Computation ab initio of enthalpies of formation of the composes ZrAl3 and HfAl3

The relative stabilities of L1(2), D0(22), and D0(23) structures in ZrAl3 and HfAl3 compounds are investigated employing the Vienna ab initio simulation package (VASP). In ZrAl3 and HfAl3 compounds, the energetic effects related to the tetragonal distortion are important and lead to the stabilization of the D0(22) and D0(23) structures with respect to the L1(2) structure. The effect of the cell internal displacements of the atoms in the D0(23) structure is studied. In the case of the HfAl3 compound, the D0(23) structure appears as the most stable structure after this last stage of relaxations. In the case of ZrAl3 compound, the D0(23) structure is the most stable structure in both distorted and fully relaxed stages of the relaxation. The results are discussed in the framework of an antiphase boundary model.