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