DFT study of the phase equilibria in a titanium-carbon system under high-pressures

The thermodynamic stability of titanium carbide and the solid solution of carbon in titanium under extreme high-pressure conditions was investigated using density functional theory (DFT). The calculations indicate that in the range of 0 – 20 GPa, the TiC phase exhibits a lower formation energy than the carbon solid solution in titanium, which leads to its thermodynamic dominance. At pressures exceeding 20 GPa, the thermodynamic stability shifts in favor of the solid solution phase, thereby driving the dissolution of metastable nanoscale TiC inclusions. The released carbon diffuses towards lattice defects, such as dislocations and grain boundaries, where the locally high concentration promotes the growth of larger and more stable TiC particles. With a subsequent decrease in pressure, as well as with a further pressure increase to 130 GPa and above, the formation energy of TiC once again becomes significantly lower than the dissolution energy. This makes the carbide phase thermodynamically stable and promotes the transition of carbon-enriched regions into the TiC phase. Based on the analysis of the formation energies, it is concluded that carbon is redistributed in the Ti-C system under pressure, including the decomposition and reformation of carbide phases. The data obtained explain the possible mechanisms of microstructure reconfiguration associated with carbon migration to crystal lattice defects.

1. Ministry of Education and Science of the Russian Federation - This  work  was  performed  in  accordance  with  the state task FFSG-2024-0018, state registration No. 124020700089-3