Modeling and Simulation of the Percolation Problem in High-T c Superconductors: Role of Crystallographic Constraints on
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Modeling and Simulation of the Percolation Problem in High-Tc Superconductors: Role of Crystallographic Constraints on Grain Boundary Connectivity Megan Frary and Christopher A. Schuh Department of Materials Science and Engineering, Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge, MA 02139 ABSTRACT Superconductivity in high-Tc materials is often modeled as a percolation problem in which grain boundaries are classified as strong or weak-links for current transmission based on their disorientation angle. Using Monte Carlo simulations, we have explored the topology and percolation thresholds for grain boundary networks in orthorhombic and tetragonal polycrystals where the grain boundary disorientations are assigned in a crystallographically consistent manner. We find that the networks are highly nonrandom, and that the percolation thresholds differ from those found with standard percolation theory. For biaxially textured materials, we have also developed an analytical model that illustrates the role of local crystallographic constraint on the observed nonrandom behavior. INTRODUCTION Grain boundaries play a significant role in determining the critical current densities of hightemperature oxide superconductors, as Jc varies inversely with grain boundary misorientation [13]. In order to optimize the microstructure of the oxide film, substrates are processed in such a way as to impart a high fraction of low-angle (strong-link) boundaries to the oxide films [1, 2, 4]. A small fraction of weak-link boundaries can be tolerated in the microstructure as long as they do not form a connected path across the film, so the connectivity and percolative properties of the grain boundary network are of prime importance to the resulting properties. The local connectivity among strong- and weak-link boundaries may be quantified by the triple junction distribution (TJD) which gives the population of junctions Ji coordinated by i (= 0, 1, 2, or 3) strong-link boundaries. If boundaries are randomly assigned as strong-links (with probability p) or weak-links (with probability 1 – p), these populations are: 3 3−i J i = p i (1 − p ) i
(1)
3 where the combinations are equal to 1, 3, 3, and 1 for i = 0, 1, 2, and 3 respectively. We have i recently performed a survey of existing experimental data [5], and find that these data do not follow the predictions of Eq. (1), but instead fall on different universal curves, independent of material class or crystal structure. This is illustrated in Fig. 1, which includes data points from high-Tc superconductors [6-8] as well as the biaxially-textured Ni substrates that are often used in their production [1, 2, 9]. Here we see that triple junctions coordinated by two strong-link and one weak-link boundary (J2 junctions) occur less frequently than expected on the basis of a random assignment process, with a concurrent increase in the population of J3 junctions.
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Superconducting Oxides Nickel Substrates
J0
J1
J2
J3
Figure 1. Triple junctio
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