Understanding the nanoscale chemistry of as-received and fast neutron irradiated Nb<sub>3</sub>Sn RRP<sup>®</sup> wires using atom probe tomography

Wheatley, Laura; Baumgartner, T.; Eisterer, M.; Speller, Susannah; Moody, Michael P.; Grovenor, C.R.M.

doi:10.1088/1361-6668/acdbed

“…Dew-Hughes [36] calculated theoretical characteristic values for p and q for different pinning mechanisms, in particularly for point defect (PD) and grain boundary (GB) pinning. The evolution of the dominant pinning mechanism from GB-to PD-pinning in Nb3Sn under neutron irradiation was recently reported by Wheatley et al [39], who showed that the unirradiated Nb3Sn alloy exhibits |𝐹 𝑝 ⃗⃗⃗ (𝐵, 𝑇)| form indicating the dominance of the GB-pinning, and after the neutron irradiation the |𝐹 𝑝 ⃗⃗⃗ (𝐵, 𝑇)| form transforms towards the PD-pinning mode.…”

mentioning

confidence: 58%

“…In this report we re-analysed experimental data on the dependence of the maximum pinning force density, |𝐹 𝑝,𝑚𝑎𝑥 (𝑑, 𝑇 = 4.2 K)| (deduced from the |𝐹 𝑝 (𝐵)| [35][36][37] projection) from the average grain size in practical low-Tc multifilamentary Nb3Sn conductors [38][39][40][41][42][43][44][45][46]55,56,58] fabricated by bronze and power-in-tube technologies.…”

Section: Discussionmentioning

confidence: 99%

Characteristic Length for Pinning Force Density in Nb3Sn

Talantsev¹,

Valova-Zaharevskaya²,

Deryagina³

et al. 2023

Preprint

0

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The pinning force density FpJc,B=Jc×B (where Jc is the critical current density and B is the applied magnetic field) is one of the main parameters that characterize the resilience of a superconductor to carry a dissipative-free transport current in an applied magnetic field. Kramer (1973 J. Appl. Phys. 44 1360), and Dew-Hughes (1974 Phil. Mag. 30 293) proposed a widely used scaling law for the pinning force density amplitude: FpB=Fp,max×p+qp+qppqq×BBc2p×1-BBc2q, where Fp,max, Bc2, p, and q are free-fitting parameters. Since the late 1970-s till now, several research groups have reported experimental data on the dependence of Fp,max on the average grain size, d, in Nb3Sn-based conductors. Godeke (2006 Supercond. Sci. Techn. 19 R68) proposed that the dependence obeys the law Fp,maxd=A×ln1d+B. However, this scaling law has several problems, for instance, the logarithm is taken from a non-dimensionless variable, and Fp,maxd&lt;0 for large grain sizes, and Fp,maxd→∞ for d→0. Here, we reanalysed the full inventory of publicly available Fp,maxd data for Nb3Sn conductors and found that the dependence can be described by Fp,maxd=Fp,max0×exp-dδ law, where the characteristic length, δ, varies within a remarkably narrow range, that is, δ=175±13 nm, for samples fabricated by different technologies. The interpretation of the result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of δ) near the grain boundary surfaces (similar to London’s law, where the self-field supercurrent flows within a thin surface layer with a thickness of the London penetration depth, λ, and the surface is a superconductor-vacuum surface). An alternative interpretation is that δ represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb3Sn superconductors, which are grain boundaries.

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“…In this report, we reanalyzed experimental data on the dependence of the maximum pinning force density, F p,max , from the average grain size, d, in practical low-T c multifilamentary Nb 3 Sn conductors [38][39][40][41][42][43][44][45][46]55,56,58] fabricated by bronze and power-in-tube technologies.…”

Section: Discussionmentioning

confidence: 99%

Characteristic Length for Pinning Force Density in Nb3Sn

Talantsev

¹

,

Valova-Zaharevskaya

²

,

Deryagina

³

et al. 2023

Materials

2

0

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The pinning force density, Fp, is one of the main parameters that characterize the resilience of a superconductor to carrying a dissipative-free transport current in an applied magnetic field. Kramer (1973) and Dew-Hughes (1974) proposed a widely used scaling law for this quantity, where one of the parameters is the pinning force density maximum, Fp,max, which represents the maximal performance of a given superconductor in an applied magnetic field at a given temperature. Since the late 1970s to the present, several research groups have reported experimental data on the dependence of Fp,max on the average grain size, d, in Nb3Sn-based conductors. Fp,maxd datasets were analyzed and a scaling law for the dependence Fp,maxd=A×ln1/d+B was proposed. Despite the fact that this scaling law is widely accepted, it has several problems; for instance, according to this law, at T=4.2 K and d≥650 nm, Nb3Sn should lose its superconductivity, which is in striking contrast to experiments. Here, we reanalyzed the full inventory of publicly available Fp,maxd data for Nb3Sn conductors and found that the dependence can be described by the exponential law, in which the characteristic length, δ, varies within a remarkably narrow range of δ=175±13 nm for samples fabricated using different technologies. The interpretation of this result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of δ) near grain boundary surfaces (similar to London’s law, where the self-field supercurrent flows within a thin surface layer with a thickness of the London penetration depth, λ, and the surface is a superconductor–vacuum surface). An alternative interpretation is that δ represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb3Sn superconductors, which are grain boundaries.

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“…To obtain a continuous function, the experimental measurements of material parameters need to be fitted as a function of Sn content. Following the treatment in [21], we use global fits to the experimental T , c g and r versus b in the entire A15 range (table 1), One can see the fitting curves as figure A1 below. With sufficient data available for the critical temperature T c and the transport scattering resistivity r, we choose cubic fit to achieve an exact representation.…”

Section: Appendix the Dependence Of Materials Parameters With Tin Con...mentioning

confidence: 99%

“…It is assumed that this tin variation is a non-negligible contribution to the disagreement between the scaling laws and the experimental results. To improve the scaling law it is useful to understand how B c2 varies with Sn content (see [21][22][23] for recent advances in composition dependences of superconducting properties), since a Nb 3 Sn conductor has practically tin composition content that covers the full range of A15 phase (generally thought to range from ∼18-25 at.% Sn). Following the approach proposed by the same author [24], we begin with the dependence of GL (Ginzburg-Landau) parameters k on the three independent material parameters that are the transport scattering resistivity r W , m low-temperature coefficient of electronic heat capacity g mJ and transition temperature T c [25].…”

Section: Introductionmentioning

confidence: 99%

A semi-empirical formula for the dependence of upper critical field with component and strain in Nb₃Sn

Xu,

Li,

Salmi

2023

Phys. Scr.

0

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We include the effects of Sn content β in the scaling law to generalize the upper critical field B c 2 ( T , ε ) function of temperature and strain in Nb3Sn. The basis for this generalization comes from a theory developed by the same author [Scientific Reports 7, 1133 (2017)]. The important assumption in the current work is that, in determining the upper critical field B c 2 , the contributions of strain, temperature and Sn content are independent of each other. It is followed that we write down a semi-empirical expression B c 2 ( T , ε , β ) = B c 2 ( T 0 , ε 0 , β ) s ( ε ) ( 1 − t 1.52 ) where the strain function s ( ε ) and t ≡ T / T c ( ε ) are affected only by strain and temperature, respectively, and the variation of tin content β enters in the function B c 2 through B c 2 ( T 0 , ε 0 , β ) . This separable form of B c 2 ( T , ε , β ) allows one to incorporate Sn content β in the scaling law in a natural way, while this variable is not considered by traditional scaling laws. In addition to this advance, one can see a more flexible function with triple variables which could be an effective tool to fit or predict experiments. As the last but most important outcome, this semi-empirical function instructs one how to understand the role of component content played in scaling behaviors of Nb3Sn, so as to reduce the off-stoichiometric composition inducing discrepancy between the results by scaling laws and experiments.

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Understanding the nanoscale chemistry of as-received and fast neutron irradiated Nb₃Sn RRP^® wires using atom probe tomography

Cited by 5 publications

References 38 publications

Characteristic Length for Pinning Force Density in Nb3Sn

Characteristic Length for Pinning Force Density in Nb3Sn

Characteristic Length for Pinning Force Density in Nb3Sn

A semi-empirical formula for the dependence of upper critical field with component and strain in Nb₃Sn

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Understanding the nanoscale chemistry of as-received and fast neutron irradiated Nb3Sn RRP® wires using atom probe tomography

Cited by 5 publications

References 38 publications

Characteristic Length for Pinning Force Density in Nb3Sn

Characteristic Length for Pinning Force Density in Nb3Sn

Characteristic Length for Pinning Force Density in Nb3Sn

A semi-empirical formula for the dependence of upper critical field with component and strain in Nb3Sn

Contact Info

Product

Resources

About

Understanding the nanoscale chemistry of as-received and fast neutron irradiated Nb₃Sn RRP^® wires using atom probe tomography

A semi-empirical formula for the dependence of upper critical field with component and strain in Nb₃Sn