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Titre complet: Study of the Structural ,Elastic, Electronic and Magnetic properties of full Heusler alloy Zr2RhGa. NOM : Sofrani Prénom: Fatima Affiliation:1Laboratory of Physical Chemistry of Advanced Materials, University of Djillali Liabes, BP 89, Sidi-Bel-Abbes 22000, Algeria University canter El-Wancherisi of Tissmesilt-Algeria. Courriel : sofranifatima14@gmail.com Résumé : The structural ,elastic, electronic and magnetic properties of full Heusler alloy Zr2RhGa, have been investigated by using the first-principles calculations within were based on (DFT) with GGA using FPLAPW As applied within the WIEN2k code . The results of our calculations show that Ti2RhGa is more stable for (FM) configuration among three possible configurations. The mechanical properties of bulk modulus, shear modulus, Young’s modulus E, anisotropic ratio, Poisson’s ratio ν and B/G ratio are also investigated to explore the ductile and brittle nature of this compound. Our calculated values are in agreement with other calculated data. The negative formation energy of –2.26 eV, indicate its stability . The Curie temperature obtained, is higher than room temperature shows this alloy is suitable for spintronic applications. The electronic structure calculations by Zhang et al,of this compound show that Zr2RhGa is half-metallic ferrimagnets (HMF), with an indirect band gap of 0.66 eV ,in the minority-spin energy channel. The Ti2RhGa, alloy has an integer total magnetic moment of 2 μB