THEORY OF NONCLASSICAL SURFACE NUCLEATION AT CHANGE OF VOLUME TRANSITIONS

We consider first-order transitions of isotropic, elastic solids under going a change of volume and determine all symmetric (i.e., depending on only the radial component of the displacement vector) saddle-point solutions that are potential critical nuclei. In one dimension these s olutions can be found analytically, whereas in higher dimensions we ha ve managed to find these states numerically. We show that in all dimen sions (d) the states corresponding to both the displacement and strain fields being localized in the region of the surface are the lowest-en ergy saddle-point solutions and, thus, the critical nuclei of these tr ansitions;Also, if the radius of the system is very large, we find tha t the d = 1 analytical strain profile of the critical surface nucleus provides an extremely accurate representation of the exact surface cri tical nuclei for any d > 1. We provide further support to our claim th at these states are the critical nuclei of these transitions by formul ating a complete hydrodynamical theory of the evolution of the symmetr ic strain and then integrating the associated equation of motion. The transition proceeds by nucleation and growth, and our dynamics demonst rates that the system always evolves by passing through these surface nuclei. The applicability of these results in describing (i) the (elec tronic-band-induced) symmetric transition undergone by the mixed-valen ce alloy Ce1-xThx or (ii) the nature of the nucleation centers inferre d from the ordering kinetics of diblock copolymers is discussed.