Josephson-junction model of critical current in granular<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Y</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ba</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn><mml:mo>−</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductors

We calculate the transport critical-current density in a granular superconductor in magnetic fields below about 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ T. The field dependence in this region is assumed to be controlled by intragranular or intergranular Josephson junctions. Various model calculations are fitted to transport critical-current data on bulk ${\mathrm{Y}}_{1}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ ceramic superconductors, whose average grain size somewhat exceeds 10 \ensuremath{\mu}m. The results yield an average junction cross-sectional area (thickness x length) of 4-6 \ensuremath{\mu}${\mathrm{m}}^{2}$. If the junctions are at the grain boundaries, a London penetration depth of about 150-300 nm is inferred, consistent with other estimates. We conclude that Josephson junctions are limiting the transport critical current in these samples and that they lie at the grain boundaries. The parameters of the fit are not consistent with Josephson junctions at twinning boundaries.

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