Stress effect on atomic diffusion

In this work, we incorporate strain energy in the potential energy for the migration/diffusion of atoms in a stress field under the frameworks of linear elasticity and statistical thermodynamics. Analytical expressions of the diffusivity and net flux of atoms are derived. Both hydrostatic stress and effective stress play important roles in the diffusivity and net flux of atoms for the migration/diffusion of atoms in a deformed material. The gradients of the hydrostatic stress and the effective stress also contribute to the net flux of atoms in a deformed material.