques have matured to a state where the microstructure evolution paths, and the morphologies of the resulting precipitate phases can be predicted reasonably accurately, considering alloy-specific thermodynamic and kinetic aspects of the nucleation and growth processes. However, phase-field simulations are computationally intensive, which precludes the ability to apply the simulations directly to the length scale of the entire component. Therefore, it is highly desirable to develop low-computational-cost surrogate models that effectively capture the physics at the microstructural length scale, while facilitating the design of optimized processing conditions resulting in location-specific targeted microstructures at the component scale. The work presented here demonstrates the application of the materials knowledge system framework to develop a surrogate model that effectively captures the microstructural path during annealing of a Ni–Mo–Nb alloy containing different Mo and Nb compositions known to segregate during solidification under additive manufacturing conditions. Specifically, the surrogate model built in this work is based on a Gaussian process autoregressive model informed by statistical representation of simulated microstructures using two-point correlations and dimensionality reduction through principal component analysis. In conclusion, this surrogate model is shown to capture the bifurcation of the microstructural path during precipitation, which yields a microstructure dominated by the $\gamma^{\prime\prime}$ phase at high Nb concentrations and the $\delta$ phase at low Nb concentrations.

36 MATERIALS SCIENCE↗