Basic equations of diffusion in metals considering nonlocality

Polycrystalline metals usually have internal structures, thus there are cases where it is difficult to apply Fick's laws to diffusion. In the present paper, the authors introduce mesodomains, which are regarded as the grains in metals, to the conventional diffusion theory. State variables are varied in mesodomains and are divided into the average value and fluctuating value. Consequently, the mass balance is expressed by not only the mass concentration but also the mesoscopic average mass concentration considering nonlocality. A new entropy flux is introduced to entropy inequality and a new mesoscopic variable is added to Helmholtz free energy. Furthermore, the constitutive equations of Cauchy's stress and of diffusion flux are influenced by mesoscopic average mass concentration which is one of the behaviors of materials in grains.