Phonon spectrum, IR and Raman modes, thermal expansion tensor and thermal physical properties of M₂TiAlC₂ (M = Cr, Mo, W)

The phonon spectra, phonon optical activities, thermal expansion and thermodynamic properties of ordered quaternary carbides M₂TiAlC₂ (M = Cr, Mo, W) and their ternary counterparts Ti₃AlC₂ and Cr₃AlC₂ are studied by first-principles phonon calculations. Phonon eigenvectors of all Raman and infrared modes are analyzed. We find that vibrational frequencies of some Raman active modes (A_1g and E_2g) can be correlated to the strength and reduced mass of covalent M (4f)[sbnd]C or metallic M (4f)[sbnd]Al bond in all studied structures. Phonon mode-Grüneisen parameter and macroscopic Grüneisen constants are evaluated from phonon spectra. The thermal expansion coefficients, specific heats and isothermal bulk moduli at finite temperatures are obtained under the quasiharmonic approximation (QHA). The average linear thermal expansion coefficient (LTEC) values are found to be α_L = 11.30 × 10⁻⁶ K⁻¹, 7.15 × 10⁻⁶ K⁻¹, 8.67 × 10⁻⁶ K⁻¹, 10.29 × 10⁻⁶ K⁻¹ and 15.70 × 10⁻⁶ K⁻¹ for Cr₂TiAlC₂, Mo₂TiAlC₂, W₂Ti₂AlC₂, Ti₃AlC₂ and Cr₃AlC₂ in a range from 300 K to 1400 K, respectively. The hypothetical Cr₃AlC₂ phase shows strong anharmonic effects in the calculated thermal expansion profile above 600 K. Using Slack-model, the thermal conductivities are also evaluated, and the values are κ = 36.1 W/m K (34.4 W/m K, 27.2 W/m K) for Cr₂TiAlC₂ (Mo₂TiAlC₂, W₂Ti₂AlC₂) at room temperature.