Concept of Collective Pinning Applied to Solution Hardening of Crystals

The concept of collective pinning, which has proven successful in the theories of flux-line and charge-density-wave pinning, is outlined and its applicability to problems of various dimensionality is discussed. This concept is applied to the one-dimensional problem of dislocations weakly pinned by solute atoms. Within a self-consistent approach the critical shear stress for the onset of solution hardening is obtained. The qualitative agreement of the result with those of other approaches is explained by scaling laws.