A change in the free energy of a grain boundary was analyzed for the case where lattice vacancies came to the boundary and were then delocalized in its disordered atomic structure. It was shown that the free energy of the boundary was minimized at some excess atomic volume whose value depended upon the energy of vacancy formation in the crystal lattice, and the boundary energy. The formation of a metastable localized grain-boundary vacancy, as a result of thermal fluctuations of the density in a group of atoms followed by the jumping of an adjacent atom into this vacancy, was taken to be an elementary event of grain-boundary diffusion. Expressions for the activation energy of diffusion, and the diffusion coefficient, were derived for equilibrium and non-equilibrium grain boundaries.

Self-Diffusion at Grain Boundaries with a Disordered Atomic Structure. V.N.Perevezentsev: Technical Physics, 2001, 46[11], 1481-3