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.