Model of grain-boundary self-diffusion in $\alpha$- and $\beta$-phases of titanium and zirconium

A model of the grain-boundary self-diffusion process in metals undergoing phase transitions in the solid state is proposed. The model is based on the ideas and approaches of the theory of nonequilibrium grain boundaries. It is shown that the range of application of basic relations of this theory can be extended, and they can be used to calculate the parameters of grain-boundary self-diffusion in high-temperature and low-temperature phases of metals with phase transition. Based on the constructed model, activation energies of grainboundary self-diffusion in titanium and zirconium are calculated, and their anomalously low values in the low-temperature phase are explained. The calculated activation energies of grain-boundary self-diffusion are in good agreement with experimental data.