Grain-boundary flux pinning by the electron-scattering mechanism

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Abstract
The pinning force exerted by an isolated grain boundary upon the flux line lattice (FLL) of a type-II superconductor has been computed, based upon the assumption that electron scattering at the boundary is the most significant source of pinning. The approach is valid at all fields, and takes into consideration both second-order FLL energy terms and high-order Fourier components of the order parameter of the FLL. No attempt has been made in the ‘Electron Scattering Flux Pinning’ (ESFP) model to account for relaxation in the FLL or summation effects due to pinning forces exerted by neighbouring grain boundaries. Nevertheless, calculations based on the model are in reasonable agreement with the published values for grain-boundary flux pinning in a variety of materials. The ESFP model predicts a strong dependence of grain-boundary pinning upon material purity. If the impurity atoms have little effect on parameters such as the thermodynamic critical field H c or the critical temperature T c, then maximum pinning is predicted to occur for an electron mean free path roughly 0·1 times the BCS coherence length ξ0.