The elastic properties and lattice dynamics for selected 211 MAX phases: A DFT study

TL;DR

This study uses density functional theory to analyze the elastic properties, lattice dynamics, and thermal conductivity of selected MAX phases, confirming their stability and potential industrial applications.

Contribution

It provides a comprehensive DFT-based analysis of elastic and lattice dynamic properties of seven MAX phases, including thermal conductivity estimates, with validation against experimental data.

Findings

All studied MAX phases are dynamically stable.

Ti2PbC and Ti2CdC are more stable and ductile.

Ti2PbC has the lowest thermal conductivity.

Abstract

The elastic properties and lattice dynamics of Ti$_2$AlC, Ti$_2$AlN, Ti$_2$GaC, Ti$_2$GaN, Ti$_2$PbC, Ti$_2$CdC and Ti$_2$SnC have been investigated using the density functional theory within the generalized gradient approximations as expressed in Quantum Espresso and VASP codes. The obtained lattice parameters are in agreement with the previous theoretical research and available experimental data. The elastic properties of the MAX phases under study have been calculated. The values of elastic anisotropy, Young's modulus, Poisson ratio and shear modulus reveal that the compounds are stable and ductile and that Ti$_2$PbC and Ti$_2$CdC are more stable than the other considered compounds. Thus, the seven compounds may be useful for industrial applications. The calculated phonon spectra confirm that the studied MAX phases are dynamically stable because of the absence of imaginary phonon modes. The temperature dependent lattice thermal conductivity of MAX phases have been determined using the Debye theory as outlined by Slack. The obtained $\kappa_{ph}$ for Ti$_2$AlC at 1300 K agree with experimental findings within 9$\%$. The estimated minimum thermal conductivities ($\kappa_{min}$) of the MAX phases obtained by using empirical formula suggested by Clarke show that Ti$_2$PbC possesses the lowest minimum thermal conductivity.