Nucleation barrier for phase transformations in nanosized crystals

Abstract

The nucleus of a new phase is considered as an inclusion embedded into a small grain of a polycrystalline matrix. The calculation of the nucleation barrier of dilatational phase transformation in nanosized crystals is carried out based on the concepts of surface stress associated with phase equilibria suggested by Cahn and Larch\'e and the interface equilibrium given by Gurtin and Murdoch. As an example, the $\mathrm{fcc}\ensuremath{\rightarrow}\mathrm{bcc}$ allotropic transformation in Fe is calculated. By further addition of the shear energy using the Eshelby's shear energy equation, the nucleation barrier of martenstic transformation in nanosized crystals for Fe-30Ni alloy is calculated. The results indicate that the nucleation barrier and critical size of phase transformation in nanosized crystals are predominantly dependent on the strain energy, interphase boundary energy from phase transformation, and the grain size, however, the effect of grain size can be ignored when grain size is more than 100 nm. In the basis of these results, the different behavior of martenstic transformation between nanocrystals of Fe-Ni and NiTi alloys is reasonably explained. The factors influencing the nucleation barrier and critical sized of structural phase transformation in nanocrystals are discussed in detail.