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 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 (A1g and E2g) 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-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 αL=11.30×10−6K−1, 7.15×10−6K−1, 8.67×10−6K−1, 10.29×10−6K−1 and 15.70×10−6K−1 for Cr2TiAlC2, Mo2TiAlC2, W2Ti2AlC2, Ti3AlC2 and Cr3AlC2 in a range from 300K to 1400K, respectively. The hypothetical Cr3AlC2 phase shows strong anharmonic effects in the calculated thermal expansion profile above 600K. Using Slack-model, the thermal conductivities are also evaluated, and the values are κ=36.1W/mK (34.4W/mK, 27.2W/mK) for Cr2TiAlC2 (Mo2TiAlC2, W2Ti2AlC2) at room temperature.