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DOE OSTI2024

Optimality and Noise Resilience of Critical Quantum Sensing

We compare critical quantum sensing to passive quantum strategies to perform frequency estimation, in the case of single-mode quadratic Hamiltonians. We show that, while in the unitary case both strategies achieve precision scaling quadratic with the number of photons, in the presence of dissipation this is true only for critical strategies. We also establish that working at the exceptional point or beyond threshold provides suboptimal performance. This critical enhancement is due to the emergence of a transient regime in the open critical dynamics, and is invariant to temperature changes. When considering both time and system size as resources, for both strategies the precision scales linearly with the product of the total time and the number of photons, in accordance with fundamental bounds. However, we show that critical protocols outperform optimal passive strategies if preparation and measurement times are not negligible. Our results are applicable to a broad variety of critical sensors whose phenomenology can be reduced to that of a single-mode quadratic Hamiltonian, including systems described by finite-component and fully connected models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Nontrivial critical behavior at magnetic transitions: A case study of Sm 7 ⁢Pd 3

We present a comprehensive analysis of the critical behavior of Sm 7 ⁢Pd 3 in the vicinity of its second-order magnetoelastic transition at 𝑇 c =173 K. The critical exponents (CEs) 𝛽 and 𝛾, determined using both the standard convergence procedure and the average normalized slope (ANS) method, diverge at 𝑇 c –-a characteristic typically associated with first-order transitions. Notably, none of the established universality classes satisfactorily describe the critical behavior of Sm 7 ⁢Pd 3 , and we discuss the possible origins of this deviation in the context of the strong spin-lattice coupling intrinsic to the sample. We emphasize the importance of accurately selecting the critical temperature and magnetic field ranges to ensure robust critical behavior analysis, and propose a quantitative approach to assess the reliability of the extracted CEs. Additionally, we demonstrate that in the ANS method, the critical exponents 𝛽 and 𝛾 should be calculated separately using data for 𝑇 ⩽ 𝑇 c and 𝑇 ⩾ 𝑇 c , respectively. In conclusion, our findings underscore the need for a revised theoretical framework to accurately describe second-order magnetoelastic transitions.

Ferrimagnets↗

DOE OSTI2023

Review—Effects of Solution and Alloy Composition on Critical Crevice Temperature

Critical temperature for localized corrosion can be a good design parameter because localized corrosion is not likely to occur below that temperature. The critical temperature depends on alloy composition, microstructure, and environment chemistry (including its redox potential). This paper reviews the literature on critical temperature for localized corrosion, expressed either as Critical Pitting Temperature (CPT) or Critical Crevice Temperature (CCT). A history of various testing methods is presented. Different approaches for modeling the temperature of transition to active pit growth are reviewed, including probabilistic aspects of critical temperature. A semi-empirical, electrolyte-based, model is described that can be useful in predicting CCT in service environments that differ from standard laboratory test environments. The model predictions are compared to experimental data for various alloys. The effect of solvent on CCT/CPT is described briefly and future avenues of research are recommended.

02 PETROLEUM↗

DOE OSTI2022

Criticality in the Shallow-to-Deep Transition of Simulated Tropical Marine Convection

Idealized simulations of tropical, marine convection depict shallow, nonprecipitating cumuli located beneath the 0°C level transitioning into cumulonimbi that reach up to 12 km and higher. The timing of the transition was only weakly related to environmental stability, and 13 of the 15 simulations run with 5 different lapse-rate profiles had rain develop at nearly the same time after model start. The key quantity that apparently controlled deep convective formation was vertical acceleration inside cloudy updrafts between cloud base and the 0°C level. Below a critical value of updraft vertical acceleration, little rainfall occurred. Just as the domain-mean updraft acceleration reached the critical value, the first convection quickly grew to past 12 km altitude. Then, as acceleration increased above the critical value, rain rate averaged in the model domain increased quickly over about a 3-h-long period. The specific value of the critical updraft acceleration depended on how updrafts were defined and in what layer the acceleration was averaged; however, regardless of how criticality was defined, a robust relationship between domain-mean updraft vertical acceleration and rain rate occurred. Positive acceleration of updrafts below the 0°C level was present below 2.75 km and was largest in the 500 m above cloud base. However, the maximum difference between updraft and environmental temperatures occurred between 2 and 3 km. The domain-mean Archimedean buoyancy of updrafts relative to some reference state was a poor predictor for domain-mean rain rate. In conclusion, the exact value of the critical updraft acceleration likely depends on numerous other factors that were not investigated.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Synchronization of Alternative Models in a Supermodel and the Learning of Critical Behavior

“Supermodeling” climate by allowing different models to assimilate data from one another in run time has been shown to give results superior to those of any one model and superior to any weighted average of model outputs. The only free parameters, connection strengths between corresponding variables in each pair of models, are determined using some form of machine learning. It is demonstrated that supermodeling succeeds because near critical states, interscale interactions are important but unresolved processes cannot be effectively represented diagnostically in any single parameterization scheme. In two examples, a pair of toy quasigeostrophic (QG) channel models of the midlatitudes and a pair of ECHAM5 models of the tropical Pacific atmosphere with a common ocean, supermodels dynamically combine parameterization schemes so as to capture criticality, associated critical structures, and the supporting scale interactions. The QG supermodeling scheme extends a previous configuration in which two such models synchronize with intermodel connections only between medium-scale components of the flow; here the connections are trained against a third “real” model. Intermittent blocking patterns characterize the critical behavior thus obtained, even where such patterns are missing in the constituent models. In the ECHAM-based climate supermodel, the corresponding critical structure is the single ITCZ pattern, a pattern that occurs in neither of the constituent models. In conclusion, for supermodels of both types, power spectra indicate enhanced interscale interactions in frequency or energy ranges of physical interest, in agreement with observed data, and supporting a generalized form of the self-organized criticality hypothesis.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Uranium–Molybdenum Alloy Critical Experiments for the Design of the Health Physics Research Reactor

Clean critical experiments with a uranium-molybdenum alloy (average of 10.1616 wt. % Mo with a density of 17.08 g/cm 3 ) were performed at the Oak Ridge Critical Experiments Facility in 1961 to support the design of the Health Physics Research Reactor (HPRR). The HPRR was similar to the Godiva burst reactor at Los Alamos National Laboratory and was designed to produce 50 microseconds burst of 10 17 fission pulses of radiation for dosimetry measurements, initially in support of the determination of the doses from the nuclear detonations in Japan during World War II. These experiments reported here were used to verify the calculational methods used to design the HPRR. These delayed critical measurements were:1) a solid unreflected and unmoderated 8-in.-dimeter U-Mo cylinder, 2) an unmoderated and unreflected annulus with 8-in.-outside diameter, 2-in.-inside diameter cylinder with a central void, 3) an unmoderated and unreflected annulus with 8-in.-outside diameter, 2-in.-inside diameter cylinder with a central void filled with stainless steel, 4) Same as 3) but with 3-in-thick Plexiglas reflector on top with and without cadmium between the reflector and the U-Mo alloy assembly with steel in the center, and 5) an unmoderated and unreflected annulus which was a modification of the second but with the lower 5 inches of the central hole enlarged to 3.5 in. with various reflector conditions. The reflector conditions were: 1-in.-thick Plexiglas on all outer surfaces-void in the center; 1-in.-thick Plexiglas on all outer surfaces-Plexiglas in the center; 2-in.- thick Plexiglas on radial surface-void in the center; 6-in.-thick Plexiglas on the bottom only-Plexiglas in the center; and 6-in.-thick Plexiglas on bottom, 1-in.-thick on top and on the lower 8.25-cm.-section of the radial surface-void in the center. For some of these reflector conditions 0.025-cm.thick cadmium was located between the reflector and the U-Mo alloy. The uranium contained 93.17 wt. % 235 U. Reflection was a safety concern for this unmoderated and unreflected reactor and reduction of reflection effects was also investigated by insertion of neutron absorber around the U-Mo alloy. The stainless steel 304 contained 18% nickel and 8% chromium and the rest iron. The reflector material was a methacrylate plastic (Plexiglas) containing 5.8 x 10 22 atoms/cm 3 of hydrogen and 3.6 x 10 22 atoms/cm 3 of carbon with a density of 1.20 g/cm 3 . The purpose of this report is to document the experimental information for the measurements performed so that at a later date researchers could perform the required uncertainty and calculational analyses and documentation to use these data for an International Nuclear Criticality Safety Benchmark Program (ICSBEP) or a EURATON Nuclear Energy Agency (NEA) benchmark. The data from the experiments described should be acceptable for use as criticality safety benchmark experiments for the ICSBEP and the NEA nuclear criticality safety benchmark program, once the uncertainty analysis is completed. Based on previous ICSBEP benchmarks with this enriched uranium metal at ORCEF, the uncertainties in k eff could be as low as ±0.0002 for some configurations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Theoretical Studies of Polar Systems near Ferroelectrics Quantum Critical Points (Final Report)

The PI has studied emergent quantum phases near polar quantum critical points. A first challenge was to develop a theoretical description of the observation that many polar materials undergo classical first-order transitions while displaying quantum criticality. The possibility of novel metallic states near polar quantum critical points was then studied; identification and characterization of a non-Fermi liquid phase was made in a multiband system. In dilute quantum critical polar metals, electronic coupling to polar energy fluctuations was shown to result in attractive electron-electron interactions and to superconductivity. A spin-phonon resonance measurement in applied magnetic field was proposed to determine the magnitude of spin-orbit mediated electron-phonon coupling; furthermore in the polar phase new field-induced phonon collective modes were identified with specific signatures for experiment. In order to keep current, the PI has also worked on other types of strongly correlated problems. With experimental groups, she has developed phenomenologies to identify and explain observed dynamical critical behaviors. The PI has studied the interplay of topology, fractionalization and deconfinement in a minimalist spin model. An emergent phase transition in a 1 + 1 frustrated spin nanotube has also been identified and characterized. The PI has also begun exploring criticality out of equilibrium, characterizing rich dynamical phases associated with photoinduced polar transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Strategic Plan: Decrease Critical Minerals Waste Through Enabling Advanced Manufacturing Techniques

In this report we developed a strategic outlook derived from previous findings by our Phase-2 Scorecard Report and the Critical Mineral Evaluation Report. In addition, Phase 2 Materials Scorecards have been developed in 2022 to provide a detailed justification and traceability for the adoption of additively manufactured structural materials and ceramics for nuclear deployment. The report provides a strategic vision to harvest the benefits of reduced material and energy demands by enhanced deployment of advanced manufacturing in nuclear technology. The objective of this report is to address the needs for imminent experimental/computational studies to optimize the deployment of advanced manufacturing for its energy-, cost-, and critical materials saving potentials. We display what further actions are needed to minimize supply risks of critical minerals and to lower the economic vulnerability when implementing the additional nuclear capacity projected by 2050, in support of the U.S. goal of net-zero carbon emission. The critical minerals essential for Gen-IV nuclear technology show either low disruption potential (supply risks) combined with high economic vulnerability, such as: copper, nickel, and chromium; or low supply risks combined with medium economic vulnerability, such as: manganese, molybdenum, tungsten, vanadium, tantalum, and zirconium. Enhancements in quality and yield of critical mineral recycling and the recovery of critical minerals from solid and industrial waste streams are needed to enhance supply security for stainless-steel production and to shift the time to scarcity for society to future years.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Critical Infrastructure Classification via CNN-based Modeling and Image Analysis

With recent advances in the fields of satellite imagery and machine learning we now have the ability to develop explainable deep learning models that enhance critical infrastructure analysis. Funded through Idaho National Laboratory’s (INL) Laboratory Directed Research and Development (LDRD) office we are in the process of developing a deep learning model capable of identifying critical infrastructure facilities and embedded features within those facilities. Utilizing current limit of practice techniques in the machine learning areas of explainability and transfer learning our model, once complete, will have the capacity to be used on multiple different imagery data sets and produce results that not only classify critical infrastructure facilities, but also explain why a critical infrastructure facility was classified as a certain type of facility. These advancements eliminate the ‘black box’ approach deep learning models have had in the past, where a user will have to trust the conclusion of a model without understanding what reasoning when into the model’s classification process. They also expand a model’s usefulness, traditionally a deep learning model will have to use the same data set it was originally trained on. Given the long training times of deep learning models this is impractical in a number of scenarios. By utilizing transfer learning advancements, we are eliminating the need to train our model on the same data set it is then run on to classify critical infrastructure facilities. We are also enabling the analysis and classification of data sets that are potentially too small to be divided into a training and testing data set. Once completed this model can provide a foundation to enhanced critical infrastructure analysis, dependency analysis, and potential disaster relief efforts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A Quenched Disorder in the Quantum-Critical Superconductor CeCoIn 5

Emergent inhomogeneous electronic phases in metallic quantum systems are crucial for understanding high- T c superconductivity and other novel quantum states. In particular, spin droplets introduced by nonmagnetic dopants in quantum-critical superconductors (QCSs) can lead to a novel magnetic state in superconducting phases. However, the role of disorders caused by nonmagnetic dopants in quantum-critical regimes and their precise relation with superconductivity remain unclear. Here, the systematic evolution of a strong correlation between superconductive intertwined electronic phases and antiferromagnetism in Cd-doped CeCoIn 5 is presented by measuring current–voltage characteristics under an external pressure. In the low-pressure coexisting regime where antiferromagnetic (AFM) and superconducting (SC) orders coexist, the critical current ( I c ) is gradually suppressed by the increasing magnetic field, as in conventional type-II superconductors. At pressures higher than the critical pressure where the AFM order disappears, I c remarkably shows a sudden spike near the irreversible magnetic field. In addition, at high pressures far from the critical pressure point, the peak effect is not suppressed, but remains robust over the whole superconducting region. These results indicate that magnetic islands are protected around dopant sites despite being suppressed by the increasingly correlated effects under pressure, providing a new perspective on the role of quenched disorders in QCSs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Evaluation of the critical behavior near ferromagnetic to paramagnetic phase transition in CrTe 1-x Se x alloys: An experimental study

For this study, we used the conventional solid-state reaction method to prepare stoichiometric samples of CrTe 1-x Se x , where 0 ≤ x ≤ 0.10, and investigated the structural and critical behavior of the prepared samples. Room temperature powder X-ray diffraction, along with Rietveld refinement, revealed the emergence of the NiAs structure with P6 3 /mmc (194) space group with increasing Se substitution. The high-temperature linear fit to inverse of the dc-susceptibility versus temperature for the mother sample resulted in an effective moment of 3.65μ B Cr with Curie-Weiss temperature near 335K, which is slightly higher than the Tc of ~332K obtained from the inflection point of magnetization versus temperature. Magnetization isotherms were employed to investigate the critical behavior of ferromagnetic CrTe 1-x Se x with 0.0 ≤ x ≤ 0.10 near their Curie temperatures (Tc). The magnetic behavior near Tc was found to follow 3D mean-field critical exponents with a second-order phase transition in all samples investigated. We fine-tuned the critical exponents (β, γ, and δ) using a combination of an iteration technique, the Kouvel-Fisher method, and modified Arrott plots. All samples follow a mean field behavior, with Tc ranging from 298 to 340K. The acquired values exhibit self-consistency, as indicated by the results from the Widom scaling relation. Furthermore, the magnetization isotherms exhibit a universal scaling behavior, providing additional credence to the calculated critical exponents.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Design Optimization of a Criticality Experiment for the Molten Chloride Reactor Experiment Facility

Neutronics simulations of Molten Chloride Fast Reactors have quantifiable biases that arise from nuclear data, modeling choices, or numerical methods. The multiphysics nature of molten salt reactors makes it challenging to disentangle neutronics modeling biases from biases originating from other physical phenomena. In comparison to a mock-up reactor, criticality experiments can specifically assess the neutronics modeling bias while limiting multiphysics effects. The criticality experiment must be neutronically representative of the full-scale reactor to be valuable. Here, in this paper, we describe the design of a criticality experiment to validate only the neutronics of TerraPower’s Molten Chloride Reactor Experiment (MCRE) and its criticality safety upset scenarios. The proposed experiment uses different chlorine-containing materials to maximize its similarity to the MCRE. The design process uses a constrained Bayesian optimization algorithm to investigate different objective functions that use covariance information for 35 Cl nuclear data. The experiments could reduce the nuclear data–induced uncertainty in k eff of the MCRE from 2161 to 886 pcm. They would also increase the upper subcritical limit of the MCRE criticality safety upset scenario from 0.94101 to 0.94476 when using the WHISPER analysis framework.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Nanoscale Critical Phenomena in a Complex Fluid Studied by X-ray Photon Correlation Spectroscopy.

The advent of high-speed x-ray photon correlation spectroscopy now allows the study of critical phenomena in fluids to much smaller length scales and over a wider range of temperatures than is possible with dynamic light scattering. We present an x-ray photon correlation spectroscopy study of critical fluctuation dynamics in a complex fluid typical of those used in liquid-liquid extraction (LLE) of ions,dodecane-DMDBTDMA with extracted aqueous Ce(NO 3 ) 3 . We observe good agreement with both staticand dynamic scaling without the need for significant noncritical background corrections. Critical exponents agree with 3D Ising values, and the fluctuation dynamics are described by simple exponential relaxation.The form of the dynamic master curve deviates somewhat from the Kawasaki result, with a more abrupt transition between the critical and noncritical asymptotic behavior. The concepts of critical phenomena thus provide a quantitative framework for understanding the structure and dynamics of LLE systems and a path forward to new LLE processes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Validation of MCNP Critical Benchmark Models of Moderated Highly Enriched Uranium Slabs

A new centralized repository of high-quality MCNP models of critical benchmark experiments is currently under development at Los Alamos National Laboratory (LANL). The benchmark experiments are described in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook, and the initial set of benchmark models are derived from the Whisper Suite provided with MCNP6.2. This effort is a collaboration among the Nuclear Criticality Safety, Nuclear Data, and Monte Carlo code development/application organizations at LANL. The goal is to build a single LANL benchmark collection that is up to date with the latest ICSBEP revision, has a formal review and revision process, is contained in an open-source repository, and utilizes new Python tools for improved input and output file review. This paper describes the validation of the models associated with HEU-MET-FAST-007, “Uranium Metal Slabs Moderated with Polyethylene, Plexiglas, and Teflon”. The Monte Carlo n-Particle (MCNP) models were compared to the second revision of HEU-MET-FAST-007. The experiment considered critical configurations of highly enriched uranium (HEU) metal slabs and various moderators in 43 unique cases. The slabs of uranium were separated by layers of moderating material, forming an assembly. The assembly was separated in two halves with one half placed on a stationary table and the other attached to a moveable table that could be raised and lowered via pulleys connected to the ceiling of the shielded room. To reach criticality, the two halves were brought together with a negligible gap between the assemblies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Experiments at Sandia to Measure the Effect of Temperature on Critical Systems

Estimation of the uncertainty in a critical experiment attributable to uncertainties in the measured experiment temperature is done by calculating the variation of the eigenvalue of a benchmark configuration as a function of temperature. In the low-enriched water-moderated critical experiments performed at Sandia, this is done by 1) estimating the effects of changing the water temperature while holding the UO 2 fuel temperature constant, 2) estimating the effects of changing the UO 2 temperature while holding the water temperature constant, and 3) combining the two results. This assumes that the two effects are separable. The results of such an analysis are nonintuitive and need experimental verification. Critical experiments are being planned at Sandia National Laboratories (Sandia) to measure the effect of temperature on critical systems and will serve to test the methods used in estimating the temperature effects in critical experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Experiments at Sandia to Measure the Effect of Temperature on Critical Systems [Slides]

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Delayed Critical Highly Enriched Uranium Metal Cylinders with Thin Graphite Top and Bottom Reflectors

Nine 7, 11, and 15 in. diam highly enriched uranium (HEU, 93.15 wt % 235 U) metal cylinders were assembled on the vertical assembly machine in the Oak Ridge Critical Experiments Facility (ORCEF) and had 1, 2, or 3 in. thick HLM graphite reflectors on the top and bottom. The experiments, which were performed between April 3, 1970, and February 18, 1971, used 23 operational days at ORCEF. Before those experiments were carried out, unreflected and unmoderated, graphite- and polyethylene-reflected, and polyethylene-moderated HEU metal cylinders had been assembled to obtain delayed criticality at ORCEF in the 1960s and reported by the International Criticality Safety Benchmark Evaluation Project (ICSBEP) at the Nuclear Energy Agency (NEA)*. The data from the nine critical experiments are acceptable for use as criticality safety benchmark experiments for the NEA’s ICSBEP once the uncertainty analysis is completed. Based on previous ICSBEP benchmarks with HEU metal at ORCEF, the uncertainties in k eff are expected to be as low as ±0.0004.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Criticality Experiments to Reduce Compensating Errors in Plutonium Nuclear Data

Compensating errors between nuclear data observables in a library can adversely impact application simulations. The primary goal of the EUCLID project (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) is to reduce compensating errors in nuclear data. A new criticality experiment, described in this work, was designed with the specific target nuclear data of 239 Pu fission, inelastic scattering, elastic scattering, capture, nu-bar, and prompt fission neutron spectrum (PFNS). This work will focus on the design and execution of the EUCLID experiment, performed on the Planet vertical lift critical assembly machine at the National Criticality Experiments Research Center (NCERC). The criticality experiment includes two different configurations with very different geometries: one is cube-like to minimize neutron leakage while the other is slab-like to maximize leakage. Having these two widely varying configurations allows the scattering sensitivities of 239 Pu to the neutron multiplication factor to be greatly changed while minimally impacting the other cross section sensitivities. Both configurations utilize the Pu ZPPR (Zero Power Physics Reactor) plates as fuel. The experiments were designed using a D-Optimality criteria, which is an optimization method minimizing the log-determinant of the adjusted nuclear data covariance for the target reactions. These experiments include not only inference of k eff , as done in all critical benchmark experiments, but several other responses as well, such as neutron multiplication measurements and reaction rate ratios. After analysis of the measured data is complete, adjustment of nuclear data will be performed to assess whether the new experimental data successfully reduced compensating errors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗