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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Suppression of ferromagnetism governed by a critical lattice parameter in CeTiGe 3 with hydrostatic pressure or V substitution

We combine structural and magnetic measurements to compare the different magnetic phase diagrams between the pressure and substitution studies in CeTiGe 3 . We report on the structural, magnetic, and electrical transport properties of single crystals of CeTi 1–x V x Ge 3 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.9, and 1), and of polycrystalline samples (x = 0.5, 0.6, 0.7, 0.8), as well as structural properties of CeTiGe 3 under pressure up to 9 GPa. The ferromagnetic ordering in CeTiGe 3 is suppressed with V doping in CeTi 1–x V x Ge 3 , and suggests a possible ferromagnetic quantum critical point near x = 0.45. We perform a detailed crystalline electric field (CEF) analysis, and the magnetic susceptibility data in pure CeTiGe 3 and CeVGe 3 can be well explained by the CEF model. The proposed CEF energy levels suggest that there is a gradual change of the ground state from |±5/2 in CeTiGe 3 to |±1/2 in CeVGe 3 , and a suppression of CEF splitting energies near the quantum critical region. When hydrostatic pressure is used instead of chemical substitution, the quantum critical point is avoided by the appearance of magnetic phases above around 4.1 GPa. In the substitution study, the ferromagnetic and antiferromagnetic regions are well separated, whereas they touch in the pressure study. We observe a different trend in the temperature dependence of the resistivity maximum in both studies, suggesting that the CEF splitting energy is suppressed by V substitution but enhanced by pressure. Here, we also observe different responses in lattice constants between the two studies, highlighting the fact that substitution effects cannot be reduced to chemical pressure effects only. Nevertheless, when the magnetic phase diagrams of both hydrostatic pressure and substitution are compared, we find a common critical lattice constant c = 5.78 Å where the ferromagnetic ordering is suppressed in both studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Lattice Parameter Evolution during the β-to-α and β-to-ω Transformations of Iron- and Aluminum-Modified Ti-11Cr(at.%)

β-titanium (β-Ti) alloys are useful in diverse industries because their mechanical properties can be tuned by transforming the metastable β phase into other metastable and stable phases. Relationships between lattice parameter and β-Ti alloy concentrations have been explored, but the lattice parameter evolution during β-phase transformations is not well understood. In this work, the β-Ti alloys, Ti-11Cr, Ti-11Cr-0.85Fe, Ti-11Cr-5.3Al, and Ti-11Cr-0.85Fe-5.3Al (all in at.%), underwent a 400 °C aging treatment for up to 12 h to induce the β-to-ω and β-to-α phase transformations. Phase identification and lattice parameters were measured in situ using high-temperature X-ray diffraction. Phase compositions were measured ex situ using atom probe tomography. During the phase transformations, Cr and Fe diffused from the ω and α phases into the β matrix, and the β-phase lattice parameter exhibited a corresponding decrease. The decrease in β-phase lattice parameter affected the α- and ω-phase lattice parameters. The α phase in the Fe-free alloys exhibited α-phase c/a ratios close to those of pure Ti. A larger β-phase composition change in Ti-11Cr resulted in larger ω-phase lattice parameter changes than that for Ti-11Cr-0.85Fe. This work illuminates the complex relationship between diffusion, composition, and structure for these diffusive/displacive transformations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Automated prediction of lattice parameters from X-ray powder diffraction patterns

A key step in the analysis of powder X-ray diffraction (PXRD) data is the accurate determination of unit-cell lattice parameters. This step often requires significant human intervention and is a bottleneck that hinders efforts towards automated analysis. This work develops a series of one-dimensional convolutional neural networks (1D-CNNs) trained to provide lattice parameter estimates for each crystal system. A mean absolute percentage error of approximately 10% is achieved for each crystal system, which corresponds to a 100- to 1000-fold reduction in lattice parameter search space volume. The models learn from nearly one million crystal structures contained within the Inorganic Crystal Structure Database and the Cambridge Structural Database and, due to the nature of these two complimentary databases, the models generalize well across chemistries. A key component of this work is a systematic analysis of the effect of different realistic experimental non-idealities on model performance. It is found that the addition of impurity phases, baseline noise and peak broadening present the greatest challenges to learning, while zero-offset error and random intensity modulations have little effect. However, appropriate data modification schemes can be used to bolster model performance and yield reasonable predictions, even for data which simulate realistic experimental non-idealities. In order to obtain accurate results, a new approach is introduced which uses the initial machine learning estimates with existing iterative whole-pattern refinement schemes to tackle automated unit-cell solution.

42 ENGINEERING↗
DOE OSTI2020

The dependence of aluminum lattice orientation on semiconductor lattice parameter in planar InAs/Al hybrid heterostructures

We present a detailed study of 7-nm thick Al layers epitaxially grown on In x Al 1-x As or Al 1-x Ga x Sb y As 1-y (0 0 1) semiconductors using high-resolution transmission electron microscopy (HRTEM) and synchrotron X-ray diffraction (XRD). These techniques provide high spatial and high reciprocal space resolution information about Al lattice orientations and interfacial structure, highlighting the existence of a strong correlation between the surface lattice parameter of the semiconductor and the normal orientation of the aluminum film. The normal orientation of Al layers is found to be [1 1 1] when the in-plane semiconductor surface lattice parameter, a S , is smaller than 5.98 Å, and is [1 1 0] when aS is larger than this value. In the transition between these lattice parameters where one orientation is preferred, both orientations may be observed. Concomitant with the change in normal orientation is an inversion in the strain state of the aluminum film. When the normal orientation is [1 1 1], the Al film is compressively strained; while for [1 1 0] normal orientations, the Al in-plane strain is tensile. An energy balance model, accounting for surface, interfacial, side-face, and strain energy, and the registry of lattice planes across the semiconductor/aluminum interface provide explanations for the observed normal orientation and strain inversion.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Carbonated apatite lattice parameter variation across incremental growth lines in teeth

Here, results of microbeam mapping (x-ray excited x-ray fluorescence and transmission x-ray diffraction) of Beluga whale cementum and of beaver dentin reveal growth bands are defined by variation in mineral content (carbonated hydroxyapatite, cAp), by variation in Zn content and by variation in cAp lattice parameter a. For both tissues, diffraction and fluorescence data show that Zn signal and a are anti-correlated, that is high Zn signal is co-located with low a, and vice versa. In cementum and bone, treatment with acid removes Ca, Zn and cAp. The data are strong evidence that Zn is incorporated into the cAp lattice in these tissues and that the amount of Zn incorporated varies across two very different types of growth bands, annual bands in Beluga cementum and daily incremental bands in beaver dentin. To the best of the authors’ knowledge, this is the first observation of spatial variation of lattice parameter within growth bands.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The lattice parameter – composition relationship of the body centered cubic uranium-niobium alloys

In this paper, in-situ time-of-flight neutron diffraction experiments were performed on uranium-niobium alloy with 6 wt% Nb to study the lattice parameter-composition relationship for the body centered cubic (bcc) alloys. Based on lattice-parameter measurements of Nb-supersaturated γs phase over the range of 450 – 790 °C, an improved Vegard's-type relationship was established for determination of Nb concentrations at elevated temperatures. Neutron diffraction data were also collected as a function of aging time over the 450 - 600 °C range when γs phase decomposed isothermally into the mixture of orthorhombic α-U and Nb-rich bcc phase, as well as at room-temperature on the alloys aged ex-situ at 500 °C up to five years. From these measurements, the average Nb concentrations in the bcc phase were determined based on the Rietveld refinements of weight fraction and mass conservation relations (lever rule). Over the 15at% – 78at% range of Nb concentrations that correspond to different experimental aging times, the lattice parameters at constant temperatures exhibit a nonlinear S-shaped variation with Nb concentration, and the associated excess volumes of mixing can be described by a subregular solution model of the Redlich–Kister type of polynomial. Over the full range of composition the S-shaped deviation from Vegard's law can be modeled using a combination of an elastic continuum model and a perturbation to the radii of the solute atoms in the solvent, suggesting that electronic interactions between solute and solvent atoms could play an important role in the compositional dependence of lattice parameter for the γ-phase U-Nb alloys. While Vegard's law is a straightforward and reasonably good approximation for the bcc solid solutions in the U-Nb system, the Nb concentrations determined from the weight fraction refinements of diffraction data provide internally consistent, mass-conserving estimates of solute redistribution for the monotectoid reaction.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Size Dependence of Lattice Parameter and Electronic Structure in CeO2 Nanoparticles

Intrinsic properties of a compound (e.g. electronic structure, crystallographic structure, optical and magnetic properties) define notably its chemical and physical behavior. In the case of nanomaterials, these fundamental properties depend on the occurrence of quantum mechanical size effects and on the considerable increase of the surface to bulk ratio. However, the literature on this size-dependence and on the involved mechanisms is quite elusive and scarce. Here, we explore the size-dependence of both crystal and electronic properties of CeO2 nanoparticles (NPs) with different sizes by state-of-the art spectroscopic techniques. XRD, XPS and HERFD-XANES demonstrate that the as-synthesized NPs crystallize in the fluorite structure and they are predominantly composed of CeIV ions. The strong dependence of the lattice parameter with the NPs size was attributed to the presence of adsorbed species at the NPs surface thanks to FTIR and TGA measurements. In addition, the size-dependence of the eg level in the Ce LIII XANES spectra was experimentally observed by HERFD-XANES and confirmed by theoretical calculations.

Lanthanide, CeO2, HEFRD-XANES, Electronic structur↗
DOE OSTI2022

Beam-Based Diagnostics of Electric Guide Fields and Lattice Parameters for Run-1 of the Muon g-2 Storage Ring at Fermilab

A portion of the Muon g-2 Storage Ring electric system, which provides vertical beam focusing, exhibited an unexpected time dependence that produced a characteristic evolution of the stored beam during Run-1 of the Muon g-2 Experiment at Fermilab (E989). A method to reconstruct the Run-1 electric guide fields has been developed, which is based on a numerical model of the muon storage ring and optimization algorithms supported by COSY INFINITY. This method takes beam profile measurements from the Muon g-2 straw tracking detectors as input, and it produces a full reconstruction of the time-dependent fields. The fields can then be used for the reproduction of detailed beam tracking simulations and the calculation of ring lattice parameters for acceptance studies and systematic error evaluations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Isotopic and Fuel Lattice Parameter Trends in Extended Enrichment and Higher Burnup LWR Fuel Vol I: PWR fuel

Commercial light water reactor (LWR) operators and fuel vendors in the United States are pursuing changes to nuclear fuel that include extended enrichment (EE) and accident-tolerant fuel (ATF) designs. The term EE (8% > 235 U > 5%) is used in this report to refer to a subset of high assay low-enriched uranium (HALEU) that is considered usable in commercial US LWRs in the near term. ATF features are designed to improve fuel system performance under accident conditions. One goal of EE is to improve fuel cycle economy by enabling fuel to be depleted to higher burnup than the typical current maximum pin burnup limits (62 gigawatt-days per metric ton of uranium [GWd/MTU]). Adoption of EE, ATF, and high burnup (HBU) fuels in the US commercial fleet requires a clear understanding of the effects on core physics parameters and used fuel isotopic content, as well as confidence in the accuracy of computer code predictions over an expanded range of materials, enrichment, and burnup. A thorough understanding of the applicability and adequacy of benchmark data (e.g., criticality, decay heat, isotopic content) for computer code validation is necessary to ensure that appropriate safety margins are maintained. To prepare for and support these potential changes, the effects of EE, ATF, and HBU are being assessed for selected representative LWR fuel designs. The project is divided into phases: this report summarizes the findings of Phase 1, which focuses on the lattice physics parameter and used fuel isotopic changes for a conventional Westinghouse 17×17 pressurized water reactor (PWR) design. The primary investigation tool is the SCALE Polaris code using the SCALE 56-group Evaluated Nuclear Data File (ENDF)/B-VII.1 cross sections. The goal of the current work is to (1) identify and explain important effects of EE and HBU (reactivity, lattice physics, and isotopic effects) assuming that PWR fuel design and usage remain similar to those for current enrichment fuel, (2) provide limited code-to-code comparisons with higher order cross section libraries and/or codes, and (3) identify any apparent anomalous trends in the results for further investigation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Isotopic and Fuel Lattice Parameter Trends in Extended Enrichment and Higher Burnup LWR Fuel, Volume II: BWR

Commercial light water reactor (LWR) operators and fuel vendors in the United States are pursuing changes to nuclear fuel that include extended enrichment (EE) and accident-tolerant fuel (ATF) designs to further improve reactor safety and plant economics. Extended fuel enrichments above 5% 235 U pin enrichment and up to 10% 235 U are a subset of high assay low-enriched uranium (HALEU) that may be deployed in commercial US LWRs in the near term. ATF features, such as cladding coatings or alternative cladding materials, are designed to improve fuel system performance under accident conditions. One goal of EE is to improve fuel cycle economy by enabling fuel to be depleted to higher burnup than the typical current limits (62 gigawatt-days per metric ton of uranium [GWd/MTU]). Adoption of EE, ATF, and high burnup (HBU) fuels in the US commercial fleet requires a clear understanding of the effects on core physics parameters and used fuel isotopic content, as well as confidence in the accuracy of computer code predictions over an expanded range of materials, enrichment, and burnup. A thorough understanding of the applicability and adequacy of benchmark data (e.g., criticality, decay heat, isotopic content) for computer code validation is necessary to ensure that appropriate safety margins are maintained. As part of the US Nuclear Regulatory Commission (NRC) agreement number 31310019N0008, “SCALE Code Development, Assessment and Maintenance,” the effects of EE, ATF, and HBU are being assessed for selected representative LWR fuel designs. The project is divided into phases, and this report summarizes the findings of the Phase 1 work, which focuses on lattice physics parameter and used fuel isotopic changes for a conventional GE14 10 x 10 boiling water reactor (BWR) design with GNF-2 part length rod patterns to model a modern BWR assembly design.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

A multiscale approach to analyze the effect of radial void fraction distributions on BWR neutronic lattice parameters

The goal of this study is to analyze the effect of radial void fraction distribution, considered at three degrees of fidelity, on lattice and 2-group homogenized cross sections. The novelty of this work lies in its use of experimentally-determined radial void fraction distributions which allows for fine-scale coolant density data with no predictive uncertainty and which could be prohibitively expensive to simulate over the range of operational parameters used in the experiments. The experimentally-determined radial void fraction distributions are also characterized using a statistical tool called a semi-variogram in order to determine the scale of continuity. Void fraction distributions are averaged at the lattice and subchannel level for comparison with the fine-scale model. Models averaged at the subchannel and lattice level show a difference in about 68% of the time. Also, by comparing 2-group homogenized cross-sections, the differences between the subchannel and homogeneous cases are measurable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Extended Enrichment Accident Tolerant LWR Fuel Isotopic and Lattice Parameter Trends

Commercial light water reactor (LWR) operators and fuel vendors in the United States (US) are pursuing changes to the reactor fuel that include increased enrichment and accident-tolerant fuel (ATF) designs. Enrichments under consideration are between 5 wt % and 10 wt % 235 U, which are a subset of high-assay low-enriched uranium fuels. ATF features are designed to improve fuel system performance under accident conditions. With increased enrichment, fuel cycle economics can be improved if fuel can be licensed for higher burnup (HBU) than typical current limits (e.g., 62 GWd/MTU maximum fuel pin).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Thermal stability of dopants in boron carbide

Undoped (B 4 C), B rich (B 5.5 C), and B/Si co-doped (Si-B 6.5 C) boron carbides were annealed at 500 °C for up to 21 days to investigate the thermal stability of primary dopants, B and Si. Structural changes associated with dedoping were investigated by X-ray diffraction (XRD) and Raman spectroscopy. The stable phase B 4 C showed no microstructural or lattice parameter changes. Similarly, lattice parameters of B 5.5 C remained constant, suggesting that B dopant is stable at the given conditions. However, the shortened lattice parameters and reduced Si content of Si-B 6.5 C over the annealing time indicated that Si dopant was in a metastable state at the annealing temperature. Consequently, Si dedoping led to an increase in amorphization (a loss of local crystalline order) which degrades the ballistic performance of boron carbide. The insight highlights the importance of Si dopant in boron carbide and suggests that rapid processing may be necessary to retain more silicon for better performance.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Comparing the influence of cation order and composition in simulated Zn(Sn, Ge)N 2 on structure, elastic moduli, and polarization for solid state lighting

Alloying and site ordering play complementary roles in dictating a material’s properties. However, deconvolving the impacts of these separate phenomena can be challenging. In this work, we simulate structures of Zn(Sn,Ge)N 2 with varied Sn content and site ordering to determine the impacts of order and composition on structural and electronic properties. We assess the formation enthalpy, lattice parameters, elastic constants, spontaneous polarization, and piezoelectric coefficients. In mostly disordered structures (order parameters ranging from 0.2 to 0.4), the formation enthalpy exhibits local extrema as a function of the order parameter, deviating from the more linear trends seen in both fully disordered and fully ordered systems. This anomalous deviation from the otherwise linear trend in formation enthalpy with order manifests in each of the other properties calculated. This range of order parameters of interest may be caused by a transition in the ordering of the quaternary material similar to phase changes seen in ternary compounds but stretched over a region inclduing 20% of the order parameter range. Most parameters calculated are more sensitive to order than to composition in the limited composition range tested; however, the lattice parameter c, piezoelectric coefficient e 33 , and elastic moduli C 12 , C 13 , and C 23 are more sensitive to composition. Of the properties compared, the piezoelectric coefficients are influenced most significantly by changes in both the composition and order parameter. Lattice parameters undergo the smallest changes with order and composition, but these small differences appear to impart large trends in the other properties. Better understanding the effects of disorder and group IV alloying in Zn(Sn,Ge)N 2 allows for more accurate modeling of characteristics of this material system for solid state lighting and other applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Structural changes upon magnetic ordering in magnetocaloric AlFe 2 B 2

With a Curie temperature just above room temperature, AlFe 2 B 2 is a useful magnetocaloric material composed of earth-abundant elements. Here, we employ temperature-dependent high-resolution synchrotron X-ray diffraction to establish with high certainty that the paramagnetic to ferromagnetic transition in AlFe 2 B 2 is of second order, showing no discontinuity in lattice parameters or cell volume. Nevertheless, the lattice parameters undergo anisotropic changes across the transition with distinct differences in the thermal expansion coefficients. While the $a$ and $b$ lattice parameters show a positive thermal expansion, $c$ shows a negative thermal expansion. We link these changes to the respective interatomic distances to determine the contribution of magnetism to the anisotropic structural evolution. The work underpins the possible role of magnetostructural coupling in driving the magnetocaloric effect in AlFe 2 B 2 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

High-Pressure Equation of State of 1,3,5-triamino-2,4,6-trinitrobenzene: Insights into the Monoclinic Phase Transition, Hydrogen Bonding, and Anharmonicity

The high-pressure equation of state (EOS) of energetic materials (EMs) is important for continuum and mesoscale models of detonation performance and initiation safety. Additionally, obtaining a high-fidelity EOS of the insensitive EM 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) has proven to be difficult because of challenges in experimental characterization at high pressures (HPs). In this work, powder X-ray diffraction patterns were fitted using the recently discovered monoclinic I2/a phase above 4 GPa, which shows that TATB is less compressible than when indexed with the triclinic $P\bar{1}$ phase. First-principles calculations were performed with Perdew–Burke–Ernzerhof (PBE) and PBE0 functionals including thermal effects using the $P\bar{1}$ phase. PBE0 improves the description of hydrogen bonding and thus predicts accurate planar a and b lattice parameters under ambient conditions. However, discrepancies in the predicted lattice parameters above 4–10 GPa compared with experimental measurements indexed with $P\bar{1}$ are further evidence of a structural modification at high pressure. Layer sliding defects are formed during molecular dynamics simulations, which induces an anharmonic effect on the thermal expansion of the c lattice parameter. In short, the results provide several insights into determining high-fidelity EOS parameters for TATB and other molecular crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Intact archeological human bones and age at death studied with transmission x–ray diffraction and small angle x–ray scattering

In this work, high-energy, wide-angle x-ray scattering (WAXS, x-ray diffraction) and small-angle x-ray scattering (SAXS) were used to study intact human second metacarpal bones (mc2) from two UK archeological sites. A novel method correcting for irregular mass distribution was applied in these transmission geometry experiments done at beamline 1-ID of the Advanced Photon Source. The authors asked whether there were age-at-death-related changes in carbonated apatite (cAp) lattice parameters and whether SAXS could detect collagen D-period peaks in the archeological mc2. For each of the two sites, Ancaster and Wharram Percy in England, six female mc2s were studied; for each site, two were from each of three age-at-death cohorts (young, 18-29 years; middle, 30-49 years; old >= 50 years) along with a modern control mc2. The Rietveld method was applied to the WAXS patterns to provide precise lattice parameter values. The cAp lattice parameters did not correlate with age-at-death estimated from dental wear. From WAXS and the 00.2 diffraction peak widths, four archeological mc2s possessed coherently scattering domain lengths (crystallite c-axis sizes) that matched that of the modern mc2; SAXS revealed the same four archeological mc2 had D-period peak intensities equivalent to that of the modern mc2. The other eight archeological mc2s had significantly larger crystallite sizes (than the modern mc2) and weak or absent D-period peaks, differences attributed to diagenetic changes. Based on these data, the authors suggest that WAXS 00.2 peak width and SAXS D-period peak intensity can be used with intact bones to select those likely to retain largely unaltered tissue nanostructure, which might be required for other analyses. Taken as a whole, the results suggest detecting age-related deterioration in nanostructural features may be difficult in bone showing significant bioerosion.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Quantum critical behavior of the hyperkagome magnet Mn 3 CoSi

β -Mn-type family alloys Mn 3 T X ( T = Co , Rh, and Ir; X = Si and Ge) have a three-dimensional antiferromagnetic (AF) corner-shared triangular network, i.e., the hyperkagome lattice. The antiferromagnet Mn 3 RhSi shows magnetic short-range order over a wide temperature range of approximately 500 K above the Néel temperature T N of 190 K. In this family of compounds, as the lattice parameter decreases, the long-range magnetic ordering temperature decreases. Mn 3 CoSi has the smallest lattice parameter and the lowest T N in the family. The quantum critical point (QCP) from AF to the quantum paramagnetic state is expected near a cubic lattice parameter of 6.15 Å . Although the Néel temperature of Mn 3 CoSi is only 140 K, the emergence of the quantum critical behavior in Mn 3 CoSi is discussed. We study how the magnetic short-range order appears in Mn 3 CoSi by using neutron scattering, μ SR , and bulk characterization such as specific heat capacity. According to the results, the neutron scattering intensity of the magnetic short-range order in Mn 3 CoSi does not change much at low temperatures from that of Mn 3 RhSi , although the μ SR short-range order temperature of Mn 3 CoSi is largely suppressed to 240 K from that of Mn 3 RhSi . Correspondingly, the volume fraction of the magnetic short-range order regions, as shown by the initial asymmetry drop ratio of μ SR above T N , also becomes small. Instead, the electronic-specific heat coefficient γ of Mn 3 CoSi is the largest in this Mn 3 T Si system, possibly due to the low-energy spin fluctuation near the quantum critical point. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗