Microwave surface resistance in superconductors with grain boundaries
  Microwave-field distribution, dissipation, and surface impedance are theoretically investigated for superconductors with laminar grain boundaries (GBs). In the present theory we adopt the two-fluid model for intragrain transport current in the grains, and the Josephson-junction model for intergrain tunneling current across GBs. Results show that the surface resistance $R_s$ nonmonotonically depends on the critical current density $J_{cj}$ at GB junctions, and $R_s$ for superconductors with GBs can be smaller than the surface resistance $R_{s0}$ for ideal homogeneous superconductors without GBs. 
Yasunori Mawatari