A Statistical Mechanical Model of Critical Currents in Superconductors

Long, N.J.

doi:10.1007/s10948-012-2063-6

Cited by 7 publications

(7 citation statements)

References 11 publications

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“…This in fact turns out to be the case. We have previously shown that combinations of Equations (3a), (3b) and (3c) can fit data for J c () [10]. In Figure 8 we show data for a YBCO sample measured at 85 K, 1 T [30].…”

Section: In-plane Field Angular Dependence Of J C Under Variable Lorementioning

confidence: 90%

“…In [10] we give an example where J c (B) data with a secondary maximum at intermediate fields (a so-called "peak effect") can be described using this form.…”

Section: Magnetic Field Dependence Of J Cmentioning

confidence: 99%

“…It is difficult to foresee how a deterministic model would ever predict a J c peak which is not aligned with the direction of correlated pinning, but this comes quite naturally from Equation (3b). Further examples of the use of these equations to explain J c () from complex pinning structures are given in [7][8][9][10]26,27]. Table 1.…”

Section: Out-of-plane Field Angular Dependence Of J C Under Maximum Lmentioning

confidence: 99%

“…That is, there is no reliable methodology to sum the effects of all the defects distributed throughout a material in order to find p F  . We have shown previously [7][8][9][10] how by adopting a maximum entropy approach we can model J c while avoiding the need to construct a model of p F  . Although we do not solve the pinning summation problem in the sense of making direct predictions of the magnitude of J c we do gain insight into how nature averages over all defects and interactions and what information is available from any experiment.…”

Section: Introductionmentioning

confidence: 99%

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Maximum Entropy Distributions Describing Critical Currents in Superconductors

Long

2013

Entropy

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Maximum entropy inference can be used to find equations for the critical currents (J c ) in a type II superconductor as a function of temperature, applied magnetic field, and angle of the applied field, θ or . This approach provides an understanding of how the macroscopic critical currents arise from averaging over different sources of vortex pinning. The dependence of critical currents on temperature and magnetic field can be derived with logarithmic constraints and accord with expressions which have been widely used with empirical justification since the first development of technical superconductors. In this paper we provide a physical interpretation of the constraints leading to the distributions for J c (T) and J c (B), and discuss the implications for experimental data analysis. We expand the maximum entropy analysis of angular J c data to encompass samples which have correlated defects at arbitrary angles to the crystal axes giving both symmetric and asymmetric peaks and samples which show vortex channeling behavior. The distributions for angular data are derived using combinations of first, second or fourth order constraints on cot θ or cot . We discuss why these distributions apply whether or not correlated defects are aligned with the crystal axes and thereby provide a unified description of critical currents in superconductors. For J//B we discuss what the maximum entropy equations imply about the vortex geometry.

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Section: In-plane Field Angular Dependence Of J C Under Variable Lorementioning

confidence: 90%

“…In [10] we give an example where J c (B) data with a secondary maximum at intermediate fields (a so-called "peak effect") can be described using this form.…”

Section: Magnetic Field Dependence Of J Cmentioning

confidence: 99%

Section: Out-of-plane Field Angular Dependence Of J C Under Maximum Lmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Maximum Entropy Distributions Describing Critical Currents in Superconductors

Long

2013

Entropy

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“…At high fields, the pinning potential of the correlated defects (both ab-directional stacking faults and c-directional growth defects such anti-phase boundaries and dislocations) is higher leading to peaks in n value and J c . The dip in n value can be described and explained by scaling approaches taken into account the size of random pinning centres [31] or in statistical, maximum-entropy considerations [32].…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Pinning analyses of a BaHfO₃-containing GdBa₂Cu₃O_7‐δ thin film grown by chemical solution deposition

Iida¹,

Cayado²,

Rijckaert³

et al. 2020

Supercond. Sci. Technol.

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The electric transport properties of a GdBa 2 Cu 3 O 7−δ thin film containing 12 mol% nano-sized BaHfO 3 (BHO) particles grown by chemical solution deposition were investigated in a wide range of temperatures (4.2 ≤ T ≤ 77 K) and magnetic fields up to µ 0 H=19 T. The exponent n of the electric field-current density characteristics (E∝J n ) has the following relation (n-1)∝J α c (α∼0.45) irrespective of measurement temperature for H ∥ c. On the other hand, this relation does not hold for H ∥ ab. The angular dependence of J c was almost similar to that of n except for the angle close to the ab-plane. A dip of n around this angle regime was observed below 77 K, whereas J c exhibited a maximum. At T ≤ 50 K a tiny peak in the dip was observed that grew with decreasing temperatures. These results suggest that the pinning mechanism changes with temperature for H ∥ ab.

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Polar projections for big data analysis in applied superconductivity

Talantsev

Mataira

2018

AIP Advances

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There is a growing problem to represent and analyse large experimental datasets in many emerging fields of science aside of traditional big data-based disciplines, i.e., elementary particles, genetics/genomics and geoscience. One of these emerging fields is applied superconductivity where recently a large, regularly up-dated, public database of critical currents of commercial superconductors was established. The size, dimensionality and resolution of this data makes current methods of display and analysis inadequate. As is often the case in physics and materials science, when dealing with any anisotropic properties, one measures the effects of rotations around a low symmetry axis, this is also the case in critical current measurements as found in applied superconductivity. In this paper we propose the use of polar projected images to map these much larger data sets into useful visualizations for analysis. Where we suggest the radial coordinate and the colour represent amplitudes of two measured parameters, and sample rotation angle is naturally mapped to the polar coordinate. We demonstrate the advantage of this projection for analysing, otherwise unwieldy large, critical current datasets, and naturally recover previously used empirical relations.

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A Statistical Mechanical Model of Critical Currents in Superconductors

Cited by 7 publications

References 11 publications

Maximum Entropy Distributions Describing Critical Currents in Superconductors

Maximum Entropy Distributions Describing Critical Currents in Superconductors

Pinning analyses of a BaHfO₃-containing GdBa₂Cu₃O_7‐δ thin film grown by chemical solution deposition

Polar projections for big data analysis in applied superconductivity

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A Statistical Mechanical Model of Critical Currents in Superconductors

Cited by 7 publications

References 11 publications

Maximum Entropy Distributions Describing Critical Currents in Superconductors

Maximum Entropy Distributions Describing Critical Currents in Superconductors

Pinning analyses of a BaHfO3-containing GdBa2Cu3O7‐δ thin film grown by chemical solution deposition

Polar projections for big data analysis in applied superconductivity

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Product

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Pinning analyses of a BaHfO₃-containing GdBa₂Cu₃O_7‐δ thin film grown by chemical solution deposition