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

Abstract The phonon spectra, phonon optical activities, thermal expansion and thermodynamic properties of ordered quaternary carbides M 2 TiAlC 2 (M = Cr, Mo, W) and their ternary counterparts Ti 3 AlC 2 and Cr 3 AlC 2 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) C or metallic M (4f) Al bond in all studied structures. Phonon mode-Gruneisen parameter and macroscopic Gruneisen 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 Cr 2 TiAlC 2 , Mo 2 TiAlC 2 , W 2 Ti 2 AlC 2 , Ti 3 AlC 2 and Cr 3 AlC 2 in a range from 300 K to 1400 K, respectively. The hypothetical Cr 3 AlC 2 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 Cr 2 TiAlC 2 (Mo 2 TiAlC 2 , W 2 Ti 2 AlC 2 ) at room temperature.