Top: Scanning electron microscope image of a cross-section of a composite. Bottom: Schematic of a typical configuration for electromagnetic measurements, showing the arrangement of magnetization current shells with respect to the applied field and the radial direction of tin diffusion.
Input profiles of tin composition as a function of radius. The index depicts the sharpness of the profile, where , and are shown here and in Figs. 4 to 7. An ideal profile, in which the tin content is constant at , is also shown. Local values of the critical temperature and upper critical field (at ) that correspond to the local composition are indicated on the right axes.
Maximum bulk pinning force plotted against the irreversibility field, derived by extrapolating Kramer plots, for a series of samples, measured at . Despite differences in heat treatment duration ( at ) and temperature, these data collapse onto the single linear fit given by Eq. (5). Data taken at to (open symbols) yield very low values of , but are still consistent with those at lower temperatures used for Eq. (5).
Moment of the shells as a function of radius simulated at and (a), and at and (b). The indices for the curves are the same as for Fig. 2. Note that the coordinate has been mapped to a radius to simulate actual composites.
Critical current density, as would be determined from a magnetization experiment of an actual strand, as a function of field simulated at (a) , and (b) . The inset of plot (a) shows a magnified view of the mid field data. The dashed and dash-dot curves correspond to the noncopper values determined by magnetization measurements in Ref. 17 for ternary and binary strands with the field parallel to the strand axis (as in Fig. 1). The large diamonds correspond to transport measurements for the same ternary strands reported in Ref. 32. The indices for the curves follow the same sequence as in Fig. 2.
Bulk flux-pinning force curves as a function of field simulated at (a) and (b) . The indices for the curves follow the same sequence as in Fig. 2.
Kramer function curves as a function of field simulated at (a) and (b) . The indices for the curves follow the same sequence as in Fig. 2. The insets in both plots show a magnified view of the region near the field axis.
Energy-dispersive x-ray spectroscopy analyses of a strand in Ref. 14 are simulated using the tin composition profile shown in plot (a), with corresponding local values of critical temperature and upper critical field indicated on the right axes. The open boxes denote data points in Ref. 14 for a , reaction. In plot (b), the simulated critical current density vs field curve at is shown over a field range of technological interest. Large diamonds denote measured values in Ref. 13 for similar strands as in Ref. 14. In plot (c), the corresponding bulk pinning force at is presented. Plot (d) shows the Kramer function, along with its extrapolation (dashed line) from data at and below. In all plots, the curve corresponding to an ideal profile of a constant is also labeled.
Comparison of the weighted mean of the upper critical field with extrapolations of simulated Kramer functions, at and .
Variation of flux-pinning quantities with tin profile index.
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