Abstract
Three-dimensional networks are interesting in their own right and as model systems for granular superconductors. We develop this idea to discuss the key concept of granularity. It is shown that for not too small grains of size a<ℓ ∞ (bulk mean free path) the phenomena of weak localization and paracoherence set in simultaneously. Also, the often-used formula for the resistivity, ρ n = R n a, that is ρ n∞ a, does not describe the dependence of ρ n on grain size. Actually ρ n∞ a −1 in this limit. The diamagnetic behaviour of sintered YBa 2Cu 3O 7 is discussed and shown to be amenable to a quantitative description in terms of critical exponents like a 3D random network. On the other hand, effects due to twin boundaries in single crystals would be expected to result in critical exponents characteristic of the X-Y model.
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