Eigenstress model for surface stress of solids

Solid films are taken here as a typical example to study surface stress of solids. When a thin film is created by removing it from a bulk material, relaxation occurs inevitably because of high energy of newly created surfaces. We separate the relaxation process into normal and parallel relaxations and propose an eigenstress model to calculate the strain energy released during parallel relaxation. After parallel relaxation, a tensile (or compressive) surface eigenstress causes a compressive (or tensile) initial strain in the thin film with respect to its bulk lattice. Due to initial deformation, surface energy density and surface stress are both dependent on the film thickness, whereas surface elastic constants are independent of the film thickness. The nominal modulus of a thin film is determined by nonlinear elastic properties of its core and surfaces with initial strain. A tensile (or compressive) eigenstress makes the nominal modulus of a thin film larger (or smaller), resulting in the thinner, the harder (or softer) elastic behavior in thin films. Atomistic simulations on Au (001), Cu (001), Si (001), and diamond (001) thin films verify the developed eigenstress model.