Frank-Read source-activated flux shear in type-II superconductors

An expression is derived for the flux-pinning force density Fₚ as a function of magnetic induction B and pinning defect center density {ρ}, based on a model of flux-line-lattice shear activated by Frank-Read source dislocations. Fₚ(b) peak positions shift with increasing {ρ} to larger b, where b=B/Bc2 is the reduced induction and Bc2 is the upper critical field. For a given B there exists an optimum defect center density, ρₒₚₜ, for which Fₚ becomes a maximum. The potential Fₚ enhancement is a function of the initial defect concentration ρᵢ. At a constant B a larger Fₚ increase is obtained for smaller ρᵢ, and at a constant ρᵢ the increase is larger for larger B. Quantitative agreement for neutron-irradiated Nb₃Sn is obtained by fitting Fₚ(b) data with three parameters ρᵢ, a pinning defect center generating linear rate constant {α}, and the third consisting of a function of the Ginzburg-Landau {κ} and Bc2. The major characteristic of Fₚ(b) for Nb₃Sn, which is Fₚ peaking at or near b=0.2, is also true for the copper-oxide-based high-Tc superconductors, and the proposed model also applies to these materials.