Elastic and thermodynamic properties of zirconium- and hafnium-doped $$\hbox {Rh}₃\hbox {V}$$ Rh 3 V intermetallic compounds: potential aerospace material

Structural, electronic, mechanical and thermodynamic properties of $$\hbox {Rh}₃\hbox {Zr}_x\hbox {V}_1-x$$ and $$\hbox {Rh}₃\hbox {Hf}_x\hbox {V}_1-x$$ ( $$x = 0$$ , 0.125, 0.25, 0.75, 0.875 and 1) combinations are investigated by means of first-principles calculations based on the density functional theory within the generalized gradient approximation. Here, $$\hbox {Rh}₃\hbox {V}$$ is chosen as the parent binary compound and the doping elements are zirconium and hafnium with the above-mentioned concentrations. The calculated lattice parameters and elastic modulus of binary $$\hbox {Rh}₃\hbox {Hf}$$ , $$\hbox {Rh}₃\hbox {V}$$ and $$\hbox {Rh}₃\hbox {Zr}$$ are in good agreement with the available experimental and other theoretical results. In this study, the following ternary materials viz., $$\hbox {Rh}₃\hbox {Zr}_0.75\hbox {V}_0.25$$ , $$\hbox {Rh}₃\hbox {Hf}_0.25\hbox {V}_0.75$$ and $$\hbox {Rh}₃\hbox {Hf}_0.75\hbox {V}_0.25$$ are found to be brittle/more brittle than the parent binary compound $$\hbox {Rh}₃\hbox {V}$$ , whereas the other ternary combinations, namely $$\hbox {Rh}₃\hbox {Zr}_0.125\hbox {V}_0.875$$ , $$\hbox {Rh}₃\hbox {Zr}_0.25\hbox {V}_0.75$$ , $$\hbox {Rh}₃\hbox {Zr}_0.875\hbox {V}_0.125$$ , $$\hbox {Rh}₃\hbox {Hf}_0.125\hbox {V}_0.875$$ and $$\hbox {Rh}₃\hbox {Hf}_0.875\hbox {V}_0.125$$ are found to be more ductile than $$\hbox {Rh}₃\hbox {V}$$ . The more brittle ternary combination, namely $$\hbox {Rh}₃\hbox {Hf}_0.75\hbox {V}_0.25$$ ( $$B = 229.32\,\hbox {GPa}$$ ) has the maximum Young’s modulus, shear modulus and hardness values; whereas the more ductile ternary $$\hbox {Rh}₃\hbox {Zr}_0.25\hbox {V}_0.75$$ combination ( $$B = 243.54\,\hbox {GPa}$$ ) is found to have the least values of Young’s modulus, shear modulus and hardness. The band structure, density of states histograms and charge density plots are drawn and discussed. Computed Debye temperature ( $$\theta _{\mathrm{D}}$$ ), Gruneisen parameter ( $$\zeta $$ ) and melting temperature ( $$T_{\mathrm{m}})$$ of the parent binary compound $$\hbox {Rh}₃\hbox {V}$$ , the more brittle $$\hbox {Rh}₃\hbox {Hf}_0.75\hbox {V}_0.25$$ combination and the more ductile $$\hbox {Rh}₃\hbox {Zr}_0.25\hbox {V}_0.75$$ combination are given by (895 K, 1.3491, 2788 K), (790 K, 1.2701, 2736 K) and (698 K, 1.7972, 2529 K), respectively.