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The structural and mechanical stability of Fe₂TaAl and Fe₂TaGa alloys along with the electronic properties are explored with the help of density functional theory. On applying different approximations, the enhancement of semiconducting gap follows the trend as GGA < mBJ < GGA + U. The maximum forbidden gaps observed by GGA + U method are E_g = 1.80 eV for Fe₂TaAl and 1.30 eV for Fe₂TaGa. The elastic parameters are simulated to determine the strength and ductile nature of these materials. The phonon calculations determine the dynamical stability of all these materials because of the absence of any negative frequencies. Basic understandings of structural, elastic, mechanical and phonon properties of these alloys are studied first time in this report.