9322687 Voorhees The properties of many alloys of engineering significance are related to the morphology and spatial distribution of coherent second-phase particles. In many cases elastic stress is present in these two-phase systems resulting from either a difference in lattice parameters between the minority phase particles and the matrix, or an applied stress. As an understanding of the factors controlling the morphology of a particle in a stressed crystalline solid is not at hand, it is difficult to predict the properties of these multiphase materials. This lack of understanding can be traced to the limited number of studies that have investigated the factors controlling the equilibrium shape of a coherent misfitting particle, i.e. the shape that minimizes the total energy of the system subject to all possible variations in particle morphology. Nevertheless, these few studies have shown that the presence of elastic stress can lead to qualitatively different phenomena than in the absence of stress, such as multiple equilibrium shapes for a given set of materials parameters, particle splitting and non convex, hourglass-like, equilibrium shapes. %%%% A major goal of this project is to provide a picture of the generic role elastic stress plays in the development of the equilibrium morphology of a misfitting three-dimensional particle. As the equations which determine the equilibrium shape of a misfitting particle are highly nonlinear, a far more complex particle shape bifurcation structure is present in three-dimensions than observed in previous work on the equilibrium shape of a particle in two- dimensions. Despite the numerical nature of the study and the specific assumptions employed in each section of the work, a general framework for understanding and predicting the morphological evolution of particles in stressed solids will be provided. Finally, this theory will be used in concert with experiments to investigate the effects of a nondilation al misfit on the morphology of misfitting particles in an elastically anisotropic system. ***
