Isotopic effect at oxygen diffusion in imperfect crystals of cerium oxide

The surface and volume diffusion of oxygen isotopes in different phase states of Ce$_{1-x}$Gd$_x$O$_{2-x/2}$ crystals are studied with the high-speed molecular dynamics method (using graphics processors). It is shown that the ratio between the oxygen isotope diffusion coefficients (the so-called isotopic effect) in the volume of simulated crystals, $D(\mathrm{O}^{16})/D(\mathrm{O}^{18})$ $\approx$ 1.05, agrees well with the well-known ratio $\sqrt{M(\mathrm{O}^{18})/M(\mathrm{O}^{16})}$ = 1.06 and does not depend on the temperature, phase state, and particle-particle interaction potential. On the surface of nanocrystals, the isotopic effect is a linear function of temperature. The ratio between diffusion coefficients of light and heavy isotopes grows with decreasing temperature and equals $D(\mathrm{O}^{16})/D(\mathrm{O}^{18}$) $\approx$ 1.12 at $T$ = 1000 K.