Electronic structures and thermodynamic properties of HfAl3 in L12, D022 and D023 structures

To better understand the relative stability and bonding characteristics of the L12, D022 and D023 structures for HfAl3, the formation enthalpies, electronic structures and thermodynamics properties were investigated by first-principles calculations. The agreement of calculated equilibrium lattice parameters and formation enthalpies with experimental results indicates the reliability of this work. The order of structural stability is D023>D022>L12. The results of densities of states, atomic Mulliken charge and bond population support the best structural stability for D023 structure. Variations of thermodynamic properties with temperature were predicted via phonon frequencies calculation. The enthalpy, entropy, free energy of D023 structure change more quickly than those of the other two structures. The Debye temperatures of L12, D022 and D023 structures are 399, 407 and 416 K, respectively. The volume thermal expansions for HfAl3 increase exponentially at the low temperature, whereas the thermal expansion coefficients increase linearly at the high temperature.