Theoretical study of kinetic isotope eff ects for vacancy diff usion of impurity in solids

<正>Theoreticalstudiesofthediff usionalisotope eff ect 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, molecularlevel theoretical models are urgently needed. Based on the microscopic defi nition of the diff usion coe ffi cient (D), a new theoretical framework for calculating the diff usional isotope eff ect(DIE(v))(intermsofD*/D)forvacancy-mediated impurity diff usion in solids is provided based on statistical mechanics formalism. The newly derived equation shows that theDIE(v)can be easily calculated as long as the vibration frequencies of isotope-substituted solids are obtained.The calculatedDIE(v)values of199 Au/195 Au and60 Co/57 Co during diff usion 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.