The behavior of self-diffusion coefficient under conditions of varying isotope composition of crystal

The variation of diffusion parameters with varying isotope composition in both the high-temperature and low-temperature region is studied in view of the dependence of the parameters of interatomic potential on the atomic mass. It is demonstrated that the isotopic dependence of the coefficient of self-diffusion is insignificant at high temperatures. However, upon transition to low temperatures, the difference between the coefficients of self-diffusion in isotopically different crystals becomes appreciable. Calculations for diamond and lithium reveal that the coefficient of self-diffusion in the low-temperature region decreases by one-three orders of magnitude during transition from $^{12}\mathrm{C}$ to $^{13}\mathrm{C}$ and increases by an order of magnitude during transition from $^7\mathrm{Li}$ to $^6\mathrm{Li}$. This effect is associated with quantum tunneling at low temperatures and is caused by the presence of "zero-point oscillations" of atoms. It is demonstrated that, in the high-temperature region, the inclusion of isotopic dependence of the parameters of interatomic potential has a marked effect on the self-diffusion coefficient. The temperature dependence of self-diffusion coefficient is calculated, and temperatures are estimated below which the Arrhenius law is no longer valid.