Influence of the lattice strain decay on the diameter of self assembled secondary phase nanorod array in epitaxial films
A theoretical model based on an analytical solution of the elastic energy of strained lattices is developed to study the diameter of self-assembled vertically-aligned secondary phase nanorods in epitaxial films. In this model, the nanorod diameter is calculated by minimizing the energy due to the formation of the nanorods, the elastic energy of the film and nanorod lattices, and the interfacial energy on the nanorod surface. The calculated nanorod diameter is consistent with experimental measurements of BaZrO3 and BaSnO3 nanorods in YBa2Cu3O7− δ films with different nanorod densities. The primary mechanism that determines the nanorod diameter is found, for the first time, to be the lattice strain decay inside the nanorods, which depends only on the ratios of elastic constants of nanorod material and is independent of film/nanorod lattice mismatch. The discovered correlation between the nanorod diameter and the elastic properties of the secondary phase oxides can be used as a guidance in the quest of the self-assembled nanorods with different diameters in epitaxial nanocomposite films.
Journal of Applied Physics 118, 164301 (2015)