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Elastic interactions arising from a difference of lattice spacing between twocoherent phases can have a strong influence on the phase separation(coarsening) of alloys. If the elastic moduli are different in the two phases,the elastic interactions may accelerate, slow down or even stop the phaseseparation process. If the material is elastically anisotropic, theprecipitates can be shaped like plates or needles instead of spheres and canform regular precipitate superlattices. Tensions or compressions appliedexternally to the specimen may have a strong effect on the shapes andarrangement of the precipitates. In this paper, we review the main theoreticalapproaches that have been used to model these effects and we relate them toexperimental observations. The theoretical approaches considered are (i)`macroscopic' models treating the two phases as elastic media separated by asharp interface (ii) `mesoscopic' models in which the concentration variescontinuously across the interface (iii) `microscopic' models which use thepositions of individual atoms.Comment: 106 pages, in Latex, figures available upon request, e-mail  addresses: fratzl@unileoben.ac.at, oliver@ma.hw.ac.uk,  lebowitz@math.rutgers.edu, submitted to the Journal of Statistical Physic

Modelling of Phase Separation in Alloys with Coherent Elastic Misfit