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The upper critical field of filamentary conductors
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10.1063/1.1890447
/content/aip/journal/jap/97/9/10.1063/1.1890447
http://aip.metastore.ingenta.com/content/aip/journal/jap/97/9/10.1063/1.1890447

Figures

Image of FIG. 1.
FIG. 1.

Field-emission scanning electron microscope (FESEM) cross-section images of the investigated wires. Top section, upper row from left to right: A ternary ITER-type bronze process wire with a Ta diffusion barrier manufactured by Furukawa (FUR) with a close-up of the filamentary region, a ternary ITER-type bronze process wire with a Ta diffusion barrier manufactured by Vacuumschmelze (VAC) with a close-up of the filamentary region, a ternary Powder-in-tube (PIT) wire enclosed by a CuNb reinforcement tube manufactured by Shape Metal Innovation (SMI) plus a close-up of the filamentary region, and a binary PIT wire produced by SMI plus a close-up of the filamentary area. Top section, bottom row from left to right: An overall cross section of a ternary PIT wire produced by SMI plus close-ups of the filamentary area for reactions of 4, 16, 64, and 768 h at 675 °C, respectively, indicating the progression of the A15 layer growth vs time. In the additional single filament close-up for the 4-h reaction an initial phase is visible in between the core region and the formed . Bottom section: Close-ups on the A15 regions in the two bronze wires and in the binary and ternary (64 h-675 °C) PIT conductors. The Sn sources in these close-ups are located at the right side of the A15 layers. More detailed conductor specifications and heat treatment data can be found in Table I.

Image of FIG. 2.
FIG. 2.

Representative resistive transitions for the ternary PIT wire (B34) as measured at the UW-ASC (open symbols) and the NMHFL (closed symbols). The upper envelope line represents an overall polynomial fit of the magnetoresistance and the thin lines represent exponential fits to individual transitions using Eq. (1) to overcome the noise that is present in the high-field data. Intersections can be made at various percentages of the normal-state resistivity, as indicated by the 10%, 50%, and 90% lines to arrive at different criteria for .

Image of FIG. 3.
FIG. 3.

SQUID magnetometer data on ternary PIT (B34) wires after 4, 16, 64, and 768 h at 675 °C taken by Fischer (see Ref. 28). The magnetic moment vs temperature was obtained through zero-field cooling of the samples to 5 K, application of a 5-mT field parallel to the wire axis to introduce shielding currents, and raising the temperature while registering the magnetic moment. The lines depict intersections at 10%, 50%, and 90% normal state for the 768-h sample where 0% is defined at the lower end of the A15 transition, depicted by the bold line. These lines represent criteria that can be used to derive .

Image of FIG. 4.
FIG. 4.

Reduction of the property gradients via extended heat treatment visualized via resistive data on SMI ternary (B34) wire. The points in these plots were derived from the resistivity fits on the data and the lines were calculated with the MDG description. The 1% and 99% lines are used to quantify the extremes of the measured transitions. The main part of the detected property distribution occurs between 10% and 90%. Clearly visible is the reduction of the transition width (10%–90%) with increasing heat treatment time from 1.2 to 0.5 T. The best A15 sections that are detected [-99%] only increase by , but the lower end of the detected property distribution ([-1%]) increases by . The reduction of the detected width, as derived from the MDG fits, is less obvious but still present, resulting in a width (10%–90%) reduction from 0.4 to 0.3 K.

Image of FIG. 5.
FIG. 5.

Summarized result from Fig. 4 depicting the effect of reaction time on the resistively measured -99%(12 K), -90%(12 K), -10%(12 K), -99%(0), -90%(0), and -10%(0) calculated from the MDG fits (dotted lines plus data points) in comparison with the SQUID and VSM data from Fig. 3 and Fischer et al. (see Ref. 27) (depicted by the shaded regions). The general trends for the critical fields vs reaction time as measured resistively are similar to the magnetic data but the detected transition widths are much smaller in the resistive characterizations. The highest values (i.e., at 99% normal state resistance) for the resistive data coincide with the VSM-determined values. A difference is visible between the detected values in addition to the reduced transition width in the resistive characterizations.

Image of FIG. 6.
FIG. 6.

Collected data for resistively characterized samples from 1% to 99% normal state. The plots are separated in temperature for enhanced visibility. Included are the range of values and detected property distribution widths for the 10%–90% normal-state criteria. The points were derived from the resistivity fits on the data and the lines were calculated with MDG. The main part of the detected property distribution occurs between 10% and 90%. The 1% and 99% lines are used to quantify the extremes of the measured transitions. The order from top to bottom is approximately of increasing inhomogeneity.

Image of FIG. 7.
FIG. 7.

Comparison of the best A15 sections that were detected in the ternary wires. The inset shows the binary PIT wire plus the binary bulk needle sample. The points were derived from the resistivity fits on the data and the lines were calculated with the MDG description. It can be seen that the best A15 regions are present in all ternary wires and very comparable, i.e., and . The binary PIT in comparison shows a reduced maximum (27.8 T) but a comparable (18.0 K). The bulk needle has a reduced fitted (16.7 K) but, in comparison to the binary PIT wire, a very high which is in the range of the ternary wires (29.3 T).

Image of FIG. 8.
FIG. 8.

Kramer plot derived from high-field transport measurements at 4.2 K with a criterion on a small diameter Ti–6Al–4V barrel for a ternary PIT wire, reacted for 64-h at 675 °C. In comparison, the small current resistive transition at 4.2 K on a Ti–6Al–4V mounted resistive sample (reacted together with the barrel sample) is also included in the plot and the and 99% normal-state resistance points of this transition are indicated. The point of the resistive transition approximately coincides with the measured point and the onset of the transition is close to the value for from the transport data. The data extrapolation (short dots) assumes a gradual reduction to -99%(4.2 K). The ideal Kramer line (long dots) assumes a hypothetical ideal A15 layer with perfectly homogeneous properties equal to the measured -99% phase transition. A similar hypothetical Kramer line can be simulated from measured Sn gradient profiles, as was recently published (see Ref. 30). The inset depicts the field-temperature boundary that is required for critical current-density scaling.

Image of FIG. 9.
FIG. 9.

Normalized plot for available data, including data taken from the literature, demonstrating that the shape of the normalized phase boundary is identical for all included Nb–Sn phases. The samples in bold are presented in this publication. The data were first fitted with the Maki–DeGennes equation and the resulting and were used as normalization parameters. The normalization is valid for 1%, 10%, 50%, 90%, and 99% normal-state criteria. The data from the literature use 50% (Orlando) and 50%–90% (Foner) criteria. The normalization also holds for Kramer-extrapolated critical fields using a 10- or criterion. The numbers behind the sample names indicate the values for and .

Tables

Generic image for table
Table I.

Overview of the investigated materials. Depicted are the sample names, a short identification number, the heat treatment for each sample, the wire type, and the way each sample was mounted. The next column gives the additional elements that were present during the formation of the A15 layers. In all the wires, Cu was present close to the A15 formation area. The next column gives the non-Cu critical current density for each wire, either measured in transport or estimated from the magnetization data. The last column gives the non-Cu current density in the samples during the measurement of resistive transitions.

Generic image for table
Table II.

Summarized zero-temperature upper critical field and zero-field critical temperature data.

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/content/aip/journal/jap/97/9/10.1063/1.1890447
2005-04-27
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The upper critical field of filamentary Nb3Sn conductors
http://aip.metastore.ingenta.com/content/aip/journal/jap/97/9/10.1063/1.1890447
10.1063/1.1890447
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