Theoretical study of kinetic isotope effects for vacancy diffusion of impurity in solids

Theoretical studies of the diffusional isotope effect in solids are still stuck in the 1960s and 1970s. With the development of high spatial resolution mass spectrometers, isotopic data of mineral grains are rapidly accumulated. To dig up information from these data, molecular-level theoretical models are urgently needed. Based on the microscopic definition of the diffusion coefficient (D), a new theoretical framework for calculating the diffusional isotope effect (DIE_(v)) (in terms of D^*/D) for vacancy-mediated impurity diffusion in solids is provided based on statistical mechanics formalism. The newly derived equation shows that the DIE_(v) can be easily calculated as long as the vibration frequencies of isotope-substituted solids are obtained. The calculated DIE_(v) values of ¹⁹⁹Au/¹⁹⁵Au and ⁶⁰Co/⁵⁷Co during diffusion in Cu and Au metals are all within 1% of errors compared to the experimental data, which shows that this theoretical model is reasonable and precise.