3.1. Determination of Crystal Structure
In present study, based on the structure of
Ti3AlC2, we set up the structure of
Ti3AlB2 and tried to design layered
ordered double-transition metals MAX compound for
Ti2ZrAlB2. Two stable phases were
determined via calculations of formation enthalpy, elastic constants and
phonon dispersion curves (This would be discussed later). Here we
recorded them as Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 respectively, and their
structures were shown in Figure 1. Lattice constants and atomic
coordinates for new predicted Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 are presented in
Supplemental Material Table S1. The formation enthalpies are defined by
△E = E(Ti3AlB2)-3E(Ti)-E(Al)-2E(B) and
△E = E(Ti2ZrAlB2)-2E(Ti)-
E(Zr)-E(Al)-2E(B) for Ti3AlB2 and
Ti2ZrAlB2, respectively; in which
E(Ti3AlB2) and
E(Ti2ZrAlB2) are the energy of
Ti3AlB2 and
Ti2ZrAlB2 crystal, respectively; and
E(Ti), E(Zr), E(Al) and E(B) are the respective total energies of pure
Ti (space group: P6/mmm), Zr(space group: P63/mmc),
Al(space group: Fm-3m) and α-B (space group: R-3m). The formation
enthalpies of them were calculated and listed in Table 1. It can be seen
that the formation enthalpy of Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 are negative, so these
phases can be considered as stable ones in energy, and are thereby
expected to be synthesizable in the laboratory.
Table 1. Calculated equilibrium structural data, bond lengths
and formation enthalpy △E for Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2