Anisotropic surface stability of TiB₂: A theoretical explanation for the easy grain coarsening

The exaggerated grain growth, anisotropic crystallite morphology, and thermal expansion are the main reasons for the microcracking of sintered TiB2, wherein grain coarsening and anisotropic crystallite morphology are believed to be controlled by the surface stabilities of TiB2. To deeply understand the grain growth mechanism, the anisotropic stability and bonding features of TiB2surfaces, including(left({11ar 20} ight)), two types of (0001), and three types of(left({10ar 10} ight)), are investigated by first-principles calculations. By employing the two-region modeling method, surface energies are calculated and the(left({11ar 20} ight))surface is found to be more stable than (0001) and(left({10ar 10} ight))surfaces. Hexagonal plate-like grain morphology is predicted. The different bonding conditions of surface Ti and B atoms contribute to the difference of surface structure relaxation between surfaces with Ti- and B-termination, which lead the B-terminated ones to be more stable. It is also found that the surface energies of TiB2are much higher than those of ZrB2with a similar structure, which may be responsible for the easy coarsening of TiB2.