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Half-Heusler alloys offer a variety of applications in the field of electronics and superconductors. They are suitable for the formation of thermoelectric materials and superconductors. Their stupendous applications arouse curiosity among many researchers. Therefore, in this paper, a systematic study of structural, electronic, and vibrational properties has been done using density functional theory and density functional perturbation theory. The structural properties such as lattice constant, bulk modulus, and pressure derivative of bulk modulus have been calculated. Electronic and bonding properties have been examined from electronic band structure, charge density contours, and Fermi surfaces. The phonon dispersion spectra and phonon density of states for LuPdBi are reported and discussed for the first time. Moreover, the eigenvector displacements for optical phonons at the zone center are also described to support the reliability of phonon calculations. The computation of phonon spectra disclosed the fact that the resulted phonons are real. Real frequencies of phonons are witness of alloy stability in the cubic phase. The superconducting properties have also been evaluated by employing electronphonon interaction and Eliashberg theory. The Coulomb pseudopotential variable m à is selected to be 0.11 and the computed value of transition temperature is found to be T c ¼ 1.802 K. This value of T c is in agreement with the experimental value of T c ¼ 1.80 K.

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