The quaternary Heusler LuCoTiSi, LuCoTiGe, and LuCoTiSn compounds’ physical properties have been investigated using the GGA approximation based on the density functional theory. These compounds are stable in the ferromagnetic phase and semi-stable in the non-magnetic phase. Elastic studies show that these compounds are quite stable and belong to the category of ductile materials. Phonon calculations also show that these two combinations are quite stable, and the phonon levels in the band structure are all in the positive region. The LuCoTiSi, LuCoTiGe, and LuCoTiSn compounds are half-metallic with 100% spin polarization with 2.0lB 3.0 lB, and 2.0lB, respectively. The maximum value of their Seebeck (S) coefficient occurred at 130 K. The figure of merit (ZT) coefficient of these compounds at 100 K equals one and decreased to room temperature with a gentle slope, indicating their thermoelectric efficiency at low and room temperatures. All compounds have accessible regions that referred to their thermodynamic stability. The LuCoTiGe case has a more extensive accessible region than other cases of the thermodynamic phase diagram.
