3.4 Thermal properties
High melting point is an advantage of ceramic materials. Debye
temperature is an important parameter to evaluate this thermal property
and it can be calculated by the Debye model which have been stated in
detail in Ref[42].
Based on this theoretical model, the Debye temperatures
ΘD of Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 are calculated and listed in
following Table 4. Compared with transition metal carbides MAX-phase,
the Debye temperatures ΘD of
Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 are not high, which means
the high temperature resistance of them are not as good as these
carbides. It is mainly caused by their low shear modulus. As shown in
Table 1, the distance between Al and Ti or Zr atoms in
Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2 are larger than the Ti-C
lengths in Ti3AlC2. It indicates
relatively weak bonding between Al and the M(2)-B-M(1)-C-M(2) (M=Ti or
Zr), so it is easier slip between two layers and lead to their low shear
modulus.
But compared with ordinary materials, these Debye temperatures are still
very high, it indicates that their high temperature resistance is also
good. Compared with Ti3AlB2 and
Ti2ZrAlB2-2, the Debye temperatures
ΘD of Ti2ZrAlB2-1 is
lower. According to the Debye model, it is due to the lower bulk modulus
and shear modulus of Ti2ZrAlB2-1 than
other two compounds. Combined the discussion in Section 3.3, this is
ultimately due to the strength and mode of chemical bond bonding in the
structure.
Table 4. Our calculated density; longitudinal, transverse sound, mean
sound velocities, and the Debye temperatures obtained from the mean
sound velocities of Ti3AlB2,
Ti2ZrAlB2-1 and
Ti2ZrAlB2-2; and corresponding data
for
Zr2Al3C4 and
Zr3Al3C5 obtained from
previous studies.