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.