Strain scaling law for flux pinning in practical superconductors. Part 1: Basic relationship and application to Nb3Sn conductors
TL;DR: In this article, the authors present the basic uniaxial-strain scaling relationship and focus on its application to Nb3Sn conductors, and propose a general scaling relation which unifies the usual temperature scaling relation with this strain-scaling relation.
About: This article is published in Cryogenics.The article was published on 1980-11-01. It has received 398 citations till now. The article focuses on the topics: Pinning force & Flux pinning.
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01 Sep 1990
TL;DR: In this article, an empirical model is presented that predicts the critical current density (J/sub c/) of Nb/sub 3/Sn wires under the combined effects of temperature, strain, and radiation damage.
Abstract: An empirical model is presented that predicts the critical current density (J/sub c/) of Nb/sub 3/Sn wires under the combined effects of temperature, strain, and radiation damage. The model, based on previous work of D.P. Hampshire et al. (1985) and J. W. Ekin (1980), predicts J/sub c/ with a reasonable degree of accuracy. The model can be used with a limited number of input parameters. eliminating the need for detailed characterization, particularly the difficult tasks of measuring critical current as a function of temperature and radiation damage.
306 citations
TL;DR: In this paper, a current transfer model is proposed in which weak conduction along the c axis plays a role in limiting critical-current density at grain boundaries, and the effect of intrinsic conduction anisotropy is discussed.
Abstract: Measurements of the transport critical‐current density (Jc), magnetization Jc, and magnetoresistance in a number of bulk sintered samples of Y1Ba2Cu3Ox from several different laboratories indicate that the transport Jc is limited by weak‐link regions between high Jc regions. The weak‐link Jc has a Josephson character, decreasing by two orders of magnitude as the magnetic field is increased from 0.1 to 10 mT at 77 K. An examination of the grain‐boundary region in Y1Ba2Cu3Ox shows no observable impurities or second phases to the scale of the [001] lattice planes (∼12 A). The effect of intrinsic conduction anisotropy is discussed. A current‐transfer model is proposed in which weak conduction along the c axis plays a role in limiting Jc at grain boundaries. Orienting the grains in the powder state during processing may result in enhanced transport Jc in bulk conductors.
283 citations
TL;DR: In this paper, an empirical model is presented that predicts the critical current density (J/sub c/) of Nb/sub 3/Sn wires under the combined effects of temperature, strain, and radiation damage.
Abstract: An empirical model is presented that predicts the critical current density (J/sub c/) of Nb/sub 3/Sn wires under the combined effects of temperature, strain, and radiation damage. The model, based on previous work of D.P. Hampshire et al. (1985) and J. W. Ekin (1980), predicts J/sub c/ with a reasonable degree of accuracy. The model can be used with a limited number of input parameters. eliminating the need for detailed characterization, particularly the difficult tasks of measuring critical current as a function of temperature and radiation damage.
266 citations
TL;DR: In this paper, a scaling relation for the upper critical field (Hc2) with temperature (T) and A15 composition was proposed, which is more consistent than the usual Ekin unification of strain and temperature dependence.
Abstract: Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available Hc2(T) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, Hc2*(T) results and can be approximated by , with t = T/Tc. Knowing Hc2*(T) implies that Jc(T) is also known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires from T up to about 80% of the maximum Hc2 can be described with Kramer's flux shear model, if nonlinearities in Kramer plots when approaching the maximum Hc2 are attributed to A15 inhomogeneities. The strain () dependence is introduced through a temperature and strain dependent Hc2*(T,) and Ginzburg–Landau (GL) parameter κ1(T,) and a strain dependent critical temperature Tc(). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependences on Hc2*(T) and Hc2*(). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkably simple relation , where C is a constant, s() represents the normalized strain dependence of Hc2*(0) and h = H/Hc2*(T,). Finally, a new relation for s() is proposed, which is an asymmetric version of our earlier deviatoric strain model and based on the first, second and third strain invariants. The new scaling relation solves a number of much debated issues with respect to Jc scaling in Nb3Sn and is therefore of importance to the applied community, who use scaling relations to analyse magnet performance from wire results.
176 citations
TL;DR: In this paper, the irreversible strain limit for the onset of permanent axial strain damage to Ag-sheathed Bi2Sr2Ca1Cu2O8+x and Bi 2Sr 2Ca2Cu3O10+x superconductors has been measured to be in the range of 0.2% −0.35%.
Abstract: The irreversible strain limit eirrev for the onset of permanent axial strain damage to Ag‐sheathed Bi2Sr2Ca1Cu2O8+x and Bi2Sr2Ca2Cu3O10+x superconductors has been measured to be in the range of 0.2%–0.35%. This strain damage onset is about an order of magnitude higher than for bulk sintered Y‐, Bi‐, or Tl‐based superconductors and is approaching practical values for magnet design. The measurements show that the value of eirrev is not dependent on magnetic field, nor does the critical current depend on strain below eirrev at least up to 25 T at 4.2 K. Both of these factors indicate that the observed strain effect in Ag‐sheathed Bi‐based superconductors is not intrinsic to the superconductor material. Rather, the effect is extrinsic and arises from superconductor fracture. Thus, the damage onset is amenable to further enhancement. Indeed, the data suggest that subdividing the superconductor into fine filaments or adding Ag to the superconductor powder prior to processing significantly enhances the damage th...
159 citations
References
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TL;DR: In this paper, the authors considered the effects of lattice rigidity on the summation of pinning forces and showed that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument.
Abstract: This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical...
1,172 citations
TL;DR: In this paper, it was shown that the peak in Fp scales as [Hc2(T)]2.5 if the temperature is changed; the maximum value of Fp occurred at the same value of reduced field regardless of temperature.
Abstract: For all hard high‐field superconductors examined to date, there is a maximum in the pinning force density Fp as a function of the reduced magnetic field h. Fietz and Webb first demonstrated in dilute Nb alloys that the peak in Fp scales as [Hc2(T)]2.5 if the temperature is changed; the maximum value of Fp occurred at the same value of reduced field regardless of temperature. Recent data on the temperature dependence of pinning in Nb3Sn, Nb–25% Zr and a Nb–Ti alloy, which exhibits the ``peak effect'', are analyzed to show that similar scaling laws are obeyed by these materials. All presently available evidence indicates however that the reduced field hp at which the maximum Fp occurs, as well as the height and shape of this maximum, can be altered by metallurgical treatment. Apparently weak pinning defects, or widely spaced ones, produce a small peak in Fp(h) at high h whereas strong closely spaced pins produce a large peak in Fp(h) at low h without producing much change in Fp(h) at high h. A model which p...
1,104 citations
TL;DR: In this article, expressions for flux-pinning in type II superconductors are derived from considerations of the nature of the interaction between individual flux-lines and pinning-centres, and of the geometry of th...
Abstract: Expressions for flux-pinning in type II superconductors are derived from considerations of the nature of the interaction between individual flux-lines and pinning-centres, and of the geometry of th...
1,011 citations
TL;DR: In this paper, critical current and pinning-force densities in a series of niobium alloys subjected to severe plastic deformation have been determined from measurements of complete hysteretic magnetization curves on alloys with Ginzburg-Landau parameter $\ensuremath{\kappa}$ between 1.3 and 13 at temperatures from the critical temperature ${T}_{c}$ down to $0.14{T}
Abstract: Critical current and pinning-force densities in a series of niobium alloys subjected to severe plastic deformation have been determined from measurements of complete hysteretic magnetization curves on alloys with Ginzburg-Landau parameter $\ensuremath{\kappa}$ between 1.3 and 13 at temperatures from the critical temperature ${T}_{c}$ down to $0.14{T}_{c}$. Systematic scaling rules were found that accurately describe all of the results over the entire range of fields and temperatures. The pinning-force density scales with magnetic induction as a single function of $\frac{B}{{H}_{c2}}$; it scales with temperature as the $\frac{5}{2}$ power of the upper critical field ${H}_{c2}(T)$, is roughly proportional to ${\ensuremath{\kappa}}^{\ensuremath{-}\ensuremath{\gamma}}$, where $1l\ensuremath{\gamma}l3$, and is otherwise independent of $T$. A model for the pinning process that takes into account deformation of the fluxoid lattice by the pinning forces is proposed to account for the observed scaling rules. The results are consistent with a pinning interaction based on a second-order elastic interaction between dislocations and the fluxoid lattice, but other mechanisms are not excluded. Cooperative effects seem to be an essential feature of the pinning process, leading to a dependence of the pinning-force density on the square of the pinning-point strength, and on the arrangement of pinning points.
465 citations
TL;DR: In this article, the elastic properties of the flux line lattice (FLL) in type II superconductors are calculated from the linearized Ginzburg-Landau (GL) theory for large inductions.
Abstract: The elastic properties of the flux line lattice (FLL) in type II superconductors are calculated from the linearized Ginzburg-Landau (GL) theory for large inductionsB≈H
c2
. They appear to be strongly nonlocal, i.e., the elastic modulic
11 andc
44 for homogeneous deformations do not apply if the strain field varies over distances λ/(1−B/H
c2
)1/2 ≫d (λ is the penetration depth,d is the FL distance). For smaller strain wavelength,c
11 andc
44 are smaller by factors (1−B/H
c2
)2/2κ
2
and (1−B/H
c2
)/ 2κ
2
, respectively. The order parameter and local field of a deformed FLL exhibit the expected spatial “frequency modulation,” but also a pronounced “amplitude modulation” whose degree of modulation increases with the strain wavelength. The results of further calculations avoiding the linearization of the GL theory are given.
197 citations