Unraveling the Scaling Characteristics of Flux Pinning Forces in Bi 1.6 Pb 0.4 Sr 2 Ca 2− x Na x Cu 3 O 10+ δ Superconductors

The temperature and magnetic field dependence of the critical current density ( J c ) and pinning force density ( F p ) in Bi 1.6 Pb 0.4 Sr 2 Ca 2− x Na x Cu 3 O 10+ δ ( x = 0, 0.02, 0.04, 0.06, 0.08, and 0.10) high-temperature superconductors is reported. Polycrystalline samples were prepared by a conventional solid-state reaction route. The influence of Na substitution on J c and F p at temperatures ranging between 65 K and 25 K was investigated. The collective pinning model is successfully applied to describe the magnetic field dependence of J c for all the samples investigated. Magnetic field–temperature phase diagrams were also constructed to illustrate the effects of Na substitution in different field regions. The power-law dependence of the maximum F p ( F p,max ) versus the irreversibility field ( B irr ) at different temperatures shows nearly unchanged exponent values, suggesting temperature independence of the flux pinning mechanism in the Na-substituted samples. The dominant pinning mechanism is confirmed to be δ l pinning, induced by fluctuations in the mean free path of charge carriers.