Crystallite size-dependent metastable phase formation of TiAlN coatings

It is well known that surface energy differences thermodynamically stabilize nanocrystalline γ-Al₂O₃ over α-Al₂O₃. Here, through correlative ab initio calculations and advanced material characterization at the nanometer scale, we demonstrate that the metastable phase formation of nanocrystalline TiAlN, an industrial benchmark coating material, is crystallite size-dependent. By relating calculated surface and volume energy contributions to the total energy, we predict the chemical composition-dependent phase boundary between the two metastable solid solution phases of cubic and wurzite Ti_1-xAl_xN. This phase boundary is characterized by the critical crystallite size d _critical . Crystallite size-dependent phase stability predictions are in very good agreement with experimental phase formation data where x was varied by utilizing combinatorial vapor phase condensation. The wide range of critical Al solubilities for metastable cubic Ti_1-xAl_xN from x _max = 0.4 to 0.9 reported in literature and the sobering disagreement thereof with DFT predictions can at least in part be rationalized based on the here identified crystallite size-dependent metastable phase formation. Furthermore, it is evident that predictions of critical Al solubilities in metastable cubic TiAlN are flawed, if the previously overlooked surface energy contribution to the total energy is not considered.