The crystal structure stability, mechanical, optical and thermodynamic properties of TiBC, Ti6Si2B and Ti6Ge2B were predicted using the first principles calculations. The analysis of phonon dispersion curves, formation enthalpies, energy bands, and density of states demonstrate that TiBC, Ti6Si2B and Ti6Ge2B exhibit structure stability and metallic properties. The tensile strength of TiBC, Ti6Si2B and Ti6Ge2B were simulated, the results showed that the tensile strength of TiBC was the best. Anisotropy was explored by anisotropy index, 3D surface constructions and 2D projections. The order of anisotropy is TiBC > Ti6Ge2B > Ti6Si2B. The optical properties showed that TiBC, Ti6Si2B and Ti6Ge2B have strong long-wave absorption capacity. Finally, Debye temperature and sound velocity were investigated, the order of Debye temperature is: TiBC > Ti6Si2B > Ti6Ge2B.
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