On the influence of elastic strains on crystallization processes in solids. I: Spherical clusters in solids of finite size

The influence of the finite size of a solid sample on evolving elastic fields and, in particular, on the energy of elastic deformations due to the formation of a new phase inside a solid is analyzed. It is shown that, depending on the ratio between the size of the matrix R M and that of the cluster R C , elastic strains may either stimulate or inhibit the growth of the newly evolving phase. Elastic strains may result in a stable two-phase equilibrium state. The discussed specific finite-size effects become important for clusters in samples which are not larger than about 5R C . The outlined model is the basis for the discussion of energies of the elastic strain field caused by the process of formation of a cluster of a new phase near or at the surface of a solid, the detailed analysis of which will be presented in Part II