Self-organization via elastic interaction between precipitates in thin layers

The present paper is concerned with the solution of the problem of a finite coherent precipitate in an elastic isotropic and homogeneous layer. The positive hydrostatic pressure in the matrix near a dilating precipitate is deduced by comparing the displacements in a layer to those in an infinite solid. The positive hydrostatic pressure gives rise to an attractive elastic interaction between like particles that increases monotonically with decreasing interparticle distance. The attractive interaction is maximal when the particles become of equal size and it increases as they grow closer to the free surfaces. The correlations that result from the elastic interaction in the thin layers generate a tendency toward clustering of equal-sized particles. The self-energy of an isolated precipitate decreases rapidly as it grows closer to the free surfaces favoring, at the advanced stages of the precipitation, precipitate coalescence rather than clustering.