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In Part 2 of these articles, an extensive analysis of pinning-force curves and raw scaling data was used to derive the Extrapolative Scaling Expression (ESE). This is a parameterization of the Unified Scaling Law (USL) that has the extrapolation capability of fundamental unified scaling, coupled with the application ease of a simple fitting equation. Here in Part 3, the accuracy of the ESE relation to interpolate and extrapolate limited critical-current data to obtain complete Ic(B,T,ε) datasets is evaluated and compared with present fitting equations. Accuracy is analyzed in terms of root mean square (RMS) error and fractional deviation statistics. Highlights from 92 test cases are condensed and summarized, covering most fitting protocols and proposed parameterizations of the USL. The results show that ESE reliably extrapolates critical currents at fields B, temperatures T, and strains ε that are remarkably different from the fitted minimum dataset. Depending on whether the conductor is moderate-Jc or high-Jc, effective RMS extrapolation errors for ESE are in the range 2–5 A at 12 T, which approaches the Ic measurement error (1–2%). The minimum dataset for extrapolating full Ic(B,T,ε) characteristics is also determined from raw scaling data. It consists of one set of Ic(B,ε) data at a fixed temperature (e.g., liquid helium temperature), and one set of Ic(B,T) data at a fixed strain (e.g., zero applied strain). Error analysis of extrapolations from the minimum dataset with different fitting equations shows that ESE reduces the percentage extrapolation errors at individual data points at high fields, temperatures, and compressive strains down to 1/10th to 1/40th the size of those for extrapolations with present fitting equations. Depending on the conductor, percentage fitting errors for interpolations are also reduced to as little as 1/15th the size. The extrapolation accuracy of the ESE relation offers the prospect of straightforward implementation of the USL in several new areas: (l) A five-fold reduction in the measurement space for unified temperature-strain apparatuses through extrapolation of minimum datasets; (2) Combination of data from separate temperature and strain apparatuses, which provides flexibility and productive use of more limited data; and (3) Full conductor characterization from as little as a single Ic(B) curve when a few core parameters have been measured in a similar conductor. Default core scaling parameter values are also given, based on analysis of a wide range of practical Nb3Sn conductors. [ABSTRACT FROM AUTHOR]

A scaling study of several thousand Nb3Sn critical-current (Ic) measurements is used to derive the Extrapolative Scaling Expression (ESE), a relation that can quickly and accurately extrapolate limited datasets to obtain full three-dimensional dependences of Ic on magnetic field (B), temperature (T), and mechanical strain (ε). The relation has the advantage of being easy to implement, and offers significant savings in sample characterization time and a useful tool for magnet design. Thorough data-based analysis of the general parameterization of the Unified Scaling Law (USL) shows the existence of three universal scaling constants for practical Nb3Sn conductors. The study also identifies the scaling parameters that are conductor specific and need to be fitted to each conductor. This investigation includes two new, rare, and very large Ic(B,T,ε) datasets (each with nearly a thousand Ic measurements spanning magnetic fields from 1 to 16 T, temperatures from ∼2.26 to 14 K, and intrinsic strains from –1.1% to +0.3%). The results are summarized in terms of the general USL parameters given in table 3 of Part 1 (Ekin J W 2010 Supercond. Sci. Technol.23 083001) of this series of articles. The scaling constants determined for practical Nb3Sn conductors are: the upper-critical-field temperature parameter v = 1.50 ± 0.04; the cross-link parameter w = 3.0 ± 0.3; and the strain curvature parameter u = 1.7 ± 0.1 (from equation (29) for bc2(ε) in Part 1). These constants and required fitting parameters result in the ESE relation, given by I c ( B , T , ε ) B = C [ b c 2 ( ε ) ] s ( 1 − t 1.5 ) η − μ ( 1 − t 2 ) μ b p ( 1 – b ) q with reduced magnetic field b ≡ B/Bc2*(T,ε) and reduced temperature t ≡ T/Tc*(ε), where: B c 2 * ( T , ε ) = B c 2 * ( 0 , 0 ) ( 1 − t 1.5 ) b c 2 ( ε ) T c * ( ε ) = T c * ( 0 ) [ b c 2 ( ε ) ] 1/3 and fitting parameters: C, Bc2*(0,0), Tc*(0), s, either η or μ (but not both), plus the parameters in the strain function bc2(ε). The pinning-force shape parameters p and q are also preferably fitted (simultaneously with the other parameters), but default values p = 0.5 and q = 2.0 also give high fitting accuracy when the range of relative magnetic fields is not extensive. Default values are also essential when the magnetic field data range is insufficient to determine p and q. The scaling constants are remarkably stable (changes less than ∼1%) with respect to different values of p and q, Nb3Sn conductor configurations, magnetic self-field corrections, and pinning-force trim values. The results demonstrate that the scaling of transport critical current holds down to the lowest temperatures measured ∼2.2 K, for both magnetic self-field corrected and uncorrected data. An initial comparison is also made between transport and magnetization scaling data in matched Nb3Sn samples and significant differences are found, especially for the upper critical field Bc2*(T,ε), which may be a result of inhomogeneous shielding currents. In Part 3 of this topical review series (Ekin J W 2017 Supercond. Sci. Technol. at press), the smallest practical minimum dataset for extrapolating full Ic(B,T,ε) datasets is derived. Application of the ESE relation is illustrated in several new areas, including full characterization of Nb3Sn conductors from as little as a single Ic(B) curve when a few core parameters have been determined for similar conductors. [ABSTRACT FROM AUTHOR]

As part of an international project to benchmark facilities for measuring the strain dependence of critical current in International Thermonuclear Experimental Reactor (ITER) Nb3Sn strands, direct measurement of local strain exerted on Nb3Sn filaments was attempted at cryogenic temperature by means of a pulsed neutron technique. The lattice axial strain increased linearly with a slope close to unity against applied strain, while the thermal axial strain was −0.22% at 8.5 K. As a result, the force-free strain was evaluated to be 0.22–0.23%. This key parameter should provide an accurate estimate of the peak location of critical current versus applied strain. The lattice transverse strain decreased linearly as a function of applied strain with a slope of 0.33–0.34. The lattice strains of the Nb and Cu components were also measured and their behavior was analyzed by computing diffraction elastic moduli based on micromechanics theories. The stress–strain curve calculated according to the rule of mixtures described quite well the macroscopic curve measured for the present ITER Nb3Sn strand. [ABSTRACT FROM AUTHOR]

Systematic studies of the intrinsic irreversible strain limit εirr,0, microstructure, and microchemistry were made on several internal-tin Nb3Sn pre-production wires, fabricated for the domestic agencies of the USA and China participating in the International Thermonuclear Experimental Reactor. These wires were produced by Luvata, Oxford Superconducting Technology (OST), and Western Superconducting Technologies (WST), and were intended for the tokamak’s toroidal-field coils. The results of this study show that, for a final heat-treatment at 650 °C to form the A15 phase, both εirr,0 and the de-pinning field Bc2* improved by increasing heat-treatment duration beyond 100 h for the Luvata wires. On the other hand, we saw no improvement in these two parameters as a function of heat-treatment duration in the OST wires. Furthermore, micro-chemical analysis of OST wires revealed that some Nb3Sn filaments have a Sn- and Ti-rich phase at the interface between Cu(Sn) matrix and Nb3Sn in the form of a shell around individual filaments. This phase is far less prominent in the Luvata and WST conductors, and could inhibit diffusion of Sn and Ti into Nb3Sn filaments during the reaction and may potentially be the reason for the lack of noticeable change in Bc2* with heat-treatment duration in the OST wires. The increase of εirr,0 and Bc2* with heat-treatment duration in the Luvata wires and the lack of increase in the OST wires may suggest a possible correlation between εirr,0 and the stoichiometry of the A15 composition. Investigation of the samples’ microstructure revealed only a small number of cracked Nb3Sn filaments despite the significant and permanent degradation of their critical current Ic when subjected to longitudinal tensile strain ε beyond εirr,0. The scarcity of cracks indicate that Ic(ε) measurements are highly sensitive to crack formation in Nb3Sn filaments, especially at low electric-field criteria ≦̸0.1 μV cm−1, even when the sizes of the individual filaments are only few micrometers. All the strands contained substantial Kirkendall porosity, but we found that the quantity and distribution of the Kirkendall voids vary significantly with strand design. Luvata wires have the least porosity, followed by WST wires, and then by OST strands. However, even though the presence of cracks in the Nb3Sn filaments that are in close proximity to Kirkendall voids suggest a correlation between crack initiation and the proximity of the filaments to these voids, the porosity investigation established no definitive relationship between porosity and εirr,0 in the wires studied. [ABSTRACT FROM AUTHOR]