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At least 379 records · Page 21

Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials (Second Annual Progress Report)

Additive manufacturing (AM) is an emerging method for cost-efficient fabrication of nuclear reactor parts. AM of metallic structures for nuclear energy applications is currently based on laser powder bed fusion (LPBF) process, which can introduce internal material flaws, such as pores and anisotropy. Integrity of AM structures needs to be evaluated nondestructively because material flaws could lead to premature failures due to exposure to high temperature, radiation and corrosive environment in a nuclear reactor. Thermal tomography (TT) provides a capability for non-destructive evaluation of sub-surface defects in arbitrary size structures. Thermal tomography is a computational method for heat diffusion-based imaging of solids, which provides 3D visualization of data from flash thermography measurements. We investigate thermal tomography imaging and nondestructive evaluation of stainless steel and nickel super alloy metallic structures produced with laser powder bed fusion (LPBF) additive manufacturing (AM) process. Metallic structures produced with LPBF contain defects, and there are limited capabilities to evaluate these structures non-destructively. Thermal tomography reconstruction of 3D apparent spatial effusivity provides information about AM structure geometry and internal material flaws. We study performance of thermal tomography in imaging of metallic structures through COMSOL computer simulations of transient heat transfer, and through reconstruction of data obtained from experimental measurements. Reconstruction of internal defects is investigated using a stainless steel 316L specimen with flat bottom hole (FBH) indentations, and Inconel 718 plate produced with laser powder bed fusion (LPBF) method, which contains imprinted hemispherical shape low density regions containing non-sintered metallic powder. The FBH’s have the same sizes as the imprinted defects in the LPBF specimens, but offer better imaging contrast. Thermal tomography reconstructions provide visualizations of internal defects, and allow for estimation of their sizes and locations. Detection sensitivity of TT is limited by noises. We investigate separation of signal from noise in thermography images using several machine learning (ML) methods, including new spatio-temporal blind source separation (STBSS) and spatio-temporal sparse dictionary learning (STSDL) methods. Performance of the ML methods is benchmarked using thermography data obtained from imaging stainless steel 316L and Inconel 718 specimens produced LPBF method with imprinted calibrated porosity defects. The ML methods are ranked by F-score and execution runtime. Finally, we investigate TT of AM stainless steel 316L specimen with imprinted internal porosity defects using relatively low-cost, small form factor infrared (IR) camera based on uncooled micro bolometer detector. Sparse coding related K-means singular value decomposition (SVD) machine learning, image processing algorithms are developed to improve quality of TT images through removal of Additive white Gaussian noise without blurring the images. Following initial qualification of an AM component for deployment in a nuclear reactor, a compact TT can also be used for in-service nondestructive evaluation (NDE). With capability to perform in-service NDE of the AM component lifecycle, TT data can be used for development of a component digital twin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Dominant Energy Carrier Transitions and Thermal Anisotropy in Epitaxial Iridium Thin Films

High aspect ratio metal nanostructures are commonly found in a broad range of applications such as electronic compute structures and sensing. The self-heating and elevated temperatures in these structures, however, pose a significant bottleneck to both the reliability and clock frequencies of modern electronic devices. Any notable progress in energy efficiency and speed requires fundamental and tunable thermal transport mechanisms in nanostructured metals. Here, in this work, time-domain thermoreflectance is used to expose cross-plane quasi-ballistic transport in epitaxially grown metallic Ir(001) interposed between Al and MgO(001). Thermal conductivities ranges from roughly 65 (96 in-plane) to 119 (122 in-plane) W m -1 K -1 for 25.5–133.0 nm films, respectively. Further, low defects afforded by epitaxial growth are suspected to allow the observation of electron–phonon coupling effects in sub-20 nm metals with traditionally electron-mediated thermal transport. Via combined electro-thermal measurements and phenomenological modeling, the transition is revealed between three modes of cross-plane heat conduction across different thicknesses and an interplay among them: electron dominant, phonon dominant, and electron–phonon energy conversion dominant. The results substantiate unexplored modes of heat transport in nanostructured metals, the insights of which can be used to develop electro-thermal solutions for a host of modern microelectronic devices and sensing structures.

36 MATERIALS SCIENCE↗

Anisotropic phase stiffness in infinite-layer nickelates superconductors

In unconventional superconductors such as cuprates and iron pnictides and chalcogenides, phase stiffness—a measure of the energy cost associated with superconducting phase variations—governs the formation of superconductivity. Here we demonstrate a vector current technique enabling in-situ angle-resolved transport measurements to reveal anisotropic phase stiffness in infinite-layer nickelate superconductors. Pronounced anisotropy of in-plane resistance manifests itself in both normal and superconducting transition states, indicating crystal symmetry breaking. Remarkably, the electric conductivity of Nd 0.8 Sr 0.2 NiO 2 peaks at 125° between the direction of the current and crystal principal axis, but this angle evolves to 160° near zero-resistance temperature. Further measurements reveal that the phase stiffness maximizes along 160°, a direction distinct from the symmetry axis imposed by both electronic nematicity and the crystal lattice. Identical measurements conducted on a prototypical cuprate superconductor yield consistent results. By identifying the contrasting anisotropy between electron fluid and superfluid in both nickelates and cuprates, our findings provide clues for a unified framework for understanding unconventional superconductors.

Xu, Minyi [University of Electronic Science and Te↗

Semihard Iron-Based Permanent-Magnet Materials

Permanent magnets generally require a favorable, but difficult-to-achieve combination of high magnetization, Curie point, and magnetic anisotropy. Thus there have been few, if any, viable permanent magnets developed since the 1982 discovery of Nd 2 Fe 14 B. In this work we point out, both by direct first-principles calculations on the iron carbides and silicides Fe 5 C 2 , Fe 5 SiC, and Fe 7 C 3 as well as a discussion of recent experimental findings, that there are numerous rare-earth-free iron-rich potential permanent-magnet materials with sufficient intrinsic magnetic properties to reasonably achieve room-temperature energy products of 20–25 MG Oe. This is substantially better than the performance of the best available rare-earth-free magnets based on ferrite, as well as shape-anisotropy-employing alnico. These magnets could plausibly fill, at low cost, the present performance “gap” between the best rare-earth-free magnets and rare-earth magnets such as Nd 2 Fe 14 B and Sm-Co.

36 MATERIALS SCIENCE↗

The influence of kinematics of deformation on polycrystalline halite dynamic recrystallization: Full-field simulation of simple shear versus pure shear

Rock salt, composed mainly of halite, flows viscoplastically over a wide range of geological conditions, strongly impacting the dynamic evolution of sedimentary basins and orogens. Understanding how dislocation creep, which involves dislocation glide, intracrystalline recovery and dynamic recrystallization, influences the microstructure and rheology of halite under various deformation kinematics and temperatures is crucial for enhancing knowledge of salt flow dynamics. Here, this study employs a full-field numerical simulation method to compare the viscoplastic deformation of polycrystalline halite under simple shear and pure shear conditions up to a natural strain of ε = 1.5 at temperatures ranging from 100 °C to 300 °C. The results are presented in terms of crystallographic preferred orientation (CPO), grain shape preferred orientation (SPO), subgrain boundary direction, grain size and strain rate distribution. The results indicate that the crystallographic anisotropy of individual halite crystals is transferred to the polycrystalline scale, resulting in strain localization, particularly in simple shear simulations. The kinematics of deformation affect the evolution and distribution of high strain-rate bands, determining the direction of intragranular substructures and the morphology of strain-induced grain boundaries, with minimal impact on grain size. The intensity of grain boundary migration increases with temperature, significantly influencing grain morphology and size, thereby obscuring strain localization, while having little effect on CPOs. At low strain (ε < 1.0), CPOs relative to both the maximum shortening direction and the grain SPO are similar regardless of the deformation kinematics. At high strain (ε > 1.0), simple shear CPOs exhibit three stronger {100} maxima with a monoclinic symmetry relative to the grain SPO compared to the six {100} maxima with an orthotropic symmetry relative to the grain SPO generated under pure shear. Therefore, microstructures and CPOs can serve as indicators of the strain path in polycrystalline halite under various conditions, aiding in determining the shear sense and elucidating the deformation kinematics of salt structures.

58 GEOSCIENCES↗

Rare-Earth Permanent Magnet SmCo 5 for Chiral Interfacial Spin-Orbitronics

Interfacially asymmetric magnetic multilayers made of heavy metal/ferromagnet have attracted considerable attention in the spintronics community for accommodating spin-orbit torques (SOTs) and meanwhile for hosting chiral spin textures. In these multilayers, the accompanied interfacial Dzyaloshinskii–Moriya interaction (iDMI) permits the formation of Néel-type spin textures. While significant progresses have been made in Co, CoFeB, Co 2 FeAl, CoFeGd based multilayers, it would be intriguing to identify new magnetic multilayers that could enable spin-torque controllability and meanwhile host nanoscale skyrmions. In this report, first, thin films made of permanent magnet SmCo 5 with perpendicular magnetic anisotropy are synthesized, in which the deterministic SOT switching, enabled by the spin Hall effect, in Pt/SmCo 5 /Ta trilayer is demonstrated. Further, the stabilization of room-temperature skyrmions with diameters ≈100 nm in [Pt/SmCo 5 /Ta] 15 , together with a skyrmionium-like spin texture in [Pt/SmCo 5 /Ir] 15 multilayers is shown. Based on the material specific parameters, micromagnetic simulations are also carried out. The results confirm the presence of chiral spin textures in this new material family. Through interfacial engineering, the results thus demonstrate that rare earth permanent magnets could be a new platform for studying interfacial chiral spintronics.

36 MATERIALS SCIENCE↗

Anisotropic superconductivity of niobium based on its response to nonmagnetic disorder

Niobium is one of the most studied superconductors, both theoretically and experimentally. It is tremendously important for applications, and it has the highest superconducting transition temperature, T c = 9.32 K, of all pure metals. In addition to power applications in alloys, pure niobium is used for sensitive magnetosensing, radio-frequency cavities, and, more recently, as circuit metallization layers in superconducting qubits. A detailed understanding of its electronic and superconducting structure, especially its normal and superconducting state anisotropies, is crucial for mitigating the loss of quantum coherence in such devices. Recently, a microscopic theory of the anisotropic properties of niobium with the disorder was put forward. To verify theoretical predictions, we studied the effect of disorder produced by 3.5 MeV proton irradiation of thin Nb films grown by the same team and using the same protocols as those used in transmon qubits. By measuring the superconducting transition temperature and upper critical fields, we show a clear suppression of T c by potential (nonmagnetic) scattering, which is directly related to the anisotropic order parameter. Here, we obtain a very close quantitative agreement between the theory and the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ferrielectricity in the Archetypal Antiferroelectric, PbZrO 3

Antiferroelectric materials, where the transition between antipolar and polar phase is controlled by external electric fields, offer exceptional energy storage capacity with high efficiencies, giant electrocaloric effect, and superb electromechanical response. PbZrO 3 is the first discovered and the archetypal antiferroelectric material. Nonetheless, substantial challenges in processing phase pure PbZrO 3 have limited studies of the undoped composition, hindering understanding of the phase transitions in this material or unraveling the controversial origins of a low-field ferroelectric phase observed in lead zirconate thin films. Here, leveraging highly oriented PbZrO 3 thin films, a room-temperature ferrielectric phase is observed in the absence of external electric fields, with modulations of amplitude and direction of the spontaneous polarization and large anisotropy for critical electric fields required for phase transition. The ferrielectric state observations are qualitatively consistent with theoretical predictions, and correlate with very high dielectric tunability, and ultrahigh strains (up to 1.1%). This work suggests a need for re-evaluation of the fundamental science of antiferroelectricity in this archetypal material.

36 MATERIALS SCIENCE↗

Half-quantum vortices in nematic and chiral phases of 3 He

In this work, we report theoretical results for the stability of half-quantum vortices (HQVs) in the superfluid phases of 3 He confined in highly anisotropic Nafen aerogel. Superfluidity of 3 He confined in Nafen is the realization of a “nematic superfluid” with Cooper pairs condensed into a single p -wave orbital aligned along the anisotropy axis of the Nafen aerogel. In addition to the nematic phase, we predict a second “chiral” phase that onsets at a lower transition temperature. This chiral phase spontaneously breaks time-reversal symmetry and is a topological superfluid. Both superfluid phases are equal-spin pairing condensates that host arrays of HQVs as equilibrium states of rotating superfluid 3 He. We present results for the structure of HQVs, including magnetic and topological signatures of HQVs in both the nematic and chiral phases of 3 He-Nafen.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tunable Magnon Interactions in a Ferromagnetic Spin-1 Chain

NiNb 2 O 6 is an almost ideal realization of a 1D spin-1 ferromagnetic Heisenberg chain compound with weak unidirectional anisotropy. Using time-domain THz spectroscopy, we measure the low-energy electrodynamic response of NiNb 2 O 6 as a function of temperature and external magnetic field. At low temperatures, we find a magnonlike spin excitation, which corresponds to the lowest energy excitation at q ~ 0. At higher temperatures, we unexpectedly observe a temperature-dependent renormalization of the spin-excitation energy, which has a strong dependence on field direction. Using theoretical arguments, exact diagonalizations, and finite temperature dynamical Lanczos calculations, we construct a picture of magnon-magnon interactions that naturally explains the observed renormalization. In this work, we show how magnetic field strength and direction may be used to directly tune the sign of the magnon-magnon interaction. This unique scenario is a consequence of the spin-1 nature and has no analog in the more widely studied spin-1/2 systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Structural and magnetic properties of Pt/Co/Mn-based multilayers

Magnetic multilayers are a rich class of material systems with numerous highly tunable physical parameters that determine both their magnetic and electronic properties. Here, we present a comprehensive experimental study of the system Pt/Co/Mn, which extends the group of Pt / Co / X ( X = metal) multilayers that have been investigated thus far. We demonstrate that an increasing Co layer thickness changes the magnetic anisotropy from out of plane to in plane, whereas the deposition of thicker Mn layers leads to a decrease in the saturation magnetization. Temperature-dependent magnetometry measurements reinforce the hypothesis of antiferromagnetic coupling at the Co/Mn interfaces being responsible for the observed Mn thickness dependence of the magnetization reversal. Moreover, magneto-optical imaging experiments indicate systematic changes in magnetic domain patterns as a function of the Co and Mn layer thickness, suggesting the existence of bubblelike domains—potentially even magnetic skyrmions—in the case of sufficiently thick Mn layers, which are expected to contribute to a sizable Dzyaloshinskii-Moriya interaction in the multilayer stacks. As a result, we identify Pt/Co/Mn as a highly complex multilayer system with strong potential for further fundamental studies and possible applications.

36 MATERIALS SCIENCE↗

Magnetic properties of Lutetium and Yttrium doped Ce 2 Fe 14 B magnets

The increasing demand for Nd-Dy and Sm-Co based permanent magnets is exacerbating the current critical materials shortage, therefore improving and optimizing current candidate critical element free permanent magnets is necessary to develop future clean energy technologies. In this work, we aim to increase the thermal stability and magnetic performance of Ce 2 Fe 14 B based permanent magnets through the substitution of Ce ions with noncritical rare earth elements Lu and Y. The substitution of Lu (x=0; 0.05; 0.1; 0.15) for Ce ions in (LuxCe 2-x )Fe 14 B was unsuccessful, likely due to disparities in ionic size and valencies, and failed to exhibit improved thermal stability or magnetic performance. In contrast, Y substitution for Ce ions in (Y x Ce 2-x )Fe14B (x= 0.1; 0.2; 0.3; 0.4; 0.5) alloys was successful. Notably, these alloys demonstrated enhanced thermal stability, as evidenced by an increase in the Curie temperature, reaching a peak of 443 K at x= 0.5. Y substitution also helped to suppress the CeFe2 Laves phase. Without loss of the anisotropy field Y substitution increased the saturation magnetization, MS, peaking at MS = 125 emu/g for a Y concentration of x= 0:4, demonstrating (Y 0.4 Ce 1.6 )Fe 14 B as a potential critical element free permanent magnet with an energy product as high as 29 MGOe. This work is advantageous in developing low cost high performance permanent magnets with reduced or little to no critical rare earth elements.

Rai, Binod K.↗

Mechanical and Thermophysical Properties of 3D-Printed SiC before and after Neutron Irradiation – FY21

This report presents the mechanical and thermophysical properties of 3D-printed SiC before and after neutron irradiation that have been evaluated to assess the fuel matrix material for the Transformational Challenge Reactor (TCR). The TCR fuel form consists of an additively-manufactured silicon carbide (SiC) matrix and uranium nitride tristructural isotropic (UN TRISO) fuel particles, which is manufactured through a newly developed processing route combining binderjet 3D printing, TRISO fuel particle loading, and chemical vapor infiltration (CVI). Because the fuel matrix is a primary component of the TCR core and its response to mechanical and thermal loads during operation is one of the most influential factors on the integrity of TCR core, testing and evaluation have focused on producing mechanical and thermophysical properties data for the binderjet/CVI SiC. Baseline mechanical and thermophysical properties were measured from the disk specimens printed for different and sizes orientations, which included equibiaxial flexural failure strength, elastic constants, thermal diffusivity and conductivity, density, and the coefficient of thermal expansion. Flexural failure strength datasets showed similar Weibull distributions regardless of sample variants including different orientations. The mean failure strengths of the 3D-printed SiC variants were in the range of 280–310 MPa, which are slightly lower than that of the chemical vapor deposition (CVD) SiC. Thermophysical test results showed that specific heat and thermal expansion are not sensitive to the build direction of SiC samples, while thermal conductivity is highly dependent on the build direction and can be correlated to the anisotropic character of the 3D-printed SiC. Neutron irradiation tests were carried out on the 3D-printed 6-mm diameter SiC disk specimens. Irradiation was carried to 2.3 dpa over a temperature range of 360–880°C. No significant degradation in strength was observed in SiC after irradiations in various conditions and with different orientations. Anisotropy that had been observed in the thermal conductivity of 3D-printed SiC prior to irradiation vanished after irradiation as the irradiation defect thermal resistivity accumulated in the material. Electron microscopy of the microstructure after neutron irradiation showed distinct defect morphologies in the heterogenous material, but no evidence for irradiation-induced cracking or degradation in the microstructure was observed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Physical vapor deposition of organic glasses (Final Report)

As of 2009, when this project began, it had been established that physical vapor deposition (PVD) could produce high density and high stability (“ultrastable”) glasses of two organic molecules. With this project, we established that ultrastability was a quite general result for PVD glasses of organic molecules and, in particular, for the organic semiconductors used to produce organic light emitting diodes (OLEDs). We established that ultrastable glasses have enhanced photochemical and chemical stability, and increased resistance to crystallization. We developed a temperature-gradient deposition stage to more efficiently screen the properties of PVD glasses. We established that PVD glasses are usually anisotropic and that this anisotropy can be controlled. We characterized the unusual transformation mechanism of PVD glasses, which superficially is more similar to crystals than liquid-cooled glasses. In the most recent grant cycle, we extended these results to co-deposition of two organic semiconductors, showing that mixed PVD glasses of these systems usually showed ultrastability and high density; in two cases, co-deposition results in component segregation, and deposition conditions can be adjusted to control domain size. In our work since 2009, we established that the surface equilibration mechanism can successfully explain almost all of the properties of PVD glasses, and that this mechanism can provide useful predictions regarding stability and anisotropy.

36 MATERIALS SCIENCE↗

Manipulation of Emergent Collective Excitations via Composition Control in Mixed MPX 3 Correlated 2D Antiferromagnets

Transition metal (i.e., Mn, Fe, Cr) and chalcogen (Se) substituents are introduced into single-crystalline NiPS 3 , and the evolution of the two emergent quasi-particle excitations characteristic to the XXZ correlated antiferromagnetism of NiPS 3 (i.e., spin orbit entangled exciton (SOX) and two-magnon scattering (2M )) are investigated as functions of substituent concentration through comprehensive room- and low-temperature photoluminescence (PL) and Raman spectroscopy studies. These findings are further correlated with the magnetic properties of the same set of compounds reported in prior studies. The work revealed that the SOX emission intensities and linewidths are mainly controlled by the magnetic anisotropy and spin orientations, and are strongly suppressed by the introduction of substituents. The suppression depends on the type of substituent, with Fe affecting the SOX emission more than Mn and Cr. The 2 M scattering is linked to short-range correlations and exhibits greater resiliency against metal atom substitution. While the 2M peak at low temperature gets suppressed and red-shifted in frequency with increasing concentrations of all the substituents, Fe induces the weakest suppression compared to all other substituents. Altogether, these findings revealed the introduction of substituents as a powerful route to control the emergent collective excitations in NiPS 3 and mixed-MPX 3 materials.

2D magnet↗

Local strain-dependent electronic structure and perpendicular magnetic anisotropy of a MnGaN 2D magnetic monolayer

Local strain-dependent spin-polarized electronic structure of a two-dimensional (2D) magnetic layer is an exciting property for practical applications. For example, it holds the promise for advanced ultrathin spintronic nanodevices with customized electronic and magnetic properties by local strain engineering. Here, we demonstrate that the spin-polarized electronic structure of a 2D manganese gallium nitride (MnGaN-2D) magnetic monolayer is sensitive to intrinsic local lattice strain, as proven by first-principles calculations and indicated by scanning tunneling spectroscopy measurements. Atomic resolution images reveal a highly non-Gaussian lattice spacing/strain distribution, while the spectroscopy reveals variations in the electronic density of states. Simulations of the MnGaN-2D monolayer based on first-principles calculations, including both isotropic and anisotropic strains, confirm a highly strain-dependent manganese partial density of states. Spin-orbit coupling is included which indicates either out-of-plane perpendicular magnetic anisotropy (PMA) or in-plane magnetic anisotropy, dependent on the type of strain whether compressive or tensile, suggesting that MnGaN-2D is magnetoelastic. The MnGaN-2D PMA is further supported by superconducting quantum interference device magnetometry measurements which reveal a high spin polarization of ~ 79 % at room temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Competing Electronic Ground States in the Heavy-Fermion Superconductor CeRh 2 As 2

CeRh 2 ⁢As 2 is rare among superconductors, in that the magnetic field tunes it between two distinct superconducting phases. Combined with a lack of local inversion symmetry and an upper critical field exceeding the Pauli paramagnetic limit, this excitingly suggests triplet multicomponent superconductivity. Preceding the superconducting onset, 𝑓-electron correlations cause long-range order, attributed both to local antiferromagnetism and itinerant (quadrupole) density waves. A magnetic field provides a significant perturbation of the 𝑓 electrons and may reveal the nature of the many-body correlations. Therefore, we report comprehensive magnetization and magnetotransport studies on microstructured devices in fields of up to 73 T. Applied along the 𝑐 axis, the field causes a low-temperature change of majority (hole) carrier density at 𝜇 0⁢ 𝐻 ≈ 2⁢4 T. By contrast, in-plane fields produce a cascade of phase transitions; the field-induced in-plane conductivity anisotropy and lack of accompanying magnetic features, plus the closed-dome nature of the overall phase boundary is consistent with a hierarchy of field-induced density-wave states.

36 MATERIALS SCIENCE↗

Multichannel Topological Kondo Effect

A Coulomb blockaded M-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity “spin” transforms under the orthogonal group SO⁡(M). The impurity spin stems from the nonlocal topological ground state degeneracy of the island and thus the effect is known as the topological Kondo effect. We introduce a physically motivated N-channel generalization of the topological Kondo model. Starting from the simplest case N =2, we conjecture a stable intermediate coupling fixed point and evaluate the resulting low-temperature impurity entropy. The impurity entropy indicates that an emergent Fibonacci anyon can be realized in the N =2 model. We also map the case N =2, M =4 to the conventional four-channel Kondo model and find the conductance at the intermediate fixed point. By using the perturbative renormalization group, we also analyze the large-N limit, where the fixed point moves to weak coupling. In the isotropic limit, we find an intermediate stable fixed point, which is stable to “exchange” coupling anisotropies, but unstable to channel anisotropy. We evaluate the fixed point impurity entropy and conductance to obtain experimentally observable signatures of our results. Here, in the large-N limit, we evaluate the full crossover function describing the temperature-dependent conductance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗