According to the mechanical stability criterion for hexagonal crystals
[35] and the calculated elastic constants of
Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 listed in Table 2, it can be
said that they are all stable in mechanics.
Based on the investigation of formation enthalpy, phonon dispersion
curve and elastic constants of Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2, it can be concluded that
these three compounds are stable at normal pressure. However, we still
know little about their performance, which needs further exploration.
Here, we first studied their bulk modulus B and shear modulus G
according to the Voigt-Reuss-Hill approximation [36-37] and listed
the results in Table 3.
The B/G ratio is a parameter to evaluate the brittleness of materials
proposed by Pugh [38-39]. In present work, the B/G ratio of
Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 are larger than 1.75, which
means they have good ductility. This is an obvious advantage that the
MAX materials studied previously does not have. This excellent
characteristic shows that the three layered ceramic materials have good
toughness and are not fragile. Fragile is the weakness of traditional
ceramic materials, none of the three materials in this study has this
disadvantage.
The
Poisson
ratio values, ν=(3B-2G)/2(3B+G), are calculated to evaluate the degree
of the covalent bonding [40]. For
Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2, their Poisson ratios are
larger than 0.25, which means ionic bonds dominate in these three
crystal materials. And the specific bonding characteristics will be
discussed in the following study of electronic properties.
Table 3. Calculated bulk Modulus B (GPa), Shear Modulus G (GPa), Young’s
Modulus E (GPa), Poisson’s Ratio ν, and B/G of
Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 at atmospheric pressure.