2. Computational methods and details
In this work, we set up the theoretical models of chemically ordered MAX
phase compositions Ti3AlB2 and two
Ti2ZrAlB2 structures based on the
structure of Ti3AlC2 reported by Pietzkaet al [27]. The predicted structural parameters of these
three new compounds are presented in the Supplement Material. Then
first-principles calculations were carried out by VASP software to study
the structural stability, electronic, elastic and thermophysical
properties of the ternary ceramic
Ti3AlB2 and two quaternary ceramic
Ti2ZrAlB2. The crystal structures of
these ceramic compounds were optimized by the conjugate gradient (CG)
algorithm. The plane-wave pseudopotential method within the PBE-GGA
designed by Perdew, Burke, and Ernzerhof [28-29] is employed in the
calculations. The cut-off energy for the plane wave basis set was
configured as 520 eV. A 12×12×2 Monkhorst-pack grid [30] of k-point
sampling was set for the first electronic Brillouin zone (BZ). In the
structural optimizations, the calculated systems are relaxed until the
total energy change and the band structure energy change between two
steps are both smaller than 1×10−6 eV in the
relaxation of the electronic degrees of freedom, and the forces of all
atoms are smaller than 0.02 eV/Å in the ionic relaxation.
Phonon dispersions were calculated in the Phonopy software based on the
density functional linear-response method [31].