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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms

Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan's law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test was first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. Finally, the simulations show that dislocations exhibit some self-organized structures as the strain is increased.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Defect filtering for thermal expansion induced dislocations in III–V lasers on silicon

Epitaxially integrated III–V semiconductor lasers for silicon photonics have the potential to dramatically transform information networks, but currently, dislocations limit performance and reliability even in defect-tolerant InAs quantum dot (QD)-based lasers. Despite being below the critical thickness, QD layers in these devices contain previously unexplained misfit dislocations, which facilitate non-radiative recombination. We demonstrate here that these misfit dislocations form during post-growth cooldown due to the combined effects of (1) thermal-expansion mismatch between the III–V layers and silicon and (2) mechanical hardening in the active region. By incorporating an additional sub-critical thickness, indium-alloyed “misfit dislocation trapping layer,” we leverage these mechanical hardening effects to our advantage, displacing 95% of misfit dislocations from the QD layer in model structures. Unlike conventional dislocation mitigation strategies, the trapping layer reduces neither the number of threading dislocations nor the number of misfit dislocations. It simply shifts the position of misfit dislocations away from the QD layer, reducing the defects' impact on luminescence. In full lasers, adding a misfit dislocation trapping layer both above and below the QD active region displaces misfit dislocations and substantially improves performance: we measure a twofold reduction in lasing threshold currents and a greater than threefold increase in output power. Overall, our results suggest that devices employing both traditional threading dislocation reduction techniques and optimized misfit dislocation trapping layers may finally lead to fully integrated, commercially viable silicon-based photonic integrated circuits.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Hydrogen diffusion in the elastic fields of dislocations in iron

The effect of dislocation stress fields on the sink efficiency thereof is studied for hydrogen interstitial atoms at temperatures of 293 and 600 K and at a dislocation density of 3 × 10{sup 14} m{sup –2} in bcc iron crystal. Rectilinear full screw and edge dislocations in basic slip systems 〈111〉(110), 〈111〉(112), 〈100〉(100), and 〈100〉(110) are considered. Diffusion of defects is simulated by means of the object kinetic Monte Carlo method. The energy of interaction between defects and dislocations is calculated using the anisotropic theory of elasticity. The elastic fields of dislocations result in a less than 25% change of the sink efficiency as compared to the noninteracting linear sink efficiency at a room temperature. The elastic fields of edge dislocations increase the dislocation sink efficiency, whereas the elastic fields of screw dislocations either decrease this parameter (in the case of dislocations with the Burgers vector being 1/2〈111〉) or do not affect it (in the case of dislocations with the Burgers vector being 〈100〉). At temperatures above 600 K, the dislocations affect the behavior of hydrogen in bcc iron mainly owing to a high binding energy between the hydrogen atom and dislocation cores.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Characterization of dislocation structures and deformation mechanisms in as-grown and deformed directionally solidified NiAl–Mo composites

In this paper, directionally solidified (DS) NiAl–Mo eutectic composites were strained to plastic strain values ranging from 0% to 12% to investigate the origin of the previously observed stochastic versus deterministic mechanical behaviors of Mo-alloy micropillars in terms of the development of dislocation structures at different pre-strain levels. The DS composites consist of long, [1 0 0] single-crystal Mo-alloy fibers with approximately square cross-sections embedded in a [1 0 0] single-crystal NiAl matrix. Scanning transmission electron microscopy (STEM) and computational stress state analysis were conducted for the current study. STEM of the as-grown samples (without pre-straining) reveal no dislocations in the investigated Mo-alloy fibers. In the NiAl matrix, on the other hand, a(1 0 0)-type dislocations exist in two orthogonal orientations: along the [1 0 0] Mo fiber axis, and wrapped around the fiber axis. They presumably form to accommodate the different thermal contractions of the two phases during cool down after eutectic solidification. At intermediate pre-strain levels (4–8%), a/2(1 1 1)-type dislocations are present in the Mo-alloy fibers and the pre-existing dislocations in the NiAl matrix seem to be swept toward the interphase boundary. Some of the dislocations in the Mo-alloy fibers appear to be transformed from a(1 0 0)-type dislocations present in the NiAl matrix. Subsequently, the transformed dislocations in the fibers propagate through the NiAl matrix as a(1 1 1) dislocations and aid in initiating additional slip bands in adjacent fibers. Thereafter, co-deformation presumably occurs by (1 1 1) slip in both phases. With a further increase in the pre-strain level (>10%), multiple a/2(1 1 1)-type dislocations are observed in many locations in the Mo-alloy fibers. Interactions between these systems upon subsequent deformation could lead to stable junctions and persistent dislocation sources. Finally, the transition from stochastic to deterministic, bulk-like behavior in sub-micron Mo-alloy pillars may therefore be related to an increasing number of multiple a(1 1 1) dislocation systems within the Mo fibers with increasing pre-strain, considering that the bulk-like behavior is governed by the forest hardening of these junctions.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Nanoscale dislocation shear loops at static equilibrium and finite temperature

Atomistic simulations are used to determine the resolved shear stress necessary for equilibrium and the resulting geometry of nanoscale dislocation shear loops in Al. Dislocation loops with different sizes and shapes are created via superposition of elemental triangular dislocation displacement fields in the presence of an externally imposed shear stress. First, a bisection algorithm is developed to determine systematically the resolved shear stress necessary for equilibrium at 0 K. Here, this approach allows for the identification of dislocation core structure and a correlation between dislocation loop size, shape and the computed shear stress for equilibrium. It is found, in agreement with predictions made by Scattergood and Bacon, that the equilibrium shape of a dislocation loop becomes more circular with increasing loop size. Second, the bisection algorithm is extended to study the influence of temperature on the resolved shear stress necessary for stability. An approach is presented to compute the effective lattice friction stress, including temperature dependence, for dislocation loops in Al. The temperature dependence of the effective lattice friction stress can be reliably computed for dislocation loops larger than 16.2 nm. However, for dislocation loops smaller than this threshold, the effective lattice friction stress shows a dislocation loop size dependence caused by significant overlap of the stress fields on the interior of the dislocation loops. Combined, static and finite temperature atomistic simulations provide essential data to parameterize discrete dislocation dynamics simulations.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

Situating the Vector Density Approach Among Contemporary Continuum Theories of Dislocation Dynamics

Abstract For the past century, dislocations have been understood to be the carriers of plastic deformation in crystalline solids. However, their collective behavior is still poorly understood. Progress in understanding the collective behavior of dislocations has primarily come in one of two modes: the simulation of systems of interacting discrete dislocations and the treatment of density measures of varying complexity that are considered as continuum fields. A summary of contemporary models of continuum dislocation dynamics is presented. These include, in order of complexity, the two-dimensional statistical theory of dislocations, the field dislocation mechanics treating the total Kröner–Nye tensor, vector density approaches that treat geometrically necessary dislocations on each slip system of a crystal, and high-order theories that examine the effect of dislocation curvature and distribution over orientation. Each of theories contain common themes, including statistical closure of the kinetic dislocation transport equations and treatment of dislocation reactions such as junction formation. An emphasis is placed on how these common themes rely on closure relations obtained by analysis of discrete dislocation dynamics experiments. The outlook of these various continuum theories of dislocation motion is then discussed.

Engineering↗
DOE OSTI2016

Solute drag on perfect and extended dislocations

The drag force exerted on a moving dislocation by a field of mobile solutes is studied in the steady state. The drag force is numerically calculated as a function of the dislocation velocity for both perfect and extended dislocations. The sensitivity of the non-dimensionalized force–velocity curve to the various controlling parameters is assessed, and an approximate analytical force–velocity expression is given. A non-dimensional parameter S characterizing the strength of the solute-dislocation interaction, the background solute fraction , and the dislocation character angle , are found to have the strongest influence on the force–velocity curve. Within the model considered here, a perfect screw dislocation experiences no solute drag, but an extended screw dislocation experiences a non-zero drag force that is about 10 to 30% of the drag on an extended edge dislocation. The solutes can change the spacing between the Shockley partials in both stationary and moving extended dislocations, even when the stacking fault energy remains unaltered. Under certain conditions, the solutes destabilize an extended dislocation by either collapsing it into a perfect dislocation or causing the partials to separate unboundedly. It is proposed that the latter instability may lead to the formation of large faulted areas and deformation twins in low stacking fault energy materials containing solutes, consistent with experimental observations of copper and stainless steel containing hydrogen.

42 ENGINEERING↗
DOE OSTI2018

Line tension of a dislocation moving through an anisotropic crystal

Plastic deformation, at all strain rates, is accommodated by the collective motion of crystalline defects known as dislocations. In this paper, we extend an analysis for the energetic stability of a straight dislocation, the so-called line tension (Γ), to steady-state moving dislocations within elastically anisotropic media. Upon simplification to isotropy, our model reduces to an explicit analytical form yielding insight into the behaviour of Γ with increasing velocity. We find that at the first shear wave speed within an isotropic solid, the screw dislocation line tension diverges positively indicating infinite stability. The edge dislocation line tension, on the other hand, changes sign at approximately 80% of the first shear wave speed, and subsequently diverges negatively indicating that the straight configuration is energetically unstable. In anisotropic crystals, the dependence of Γ on the dislocation velocity is significantly more complex; at velocities approaching the first shear wave speed within the plane of the crystal defined by the dislocation line, Γ tends to diverge, with the sign of the divergence strongly dependent on both the elastic properties of the crystal and the orientation of the dislocation line. We interpret our analyses within the context of recent molecular dynamics simulations of the motion of dislocations near the first shear wave speed. Both the simulations and our analyses are indicative of instabilities of nominally edge dislocations within fcc crystals approaching the first shear wave speed. Finally, we apply our analyses towards predicting the behaviour of dislocations within bcc crystals in the vicinity of the first shear wave speed.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Column-by-column observation of dislocation motion in CdTe: Dynamic scanning transmission electron microscopy

The dynamics of partial dislocations in CdTe have been observed at the atomic scale using aberration-corrected scanning transmission electron microscopy (STEM), allowing the mobility of different dislocations to be directly compared: Cd-core Shockley partial dislocations are more mobile than Te-core partials, and dislocation cores with unpaired columns have higher mobility than those without unpaired columns. The dynamic imaging also provides insight into the process by which the dislocations glide. Dislocations with dangling bonds on unpaired columns are found to be more mobile because the dangling bonds mediate the bond exchanges required for the dislocations to move. Furthermore, a screw dislocation has been resolved to dissociate into a Shockley partial-dislocation pair along two different directions, revealing a way for the screw dislocation to glide in the material. The results show that dynamic STEM imaging has the potential to uncover the details of dislocation motion not easily accessible by other means. This research was sponsored by the U.S. DOE, Office of Energy Efficiency and Renewable Energy, Foundational Program to Advance Cell Efficiency (F-PACE, DE-FOA-0000492), (CL, YLW, NP, YFY, SJP), the Office of DOE-BES, Materials Science and Engineering Division (ARL), DOE Grant No. DE-FG02-09ER46554 (YYZ, STP), and a user project supported by ORNL's Center for Nanophase Materials Sciences (CNMS), which is also sponsored by DOE-BES. Supercomputer time was provided by the National Center for Supercomputing Applications which is supported by the DOE Office of Science under Contract No. DE-AC02-05CH11231, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575. Chen Li [No. 656378] and Timothy Pennycook [No.655760] are currently funded by the European Union's Marie Sklodowska-Curie Grants.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Phase field modeling of dislocations and obstacles in InSb

We present a phase-field dislocation dynamics (PFDD) model informed by first-principle calculations to elucidate the competitive dislocation nucleation and propagation between the glide and shuffle sets in InSb diamond cubic crystal. The calculations are directly informed with generalized stacking fault energy curves on the (111) slip plane for both the “glide set,” with the smaller interplanar spacing, and the “shuffle set,” with the larger interplanar spacing. The formulation also includes elastic anisotropy and the gradient term associated with the dislocation core. The PFDD calculations show that under no stress the equilibrium structure of screw glide set dislocations dissociates into Shockley partials, while those of the shuffle set dislocations do not dissociate, remaining compact. The calculated dislocation core widths of these InSb dislocations agree well with the measured values for other semiconductor materials, such as Si and GaN. We find that a shuffle set dislocation emits from a dislocation source at an applied stress about three times smaller than that needed to emit leading and trailing partials successively on the glide set plane. Once the partial dislocations in the glide set are emitted, they propagate faster than the shuffle set perfect dislocation at the same stress level.

36 MATERIALS SCIENCE↗
DOE OSTI2021

On the three-dimensional spatial correlations of curved dislocation systems

Abstract Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

Anderson, Joseph Pierre (ORCID:0000000329760903)↗
DOE OSTI2022

Hydrogen induced dislocation core reconstruction in bcc tungsten

Dislocation, playing a crucial role in the plastic deformation of metals, can be significantly affected by introducing solute elements. Hydrogen (H) embrittlement is one such example, while the underlying mechanism for H affected dislocation structural stability and mobility remains unclear and the role of H has been controversial. Here, using first-principles calculations, we demonstrate that the effect of H on screw dislocation in bcc tungsten (W) is H concentration-dependent, signified by a H-induced transition of SD core structure. At low concentrations of H segregation, dislocation maintains the intrinsic easy-core structure, and H atoms are attached to the “periphery” of dislocation to enhance dislocation motion. In contrast, at high H concentrations, dislocation transforms into a hard-core, metal hydride-like structure, as H atoms become the “body” of dislocation to significantly reduce the dislocation mobility in W. Further, such local easy-to-hard transition can also be induced by the other solutes, including helium, carbon, nitrogen and oxygen. Our work sheds new light on the H-dislocation interactions in bcc W, having broad implications in the interstitial solute-related phenomena.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Modal analysis of dislocation vibration and reaction attempt frequency

Transition state theory is a fundamental approach for temporal coarse-graining. It estimates the reaction rate for a transition processes by quantifying the activation free energy and attempt frequency for the unit process. To calculate the transition rate of a gliding dislocation, the attempt frequency is often obtained from line tension estimates of dislocation vibrations, a highly simplified model of dislocation behavior. This work revisits the calculation of attempt frequency for a dislocation bypassing an obstacle, in this case a self-interstitial atom (SIA) loop. First, a direct calculation of the vibrational characteristics of a finite pinned dislocation segment is compared to line tension estimates before moving to the more complex case of dislocation-obstacle bypass. The entropic factor associated with the attempt frequency is calculated for a finite dislocation segment and for an infinite glide dislocation interacting with an SIA loop. Lastly, it is found to be dislocation length independent for three cases of dislocation-self interstitial atom (SIA) loop interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Origin of dislocation structures in an additively manufactured austenitic stainless steel 316L

In this experiment, the origin of dislocation structures in AM stainless steels was systematically investigated by controlling the effect of thermal stress through geometric constraints for the first time. Stainless steel 316L parts were produced in the form of “1D” rods, “2D” walls, and "3D" rectangular prisms to evaluate the effect of constraints to thermal expansion/shrinkage on the development of defect microstructures and to elucidate the origin of additively manufactured (AM) dislocation microstructures. Dislocation density, organization, chemical micro-segregation, precipitate structures, and misorientations were analyzed as a function of increasing constraints around solidifying material in 1D, 2D, and 3D components built using both directed energy deposition (DED) and powder-bed selective laser melting (SLM). In DED parts, the dislocation density was not dependent on local misorientations or micro-segregation patterns, but evolved from approximately ρ ⊥ = 10 12 m -2 in 1D parts to ρ ⊥ = 10 14 m -2 in 3D parts, indicating that it is primarily thermal distortions that produce AM dislocation structures. In DED 3D parts and SLM parts, dislocation densities were highest (ρ ⊥ ≈ 10 14 m -2 ) and corresponded to the formation of dislocation cells approximately 300-450 nm in diameter. Dislocation cells overlapped with dendrite micro-segregation in some but not all cases. The results illustrate that dendritic micro-segregation, precipitates, or local misorientations influence how the dislocations organize during processing, but are not responsible for producing the organized cell structures. Furthermore, this work shows that AM dislocation structures originate due to thermal distortions during printing, which are primarily dictated by constraints surrounding the melt pool and thermal cycling.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Laser shock peening effect on the dislocation transitions and grain refinement of Al–Mg–Si alloy

This paper systematically investigates the effect of laser shock peening without coating parameters on the microstructural evolution, and dislocation configurations induced by ultra-high plastic strains and strain rates. Based on an analysis of optical microscopy, polarized light microscopy, transmission electron microscopy observations and residual stress analysis, the significant influence of laser shock peening parameters due to the effect of plasma generation and shock wave propagation has been confirmed. Although the optical microscopy results revealed no significant microstructural changes after laser shock peening, i.e. no heat effect zone and differences in the distribution of second-phase particles, expressive influence of laser treatment parameters on the laser shock induced craters was confirmed. Moreover, polarized light microscopy results have confirmed the existence of well-defined longish grains up to 455 μm in length in the centre of the plate due to the rolling effect, and randomly oriented smaller grains (20 μm × 50 μm) in the surface due to the static recrystallization effect. Laser shock peening is reflected in an exceptional increase in dislocation density with various configurations, i.e. dislocation lines, dislocation cells, dislocation tangles, and the formation of dense dislocation walls. More importantly, the microstructure is considerably refined due to the effect of strain deformations induced by laser shock peening process. The results have confirmed that dense dislocation structures during ultra-high plastic deformation with the addition of shear bands producing ultra-fine (60–200 nm) and nano-grains (20–50 nm). Furthermore, dislocation density was increased by a factor of 2.5 compared to the untreated material (29 × 10{sup 13} m{sup −2} vs. 12 × 10{sup 13} m{sup −2}). - Highlights: • LSPwC imparts high compressive residual stresses up to − 362 ± 31 MPa. • After LSPwC the microstructure is considerably refined via dislocation transitions. • Results confirmed ultra-fine (60–200 nm) and nano-grains (20–50 nm) after LSPwC. • Reasonable agreements between dislocation density and residual stress are obtained.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Characterizing dislocation configurations and their evolution during creep of a new 12% Cr steel

Highlights: • Applicability of different techniques to characterize particular dislocation configuration. • XRD models in combination with TEM and EBSD to measure the dislocation density. • Substructure evolution during creep of a new 12% Cr steel is discussed. - Abstract: In this research, different types of dislocations are characterized and quantified in a newly developed 12% Cr steel in as-received as well as in crept conditions. X-ray diffraction (XRD) patterns are analyzed using three different models. The dislocation densities are determined employing the Convolution Multiple Whole Profile (CMWP) fitting, the analysis of the asymptotic part of the X-ray line profile (Groma's method), and the Rietveld refinement coupling Popa's and Williamson-Smallman approaches. CMWP method is used to measure the internal dislocation density inside the subgrains consisting of mobile and dipole dislocations, and the results show good agreement with Transmission Electron Microscopy (TEM) measurements. Groma's method is used to evaluate the total dislocation density, with results comparable to those obtained from the combination of Electron Backscatter Diffraction (EBSD) and TEM. Rietveld method gives the internal dislocation density or mobile dislocation density depending on the model chosen. The experimentally determined results such as creep strain, dislocation densities and subgrain size are compared with theoretical predictions and they are found in good agreement.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Dynamics and Removal Pathway of Edge Dislocations in Imperfectly Attached PbTe Nanocrystal Pairs: Toward Design Rules for Oriented Attachment

Using in situ high-resolution TEM, we study the structure and dynamics of well-defined edge dislocations in imperfectly attached PbTe nanocrystals. In this work, we identify that attachment of PbTe nanocrystals on both {100} and {110} facets gives rise to b = a/2⟨110⟩ edge dislocations. Based on the Burgers vector of individual dislocations, we can identify the glide plane of the dislocations. We observe that defects in particles attached on {100} facets have glide planes that quickly intersect the surface, and HRTEM movies show that the defects follow the glide plane to the surface. For {110} attached particles, the glide plane is collinear with the attachment direction, which does not provide an easy path for the dislocation to reach the surface. Indeed, HRTEM movies of dislocations for {110} attached particles show that defect removal is much slower. Further, we observe conversion from pure edge dislocations in imperfectly attached particles to dislocations with mixed edge and screw character, which has important implications for crystal growth. Lastly, we observe that dislocations initially closer to the surface have a higher speed of removal, consistent with the strong dislocation free surface attractive force. Our results provide important design rules for defect-free attachment of preformed nanocrystals into epitaxial assemblies.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Origins of electrostatic potential wells at dislocations in polycrystalline Cu(In,Ga)Se{sub 2} thin films

Thin-film solar cells based on Cu(In,Ga)Se{sub 2} (CIGSe) reach high power-conversion efficiencies in spite of large dislocation densities of up to 10{sup 10}–10{sup 11} cm{sup −2}. The present work gives insight into the structural and compositional properties of dislocations in CIGSe thin films, which are embedded in a complete solar cell stack. These properties are related to the average electrical potential distributions obtained by means of inline electron holography. At a part of the dislocations studied, the average electrostatic potential shows local minima, all with depths of about −1.4 V. The measured average electrostatic potential distributions were modeled in order to reveal possible influences from strain fields, excess charge, and also compositional changes at the dislocation core. Cu depletion around the dislocation core, as evidenced by atom-probe tomography, explains best the measured potential wells. Their influences of the strain field around the dislocation core and of excess charge at the dislocation core are small. A structural model of dislocations in CIGSe thin films is provided which includes a Cu-depleted region around the dislocation core and gives a possible explanation for why decent photovoltaic performances are possible in the presence of rather large dislocation densities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗