Uranium Molybdenum Research Articles

Multiphysics analysis of mechanical responses in micro-reactors under varied operating conditions

Micro-reactors are a promising alternative for power production applications where traditional methods may not be feasible (e.g., space missions). Their design requires critical selection of materials, especially for moderator and fuel, to ensure long-term operation and optimal performance. This research focuses on developing computational analysis models for micro-reactors, aiming to explore their structural behavior under thermal and mechanical loadings. The micro-reactor model is based on the Zero Energy Breeder Reactor Assembly (Zebra) Kilowatt (kW) reactor design conceptualized at Los Alamos National Laboratory. This study investigates the thermal and mechanical responses of three distinct reactor models considering factors, such as boundary conditions, material properties, and thermal-mechanical loading. In this study, Beryllium Oxide (BeO), Beryllium (Be), Aluminum Oxide (Al2O3), and Magnesium Oxide (MgO) are chosen as materials for the reflector. Yttrium Hydride (YH) and Zirconium Hydride (ZH) are chosen as moderators. Uranium Nitride (UN) and Uranium Molybdenum (UMo) are chosen as reactor fuel materials. The thermal analysis predicts the deformation due to the thermal expansion within the reactor under steady operating conditions at 25 kWth, mimicking the maximum rated power of the Zebra kW design. The mechanical study simulates the system's response to forced vibration loads applied along the cooling channels, matching the natural frequency of the system. The results from both analyses show that Beryllium Oxide, Yttrium Hydride, and Uranium Nitride demonstrate the most optimal stress distribution in the system compared to other configurations investigated here. The results of this study can be developed into datasets to facilitate future machine learning studies, enabling the prediction of mechanical and thermal responses for micro-reactors.

Formation of uranium nitride nanoparticles via mechanical alloying of uranium-molybdenum alloy fuels in gaseous nitrogen

Uranium-molybdenum (U-Mo) alloys show promise as a nuclear fuel system due to their high thermal conductivity and fuel loading capability. However, U-Mo systems are susceptible to irradiation induced swelling ultimately affecting the cladding via mechanical and chemical interactions. To address these shortcomings, this research investigated the formation of uranium mononitride (UN) nanoparticles within a 90 wt% U/ 10 wt% Mo (U-10Mo) matrix to act as a prospective defect sink for fission products at nanometric hetero-interfaces. To promote the formation of UN, U-10Mo powders were mechanically alloyed under a high purity nitrogen atmosphere. Variations of the milling process investigated included media size, duration of milling, and number of times the milling jar was re-aerated with nitrogen gas. Characterization of the fuel microstructure was completed using light element analysis, X-ray diffraction, scanning and transmission-electron microscopy, electron energy loss spectroscopy, and atom probe tomography. UN nanoparticles measuring 1–5 nm in radius were observed in the U-Mo matrix as early as 1 h into the mechanical alloying process. Milling time in excess of 10 h was found to lead to deleterious effects induced by the stainless-steel milling media.

A European manufacturing line for monolithic U–Mo bare foil production

The nuclear research reactor Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM II), operated by the Technical University of Munich (TUM) in Germany, provides intense thermal neutron beams for the international scientific community. The uranium fuel currently used for the compact core is an assembly of fuel plates composed of dispersed U3Si2 powder with an enrichment up to 93%, dispersed in aluminium (Al) powder and cladded with an Al alloy. Within the international efforts to minimise the usage of HEU (Highly Enriched Uranium), the FRM II aims to convert its compact core to LEU (Low Enriched Uranium), i.e., a fuel with an enrichment in 235U lower than 20%. The most promising candidate is the metallic monolithic uranium–molybdenum alloy (U–Mo) with zirconium (Zr) coating and Al-based cladding. Here, we show the first European pilot line for U–Mo bare foil manufacturing, implemented in collaboration with the European fuel manufacturer Framatome-CERCATM in Romans-sur-Isère, France. This line involves innovative manufacturing processes, including casting, laser welding, hot rolling, and laser cutting. An overview of the bare foil development with the first results is presented, including visual inspections of foils produced from the hot rolling, the laser cutting and the manufacturing tools used. These first depleted uranium (DU) bare foils are analysed to extract the best manufacturing parameters for future industrialisation. This European manufacturing process gives an alternative solution to the US development for U–Mo monolithic bare foil manufacturing. It represents the first step for European monolithic fuel manufacturing, which could push other European research reactors to use the monolithic U–Mo for their conversion.

Effect of heat treatment on the microstructure of medium burn-up U-Mo monolithic fuel foils

Using scanning electron microscopy (SEM), this study evaluates the microstructure evolution of uranium-molybdenum (U-Mo) fuel foils made with and without heat treatment at medium burn-up (of approximately 5 × 1021 f/cm3). The impact of annealing treatments on critical microstructural properties of the U-Mo fuel foils, including porosity, grain structure, Mo homogeneity, and fuel interaction with the Zr interlayer, was examined using large area lift outs (LALOs). The heat-treated specimens presented less grain refining at these burnups when compared to the non-heat-treated specimens. Grain refinement was associated with porosities and fission products precipitation. These observations may indicate that heat treatment can influence fuel swelling during irradiation. Chemical inhomogeneity (Mo banding) was found to persist in the non-heat-treated samples but was not present in the heat-treated samples. Thus, heat-treated U-Mo foils allow for more predictable fuel behavior under irradiation with respect to non-heat-treated foils. The U-Mo and Zr interaction layer appears to be thicker and more continuous in the heat-treated sample which has been associated with stronger interface integrity during irradiation, as observed in previous studies. These observations may indicate an overall improved performance of heat-treated fuel foil in a reactor, which needs to be confirmed with higher burnup samples. The effect of local burn-up on grain size/refinement and porosities in each LALO specimen, sampled from different positions in the fuel foil, was difficult to analyze due to the large standard deviation of these parameters. Finally, evidence of grain refinement by polygonization may be present in these specimens.

Evidence of Xe-incorporation in the bubble superlattice in irradiated U-Mo fuel

For years, researchers have reported competing ideas on the formation of fission gas bubble superlattices in metallic fuels, which was postulated to be comprised of elemental xenon (Xe) atoms. However, the chemical and physical arrangement of these elements within this gas bubble superlattice had not been verified. In this contribution, Xe was chemically profiled using atomic resolution scanning transmission electron microscopy (STEM) and atom probe tomography (APT) techniques in irradiated uranium-molybdenum (U-Mo) fuels. These complementary techniques provide conclusive evidence of Xe presence in the bubble superlattice up to fission densities of 4.5 × 1021 fissions/cm3 and give a quantitative assessment of Xe content within the bubble superlattice. Based on the results of simultaneous imaging and spectroscopy using STEM, the chemical composition of the Xe bubble superlattice was measured and found to be up to 8±1.3 atomic %. APT data complemented STEM findings on Xe distribution in irradiated U-Mo fuel sample. This study provides conclusive evidence that Xe is not only present within an atomically arranged bubble superlattice but provides fundamental insight into the physical state of Xe in low enriched U-Mo monolithic fuel.

Fuel cycle depletion validation and code-to-code verification studies for High Flux Isotope Reactor highly and low-enriched uranium fuel designs

This paper documents fuel cycle depletion validation and code-to-code verification studies for the High Flux Isotope Reactor (HFIR) highly enriched uranium (HEU) and proposed low-enriched uranium (LEU) fuel designs. In support of HFIR’s world-leading performance, transport and depletion simulations are performed to ensure safe operations, design and qualify irradiation experiments, enhance core components and irradiation facilities, and design and characterize LEU fuel designs. Identifying well-validated, computationally efficient codes is required for the success of these efforts. The HFIR Controller, Shift, and VESTA codes were deployed to simulate HEU uranium–oxide dispersion fuel cycles at 85, 95, and 100 MW operations, as well as LEU fuel cycles operating at 95 MW with uranium–silicide dispersion and uranium–molybdenum monolithic alloy fuel forms. Excellent agreement between the codes and with experimentally obtained 235U enrichment distributions provides increased confidence in the ability of these codes to model and simulate HFIR’s unique core design.

The role of UC inclusions in the development of fission gas bubble superlattice neutron-irradiated monolithic U-10Mo fuels

Uranium Carbide (UC) inclusions are the most prevalent impurities in Uranium-Molybdenum (U-Mo) fuel and are considered undesirable because they could potentially affect fuel performance. This work revealed that, like grain boundaries, UC inclusions could help facilitate the formation of the fission gas bubble superlattice (GBS). The GBS is a highly organized complex defect structure that can effectively store fission gases, thereby inhibiting fuel swelling. Transmission electron microscopy (TEM) showed that GBS self-organization can initiate at the UC/U-Mo interfaces in U-10Mo fuel irradiated to low fission density. This study also revealed that the UC/U-Mo phase boundary in U-10Mo irradiated to low fission density is wavy and periodic in morphology and that GBS formation is semi-coherent with the UC boundary. Because the initiation of GBS preferentially occurs at grain boundaries and UC/U-Mo phase boundaries, it is expected that following GBS collapse at higher fission densities, high burnup structure development may initiate first at grain boundaries and UC/U-Mo interfaces.

DETERMINING GAMMA SOURCE IN URANIUM MOLYBDENUM OF FUEL IN G.A SIWABESSY MULTI PURPOSE REACTOR

Nuclear fission reactions produce a lot of radionuclides that release energy, one of which is in the form of gamma radiation. Gamma radiation is produced by various types of radionuclides, and nuclear reactor fuel will produce different values of gamma intensity. Uranium Molybdenum (U7Mo-Al) is the type of nuclear fuel for future research reactors that possesses many advantages. For the application of molybdenum-based fuel, it is necessary to determine the resulting gamma radiation. The purpose is to determine the gamma radiation produced from molybdenum-based fuel with various densities. This study begins with the determination of the mass composition of the reactor component, calculations with ORIGEN2.1, and data output analysis. The U7Mo-Al density was varied, namely 2.96 gU/cm3, 3.85 gU/cm3, 4.44 gU/cm3, 5.43 gU/cm3, 6.91 gU/cm3, and 8.29 gU/cm3. The gamma radiation yield of U7Mo-Al is lower than that of uranium silicide (U3Si2) with the same density of 2.96 gU/cm3. The result will add to the justification for the superiority of U7Mo-Al compared to U3Si2/Al. For U7Mo-Al with densities of 3.85 gU/cm3, 4.44 gU/cm3, 5.43 gU/cm3, 6.91 gU/cm3, and 8.29 gU/cm3, the one that produced the lowest gamma radiation intensity is 3.85 gU/cm3 while the highest is 8.29 gU/cm3. This explains that the intensity of the gamma radiation produced is directly proportional to the fuel density. The low intensity of gamma radiation in molybdenum-based fuel can be used as a suggestion in shielding design to ensure the operational safety of reactors.

Early self-organization of fission gas bubble superlattice formation in neutron-irradiated monolithic U-10Mo fuels

Self-organization of defect superlattices in far-from-equilibrium systems presents a promising way to mitigate swelling concerns in nuclear materials. The gas bubble superlattice (GBS) is a highly ordered, three-dimensional complex defect structure that can retain fission gasses in Uranium-Molybdenum (U-Mo) fuels. Transmission electron microscopy (TEM) investigation of monolithic U-10Mo fuel irradiated to 1.15 × 1021 fissions/cm3 and 1.30 × 1021 fissions/cm3 revealed that early-stage ordering preferentially occurs at the grain boundaries (GB) and that the critical bubble size for complete ordering is ∼3 nm. Once formed at the GB, the GBS extends towards the grain interior; however, the spread in distance from the GB varies likely depending on the type and strength of the GB sink. TEM results also showed a possible correlation between the growth and evolution of the intragranular disordered bubbles and large dislocation networks. The fission product distribution in and outside of the GBS was also investigated confirming the presence of xenon in the GBS, as well as other fission products including cesium, barium, lanthanum, and cerium.

Molecular dynamics studies of grain boundary mobility and anisotropy in BCC γ-uranium

Grain morphologies such as grain size and aspect ratio in uranium-based metallic fuels are important microstructural features that can impact various fuel performance properties such as fission-gas-induced swelling, thermal transport, high burnup structure formation, and radiation resistance. Accurate prediction of the fuel grain morphologies requires knowledge of critical grain growth parameters such as grain boundary (GB) mobility and anisotropy. In this work, molecular dynamics (MD) simulations were performed to study the GB mobility and its anisotropy in pure body-centered-cubic (BCC) γ uranium. Nine GBs with different combinations of misorientation angles (20°, 30°, 45°) and rotation axes (<100>, <110>, <111>), as well as an additional <111> 38.2° GB were studied using three interatomic potentials. It is found that the GB mobility anisotropy has complex trends, depending on both rotation axis and misorientation. However, in general the <110> rotation axis has the fastest GB mobility at the same misorientation. The results of this work can be used as not only a baseline for future studies of GB mobility in uranium-based alloys such as uranium-molybdenum (U-Mo) fuels, but also input for mesoscale modeling of grain growth in uranium-based alloys.

Non-destructive analysis of swelling in the EMPIrE fuel test

The European Mini-Plate Irradiation Experiment (EMPIrE) was designed to support the development and testing of a coated uranium-molybdenum (U-Mo) dispersion fuel for the conversion of select high-performance research reactors (HPRRs) to utilize low-enriched uranium (LEU). To aid in the development of the coated fuel form, the EMPIrE test included several plate designs and irradiated them in the Idaho National Laboratory (INL) Advanced Test Reactor (ATR) at a high meat power density (∼21 kW/cm3) and to high fuel particle fission densities (∼6.4 × 1021 fissions/cm3). These conditions mimic the bounding conditions of the BR-2 reactor in Belgium, where a concurrent irradiation experiment was performed, and exceed those previously explored in dispersion U-Mo fuel plates. A local fuel swelling analysis, as determined through high-fidelity, post-irradiation mini-plate profilometry, was used along with statistical methods to non-destructively evaluate the overall performance and separate the effects of convoluted fabrication variables. While some effects observed with this non-destructive analysis were subtle, others had more significant, and possibly competing, effects on the fuel swelling behavior. These observations will be examined further with destructive examinations to more fully assess them as the fuel design is developed and qualified.

Effect of Concentration of Mo on the Mechanical behavior of γ UMo: an Atomistic Study

We performed molecular dynamics simulation on nanoindentation ofγ phase Uranium Molybdenum alloys using spherical indenter. A ternary potential developed for UMoXe was utilized. We calculated the updated values for hardness and reduced elastic modulus at different concentrations of Mo. The whole process of deformation and dislocation analysis was visualized using OVITO. We found an increase in deformation withincreasein stress while dislocations are not found anyhow induced defects have been distributed throughout the simulation cell randomly. The increase in concentration affected the hardness and reduced elastic modulus significantly. This study provides insights into the structure and mechanical characteristics of γ UMo under deformation.

Benchmark of the Kilowatt Reactor Using Stirling TechnologY (KRUSTY) Component Critical Configurations

Kilowatt Reactor Using Stirling TechnologY (KRUSTY) was a prototype for the U.S. National Aeronautics and Space Administration’s Kilopower Program. KRUSTY has a highly enriched uranium–molybdenum alloy (with 7.65 wt% molybdenum) annular core reflected by beryllium oxide with an outer stainless steel shield. Five configurations from the experimental campaign were chosen to be evaluated as benchmark cases. Uncertainties were evaluated in five categories: (1) criticality measurement, (2) mass and density, (3) dimensions, (4) material compositions, and (5) positioning. The largest contribution to the overall uncertainty in each case was from the radial alignment of the movable platen. A simplified model was created to increase computational efficiency, and an average bias of –16 pcm was calculated due to the simplifications. Sample calculations were completed for each case using MCNP6.2, COG, and MC21, all with ENDF/B-VIII.0 nuclear data. For MCNP6.2, the average difference (absolute value) between the calculated and experimental keff for the five configurations was 14 pcm for both the detailed and the simplified models. The keff results from all three codes are within 1σ of the benchmark values. KRUSTY’s value as a benchmark is due to its sensitivity to beryllium and molybdenum. For beryllium, KRUSTY adds an 18th benchmark with a total cross-section sensitivity greater than 0.05%/%/(unit lethargy). For molybdenum, KRUSTY adds a 9th benchmark with a total cross-section sensitivity greater than 0.004%/%/(unit lethargy).

An atomistic study of defect energetics and diffusion with respect to composition and temperature in γU and γU-Mo alloys

• Vacancy and self-interstitial formation energies were calculated in γ U and γ U-Mo. • Self-diffusion and interdiffusion coefficients in γ U- x Mo ( x = 7 , 10, 12 wt.%) were calculated. • Results can be used as input parameters in mesoscale and engineering scale fuel modeling. Uranium-molybdenum (U-Mo) alloys are promising candidates for high-performance research and test reactors, as well as fast reactors. The metastable γ phase, which shows acceptable irradiation performance, is retained by alloying U with Mo with specific quenching conditions. Point defects contribute to the atomic diffusion process, defect clustering, creep, irradiation hardening, and swelling of nuclear fuels, all of which play a role in fuel performance. In this work, properties of point defects in γ U and γ U- x Mo ( x = 7, 10, 12 wt. % ) were investigated. Vacancy and self-interstitial formation energies in γ U and γ U- x Mo were calculated with molecular dynamics (MD) simulations using an embedded atom method interatomic potential for the U-Mo system. Formation energies of point defects were calculated in the temperature range between 400 K and 1200 K. The vacancy formation energy was higher than the self-interstitial formation energy in both γ U and γ U- x Mo in the evaluated temperature range, which supports the previous results obtained via first-principles calculations and MD simulations. In γ U- x Mo, the vacancy formation energy decreased with increasing Mo content, whereas the self-interstitial formation energy increased with increasing Mo content in the temperature range of 400 K to 1200 K. The self-diffusion and interdiffusion coefficients were also determined in γ U- x Mo as a function of temperature. Diffusion of U and Mo atoms in γ U- x Mo were negligible below 800 K. The self-diffusion and interdiffusion coefficients decreased with increasing Mo concentration, which qualitatively agreed with the previous experimental observations. Point defect formation energies, self-diffusion coefficients, and interdiffusion coefficients in γ U- x Mo calculated in the present work can be used as input parameters in mesoscale and engineering scale fuel performance modeling.

Processing technology for carbonate ore from the Argun deposit

Priargun Mining and Chemical Association has been producing uranium in the Streltsov ore field for more than 50 years. The main ore bodies with high content of uranium have been mined out during this period of time, and the uranium content has dropped in ore which is currently extracted. In connection with this, appraisal of the mineral resources and mineral reserves of Priargun MCA has been accomplished. The Argun ore is composed of a few process types—iron silicate and uranium, silicate–uranium–molybdenum, carbonate and uranium, carbonate and molybdenum, carbonate–uranium–molybdenum and rebellious ore (contains zirconium and brannerite). It is required to undertake technology-based rating and certification of the Argun ore. The autoclave leaching technology is found to be higher economically efficient as against the atmospheric leaching technology due to lower operating expenses. From the preliminary studies, four samples of anion-exchange resins are recommended for further testing: A500Y, BM77-14, D299 and Ambersep 920UXL SO4. These ion-exchangers were used to analyze their influence on sorption–desorption of uranium and molybdenum. All these ion exchangers had preserved their sorption capacity in 10 sorption–desorption cycles. Based on the studies into adsorption of uranium and molybdenum from leached slurry at the Argun deposit, the optimal sorbent for extraction and separation of uranium and molybdenum is Ambersep 920UXL SO4. Producibility of natural uranium to meet ASTM C 967-13 standards is analyzed on a laboratory scale. The produced uranium concentrate contains much less impurities than it is stipulated by International Standard Specification ASTM С 967-13. The action chart of processing of carbonate ore from the Argun and Zherlovoe deposits is developed and economically justified.

Analysis and comparison of computer programs to analyze the irradiation performance of Uranium Molybdenum monolithic fuel plates and Uranium dioxide cylindrical fuel rods in power reactors.

The aim of this work is to present a comparative analysis in terms of the irradiation performance of cylindrical uranium dioxide fuel rods and monolithic uranium molybdenum fuel plates in pressurized light water reactors.To analyze the irradiation performance of monolithic uranium molybdenum fuel plates when subjected to steady state operating conditions in light water pressurized reactors, the computer program PADPLAC-UMo was used, which performs thermal and mechanical analysis of the fuel taking into account the physical , chemicals and irradiation effects to which this fuel is subjected. For the analysis of the uranium dioxide fuel rods, the code FRAPCON was used, which is an analytical tool that verifies the irradiation performance of fuel rods of pressurized light water reactor, when the power variations and the boundary conditions are slow enough for the term permanent regime to be applied. The analysis for a small nuclear power reactor, despite the higher power density applied to the fuel plate in relation to the fuel rod, showed that the fuel plates have lower temperatures and lower fission gas releases throughout the analyzed power history, allowing the use of a more compact reactor core without exceeding the design limits imposed on nuclear fuel.

Crystallographic texture of hot rolled uranium-molybdenum alloys

The uranium molybdenum (U-Mo) alloys have potential to be used as low enriched uranium nuclear fuel in research, test and power nuclear reactors. U-Mo alloy with composition between 7 and 10 wt% molybdenum shows excellent body centered cubic phase (γ phase) stabilization and presents a good nuclear fuel testing performance. Hot rolling is commonly utilized to produce parallel fuel plate where it promotes the cladding and the fuel alloy bonding. The mechanical deformation generates crystallographic preferential orientation, the texture, which influences the material properties. This work studied the texture evolution in hot rolled U-Mo alloys. The U7.4Mo and U9.5Mo alloys were melted in a vacuum induction furnace, homogenized at 1000°C for 5 h and then hot rolled at 650°C in three height reductions: 50, 65 and 80%. The crystalline phases and the texture were evaluated by X-ray diffraction (XRD). The as-cast and processed alloys microstructures were characterized by optical and electronic microscopies. The as-cast, homogenized and deformed alloys have γ phase. It was found microstructural differences between the U7.4Mo and U9.5Mo alloys. The homogenized treatment showed effective for microsegregation reduction and were not observed substantial grain size increasing. The deformed uranium molybdenum alloys presented α, γ, θ texture fibers. The intensity of these texture fibers changes with deformation step.

DESIGN OF NEUTRONIC PARAMETERS OF MTR REACTOR USING WIMSD-5B/BATAN-FUEL CODES

BATAN has three aging research reactors, so it is necessary to design a new, more modern MTR type reactor using high-density, low enrichment uranium molybdenum fuel. The thermal neutron flux at the irradiation position is an important concern in the design of research reactors. This analysis is performed using standard computer codes WIMSD-5B and Batan-FUEL. The purpose of this study is to analyze the effect of the core configuration with safety control rods and neutronic parameters using the diffusion method calculation. The reactor core consists of 16 fuel elements and four control rods placed in the 5 x 5 position of the grid plate and is loaded the reflector elements outside the core. The cycle length is also a concern, not less than 20 days, and the reactor can be operated safely with a power of 50 MW. The calculation results show that for the highest fuel loading, which is 450 grams of U7Mo/Al fuel with D2O as a reflector, it will provide the lowest thermal neutron flux at the center of the core irradiation position, namely 1.0 x1015 n/cm2s. The core fuel cycle length will be up to 39 days, meeting the expected acceptance and safety criteria.

Accident tolerant fuels to replace uranium dioxide

The thermal conductivities for the traditional fuel UO2 and for the Accident Tolerant Fuel (uranium Molybdenum alloy, U-10Mo and uranium silicide, U3Si2) are calculated and compared. Then the temperature distributions on these core reactor, namely on the surface of the rod and in the center line of the rod were determined. The calculation is carried out using MATHCAD program. The calculations showed enhancement of thermal conductivity of the Accident Tolerant Fuel as they increased linearly with increasing temperature, and reduction of their center line temperatures of the rods. Beside, their steep thermal gradient, which may reduce the induced heat stresses in the core of the reactor.

Image-driven discriminative and generative machine learning algorithms for establishing microstructure–processing relationships

We investigate the methods of microstructure representation for the purpose of predicting processing condition from microstructure image data. A binary alloy (uranium–molybdenum) that is currently under development as a nuclear fuel was studied for the purpose of developing an improved machine learning approach to image recognition, characterization, and building predictive capabilities linking microstructure to processing conditions. Here, we test different microstructure representations and evaluate model performance based on the F1 score. A F1 score of 95.1% was achieved for distinguishing between micrographs corresponding to ten different thermo-mechanical material processing conditions. We find that our newly developed microstructure representation describes image data well, and the traditional approach of utilizing area fractions of different phases is insufficient for distinguishing between multiple classes using a relatively small, imbalanced original dataset of 272 images. To explore the applicability of generative methods for supplementing such limited datasets, generative adversarial networks were trained to generate artificial microstructure images. Two different generative networks were trained and tested to assess performance. Challenges and best practices associated with applying machine learning to limited microstructure image datasets are also discussed. Our work has implications for quantitative microstructure analysis and development of microstructure–processing relationships in limited datasets typical of metallurgical process design studies.