Phonon-mediated superconductivity in [Formula: see text] compounds: a crystal prediction via cluster expansion and particle-swarm optimization

Investigating superconductivity represents one of the most significant phenomena in the field of condensed matter physics. Our simulations aim to elucidate the structures in the metallic state of Mg(1−x)Mo(x)B(2), which is essential for predicting their superconducting properties. By employing a first-principle cluster expansion and particle-swarm optimization, we have predicted the structures of Mg(1−x)Mo(x)B(2) ternary alloys, including Mg(0.667)Mo(0.333)B(2), Mg(0.5)Mo(0.5)B(2), and Mg(0.333)Mo(0.667)B(2), and have determined their thermodynamically stable configurations under both atmospheric and high-pressure conditions. To investigate the potential for superconductivity in these structures, we have conducted a detailed examination of electronic properties that are pertinent to determining the superconducting state. Regarding superconducting properties, Mg(0.333)Mo(0.667)B(2) exhibits superconductivity with a critical temperature (T(c)) of 7.4 K at ambient pressure. These findings suggest that the theoretically predicted structures in Mg/Mo-substituted metal borides could play a significant role in synthesis and offer valuable insights into superconducting materials.