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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Mg vacancy and impurity-limited MgO single crystal thermal conductivity

Magnesium oxide (MgO) exhibits one of the highest thermal conductivities among oxides and is widely used as a dielectric material and substrate in semiconductor devices, in refractory applications, and as a promising filler in thermal interface materials for electronics. Its high thermal conductivity may be sensitive to impurity and defects, yet this influence is still uncertain. Here, in this study, the impact of the common impurities, i.e., Al, Ca, Ti, V, Fe, Si, B, Nb, Zr, Na, and K, as well as Mg and O vacancies on phonon scattering and thermal conductivity of MgO is studied using a fully first-principles T-matrix framework. It is found that B, Nb, and Zr impurities, along with Mg vacancies, lead to exceptionally strong reductions in thermal conductivity. By contrast, O vacancies and other impurities have modest to minimal impacts. Leveraging the T-matrix results, we reassess the perturbative, mass-only formalism whose use is pervasive in the literature and show that neglecting bond disorder does not necessarily lead to underestimation: for all transition-metal impurities studied, bond perturbations partially cancel mass disorder, causing the traditional perturbative model to overestimate scattering. We propose a simple modified perturbative expression that incorporates both mass and bond disorder and closely reproduces the T-matrix trends. Our predicted low-temperature trends by including phonon-impurity and phonon-boundary scattering match reasonably well with experiments. This work provides an in-depth study of impurity- and vacancy-limited thermal conductivity of MgO and suggests that reported “high-purity” MgO values have likely not yet reached the intrinsic upper limit, which may be substantially higher.

36 - MATERIALS SCIENCE↗
DOE OSTI2020

Unveiling the critical role of interfacial ionic conductivity in all-solid-state lithium batteries

Advancement of all-solid-state lithium-ion (Li + ) batteries (ASSLIBs) has been hindered by the large interfacial resistance mainly originating from interfacial reactions between oxide cathodes and solid-state sulfide electrolytes (SEs). To suppress the interfacial reactions, an interfacial coating layer between cathodes and SEs is indispensable. However, the kinetics of interfacial Li + transport across the coating layer has not been well understood yet. Herein, we tune the interfacial ionic conductivity of the coating layer LiNb 0.5 Ta 0.5 O 3 (LNTO) by manipulating post-annealing temperature. It is found that the interfacial ionic conductivity determines interfacial Li + transport kinetics and enhancing the interfacial ionic conductivity can significantly boost the electrochemical performance of SE-based ASSLIBs. A representative cathode LiNi 0.5 Mn 0.3 Co 0.2 O 2 coated by LNTO with the highest interfacial ionic conductivity exhibits a high initial capacity of 152 mAh.g -1 at 0.1 C and 107.5 mAh.g -1 at 1C. This work highlights the importance of increasing interfacial ionic conductivity for high-performance SE-based ASSLIBs.

25 ENERGY STORAGE↗
DOE OSTI2022

Robust and Highly Conductive Water-Stable Copper Iodide-Based Hybrid Single Crystals

High conductivity, carrier mobility as well as long diffusion length are critical for highly efficient solar cells. Here, we report new types of crystalline inorganic-organic hybrid semiconductors, 2D-Cu 2 I 2 (L) [L = benzo[c][1,2,5]thiadiazole (bs) and benzo[c][1,2,5] selenadiazole (bse)], composed of one-dimensional (1D) copper iodide staircase-like chain and benzodiazole-based ligands. These compounds possess narrow and tunable band gaps and high conductivity. High-quality large single crystals of 2D-Cu 2 I 2 (bse) were grown and used to evaluate the charge transport properties of the material. State-of-the-art time-resolved microwave conductivity (TRMC) techniques were used to investigate the charge carrier dynamics, from which a high conductivity of 2 × 10 -4 S/cm, a carrier mobility of ~1 cm 2 V -1 s -1 , a maximum doping/carrier density of 2 +/- 1 × 10 15 cm -3 , and a diffusion length of ~0.17 um were obtained. We report the excellent water/chemical stability combined with high conductivity makes this I-VII-based hybrid material family promising candidates for potential optoelectronic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

In Situ Structural and Electrical Conductivity Characterization of Sr2MMoO6-δ Double Perovskite Solid Oxide Fuel Cell Anode Materials

In this study, a series of Sr 2 MMoO 6-δ double perovskite solid oxide fuel cell (SOFC) anode materials (where 0 <= δ <= 0.041 and M = Fe, Co, or Ni) were synthesized, and the changes in their morphologies under relevant SOFC operating conditions were explored. Ultra-small-angle X-ray scattering (USAXS), small-angle X-ray scattering (SAXS), and wide-angle X-ray scattering (WAXS) were used to determine changes in the microstructures and phase compositions of the anode materials at high temperatures and under a reducing atmosphere. The stability of the double perovskite structure was found to be highly dependent on the identity of the cation M, such that when M = Fe, the material remained stable over the course of the experiments. However, when M = Co or Ni, significant changes in the microstructure and phase composition were observed. An in situ study of the M = Co sample, in which electrical conductivity and USAXS/SAXS/WAXS measurements were conducted simultaneously, revealed the structural degradation mechanisms and electrical conductivity changes over a range of temperatures. To conduct these measurements, a cell was developed that allowed for a sample mounted on Pt wires to be placed in the X-ray beam and heated under gas flow comprising 4% mass H 2 and 96% mass N 2 . The resulting measurements allowed for the direct comparison of the electrical and morphological changes occurring in the material under operating conditions, such that increases in conductivity could be attributed to the growth of new phases.

25 ENERGY STORAGE↗
DOE OSTI2020

Polymer–Ceramic Composite Electrolytes for Lithium Batteries: A Comparison between the Single-Ion-Conducting Polymer Matrix and Its Counterpart

Single-ion-conducting polymer electrolytes are attractive to use in lithium batteries as the transference number of the lithium cation approaches unity. This helps prevent concentration gradients across the electrolyte, which can result in dendrite formation. The addition of ceramic particles to polymer electrolytes at high loadings can increase the mechanical strength of the polymer, which can also help suppress dendrite formation. Here, a single-ion-conducting polymer electrolyte is blended with lithium-conducting oxide ceramic particles to make a composite electrolyte. This electrolyte is studied in comparison to a composite electrolyte containing freely dissolved lithium salt. It is found that the addition of ceramic particles to the single-ion-conducting polymer can result in increased cation dissociation and consequent increased ionic conductivity. The electrolytes are cycled in lithium symmetrical cells, and it is found that the ceramic-containing electrolytes show increased interfacial stability with the lithium metal compared to the pristine polymer electrolytes. Our findings shed light on how to optimize the polymer host chemistry to form composite electrolytes that can meet the challenging requirements to stabilize the lithium metal anode.

25 ENERGY STORAGE↗
DOE OSTI2020

Rational Designed Mixed-Conductive Sulfur Cathodes for All-Solid-State Lithium Batteries

All-solid-state lithium–sulfur batteries (ASSLSBs) hold great promise for safe and high-energy-density energy storage. However, developing high-performance sulfur cathodes has been proven difficult due to low electronic and ionic conductivities and large volume change of sulfur during charge and discharge. Here, we reported an approach to synthesize sulfur cathodes with a mixed electronic and ionic conductivity by infiltrating a solution consisting of Li 3 PS 4 (LPS) solid electrolyte and S active material into a mesoporous carbon (CMK-3). This approach leads to a uniform dispersion of amorphous Li 3 PS 7 (L 3 PS) catholyte in an electronically conductive carbon matrix, enabling high and balanced electronic/ionic conductivities in the cathode composite. The inherent porous structure of CMK-3 also helps to accommodate the strain/stress generated during the expansion and shrinkage of the active material. In sulfide-based all-solid-state batteries with Li metal as the anode, this cathode composite delivered a high capacity of 1025 mAh g –1 after 50 cycles at 60 °C at 1/8C. This work highlights the important role of high and balanced electronic and ionic conductivities in developing high-performance sulfur cathodes for ASSLSBs.

25 ENERGY STORAGE↗
DOE OSTI2023

Thickness-Dependent Cross-Plane Thermal Conductivity Measurements of Exfoliated Hexagonal Boron Nitride

Submicrometer-thick layers of hexagonal boron nitride (hBN) exhibit high in-plane thermal conductivity and useful optical properties, and serve as dielectric encapsulation layers with low electrostatic inhomogeneity for graphene devices. Despite the promising applications of hBN as a heat spreader, the thickness dependence of its cross-plane thermal conductivity is not known, and the cross-plane phonon mean free paths (MFPs) have not been measured. We measure the cross-plane thermal conductivity of hBN flakes exfoliated from bulk crystals. We find that submicrometer thick flakes exhibit thermal conductivities up to 8.1 ± 0.5 W m –1 K –1 at 295 K, which exceeds previously reported bulk values by more than 60%. Surprisingly, the average phonon mean free path is found to be several hundred nanometers at room temperature, a factor of 5 larger than previous predictions. When planar twist interfaces are introduced into the crystal by mechanically stacking multiple thin flakes, the cross-plane thermal conductivity of the stack is found to be a factor of 7 below that of individual flakes with similar total thickness, thus providing strong evidence that phonon scattering at twist boundaries limits the maximum phonon MFPs. These results have important implications for hBN integration in nanoelectronics and improve our understanding of thermal transport in twodimensional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Yttrium Contenting Compositionally Complex Medium-Entropy Li-Garnet Electrolyte with Improved Ionic Conductivity

The compositionally complex medium/high-entropy design concept can greatly expand the categories and affect the properties of the materials. With such a designing concept, a medium-entropy Li-garnet electrolyte with appropriate yttrium content (formula Li 6.6 La 3 ZrNb 0.3 Ta 0.3 Hf 0.3 Y 0.1 O 12 ) shows a record-high ionic conductivity of ∼5.7 × 10 –4 S/cm, the highest reported for any single-site substituted high/medium-entropy Li-garnet. The assembled Li metal symmetric cells also show stable long-term cycling (0.1 mA/cm 2 for over 200 h). Neutron powder diffraction and Rietveld refinement results indicate that a competing conduction mechanism between (1) occupancy on high mobility of 96h sites and (2) the associated site vacancies and the bond length requires an appropriate content of Y for enhanced ionic conductivity. Li-ion hopping through the bottleneck can also contribute to the conductivity. Finally, density functional theory and Born–Oppenheimer molecular dynamics simulations also indicate the high mobility and number of hopping transitions of Li ions, contributing to the high ionic conductivity.

Li-garnet↗
DOE OSTI2026

Proton Conducting Silicon Oxide Membranes as a Fluorine Free Alternative to Nafion for Low Temperature Water Electrolysis

Driven by environmental and health concerns related to per- and polyfluoroalkyl substances (PFAS), there has been growing interest in developing fluorine-free proton (H + ) exchange membrane (PEM) materials for fuel cells and water electrolyzers. In this study, we present a side-by-side comparison of the key transport properties of submicron thick, PFAS-free amorphous silicon dioxide (SiO 2 ) membranes to Nafion, a fluorinated polymer electrolyte membrane that represents the industry standard for PEM fuel cells and electrolyzers. Here, measurements of proton (H + ) conductivity (σ H + ), hydrogen (H 2 ) permeability (P H 2 ), and electrical resistivity (ρ e – ) were conducted using model thin films comprised of SiO 2 membranes deposited by atomic layer deposition (ALD). Although the H + conductivity of the SiO 2 membranes is 2–3 orders of magnitude lower than Nafion, the addition of phosphorus dopants (PO x ) improves H + conductivity such that the area specific membrane resistance of thin (<50 nm) PO x -doped SiO 2 membranes is more than an order of magnitude lower than Nafion-117. Importantly, the safe operation of such nanoscale membranes within a PEM electrolyzer is feasible thanks to the low H 2 permeability of dense SiO 2 -based membranes, which are predicted to limit H 2 crossover rates to acceptable levels for pressures up to ≈ 100 bar. As a proof-of-principle demonstration, a chip-scale water electrolyzer based on 100 nm thick PO x -SiO 2 membrane is shown to achieve a current density of 2 A cm –2 at a potential of 2.5 V. If this technology can be successfully scaled up, H + conducting oxide membranes offer an attractive PFAS-free alternative to Nafion for efficient and durable water electrolysis and fuel cell technologies.

Nafion↗
DOE OSTI2021

Pore-Confined Polymers Enhance the Thermal Conductivity of Polymer Nanocomposites

In this work, molecularly confined polymer fillers in nanopores were found to give superior mechanical properties of polymer nanocomposites. In this work, we study the thermal conductivity of such nanocomposites and unveil the effect of polymer confinement on thermal conductivity. Using the time-domain thermoreflectance method, we measure the cross-plane thermal conductivity of polymer nanocomposites that consist of polystyrene fillers confined within a nanoporous organosilicate matrix. Compared to unconfined bulk polystyrene fillers, we find that pore-confined polystyrene fillers enhance the thermal conductivity of the polymer nanocomposites. This enhancement is attributed to the better aligned and less entangled chains in the confined phase, where chain–chain phonon scatterings are reduced. Our work provides essential insights into the thermal conductivity of polymer nanocomposites for multifunctional thermal and mechanical applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Critical Role of Framework Flexibility and Disorder in Driving High Ionic Conductivity in LiNbOCl 4

Understanding Li-ion transport is key for the rational design of superionic solid electrolytes with exceptional ionic conductivities. LiNbOCl 4 is reported to be one of the most highly conducting materials in the recently realized new class of soft oxyhalide solid electrolytes, exhibiting an ionic conductivity of ~11 mS·cm -1 . Here, we apply X-ray/neutron diffraction and pair distribution function analysis - coupled with density functional theory/ab-initio molecular dynamics - to determine a structural model that provides a rationale for the high conductivity that we observe experimentally in this nanocrystalline solid. We show that it arises from unusually high framework flexibility at room temperature. This owes to isolated 1-D [NbOCl 4 ] - anionic chains which exhibit energetically favorable orientational disorder that is - in turn - correlated to multiple, disordered and equi-energetic Li + sites in the lattice. As the Li-ions sample the 3-D energy landscape with a fast predicted diffusion coefficient of 5.1 x 10 -7 cm 2 /s at room temperature (σ i calc = 17.4 mS·cm -1 ), the inorganic polymer chains can reorient or vice versa. The activation energy barrier for Li migration through the frustrated energy landscape is especially reduced by the elastic nature of the NbO 2 Cl 4 octahedra evident from very widely dispersed Cl-Nb-Cl bond angles in AIMD snapshots at 300 K. The phonon spectra are predominantly influenced by Cl vibrations in the low energy range, and there is strong overlap between the framework (Cl, Nb) and Li partial pDOS in the region between 1.2 - 4.0 THz. The framework flexibility is also reflected in a relatively low bulk modulus of 22 GPa. In conclusion, our findings pave the way for investigation of future “flex-ion” inorganic solids and open up a new direction for the design of high conductivity, soft solid electrolytes for all-solid-state batteries.

AIMD↗
DOE OSTI2020

A New Class of Ionically Conducting Fluorinated Ether Electrolytes with High Electrochemical Stability

Increasing battery energy density is greatly desired for applications such as portable electronics and transportation. However, many next-generation batteries are limited by electrolyte selection because high ionic conductivity and poor electrochemical stability are typically observed in most electrolytes. For example, ether-based electrolytes have high ionic conductivity but are oxidatively unstable above 4 V, which prevents the use of high-voltage cathodes that promise higher energy densities. In contrast, hydrofluoroethers (HFEs) have high oxidative stability but do not dissolve lithium salt. Here, we synthesize a new class of fluorinated ether electrolytes that combine the oxidative stability of HFEs with the ionic conductivity of ethers in a single compound. We show that conductivities of up to 2.7 × 10 –4 S/cm (at 30 °C) can be obtained with oxidative stability up to 5.6 V. The compounds also show higher lithium transference numbers compared to typical ethers. Furthermore, we use nuclear magnetic resonance (NMR) and molecular dynamics (MD) to study their ionic transport behavior and ion solvation environment, respectively. Finally, we demonstrate that this new class of electrolytes can be used with a Ni-rich layered cathode (NMC 811) to obtain over 100 cycles at a C/5 rate. The design of new molecules with high ionic conductivity and high electrochemical stability is a novel approach for the rational design of next-generation batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Machine learning-enabled discovery of ionic liquid–solvent electrolytes exhibiting high ionic conductivity

Ionic liquids (ILs), which are a class of materials with versatile nature and growing popularity, are facing impediments toward widespread usage as electrolytes due to various factors such as low ionic conductivity, high viscosity, high market price etc. One of the ways these limitations can be addressed is by mixing ILs with a molecular solvent. In a combinatorial sense, there exists an immense number of specific IL–solvent combinations. An exhaustive experimental or even simulation-based investigation of the chemical space spanned by such combinations can be extremely time-consuming, expensive, and nearly impossible. An alternative approach is to employ machine learning-based models developed from available databases. Although there exists prior literature that integrates machine learning to investigate mixtures of specific solvents with ILs, these models lack generalization necessitating development of a large number of ML models to handle various solvents. To remedy this shortcoming, as a part of designing green electrolytes with high ionic conductivity that can have potential applications in next-generation batteries and solar cells, this work aims to develop a unified machine learning model to predict ionic conductivity of any IL–solvent mixture system. In this regard, three models, namely, Random Forest, extreme gradient boosting (XGBoost), and artificial neural network (ANN) were formulated using the NIST ILThermo database. The dataset contained 549 unique ionic liquids from 16 cation families and 81 unique solvents, representing a total of 23 712 datapoints. SHAPLEY additive explanation (SHAP) method was used to assess the impact of various features on model prediction and their significance was compared with literature to gain physical insight about the model behavior. Finally, using the developed models, approximately 2.5 million IL–solvent mixtures at five different compositions were screened at room temperature. The high-throughput screening yielded nearly 19 000 IL–solvent mixtures for which ionic conductivity was found to exceed the ionic conductivity of conventional Li-ion battery electrolyte.

25 ENERGY STORAGE↗
DOE OSTI2020

A comprehensive conductivity model for drift and micro-tearing modes

The parallel electrical conductivity is a crucial parameter in the study of the linear stability of drift-modes like the micro-tearing mode (MTM). The conductivity enters by closing the electromagnetic tearing layer equations. Recent progress in the understanding of the pedestal suggests that the MTM could play an important role in its structure and evolution. For this reason, we revisit and improve previous model conductivities. This parameter is generally derived from the linearized drift kinetic equation. In the past literature, it has been computed using either simplified collision operators or neglecting the spatial dependence away from the rational surface. Here, a fully consistent expression for the conductivity that would accurately model the pedestal has not been available. By applying a novel variational procedure and with the full Fokker Plank collision operator, including electron–electron collisions, we compute a closed expression for the parallel electrical conductivity in the form of a rational function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Observation of a highly conductive warm dense state of water with ultrafast pump–probe free-electron-laser measurements

The electrical conductivity of water under extreme temperatures and densities plays a central role in modeling planetary magnetic fields. Experimental data are vital to test theories of high-energy-density water and assess the possible development and presence of extraterrestrial life. These states are also important in biology and chemistry studies when specimens in water are confined and excited using ultrafast optical or free-electron lasers (FELs). Here we utilize femtosecond optical lasers to measure the transient reflection and transmission of ultrathin water sheet samples uniformly heated by a 13.6 nm FEL approaching a highly conducting state at electron temperatures exceeding 20 000 K. The experiment probes the trajectory of water through the high-energy-density phase space and provides insights into changes in the index of refraction, charge carrier densities, and AC electrical conductivity at optical frequencies. At excitation energy densities exceeding 10 MJ/kg, the index of refraction falls to n = 0.7, and the thermally excited free-carrier density reaches ne = 5 × 1027 m−3, which is over an order of magnitude higher than that of the electron carriers produced by direct photoionization. Significant specular reflection is observed owing to critical electron density shielding of electromagnetic waves. The measured optical conductivity reaches 2 × 104 S/m, a value that is one to two orders of magnitude lower than those of simple metals in a liquid state. At electron temperatures below 15 000 K, the experimental results agree well with the theoretical calculations using density-functional theory/molecular-dynamics simulations. With increasing temperature, the electron density increases and the system approaches a Fermi distribution. In this regime, the conductivities agree better with predictions from the Ziman theory of liquid metals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Simultaneous determination of electrical conductivity and thickness of nonmagnetic metallic foils using two-sided multifrequency eddy current techniques

Here, in this paper, we describe a simple method for performing multifrequency eddy current characterization of free-standing uniform-thickness metallic foils using a forked inductive coil arrangement. The method involves measuring the mutual inductance between two coils when a foil is present between the coils, and when it is not present; the ratio of these mutual inductances is compared with an analytical solution, and foil conductivity, thickness, and sheet resistance are simultaneously estimated using numerical inversion and least-squares fitting. This method was used to characterize 34 non-ferrous metallic samples with thicknesses between 50 and 640 μm and with conductivities between 0.8 × 10 7 and 5.8 × 10 7 S/m. The estimated thicknesses from eddy current characterization agreed well with those measured using confocal optical techniques; the two approaches agreed to within 1 μm for samples that were thinner than 200 μm, and to within 0.5% for samples that had a thickness of 200 μm or greater. The estimated conductivities from eddy current characterization were in close agreement with expected values, given knowledge of the materials used. A particular strength of this approach is that the instrumentation needed is broadly available in research and development laboratories and the associated fixturing is easy to manufacture and assemble. A calibration procedure is described that can be used to reduce errors from geometric uncertainties. This calibration requires a sample that has only a known conductivity or thickness; both do not need to be known. The method described herein is likely extensible to conductivities and thickness well outside the ranges measured as part of this work.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Enhancement of Thermal Conductivity of Bentonite Buffer Materials with Copper Wires/Meshes for High-Level Radioactive Waste Disposal

In high-level radioactive waste disposal, a heat-generating waste canister is generally encased with a layer of bentonite-based buffer material acting as an engineered barrier to limit water percolation and radionuclide release. The low thermal conductivity of bentonite (~0.5 W/m∙K) combined with a high thermal loading waste package may result in a high surface temperature on the package that can potentially impact the structural integrity of the package itself as well as the surrounding buffer material. We show in this paper that the thermal conductivity of bentonite can be effectively enhanced by embedding copper wires/meshes across the buffer layer to form fully connected high heat conduction pathways. A simple calculation based on Rayleigh’s model shows that a required thermal conductivity of 5 W/m∙K for effective heat dissipation can be achieved simply by adding ~1 vol % of copper wires/meshes into bentonite. As a result, the peak surface temperature on a large waste package such as a dual-purpose canister can be reduced by up to 300°C, leading to a significant reduction in the surface storage time for waste cooling and therefore the overall cost for direct disposal of such waste packages. Because of the ensured full thermal percolation across the buffer layer, copper wires/meshes turn out to be much more effective than any other materials currently suggested (such as graphene or graphite) in enhancing the thermal conductivity of buffer material. Furthermore, the embedded copper wires/meshes can help reinforce the mechanical strength of the buffer material, thus preventing the material from a potential erosion by a possible intrusion of dilute groundwater.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Implications of phonon anisotropy on thermal conductivity of fluorite oxides

Abstract Fluorite oxides are attractive ionic compounds for a range of applications with critical thermal management requirements. In view of recent reports alluding to anisotropic thermal conductivity in this face-centered cubic crystalline systems, we perform a detailed analysis of the impact of direction-dependent phonon group velocities and lifetimes on the thermal transport of fluorite oxides. We demonstrate that the bulk thermal conductivity of this class of materials remains isotropic despite notable anisotropy in phonon lifetime and group velocity. However, breaking the symmetry of the phonon lifetime under external stimuli including boundary scattering present in nonequilibrium molecular dynamics simulations of finite size simulation cell gives rise to apparent thermal conductivity anisotropy. We observe that for accurate determination of thermal conductivity, it is important to consider phonon properties not only along high symmetry directions commonly measured in inelastic neutron or x-ray scattering experiments but also of those along lower symmetry. Our results suggests that certain low symmetry directions have a larger contribution to thermal conductivity compared to high symmetry ones.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗