The magnetic field dependence of Young's modulus of type-I and type-II superconductors is used to study the properties of the intermediate and mixed states. The density and separation of vortices in the mixed state are computed from the observed field dependence of the elasticity by use of a model which allows the vortex to expand. A residual stiffness associated with trapped flux is observed to decrease at lower temperatures as a result of reduced pinning forces acting on the vortices. The pinning forces appear to be associated with more than elastic coupling done to the imperfections. The largest total change in stiffness due to the superconducting transition is associated with the longest normal-electron mean free path. Shielding of the lattice initeractions in the superconductng state appears to be more effective the longer the coherence of the superconducting pairs between scatterings. Use of elastic measurements as a means of determining bulk characteristics of the superconductor is found to be quite accurate for materials with low acoustic losses. Anisotropies in the bulk critical fields of niobium are determined simultaneously with the magnetization.

• Received 17 July 1969

DOI:https://doi.org/10.1103/PhysRev.188.728