Native point defects in $Ti_3GeC_2$ and $Ti_2GeC$

Using density functional theory, we calculated the formation energy of native point defects (vacancies, interstitials and antisites) in MAX phase $Ti_2GeC$ and $Ti_3GeC_2$ compounds. Ge vacancy with formation energy of 2.87 eV was the most stable defect in $Ti_2GeC$ while C vacancy with formation energy of 2.47 eV was the most stable defect in $Ti_3GeC_2$. Ge vacancies, in particular, were found to be strong phonon scattering centres that reduce the lattice contribution to thermal conductivity in $Ti_2GeC$. In both compounds, the reported high thermal and electrical conductivity is attributed to the electronic contribution that originates from the high density of states at the Fermi level.