Effect of stoichiometry on the surface energies of {100} and {111} and the crystal shape of TiCx and TiNx

Abstract

The surface energies of the {100} and {111} surfaces of TiC_x and TiN_x with different stoichiometries (x ≤ 1.0) were investigated using the density-functional theory, employing Perdew Wang 91 (PW91) under the generalized gradient approximation (GGA) method. The result explains the dominating effect of the TiC_x and TiN_x stoichiometry on their growth shapes and why TiC_x and TiN_x evolve from octahedron to truncated-octahedron and finally to sphere during the self-propagating high-temperature synthesis (SHS). With the increases in stoichiometry, both the {100} and {111} surface energy values decrease. However, the surface energy of the {100} surfaces decrease more quickly than that of the {111} surfaces, which means that the {100} surfaces tend to be more stable at quite high stoichiometries. In this case, the {100} surfaces gradually expose on the crystal growth shape, while the {111} surfaces gradually shrink. According to this result, through controlling the stoichiometry during the SHS, the TiC_x and TiN_x particles with different shapes can be obtained.