Abstract
To date, the mechanism of Ti atom self-diffusion is unproven. Prior theoretical work mostly focused on Ti vacancy based mediators, but these do not reproduce the experimental activation energy or entropy. In this work, in density functional theory calculations, Ti interstitials and related defect complexes are systematically considered as possible mediators of Ti self-diffusion. Among these defects, the defect complex of two C vacancies tightly bound to a Ti dumbbell is found to have the lowest formation energy. A sustainable migration of the complex, in a translational or rotational fashion, is enabled in the presence of another (free) carbon vacancy nearby the complex, and thus the rate of Ti self-diffusion by this mechanism is dependent on the concentration of carbon vacancies. The calculated activation energy of the complex agrees well with the experimental value in TiC0.97. Similar analyses of the Ti self-diffusion mechanisms mediated by Ti interstitials or dumbbells yield much higher activation energies, but the corresponding migration energies are evaluated to be less than 1 eV, which suggests they can be possible mediators of the radiation-enhanced Ti self-diffusion in TiC. To fully enable the comparison with experiments that are typically conducted at temperatures as high as 2500 K, we also consider the temperature dependent vibrational contribution to the activation energy of the defect complex. The vibrational contribution imposes an additive effect on the defect formation energy, while the migration energies are lowered due to the thermal expansion of the lattice. When combined, these factors give an excellent agreement with the experiments. This work gives strong support to the concept that Ti interstitial based defect complexes are likely diffusion mediators for Ti atom self-diffusion in TiC, further establishes a solid basis for large-scale modeling, and may eventually pave the way to accurately predicting defect-controlled diffusional processes.
| Original language | English |
|---|---|
| Pages (from-to) | 381-387 |
| Number of pages | 7 |
| Journal | Acta Materialia |
| Volume | 165 |
| DOIs | |
| State | Published - Feb 15 2019 |
Funding
This work was financed by the Swedish Governmental Agency for Innovation Systems (VINNOVA) , Swedish industry and KTH-Royal Institute of Technology . The computing resources by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Center (NSC) in Linköping is acknowledged. P. R. C. K. was supported by the Fluid Interface Reactions, Structures, and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy , Office of Science, Office of Basic Energy Sciences. P. A. K. gratefully acknowledges the financial support of the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST “MISiS” (No. K3-2017-034 ). This work was financed by the Swedish Governmental Agency for Innovation Systems (VINNOVA), Swedish industry and KTH-Royal Institute of Technology. The computing resources by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Center (NSC) in Linköping is acknowledged. P. R. C. K. was supported by the Fluid Interface Reactions, Structures, and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. P. A. K. gratefully acknowledges the financial support of the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST “MISiS” (No. K3-2017-034).
Keywords
- Ab initio study
- Activation energy
- Defect complex
- Diffusion mechanisms
- Thermal effects
- Titanium carbide (TiC)