Figure 1. Structural model of (a) Ti3AlB2 and two new layered ordered double-transition metals MAX compound (b) Ti2ZrAlB2-1 and (c) Ti2ZrAlB2-2, where the Ti atoms are in gray, Zr atoms are in blue, Al atoms are in pink and B atoms are in orange.
Phonon dispersion curve is an important criterion to measure the stability of a crystal structure in lattice dynamics. So we calculated the phonon spectrum of Ti3AlB2 and two designed Ti2ZrAlB2, and results were shown in following Figure 2. It can be seen that the phonon frequencies are positive for all the considered structures. There is no imaginary frequency in the phonon dispersion curves, which means that Ti3AlB2 and the designed Ti2ZrAlB2 structures are stable in lattice dynamics. In addition, formation enthalpy of the ground state can be used to analyze the thermodynamic stability of crystals. The lower formation enthalpy is, the more thermodynamically stable the structure has. In Table 1, we listed the formation enthalpy of two designed Ti2ZrAlB2. Result indicates that the Ti2ZrAlB2-2 is more stable than Ti2ZrAlB2-1 at 0 GPa.