Theoretical screening, intrinsic brittleness and thermal properties of the S-containing MAX carbides and borides

To respond the recent experimental advances, the phase stability, mechanical properties, phonon as well as infrared- and Raman-active modes, thermal expansion and heat capacity were investigated by density functional theory for the S-containing MAX carbides and borides (M from III B to VIII B), of importance, well consistent with the available experimental results. After examining the thermodynamic competition with all the competing phases and intrinsic stability by their lattice dynamics, 18 MAX phases were screened out from 138 ones. Using the “bond stiffness” model as well as the associated criterion for damage tolerance and fracture toughness, the ratio of bond stiffness of weakest M−S to the strongest M-X bonds (kmin/kmax) over 1/2 indicates their intrinsic brittleness of all S-containing MAX phases except Nb4SC3. Including the contributions from phonon and electrons, their linear thermal expansion coefficients [(8.1–13.6)×10−6 K−1, 300–1 300 K] and heat capacities (Cp) as a function of temperature are predicted. Of much interest, a well-established relationship between molar Cp of the MAX and MX phases is theoretically deduced in the present work.