Resistive transition broadening in two-phase polycrystalline YBaCuO
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A model proposed by Tinkham1 to explain the resistance versus temperature broadening found in high Tc superconductors in applied magnetic fields is extended to "foot and knee"-structured data taken on polycrystalline YBa 2 Cu 3 0 6 + 5 . The proposed extension involves a series combination of two types of superconductors. For this series combination to result, a critical ratio of the two types of superconductors must be met—a result common to both percolation and randomized cellular autonoma theory. This critical ratio is investigated via statistical computer models of a polycrystalline superconductor having two phases of crystallites—one with substantially lower Jc than the other.
I. INTRODUCTION Experimental studies of the magnetic behavior of YBa2Cu306+,5 have revealed a broadening of the resistive transition (R vs T) dependent upon the strength of the applied magnetic field.2"10 Such data have been interpreted by several models, 1 ' 5 ' 1112 each assuming different mechanisms such as inhomogeneities in the material, fluctuation enhanced conductivity above Tc, and flux creep below Tc, as responsible for the dependence of resistance upon magnetic field.11 Using a scaling argument based on the Anderson-Kim 12 form of the thermal activation energy, Uo, Yeshurun and Malozemoff13 have suggested that
Uo = f3Ht£4>o/B,
(1)
where /3 is a numerical factor =1, Hc is the critical field, f the coherence length, 0 O the flux quantum, and B the flux density. Tinkham, who has offered a rationale for Eq. (1) in terms of the "thermally activated vortex lattice shear", developed a model for the width and shape of the reduced resistance versus temperature curves in various magnetic fields1: r = R/Rn =
-2
- t)m/2B]}
(2)
where Rn is the normal resistance (slightly above Tc), /o is the modified Bessel function of the first kind, A = 4CJco/Tc (Jco = Jc at B = 0 and without thermal
fluctuations; C is a material-dependent constant), and t = T/Tc. Tinkham arrives at Eq. (2) by treating the resistance caused by a network of slipping fluxons in analogy with the physics of a "single heavily damped current-driven Josephson junction". Although the mechanisms responsible for the resistive transition observed in experiments such as those displayed in Fig. 1 are a topic of current discussion,14 we use Eq. (2) in what follows because it provides a reasonably compact way to represent the experimental data. II. EXPERIMENTAL RESULTS AND ANALYSIS Equation (2) does not explain data displaying the more complicated "foot and knee" structure (Fig. 2). The purpose of this paper is to try to explain these
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Currently at School of Engineering and Applied Sciences, Washington University. b) Currently at Department of Physics, University of California at Davis. J. Mater. Res., Vol. 8, No. 5, May 1993
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