Precipitation hardening for mechanical strength, magnetic hardness and hardness of superconductors

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Abstract
If particles of a second phase form by precipitation in an alloy, the yield stress for initial plastic deformation increases, a larger coercive field is observed in a ferromagnet and a type II superconductor becomes able to carry an increased electric current in a magnetic field. These three phenomena are discussed from a unified point of view as the resistance of a statistical array of obstacles against the movement of a flexible ‘carrier’ which causes a change in state of the material. The carrier in the mechanical case is a dislocation whose movement deforms a solid. The magnetization of a ferromagnet changes by the movement of a Bloch wall. A type II superconductor in the mixed state is penetrated by magnetic flux tubes which must be prevented from moving if it is to carry a loss-free current. In each case the analysis proceeds in two steps: A discussion of the elementary interaction between one carrier and one particle, and the summation of the statistical forces acting on the carrier by all the particles it is in contact with. The results are compared with those of experiments on model substances. Quantitative differences in ‘hardening’ in the three cases and limitations of the possible ‘strength’ increases by precipitation are discussed.