Off-stoichiometry and molybdenum substitution effects on elastic moduli of B1-type titanium carbide

B1-type MX ceramics are composed of transition metals (M) and C, N, and/or O (X) occupying the M and X sites, respectively, and having M – X nearest neighbor (NN) bonds and M – M and X – X next nearest neighbor (NNN) bonds. Substitution of the elements and the formation of structural vacancies in B1-type ceramics change the numbers and strengths of the bonds, leading to novel properties. The change in elastic modulus of off-stoichiometric TiC in equilibrium with a Ti – Mo solid solution phase was experimentally investigated based on the rule of mixtures from the Voigt model. The experimentally obtained values agreed well with the results of density functional theory calculations. The bulk modulus ( K ) of TiC increased from 205.6 to 239.2 GPa as the fraction of Ti sites occupied by Mo increased from 0.11 to 0.33, whereas the Young’s modulus ( E ) and the shear modulus ( G ) remained nearly constant. On the other hand, all three elastic moduli decreased with increasing vacancy fraction at the C sites. These results suggest that the M–X bond strength should be the dominant factor in these moduli and the effect of M–M bond on K is greater than that of G and E .