Teary Mn+1AXn phases with layered hexagonal structures,as candidate materials used for next-generation nuclear reactors,have shown great potential in tolerating radiation damage due to their unique combination of ceramic and metallic properties.However,Mn+1AXn materials behave differently in amorphization when exposed to energetic neutron and ion irradiations in experiment.We first analyze the irradiation tolerances of different Mn+1AXn (MAX) phases in terms of electronic structure,including the density of states (DOS) and charge density map.Then a new method based on the Bader analysis with the first-principle calculation is used to estimate the stabilities of MAX phases under irradiation.Our calculations show that the substitution of Cr/V/Ta/Nb by Ti and Si/Ge/Ga by Al can increase the ionicities of the bonds,thus strengthening the radiation tolerance.It is also shown that there is no obvious difference in radiation tolerance between Mn+1ACn and Mn+1ANn due to the similar charge transfer values of C and N atoms.In addition,the improved radiation tolerance from Ti3AlC2 to Ti2AlC (Ti3AlC2 and Ti2AlC have the same chemical elements),can be understood in terms of the increased Al/TiC layer ratio.Criteria based on the quantified charge transfer can be further used to explore other Mn+1AXn phases with respect to their radiation tolerance,playing a critical role in choosing appropriate MAX phases before they are subjected to irradiation in experimental test for future nuclear reactors.