Abstract
The surface energies of the {100} and {111} surfaces of TiCx and TiNx 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 TiCx and TiNx stoichiometry on their growth shapes and why TiCx and TiNx 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 TiCx and TiNx particles with different shapes can be obtained.