Phase stability, elastic and electronic properties of Hf–Rh intermetallic compounds from first-principles calculations

Abstract

The phase stability, elastic and electronic properties of binary Hf–Rh compounds have been studied using first-principles calculations based on density functional theory. The equilibrium lattice constants, formation enthalpies, elastic constants, and elastic moduli are presented. Among the binary Hf–Rh compounds, Hf₃Rh₅ is the most stable with the lowest formation enthalpy. For the equiatomic HfRh phase, it tends to crystallize in the ZrIr-type structure, followed by L1₀, and then B2 at the ground state based on the analysis of formation enthalpies. Therefore, the crystal structure of the lower temperature HfRh phase is suggested to be the ZrIr-type. This conclusion is in agreement with the experimental reports in the literature. Besides, Hf₃Rh₄ are proposed to be the Pu₃Pd₄-type for the first time. Furthermore, our calculated elastic constants for Hf₂Rh, ZrIr-HfRh, L1₀-HfRh, B2-HfRh, Hf₃Rh₄, Hf₃Rh₅ and HfRh₃ can all satisfy the Born criteria, indicating their mechanical stabilities. When ZrIr-HfRh is adopted, the bulk modulus (B) increases linearly with the growing Rh atomic concentration. Meanwhile, Young's modulus linearly increases with growing shear modulus, and the compound with a higher Poisson's ratio owns a higher B/G ratio simultaneously. Overall, the results also indicate that all the considered Hf–Rh compounds should be ductile. Finally, the electronic structure is analyzed to understand the essence of structural stability of the binary compound.