Inclusion problems associated with thin fcc films: Linkage between eigenstrain and inter-atomic potential

Often, during fabrication of thin films on substrates, different types of defects may be introduced into the films. Recently, the determination of the elastic fields due to the self-assembly of quantum dots or strained islands in thin films has been of major concern. In the micromechanical studies, such strained islands are modeled by inclusions. This paper aims to develop a theory pertaining to the presence of nano-inclusions of various geometries within thin films having face centered cubic (fcc) structure. To this end, the notion of eigenstrain is combined with a many body inter-atomic potential suitable for fcc crystals. The interaction between atoms is modeled via Sutton-Chen (SC) potential. The displacements of the atoms are computed by employing the integral transform to the discretized equilibrium equation. Incorporation of the interaction between the inclusion and the free surface makes it feasible to investigate the effect of distance of the inclusion from the free surface. For the sake of comparison with the result from the continuum theory of elasticity, the problem of dislocation loop in an infinite domain is considered. Moreover, the behavior of the thin film in the presence of inclusion is studied using three-dimensional (3D) molecular dynamics (MD) simulation, and the result is compared with that obtained from the proposed theory. During the initial processes of introducing the inclusion into the film, the temperature is held at 0 K using a simple temperature scaling method. Afterwards, for the situations where thermal loading is of interest, the temperature is increased, and the pertinent thermo-mechanical fields are examined.