Elastic and thermodynamic properties of new (Zr3−xTix)AlC2 MAX-phase solid solutions

•Mechanical behavior and thermodynamic properties of (Zr3−xTix)AlC2 MAX are calculated.•The increase of Ti content x, increases the stiffness of (Zr3−xTix)AlC2.•The solid solutions (Zr3-xTix)AlC2 should be brittle in nature.•Some physical properties of (Zr3−xTix)AlC2 changes with a different trend for x = 2.0.

The elastic behavior and thermodynamic properties of recently synthesized (Zr3−xTix)AlC2 MAX phases are investigated for the first time using density functional theory and the quasi-harmonic model. The unit cell properties and elastic tensors are evaluated and the total energy is utilized to calculate the equation of state along with free energy in the scheme of the phonon-based quasi-harmonic model. The consistency between the theoretical and experimental lattice parameters is very good, with the lattice constants a and c decreasing significantly with the increase of Ti content x in (Zr3−xTix)AlC2. The mechanical stability of the (Zr3−xTix)AlC2 MAX phase solid solutions is verified. The increase of Ti content x, increases the stiffness of (Zr3−xTix)AlC2. The solid solutions (Zr3−xTix)AlC2 should be brittle in nature. The thermodynamic properties such as the thermal expansion coefficient α, Debye temperature θD, bulk modulus B, heat capacities Cp and Cv, entropy S, Grüneisen parameter γ, and normalized volume V/V0 are calculated at temperatures from 0 to 1000 K and pressures from 0 to 50 GPa, respectively. We expect that the calculated elastic and thermodynamic data can provide an essential reference as some of the physical properties can be difficult to be experimentally determined for a wide composition range.

Graphical abstractThermal expansion coefficient of (Zr3−xTix)AlC2 as a function of temperature (a) and pressure (b). Debye temperature of (Zr3−xTix)AlC2 as a function of temperature (a) and pressure (b).Download high-res image (203KB)Download full-size image