The structural, elastic, electronic and thermodynamic properties as well as the magnetism of the ternary full-Heusler alloys Rh_(2)MnZ (X = Sn, Pb and Tl) have been investigated by using the full-potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT) within the generalized gradient approximation (GGA). The AlCu_(2)Mn-type structure is energetically more favorable than the CuHg_(2)Ti-type structure for all the compounds studied here and found to be are ferromagnetic. The electronic structures calculation sare found to exhibit a metallic character for all the herein studied compounds Rh_(2)MnZ (X = Sn, Pb and Tl) alloys. The magnetic properties reveal that the Mn atom is responsible for large magnetic moment. Moreover, the mechanical behavior shows that all studied compounds are mechanically stable, ductile and anisotopic in nature. The elastic and thermodynamic properties for Rh_(2)MnTl compound have not yet been established. The obtained results for various properties of the series of Rh_(2)MnZ (X = Sn, Pb and Tl) are compared with those found experimentally and theoretically.
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