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DOE OSTI2023

Development Plan for Acoustic Emission and Vibration Sensors

This document discusses the need for high temperature, radiation tolerant sensors for monitoring vibration and acoustic emissions in advanced reactors and irradiation experiments. Testing of several commercial sensors using infrastructure available at Idaho National Laboratory was performed to benchmark currently available sensors as well as the test facilities. Finally, a strategy for developing sensors for more extreme environments is presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Bayesian Calibration of Nuclear Graphite Property Models Accounting for Model Inadequacy and Impacts on Component Performance

Nuclear-grade structural graphite is extensively utilized in the core designs of various advanced nuclear reactors. In the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, including nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity requires accurate models of graphite's thermomechanical response. This report documents the Bayesian calibration of thermomechanical properties for nuclear-grade graphite and their application to graphite component modeling and simulation using the Grizzly code. As part of this work, uncertainty-quantified models were developed for the elastic modulus, coefficient of thermal expansion, irradiation-induced dimensional change, and irradiation-induced creep for graphite grades IG-110, NBG-18, NBG-17, PCEA, and 2114. Using a hierarchical Bayesian approach, multiple experimental data sources were combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due to inadequacies in the model and the inherent spread in the experimental data were quantified for three different models. These uncertainty-quantified models, with a model-form correction, were subsequently applied to a coupled-physics simulation of representative graphite components, revealing that the uncertainties have a large impact on the components' deformation.

36 - MATERIALS SCIENCE↗

DOE OSTI2024

INSTRUMENTATION FOR IN-CORE REAL-TIME MECHANICAL TESTING OF STRUCTURAL MATERIALS (INCREASE) PROJECT

Idaho National Laboratory (INL), in collaboration with the Electric Power Research Institute (EPRI), Nuclear Regulatory Commission, French Atomic and Alternative Energies Commission (CEA), Joint Research Centre, Nuclear Research and Consultancy Group, and Research Center Rez, is the operating agent of the In-Core Real-Time Mechanical Testing of Structural Materials (INCREASE) joint experimental program (JEEP) project that operates within the Nuclear Energy Agency (NEA)’s Framework for Irradiation Experiments (FIDES-II) program. The first objective of the INCREASE project is to design a shared capsule that can house a variety of in-core mechanical testing instrumentation for enabling smart irradiation experiments. The second objective is to collect in core stress relaxation data pertaining to high priority stainless steel (SS) materials under light water reactor conditions with target temperature of 340°C +/-20°C and a minimum neutron damage of 2 displacement per atom (dpa). The INCREASE project will be demonstrated in the Massachusetts Institute of Technology Nuclear Research Reactor (MITR).

36 MATERIALS SCIENCE↗

DOE OSTI2026

Electric-field-assisted-sintering of rare-earth oxide dispersion strengthened Fe-Cr-Mo alloys

Oxide dispersion-strengthened (ODS) alloys are widely recognized for their exceptional high-temperature strength, creep resistance, and radiation tolerance, making them indispensable for advanced nuclear reactors, aerospace, and energy systems. Achieving a fine and stable dispersion of oxide nanoparticles is critical, as these particles act as strong barriers to dislocation motion and effective sinks for irradiation-induced defects, ensuring structural integrity under extreme conditions. Here, in this study, Fe–Cr–Mo-based ODS alloys were fabricated via mechanical alloying and consolidated using electric-field-assisted sintering (EFAS) with additions of Y 2 O 3 , La 2 O 3 , and CeO 2 . EFAS processing produced ultrafine-grained microstructures (average grain size <1 μm) with uniformly distributed oxide clusters (2–4 nm). Atom probe tomography revealed that La 2 O 3 -containing alloys exhibited the highest nanoparticle number density, resulting in superior tensile strength compared to yttria- and ceria-bearing counterparts. The combined effect of grain refinement and rare-earth oxide dispersion significantly enhanced mechanical performance, demonstrating the potential of EFAS for developing high-strength ferritic alloys for demanding environments such as nuclear systems.

36 - MATERIALS SCIENCE↗

DOE OSTI2021

Transmission of Images on High-Temperature Nuclear-Grade Metallic Pipe with Ultrasonic Elastic Waves

Transmission of information using elastic ultrasonic waves on existing metallic pipes provides an alternative communication option for a nuclear facility. The advantages of this approach consist of transmitting information through barriers, such as the containment building wall, with minimal modification of the existing hardware. Because bit rates on the order of kilobits per second are achievable, relatively large volumes of data, such as images, can be transmitted. A viable candidate for an ultrasonic communication channel is a stainless steel pipe of the chemical volume control system (CVCS) that penetrates through the reactor containment building wall through a sealed tunnel. To study ultrasonic communication under simulated nuclear facility conditions of high temperature, a test article was developed by installing heating tapes, temperature controllers, and thermal insulation on a laboratory CVCS-like stainless steel pipe. High temperature and radiation-resilient lithium niobate ultrasonic transducers were utilized for information transmission on the heated pipe. The amplitude shift keying (ASK) digital communication protocol was developed and implemented in a GNU Radio software-defined radio environment. A root-raised-cosine filter was introduced to suppress ultrasonic transducer ringing and thus reduce inter-symbol interference. This resulted in the enhancement of the data transmission bit rate compared to information encoding with square pulses. Demonstrations of communication at high temperature included transmission of a 90-KB image at the bit rate of 10 Kbps with a bit error rate of 10 -3 across a 6-ft-long straight pipe heated up to 230 degrees C. Additional preliminary studies were conducted to evaluate ultrasonic communication system resilience to environmental degradation and damage.

42 ENGINEERING↗

DOE OSTI2026

Irradiation of UC1+x kernels using the MiniFuel vehicle: Microstructure, phase analysis, and initial post-irradiation examination

Uranium carbide is a candidate fuel form for a wide range of advanced reactors, including larger Generation IV reactors as well as small modular reactors and microreactors. However, its commercial deployment timeline faces challenges via traditional qualification approaches. To address this issue, an accelerated fission rate irradiation test was performed to collect basic fuel performance data to inform fuel performance models and potential future integral tests. Hyperstoichiometric UC (UC1+x) kernels were irradiated in the High Flux Isotope Reactor using the MiniFuel irradiation vehicle. The test matrix spanned two temperature regimes (700 °C and 800 °C) and burnup levels (1.8 % FIMA and 2.8 % FIMA). Between 21 and 63 kernels were tested at each unique temperature and burnup condition. As-fabricated microstructural analysis revealed a multiphase composition with UC, UC2, UC2−y, and U-C-O bearing phases for the irradiated kernels. Following irradiation, fission gas release, swelling, and microstructures were analyzed. Measured fission gas release was below 5 % for all irradiation conditions, reaching a maximum at the highest temperature and burnup condition. A binary swelling response was observed; the lower burnup and temperature conditions resulted in negligible swelling, but the higher burnup and temperature conditions produced significant anisotropic swelling and densification in a subset of kernels. The basic microstructural exams of kernels following irradiation were not capable of showing a correlation between kernels that exhibited excessive swelling and those that did not. Characterization of a subset of samples using the Advanced Photon Source and more detailed microstructural examination of unirradiated kernels revealed that a subset of kernels contained very high UC2 phase fractions. The anomalous swelling response is hypothesized to have been driven by this chemical variation. The results of this irradiation highlight the potential of accelerated fission rate irradiation testing to explore such behaviors and inform the development of fuel specifications.

Adorno Lopes, Denise [ORNL] (ORCID:000900023705987↗

DOE OSTI2021

Irradiation-enhanced diffusion and diffusion-limited creep in U 3 Si 2

U 3 Si 2 is an advanced fuel candidate due to its relatively high fissile density and attractive thermal properties. Compared to standard UO 2 fuel, there are significant data gaps for the thermophysical and thermomechanical properties of U 3 Si 2 . Point defect concentrations and mobilities under irradiation govern a number of important fuel performance properties, such as creep and fission gas release. In this work, we utilized density functional theory (DFT) data to inform a cluster dynamics framework to predict point defect concentrations in U 3 Si 2 under irradiation. Molecular dynamics (MD) simulations were used to examine the contribution of atomic mixing during ballistic cascades to diffusion, as well as the diffusivity of U and Si at grain boundaries. These atomic scale models for diffusivity were then used to inform a creep model based on bulk (Nabarro-Herring) and grain boundary (Coble) diffusional creep, and climb-limited dislocation creep. The model compares well against available experimental data and has been implemented in the BISON fuel performance code. Finally, a demonstration case using simple power profiles has been carried out, showing that negligible creep occurs due to the low temperatures experienced by U 3 Si 2 in-reactor, a consequence of its high thermal conductivity.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Considerations of Radiation-Hardened Electronics for Alpha Detectors in Molten Salt Reactors

Along with advanced generations of reactors quickly becoming reality, the need for instrumentation to provide reliable information for their safety and operation is also becoming relevant. Instrumentation-wise, molten salt reactors (MSRs) represent an especially challenging case in which detectors must survive extreme temperatures, high amounts of radiation, and a highly corrosive coolant. Adding to the complexity, tight material control and accounting must be maintained with any special nuclear material (SNM), a practice made more difficult by the nature of a loop of flowing fuel. Alpha spectroscopy offers a unique window into investigating the isotopic concentrations of actinides within just such a molten salt environment. The characteristic α emissions of specific actinide isotopes in the salt enable quantification of their concentrations. Semiconductor devices based on wide bandgap materials such as silicon carbide and gallium oxide can withstand the extreme temperatures within MSRs and offer good chemical stability with the corrosive salt. Collaborators at The Ohio State University are fabricating and testing a β gallium oxide α particle sensor that could identify actinide concentrations within the fuel salt to help improve the material control and accounting required for complicated system inherent to MSRs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Proxy quality control of biomass particles using thermogravimetric analysis and Gaussian process regression models

Abstract The temperature experienced by reactants during preparation in a reactor is a key component in determining the yield and homogeneity of usable chemical products such as biomass particles. Thermocouples with sensors can be used to monitor spatial temperature gradients within reactors but these sensors are often too expensive and/or invasive. The present work proposes a strategy to identify optimal machine learning models to infer the maximum effective temperature experienced by particles during oxidative biomass torrefaction using key thermochemical combustion parameters. The maximum rate of weight loss, the corresponding temperature, and fixed carbon content on a dry‐ash‐free basis are used as literature‐based predictor variables obtained from thermogravimetric analysis. The evaluation of 24 machine‐learning models using the standard tenfold cross‐validation method suggests that the exponential Gaussian process regression (GPR) model is the most effective, followed by other GPR models. These high‐performing GPR models were also utilized to predict the effective preparation temperature distribution of reactor‐produced biomass particles under eight conditions of varying residence time and air‐to‐biomass ratio. The effective preparation temperature and residence time of individual biomass particles were then encoded into the torrefaction severity factor and used to estimate the energy yield of the reactor output as a novel quality control method. © 2023 The Authors. Biofuels, Bioproducts and Biorefining published by Society of Industrial Chemistry and John Wiley & Sons Ltd.

09 BIOMASS FUELS↗

DOE OSTI2026

Methyl formate oxidation kinetics up to 100 atm

Methyl formate (MF, CH3OCHO), the simplest ester, is a representative oxygenated fuel with high oxygen content, and low sooting tendency. However, its oxidation behavior under high-pressure and intermediate-temperature conditions remains insufficiently understood, especially where low-temperature peroxy radical chemistry, methanol chemistry, and pressure-dependent reaction pathways play a critical role. In this study, MF oxidation experiments were conducted in the Princeton supercritical-pressure jet-stirred reactor (SP-JSR) at 20 and 100 atm over the temperature range of 400–950 K under both fuel-lean and fuel-rich conditions. Based on the experimental results, an updated HP-Mech was developed by incorporating previous MF sub-mechanisms, expanded low-temperature peroxy pathways, and evaluated pressure-dependent decomposition kinetics. The newly updated HP-Mech shows greatly improved performance in predicting the onset temperature, the key intermediate species fractions, methanol formation, and the progression of MF oxidation across all the experimental conditions. Path flux analysis indicates that MF consumption at the onset stage is dominated by H-abstraction at the methyl site, forming CH2OCHO radicals that lead to the formation and isomerization of O2CH2OCHO, driving low-temperature chain propagation. Moreover, H-abstraction at the formate site forms CH3OCO radicals that preferentially decompose to CH3, initiating the methanol formation pathway linked to CH3O2 and HO2 chemistry. At the same time, HO2 formation is strongly coupled to MF oxidation through multiple MF-derived radical pathways. HCO originates from MF oxidation and acts as a key coupling species linking fuel consumption to HO2 buildup, especially under high-pressure and intermediate-temperature conditions. In addition to this dominant channel, supplementary HO2 formation pathways involving CH3, CH3O, CH2OH, and CH3O2 reacting with O2 further connect methanol chemistry and oxygenated radical chemistry to the HO2 pool, indicating the central role of HO2 in governing MF oxidation. Sensitivity analysis identifies MF with OH/HO2/CH3O2 reactions and the HO2/H2O2/OH sequence as the key factors controlling reactivity in the high-pressure and intermediate-temperature regime. MF directly reacts with OH/HO2/CH3O2 to consume the fuel and produce reactive radicals like CH2OCHO and CH3OCO that undergo subsequent oxidation pathways. Moreover, HO2 recombination suppresses oxidation at lower temperatures, while thermal decomposition of H2O2 accelerates OH production and promotes fuel consumption as temperature increases. The direct formation of active OH from HO2 radicals further completes the mechanism, improving its prediction especially during the oxidation onset stage.

Low-temperature Chemistry↗

DOE OSTI2023

Fuel Flow Modeling under Thermal Fluidics Considerations within Operational Domains of Molten Salt Reactors

Molten Salt Reactors (MSRs) offer significant versatility supported by their design flexibility and safety advantages due to high temperatures, design customization capabilities, strong negative reactivity feedback effects, and salt chemistry characteristics. Different control schedules and different mass flow rates in the MSR primary systems impact neutronics and thermal hydraulics coupling. The result is two-fold. First, it leads to adaptability in various applications when the customization of a MSR unit is desired. Second, it calls for the quantification of dynamics and safety characteristics to assess the operational domain and make sure reactor stability and inherent safety characteristics are maintained. This paper provides an in-depth transient analysis of the operational implications of MSRs having heat-generating fuel and heat-transporting salt mixed forming liquid fuel salts contained within primary systems. A coupling model was developed to simulate fuel flow in molten salt reactors. A zero-dimensional reactor kinetics model was used with a one-dimensional heat transfer model in the reactor core. The temperature reactivity feedbacks of the fuel salt resulting from the thermal-hydraulics model were used in the reactor kinetics model to complete the coupled code. The model was applied to simulate the Molten Salt Breeder Reactor (MSBR) response at steady state and transients. The developed model was shown to be a suitable tool for the dynamic analysis of molten salt reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Evaluations of Silicon Carbide Temperature Monitors

The effect of irradiation on materials properties is an important field of study for materials usage in both fission and fusion systems for energy production. Neutron flux and energy spectrums are well understood; however, the irradiation temperature can be more difficult to determine. Since the early 1960s, Silicon Carbide (SiC) has been used as a passive post-irradiation temperature monitor because the irradiation defects anneal out above the irradiation temperature. Irradiation temperature is determined by measuring a property change after isochronal annealing or during a continuously monitored annealing process. There are many properties that may be measured including electrical resistivity, bulk density, dimensions, thermal diffusivity, or lattice spacing. Electrical resistivity is accepted as a robust measurement technique; however, such method is time-consuming since the steps involved must be performed in a serial manner. The use of thermal expansion from continuous dilatometry is an automated process requiring minimal setup time. As part of a Nuclear Science User Facilities (NSUF) project, low dose silicon carbide monitors were irradiated in the BR2 material test reactor at SCK, Belgium, and were then evaluated at the Idaho National Laboratory (INL) High Temperature Test Laboratory (HTTL) to determine their peak temperature achieved during irradiation. The technical significance of this work was that the monitors were irradiated to a dose that was significantly less than recommended in published literature. This paper will discuss the evaluation processes available at HTTL and the performance of the low dose silicon carbide temperature monitors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Evaporator Temperature Transient Testing of a High-Performance Sodium Filled Heat Pipe

Heat pipes are two-phase heat transfer devices that enable passive removal of heat from the reactor core to the power conversion system in heat pipe-cooled microreactor designs. Experimental investigations of heat pipe transients are needed for technology demonstration, verification and validation of numerical codes, and the establishment of regulatory requirements. The Single Primary Heat Extraction and Removal Emulator (SPHERE) facility at Idaho National Laboratory (INL) serves as a platform for evaluating the dynamic response of high-temperature heat pipes under a variety of operating conditions. The present work details the experimental investigation of a high-performance, defined as over 2 kW sodium heat pipe subjected to rapid input power fluctuations induced by sudden changes in the evaporator temperature setpoint. In addition, the heat pipe was subjected to an asymmetrical heat load where a subset of heaters operated at 30% and 70% below their nominal power. These experimental conditions were chosen to simulate thermal and operational stresses expected to be encountered in microreactors to provide data on heat pipe behavior during such important transient events. Key data and performance metrics, including time series of temperatures and strains, axial temperature profiles, thermal response times, and heat transfer capabilities, the thermal output over thermal input, were reported and discussed. The results highlight the resilience of heat pipes, revealing their potential to maintain thermal stability and efficiency under varying power loads. Lastly, the paper concludes with a discussion on the significance of the results and their implications for future research.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Assessment of irradiation embrittlement effect on fatigue life of a pressurized-water reactor pressure vessel using the fracture toughness master curve approach

The reactor pressure vessel (RPV) is a critical structural component in pressurized-water reactors, and it is designed to withstand extreme conditions, such as high pressures, elevated temperatures, and prolonged radiation exposure. Ensuring RPV integrity is essential for the safe and reliable long-term operation of nuclear power plants, especially as aging mechanisms such as fatigue and irradiation embrittlement pose increased risks. Fatigue, caused by cyclic thermal and mechanical loading, can lead to crack initiation in localized high-stress regions. Simultaneously, neutron irradiation, particularly in the beltline region, progressively reduces fracture toughness, increasing susceptibility to brittle fracture. These combined effects of fatigue and irradiation embrittlement potentially impact the RPV structural integrity, necessitating fitness-for-service assessments. This study applies the fracture toughness master curve approach to evaluate the impact of irradiation embrittlement on RPV fatigue life. A coupled thermo-mechanical stress analysis identifies critical stress locations under normal service transients, pinpointing regions most vulnerable to fatigue crack initiation and growth. Stress intensity factors for postulated flaws at these locations are calculated, enabling an assessment of fatigue life under irradiated and unirradiated conditions. The results indicate that neutron irradiation embrittlement accelerates the conditions in which a critical crack can form and lead to failure, particularly at lower temperatures. The failure occurs where reduced fracture toughness limits the material’s resistance to crack growth. Axial cracks at nozzle corners are the most life limiting without irradiation, while circumferential cracks demonstrate longer fatigue lives. The findings highlight the importance of incorporating irradiation effects into fatigue life predictions to ensure the long-term structural integrity of RPVs.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Zigzag flow reactor for weekly thermochemical energy storage

This paper describes theoretical models and experimental performance of a novel Zigzag Flow Reactor (ZFR) for weekly thermochemical energy storage. The ZFR reduces redox-active metal oxide (MO x ) particles at high temperature (up to ~1100 °C) under inert gas sweep. A physical model demonstrates the approach to process equilibrium by minimizing the associated exergy destruction in a finite number of reaction steps, establishing the thermodynamic requirements for a practical reactor. The model results show several cost-relevant parameter tradeoffs, and the tradeoff analysis implies a cost-optimized set of boundary conditions. Numerical models and prototypes show that the ZFR enables significant gas phase homogenization while simultaneously enabling a customizable MO x residence time in the reactor, both key requirements for approaching an equilibrium process. A scaling model demonstrates the simplicity and affordability of sizing the ZFR to grid-scale levels, with fabrication costs at least five times lower than previously proposed scalable reactor concepts. As a result, a laboratory ZFR prototype achieved an energy storage density of ~90 Wh/kg with CaAl 0.2 Mn 0.8 O 3-δ as the MO x , at temperatures of ~850 °C in >10 h of total runtime.

Thermochemical energy storage↗

DOE OSTI2023

Performance Benchmark of Commercial and Developmental Fission Chambers in Elevated Temperatures

This report documents the testing of two in-core fission chamber technologies for high-temperature irradiation environments. This work is in collaboration with the French Alternative Energies and Atomic Energy Commission (CEA). The fission chamber evaluated by Idaho National Laboratory is the micro-pocket fission detector (MPFD). The fission chamber evaluated by the CEA are the 3 mm miniaturized fission chamber and the 7 mm high-temperature fission chamber. Demonstrations of the MPFD were performed at the Neutron Radiography Facility and the Massachusetts Institute of Technology Reactor. Demonstrations of the CEA fission chambers were performed at the Ohio State University Research Reactor. All demonstrations were conducted with a heated experiment rig up to 850°C.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Structural Design and Modeling of MARVEL Primary Coolant System Using the ASME Section III, Division 5, Code

This paper presents the structural design and supporting analysis for the Microreactor Applications Research Validation and Evaluation (MARVEL) primary coolant system (PCS) using the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code Section III, Division 5, rules. MARVEL is a liquid metal–cooled microreactor intended to provide experimental capabilities for the rapid testing and development of microreactor technologies. The PCS utilizes high-temperature sodium-potassium liquid metal as the primary coolant and operates at a design temperature of 570°C, necessitating the consideration of creep-related failure mechanisms. The base metal for the PCS is 316H stainless steel, and the weldments are made with a 16-8-2 filler. The design approach incorporates the current base code rules along with ASME code cases N-924, N-861, and N-862 to address primary load, ratcheting, and creep-fatigue evaluations, respectively. The reactor’s operation involves complex thermal and mechanical interactions due to natural convective flow and differential thermal expansion between components. In conclusion, this paper discusses the structural engineering challenges encountered, such as managing thermal stresses in the distribution plenum and guard vessel, and outlines the strategies implemented to meet the code requirements, including design modifications and operational constraints.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2025

Cold Spray Cobalt Magnetostrictive Electromagnetic Acoustic Transducers for High Temperature Structure Monitoring

The Department of Energy’s Advanced Sensors and Instrumentation program seeks to develop and qualify advanced sensors for the nuclear industry. Reliable high temperature and high radiation sensors for detection and characterization of structural flaws in pipes, vessels, and structurally critical components is a weakness for both conventional light water reactors with coolant T-hot approaching 350oC, and for advanced reactors with T-hot temperatures in excess of 500 to 800oC. Magnetostrictive Electromagnetic Acoustic Transducers using a cold spray cobalt coating have been proposed as a sensor design that can withstand these kinds of temperatures and radiation levels to serve as online sensors to detect flaws before cracks, pits, or erosion/corrosion flaws progress to through-wall failures. This report tests cold spray cobalt as part of a magnetostrictive EMAT for high temperature service. Cobalt is known to have strong magnetostrictive properties however the effect of cold spray application is not well studied. This program was surprised to discover that cold sprayed cobalt exhibited little or no magnetostrictive behavior until it was thermally annealed. Following annealing to 650oC however, cold spray cobalt did exhibit a magnetostrictive response. Work to date prior to this milestone report publication showed that magnetostrictive EMAT was successfully tested to 400oC with an alnico permanent magnet. The program plans to extend testing with an electromagnet to higher temperatures. This follow-on work will be reported under subsequent publications or as a revision to this report.

Glass, Samuel W.↗