The kinetics of precipitation from supersaturated solid solutions

An analysis is made of the process whereby diffusion effects can cause the precipitation of grains of a second phase in a supersaturated solid solution. The kinetics of this type of grain growth are examined in detail. Some grains grow, only to be later dissolved; others increase in size and incorporate further grains that they encounter in so doing. This latter phenomenon of coalescence is discussed in a new “kinetic” approximation. Formulae are given for the asymptotic grain size distribution, for the number of grains per unit volume and for the supersaturation as a function of time. The effects of anisotropy, strain, crystalline order and the finite size of the specimen are allowed for. It is pointed out that for a material that can be said to be “supersaturated with vacancies”, the discussion can be applied to the vacancies as solute “atoms” which cluster together to form internal cavities. The practical case of a real, finite crystal is here important, because the vacancies can in general also escape to the surface. A special analysis is made of this example, and the results are applied to the theory of sintering.