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Nuclear fusion powered Titan aircraft

This paper discusses a system for Titan exploration enabled by nuclear fusion power. Titan is one of the most interesting locations in the solar system with a thick atmosphere, surface oceans, under-ice oceans and complex terrain. This paper provides a conceptual design of a fusion-powered system to explore many parts of Titan and enable the use of high-power instruments. The design includes a fusion-powered orbital transfer vehicle and an electric Titan science aircraft. A Direct Fusion Drive (DFD) propulsive engine could bring a sizable spacecraft to Titan orbit in less than two years. A second fusion reactor, configured as a closed-loop power generator, would be used for an electric Titan science aircraft. Both reactors are based on the Princeton Field-Reversed Configuration (PFRC) concept which combines an FRC with a magnetic mirror. PFRC uses a novel radio-frequency plasma heating system and deuterium-helium-3 fuel. A lower temperature plasma flows around the closed-field FRC region removing the fusion products. In the DFD propulsive configuration, this secondary flow permits direct and variable thrust and exhaust velocity. The science aircraft would do a powered entry to Titan and then have the capability to fly anywhere on the moon at subsonic speeds. The DFD-powered transfer vehicle would allow the in-orbit transfer stage to change inclination as needed to cover different areas of the surface.

33 ADVANCED PROPULSION SYSTEMS↗

Composition and automated crystal orientation mapping of rapid solidification products in hypoeutectic Al-4 at.%Cu alloys

Rapid solidification can produce metastable phases and unusual microstructure modifications in multi-component alloys during additive manufacturing or laser beam welding. Composition and phase mapping by transmission electron microscopy have been used in this paper to characterize the morphologically distinct zones developing in hypoeutectic Al-4 at.% Cu alloy after pulsed laser melting for different crystal growth rate regimes. Deviations of the compositions of the alloy phases from equilibrium predictions and unique orientation relationships between the solidification transformation products have been determined. Specifically, for the columnar growth zone at solidification rates of 0.8 m s - 1 < v < v a = 1.8 m s - 1 , two distinct orientation relationships were established between the concomitantly forming non-equilibrium phases, supersaturated α-Al solid solution and the discontinuously distributed α-Al 2 Cu-based θ'-phase, which can be described as {110} θ ∥ {001} α , [001] θ ∥ [110] α and {001} θ ∥ {001} α , [100] θ ∥ [100] α . These orientation relationships permit formation of coherent interphase interfaces with low interfacial free energy. Finally, this endows a kinetic advantage to the thermodynamically less stable θ'-Al 2 Cu phase relative to the more stable equilibrium θ-Al 2 Cu phase during formation of the morphologically modified eutectic of the columnar growth zone grains, since repeated nucleation is required to establish the discontinuous distribution of θ'-Al 2 Cu phase.

36 MATERIALS SCIENCE↗

Quantifying and connecting atomic and crystallographic grain boundary structure using local environment representation and dimensionality reduction techniques

In this paper, the relationship between grain boundary crystallography and grain boundary atomic structure is examined, using [100] - symmetric tilt grain boundaries in nickel. The structural unit model is used as a benchmark to evaluate the atomic structure description capacities of an emerging structural descriptor, the local environment representation, which itself is a refinement of the Smooth Overlap of Atomic Positions (SOAP) descriptor. We show that the local environment representation encodes both the information of the structural unit model and additional information, such as distortion in the structural units and the arrangement of the structural units at the interface. The use of the local environment representation permits the use of a visualization tool known as SPRING to represent structural similarities between grain boundaries. With the SPRING representation, we produce objective evidence of a relationship between crystallography and atomic structure, at least for [100] - symmetric tilt grain boundaries.

36 MATERIALS SCIENCE↗

Interface velocity dependent solute trapping and phase selection during rapid solidification of laser melted hypo-eutectic Al-11at.%Cu alloy

Microstructure formation of a hypo-eutectic Al-11Cu (atom percent) alloy during solidification after laser melting has been studied by transmission electron microscopy (TEM). The evolution of the solid-liquid-interface velocity, V SL , during the solidification process has been determined from direct observation by in-situ TEM. This enabled correlating V SL with development of four distinct microstructure zones. Crystal growth mode transitions from planar to cellular, cellular to dendritic, dendritic to cellular, and cellular to planar, have been observed for the accelerating solid-liquid-interface. The transition from coupled two-phase growth to the single-phase growth occurred for V SL = V a = (0.80±0.05) m/s, where V a is the velocity of absolute stability, at the onset of banded morphology grain formation. The in-situ and post-mortem TEM uniquely permitted determination of the non-equilibrium solidus for the rapidly solidifying Al-11Cu alloy. Experimental evidence for solute clustering and chemical ordering tendencies at length scales on the order of ≤ 5nm has been detected in the single-phase regions of the banded grains. The structural features of the single-phase bands have been interpreted as signatures of ‘frozen in’ configurations present in the liquid boundary layer adjacent to the growing crystal, which has a width of about 3nm. Finally, the nano-scale spatiotemporal resolution experimental TEM studies performed here provided quantitative metrics, e.g. the solidification interface velocity dependent solute concentration of the α-Al phase and the near-atomic scale structure in the single-phase bands, that are uniquely suitable for comparison with theory and model predictions for solidification microstructure development in multicomponent alloys after laser melting.

36 MATERIALS SCIENCE↗

Differentiating the bonding states in calcium carbonate polymorphs by low-loss electron-energy-loss spectroscopy

Calcium carbonate is one of the important building components in organisms, especially the two most common polymorphs, calcite and aragonite. Here, to understand the difference in bonding state, the two polymorphs are characterized by valence (low-loss) electron energy loss spectroscopy. It is found that the difference in Ca M 23 edge originating from 3p to 3d states is consistent with the change of Ca-O bonds in the two studied polymorphs. Surprisingly, the measured Ca M 23 edge is in qualitative agreement with the calculated partial density of states (PDOS) of Ca-d states in contrast to their L edges (from 2p to 3d states) which are strongly influenced by atomic multiplet effect (spin-orbit coupling). This is because the atomic multiplet effect is much reduced for the Ca 3p orbital, which permits the corresponding Ca M 23 edge to be compared with the PDOS results. Our findings show insights that PDOS can potentially be used to interpret the M 23 edge of lighter 3d transition metals such as scandium, titanium, vanadium and chromium when such interpretation may not be achieved for their L edges.

36 MATERIALS SCIENCE↗

Mechanisms for high creep resistance in alumina forming austenitic (AFA) alloys

Castable alumina forming austenitic (AFA) alloys have demonstrated superior creep life and oxidation resistance at temperatures exceeding 800⁰C. Despite the success in the applicability of these alloys in extreme environments, there is a limited understanding of the deformation modes and the influence of each alloying element guiding the alloy design strategies that could further enhance the creep strength of these AFA alloys, particularly at temperatures at and above 900⁰C. In this study, we reveal the mechanism underpinning the superior creep performance of castable AFA alloys that involves suppressing primary carbide formation through minor compositional modification. This approach results in a three-fold increase in creep strength at 900⁰C and 50 MPa. Here, by employing integrated characterization techniques, we analyzed the microstructures of two AFA alloys, both before and after the creep process. We discovered that the suppression of primary carbides permits the in-situ clustering of now-available interstitial elements such as C, Si, and O during high-temperature creep. This improved solid solution strengthening and reduced stacking fault energy of the alloy. Moreover, it also enabled controlled secondary carbide formation during testing, further improving the creep resistance. These findings underline the important interplay between alloy composition, microstructure, and creep properties, and offer a promising design strategy for developing economical high-temperature Fe-based alloys suitable for advanced applications.

36 MATERIALS SCIENCE↗

Towards a quantitative understanding of bonding in supersonic single particle impacts: A three-dimensional FIB-SEM exploration

Particle bonding is crucial to coating quality in cold spray, but it has been a challenge to accurately quantify bonding even in single particle impacts. This paper uses FIB-SEM to explicitly map the particle-substrate interface for Cu-on-Cu single microparticle impacts in a full 3D rendering that spans a wide range of impact velocities. This approach permits a detailed quantification of the total bonding area and all of its associated components. In addition to revealing why prior 2D characterization efforts have missed important details about impact bonding, these data quantitatively reveal the evolution of bonding from its onset at the “critical velocity” V cr (where bonding is generally poor, ∼6 %) to its peak at around 1.3‧V cr (where almost 90 % of the particle bonds). Further increase in the velocity to 1.5‧V cr and beyond finds the onset of hydrodynamic penetration and a decrease in bonding. These data then support the development of a simple analytical model based on oxide rarefication and extrusion of bare metal through gaps in the oxide layer as driving the development of bonding. As a result, the model reproduces the experiments and provides guidance on optimization of bonding as a function of material and process parameters.

Analytical methods↗

Equilibrium water and solute uptake in silicone hydrogels

Equilibrium water content of and solute partitioning in silicone hydrogels (SiHys) are investigated using gravimetric analysis, fluorescence confocal laser-scanning microscopy (FCLSM), and back extraction with UV/Vis-absorption spectrophotometry. Synthesized silicone hydrogels consist of silicone monomer, hydrophilic monomer, cross-linking agent, and triblock-copolymer macromer used as an amphiphilic compatibilizer to prevent macrophase separation. In all cases, immiscibility of the silicone and hydrophilic polymers results in microphase-separated morphologies. To investigate solute uptake in each of the SiHy microphases, equilibrium partition coefficients are obtained for two hydrophilic solutes (i.e., theophylline and caffeine dissolved in aqueous phosphate-buffered saline) and two oleophilic solutes (i.e., Nile Red and Bodipy Green dissolved in silicone oil), respectively. Measured water contents and aqueous-solute partition coefficients increase linearly with increasing solvent-free hydrophilic-polymer volume fraction. Conversely, oleophilic-solute partition coefficients decrease linearly with rising solvent-free hydrophilic-polymer volume fraction (i.e., decreasing hydrophobic silicone-polymer fraction). In this paper, we quantitatively predict equilibrium SiHy water and solute uptake assuming that water and aqueous solutes reside only in hydrophilic microdomains, whereas oleophilic solutes partition predominately into silicone microdomains. Predicted water contents and solute partition coefficients are in excellent agreement with experiment. Our new procedure, discussed in this paper, permits a priori estimation of SiHy water contents and solute partition coefficients based solely on properties of silicone and hydrophilic homopolymer hydrogels, eliminating the need for further mixed-polymer-hydrogel experiments.

Liu, D. E.↗

A meshing framework for digital twins for extrusion based additive manufacturing

Additive manufacturing (AM) allows for manufacturing of complex three-dimensional geometries not typically realizable with standard manufacturing practices. The internal microstructure of AM components has a significant impact on mechanical, vibrational, and shock properties and permits richer design space when this is controllable. Due to complex interactions of internal geometry of an extrusion-based AM component, it is common practice to assume homogeneous behavior or to perform characterization testing on specific toolpath configurations. To avoid testing or material waste, it is necessary to develop a consistently accurate numerical simulation framework with relevant boundary value problems that can handle the complicated geometry of internal material microstructure present in AM components. Herein, a framework is proposed to directly create computational meshes suitable for finite element analysis (FEA) of the fine-scale features generated from extrusion-based AM tool paths to maintain a strong process–structure–property-performance linkage. This mesh can be manually or automatically analyzed using standard FEA simulations such as quasi-static preloading or modal analysis. The framework allows an in-silico assessment of a target AM geometry where fine-scale features greatly impact quantities of design interest such as in soft elastomeric lattices where toolpath infill can greatly influence the self-contact of a structure in compression, which we use as a motivating exemplar. This approach greatly reduces both time and resource waste present in traditional build and test design cycles for non-intuitive design spaces, and acts as a tool for use in the production of a key component of a digital twin, a mesh suitable for finite element analysis. In conclusion, it also further allows for the exploration of toolpath infill to optimize component properties beyond simple linear properties such as density and stiffness.

Additive manufacturing↗

Rapid imbibition of water in fractures within unsaturated sedimentary rock

The spontaneous imbibition of water and other liquids into gas-filled fractures in variably-saturated porous media is important in a variety of engineering and geological contexts. However, surprisingly few studies have investigated this phenomenon. In this paper, we present a theoretical framework for predicting the 1-dimensional movement of water into air-filled fractures within a porous medium based on early-time capillary dynamics and spreading over the rough surfaces of fracture faces. The theory permits estimation of sorptivity values for the matrix and fracture zone, as well as a dispersion parameter which quantifies the extent of spreading of the wetting front. Quantitative data on spontaneous imbibition of water in unsaturated Berea sandstone cores were acquired to evaluate the proposed model. The cores with different permeability classes ranging from 50 to 500 mD and were fractured using the Brazilian method. Spontaneous imbibition in the fractured cores was measured by dynamic neutron radiography at the Neutron Imaging Prototype Facility (beam line CG-1D, HFIR), Oak Ridge National Laboratory. Water uptake into both the matrix and the fracture zone exhibited square-root-of-time behavior. The matrix sorptivities ranged from 2.9 to 4.6 mm s -0.5 , and increased linearly as the permeability class increased. The sorptivities of the fracture zones ranged from 17.9 to 27.1 mm s -0.5 , and increased linearly with increasing fracture aperture width. The dispersion coefficients ranged from 23.7 to 66.7 mm 2 s -1 and increased linearly with increasing fracture aperture width and damage zone width. Both theory and observations indicate that fractures can significantly increase spontaneous imbibition in unsaturated sedimentary rock by capillary action and surface spreading on rough fracture faces. Fractures also increase the dispersion of the wetting front. In conclusion, further research is needed to investigate this phenomenon in other natural and engineered porous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A reduced order model to analytically infer atmospheric CO 2 concentration from stomatal and climate data

To address questions related to the acceleration or deceleration of the global hydrological cycle or links between the carbon and water cycles over land, reliable data for past climatic conditions based on proxies are required. In particular, the reconstruction of palaeoatmospheric CO 2 content (C a ) is needed to assist the separation of natural from anthropogenic C a variability and to explore phase relations between C a and air temperature T a time series. Both T a and C a are needed to fingerprint anthropogenic signatures in vapor pressure deficit, a major driver used to explain acceleration or deceleration phases in the global hydrological cycle. Current approaches to C a reconstruction rely on a robust inverse correlation between measured stomatal density in leaves (ν) of many plant taxa and C a . There are two methods that exploit this correlation: The first uses calibration curves obtained from extant species assumed to represent the fossil taxa, thereby restricting the suitable taxa to those existing today. The second is a hybrid eco-hydrological/physiological approach that determines C a with the aid of systems of equations based on quasi-instantaneous leaf-gas exchange theories and fossil stomatal data collected along with other measured leaf anatomical traits and parameters. In this contribution, a reduced order model (ROM) is proposed that derives C a from a single equation incorporating the aforementioned stomatal data, basic climate (e.g. temperature), estimated biochemical parameters of assimilation and isotope data. The usage of the ROM is then illustrated by applying it to isotopic and anatomical measurements from three extant species. The ROM derivation is based on a balance between the biochemical demand and atmospheric supply of CO 2 that leads to an explicit expression linking stomatal conductance to internal CO 2 concentration (C i ) and C a . The resulting expression of stomatal conductance from the carbon economy of the leaf is then equated to another expression derived from water vapor gas diffusion that includes anatomical traits. When combined with isotopic measurements for long-term C i /C a , C a can be analytically determined and is interpreted as the time-averaged C a that existed over the life-span of the leaf. Key advantages of the proposed ROM are: 1) the usage of isotopic data provides constraints on the reconstructed atmospheric CO 2 concentration from ν, 2) the analytical form of this approach permits direct links between parameter uncertainties and reconstructed C a , and 3) the time-scale mismatch between the application of instantaneous leaf-gas exchange expressions constrained with longer-term isotopic data is reconciled through averaging rules and sensitivity analysis. The latter point was rarely considered in prior reconstruction studies that combined models of leaf-gas exchange and isotopic data to reconstruct C a from ν. The proposed ROM is not without its limitations given the need to a priori assume a parameter related to the control on photosynthetic rate. Our work here further explores immanent constraints for the aforementioned photosynthetic parameter.

54 ENVIRONMENTAL SCIENCES↗

Transient analysis of advancing contact angle measurements on polished rock surfaces

We report that contact angle measurements for gas-liquid-rock systems are important for modeling multi-phase flow and transport in the subsurface. These data are needed in applications such as the extraction of oil and gas resources, geologic sequestration of carbon dioxide, contaminant fate and transport, and aquifer recharge through the vadose zone. Contact angles are frequently measured with the sessile drop method. Previous research has largely ignored the dynamic behavior of sessile droplets on geologic materials. This study investigates the dynamic behavior of sessile water droplets on prepared rock surfaces in the presence of air. Droplet diameter and advancing contact angle were determined at 0.5 s intervals for ~90 s on flat polished disks of Burlington limestone, Crossville sandstone, Mancos shale, Sierra White granite, Vermilion Bay granite, and Westerly granite using a Krüss DSA 30 Drop Shape Analyzer. The droplet diameter and advancing contact angle data sets were nonlinearly regressed against time using two different two-parameter models. The median coefficients of determination for the fits were 0.85 and 0.96, respectively. The resulting parameter estimates were used to compute the apparent equilibrium contact angle, θ e , for each disk following droplet diameter stabilization. Estimates of θ e ranged from 37.2° for Mancos shale to 75.6° for Burlington limestone. Analysis of variance indicated statistically significant differences in θ e between the rock types at the 95% confidence level. The variability of θe on the polished rock surfaces, as quantified by the coefficient of variation (CV) for θ e , varied between ~3 and ~9%; there were no significant differences in CV between the rock types. Neutron radiography indicated changes droplet morphology over time were due to the spontaneous imbibition of water into the rock matrix. Finally, the transient analysis employed in this study permits a more meaningful estimate of the equilibrium contact angle for rocks than taking the initial value or averaging over time as is frequently done.

58 GEOSCIENCES↗

Sequence Analysis of 20,453 Severe Acute Respiratory Syndrome Coronavirus 2 Genomes from the Houston Metropolitan Area Identifies the Emergence and Widespread Distribution of Multiple Isolates of All Major Variants of Concern

Since the beginning of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic, there has been international concern about the emergence of virus variants with mutations that increase transmissibility, enhance escape from the human immune response, or otherwise alter biologically important phenotypes. In late 2020, several variants of concern emerged globally, including the UK variant (B.1.1.7), the South Africa variant (B.1.351), Brazil variants (P.1 and P.2), and two related California variants of interest (B.1.429 and B.1.427). These variants are believed to have enhanced transmissibility. For the South Africa and Brazil variants, there is evidence that mutations in spike protein permit it to escape from some vaccines and therapeutic monoclonal antibodies. On the basis of our extensive genome sequencing program involving 20,453 coronavirus disease 2019 patient samples collected from March 2020 to February 2021, we report identification of all six of these SARS-CoV-2 variants among Houston Methodist Hospital (Houston, TX) patients residing in the greater metropolitan area. Although these variants are currently at relatively low frequency (aggregate of 1.1%) in the population, they are geographically widespread. Houston is the first city in the United States in which active circulation of all six current variants of concern has been documented by genome sequencing. Finally, as vaccine deployment accelerates, increased genomic surveillance of SARS-CoV-2 is essential to understanding the presence, frequency, and medical impact of consequential variants and their patterns and trajectory of dissemination.

60 APPLIED LIFE SCIENCES↗

A novel activation domain is essential for CIA5-mediated gene regulation in response to CO 2 changes in Chlamydomonas reinhardtii

The inducible CO 2 concentrating mechanism (CCM) of microalgae is essential for their acclimation to highly variable aquatic inorganic carbon levels. The key transcriptional regulator, CIA5, affects expression of thousands of genes in Chlamydomonas reinhardtii, but the molecular characteristics of this important protein are poorly understood. Here this study identifies a functional activation domain in CIA5 and demonstrates the functionality of a mini-CIA5 including only the zinc-binding domain and the identified activation domain. A highly conserved 130aa region from CIA5 exhibits auto-activation in yeast and appears responsible for the markedly slow migration of CIA5 when analyzed by SDS-PAGE. This 130aa region or either half of this region also effectively replaced the activation domain of a modified designer Transcription Activator-like Element (dTALE) in targeted activation of an endogenous Chlamydomonas gene. Additionally, a mini-CIA5 combining the conserved zinc-binding domain with the 130aa putative activation domain complemented the growth phenotype of the cia5 mutant and triggered CO 2 -regulated gene expression patterns similar to wild-type cells or cia5 complemented with the full-length CIA5. Although the mini-CIA5 complementation did not fully restore wild-type growth rates or full gene induction/repression amplitudes, especially in very low CO 2 , this newly identified activation domain combined with the previously described zinc-binding domain are demonstrated to be the key essential components of CIA5 that permit rapid CIA5-mediated responses to changes in CO 2 concentrations.

59 BASIC BIOLOGICAL SCIENCES↗

Phenomena Identification and Ranking Table (PIRT) study for metallic structural materials for advanced High-Temperature reactor

The Fluoride High-Temperature Reactor (FHR) technology promises many benefits including passive safety, proliferation-resistant waste forms, and improved economics. However, selection of reliable structural materials and identification of the possible degradation mechanisms for these is important for the licensure and the safe operation of FHRs. In order to address this task, the Georgia Tech led Integrated Research Project (IRP) hosted a Phenomena Identification and Ranking Table (PIRT) panel of experts to address degradation mechanisms and other materials related issues of importance to the FHRs. Futhermore, materials, ones that come in contact with FLiBe or FLiNaK molten salts or other related environments like high temperature steam etc., were considered in this PIRT. Focus of this PIRT was the metallic alloys, especially the ones that are permitted for the construction of elevated temperature Class A components by the ASME code. Degradation mechanisms considered in this PIRT included chemical degradation, mechanical degradation, radiation degradation, and synergistic effect of these mechanisms that may negatively impact operations or cause some safety concerns for the major structural components of FHRs. Main components which were considered included vessel and primary piping, primary heat exchangers, steam generator vessel, steam generator tubes, intermediate loop piping, valves and pumps. Welds in all structural components were identified as an important class of material, which varies in composition and properties, and needs more attention. Importance of impurity control in molten fluorides considered for FHR was highlighted throughout PIRT panel discussions. As a result, this paper gives a summary of important results from the PIRT panel discussions and report.

36 MATERIALS SCIENCE↗

Analysis of buffer-IPyC separation in TRISO fuel particles

During High Temperature Gas-cooled Reactor (HTGR) operation, and due to the neutron irradiation in the reactor core, damage of the nuclear fuel coating layers occurs. The mechanism of damage formation in the TRISO fuel is explored by the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program, in which the debonding process between coating layers was also investigated. The purpose of this paper is to report simulation results for two models. Firstly, the debonding restricted model, where no gap formation between buffer and IPyC layers is permitted. Secondly, a debonding enabled model, where the gap between those layers is created. The simulations were performed with the Bison code. The inputs of the simulated models are based on data from the AGR-1 experiment. Further, the research included simulations on spherical and aspherical fuel types. The simulations match results obtained by the AGR-1 experiment, which as such shows that the Bison code is a good computational method for simulating the behavior of the gap between buffer and IPyC layers in TRISO fuel. Based on the irradiation experiments, and the Bison simulations, it was concluded that the most common scenario is a gap formation along the buffer-IPyC interface, while the least possible scenario is the situation where there is no gap formation at the buffer-IPyC junction. The computational results confirmed that the sphericity of the fuel influences the thickness of the gap that occurs at the buffer-IPyC junction, in a way that with increasing aspect ratio the gap thickness increases. In addition, the fuel sphericity does not influence the Weibull failure probability. The results obtained for spherical and aspherical fuel are nearly identical.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

SCALE inventory and reactivity analysis as part of the Hermes 2021 PSAR review

The readiness of SCALE for comprehensive studies of pebble-bed reactors has been demonstrated through detailed analysis of a fluoride salt–cooled, high-temperature pebble-bed reactor (PB-FHR). The methods developed for pebble-bed reactor modeling in SCALE, particularly for inventory generation, have proven effective in gaining insights into the reactor physics of this advanced reactor. Excellent agreement with another code package has been observed, further highlighting SCALE’s strong performance. The SCALE results supported the US Nuclear Regulatory Commission’s construction permit application review of the Hermes low-power PB-FHR demonstration reactor. A SCALE model of the Hermes reactor was developed at Oak Ridge National Laboratory using information from the Preliminary Safety Analysis Report (PSAR) and supplemented with publicly available data. SCALE reactivity coefficient simulations reproduced PSAR results within 1σ statistical uncertainties. Sensitivity studies emphasized the importance of graphite specifications for accurate keff predictions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Quantum critical behavior in three-dimensional one-band Hubbard model at half-filling

A one-band Hubbard model with hopping parameter t and Coulomb repulsion U is considered at half-filling. By means of the Schwinger bosons and slave fermions representation of the electron operators and integrating out the spin–singlet Fermi fields an effective Heisenberg model with antiferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Accounting adequately for the magnon–magnon interaction the Néel temperature is calculated. When the ratio t/U is small enough (t/U ≤0.09) the effective model describes a system of localized electrons. Increasing the ratio increases the density of doubly occupied states which in turn decreases the effective spin and Néel temperature. The phase diagram in the plane of temperature (T{sub N})/U and parameter t/U is presented. The quantum critical point (T{sub N}=0) is reached at t/U =0.9. The magnons in the paramagnetic phase are studied and the contribution of the magnons’ fluctuations to the heat capacity is calculated. At the Néel temperature the heat capacity has a peak which is suppressed when the system approaches a quantum critical point. It is important to stress that, at half-filling, the ground state, determined by fermions, is antiferromagnetic. The magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order. -- Highlights: •Technique of calculation is introduced which permits us to study the magnons’ fluctuations. •Quantum critical point is obtained in the one-band 3D Hubbard model at half-filling. •The present analytical results supplement the numerical ones (see Fig. 7)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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