Thermoelastic Properties Of The Ti2AlC MAX Phase: An Ab Initio Study

Abstract

MAX phases are used on an industrial scale in the transportation, armour, and furnace development sectors, among others. However, data on the dynamical properties of these materials under varying temperature and pressure conditions are rare or unavailable. This study reports on the dynamical properties of the elastic constants of Ti2AlC, under these conditions, obtained from first-principles calculations. Both static and dynamical results are presented and discussed. The dynamical results show that the elastic moduli are degraded; specifically, the bulk and shear moduli show a reduction ranging from 15 to 29% and 13 to 31%, respectively, between pressures of 10 - 30 GPa and in the temperature range of 300 - 1200 K. The reduction in these moduli is likely caused by anharmonic lattice effects that lead to thermal-induced softening, particularly in the high-pressure and temperature range. The lattice parameters of this material under the conditions of study did not vary significantly. Such data is useful as part of decision support that can inform applications as well as the limitations of use.

Figures (6)

• Figure 1: The crystal structure of Ti$_2$AlC; (a) Optimized unit cell and (b) Basal plane showing the top view of the unit cell. The blue, grey, and brown balls represent Al, Ti, and C atoms, respectively.
• Figure 2: The $C_{ij}$'s of Ti$_2$AlC versus pressure under static calculations (LHS panel) and from thermoelastic considerations (RHS panel), at 0 K.
• Figure 3: The dynamical elastic constants, $C_{ij}$'s, of Ti$_2$AlC versus pressure at various temperatures for (a) $C_{11}$, (b) $C_{12}$, (c) $C_{13}$, (d) $C_{33}$ and (e) $C_{44}$.
• Figure 4: The dynamical elastic moduli of Ti$_2$AlC at various pressures and temperatures: (a) Bulk modulus and (b) Shear modulus
• Figure 5: Temperature dependence of the elastic moduli of Ti$_2$AlC at various pressures: (a) Bulk modulus and (b) Shear modulus.