- Letter
- Open Access
Internal structure of metal vacancies in cubic carbides
Phys. Rev. B 109, L060103 – Published 9 February, 2024
DOI: https://doi.org/10.1103/PhysRevB.109.L060103
Abstract
A combinatorial approach is employed to investigate the atomic and electronic structures of a metal vacancy in titanium carbide. It turns out that the usual relaxed geometry of the vacancy is just a metastable state representing a local energy minimum. Using ab initio calculations and by systematically searching through the configurational space of a Ti monovacancy, we identify a multitude of local minima with reconstructed geometry that are lower in energy. Among them, there is a planar configuration with two displaced carbons forming a dimer inside the vacancy. This structure has the optimal number and order of C–C bonds making it the global minimum. Further calculations show that this reconstructed geometry is also the ground state of metal vacancies in other carbides such as ZrC, HfC, and VC. The reconstructed metal vacancies are characterized by localized electron states due to the relatively short C–C bonds. The defect states lie just below the upper and lower valence bands. The existence of reconstructed vacancy configurations is essential for understanding the mechanism of metal self-diffusion in transition-metal carbides.
Physics Subject Headings (PhySH)
Article Text
References (53)
- L. E. Toth, Transition Metal Carbides and Nitrides (Academic Press, New York, 1971).
- I. L. Shabalin, Ultra-High Temperature Materials II: Refractory Carbides I (Ta, Hf, Nb and Zr Carbides) (Springer Nature, Singapore, 2019).
- I. L. Shabalin, Ultra-High Temperature Materials III: Refractory Carbides II (Ti and V Carbides) (Springer Nature, Dordrecht, 2020).
- H. Holleck, Material selection for hard coatings, J. Vac. Sci. Technol. A 4, 2661 (1986).
- W. S. Williams, Transition metal carbides, nitrides, and borides for electronic applications, JOM 49, 38 (1997).
- Ultra-High Temperature Ceramics: Materials for Extreme Environment Applications, edited by W. G. Fahrenholtz, E. J. Wuchina, W. E. Lee, and Y. Zhou (Wiley, New Jersey, 2014).
- F. Keihn and R. Kebler, High-temperature ductility of large-grained TiC, J. Less-Common Met. 6, 484 (1964).
- I. Spivak, R. Andrievskii, V. Rystsov, and V. Klimenko, Creep of titanium monocarbide in its homogeneity range, Powder Metall. Met. Ceram. 13, 574 (1974).
- J.-L. Chermant, G. Leclerc, and B. L. Mordike, Deformation of titanium carbide at high temperatures, Int. J. Mater. Res. 71, 465 (1980).
- C. J. Smith, M. A. Ross, N. D. Leon, C. R. Weinberger, and G. B. Thompson, Ultra-high temperature deformation in TaC and HfC, J. Eur. Ceram. Soc. 38, 5319 (2018).
- O. Knotek and A. Barimani, On spinodal decompositiom in magnetron-sputtered (Ti,Zr) nitride and carbide films, Thin Solid Films 174, 51 (1989).
- T. Ma, R. Borrajo-Pelaez, P. Hedström, I. Borgh, A. Blomqvist, S. Norgren, and J. Odqvist, Microstructure evolution during phase separation in Ti-Zr-C, Int. J. Refract. Hard Met. 61, 238 (2016).
- A. B. Yildiz, H. Yixuan, P. Babu, T. C. Hansen, M. Eriksson, K. M. Reddy, and P. Hedström, Design, synthesis, structure, and stability of novel multi-principal element (Ti,Zr,Hf,W)C ceramic with a miscibility gap, J. Eur. Ceram. Soc. 42, 4429 (2022).
- S. Sarian, Diffusion of carbon in TiC, J. Appl. Phys. 39, 3305 (1968).
- S. Sarian, Diffusion of in , J. Appl. Phys. 40, 3515 (1969).
- V. N. Zagryazkin, On mechanism of diffusion in monocarbides of transition metals, Fiz. Met. Metalloved. 28, 292 (1969).
- D. Kohlstedt, W. S. Williams, and J. B. Woodhouse, Chemical diffusion in titanium carbide crystals, J. Appl. Phys. 41, 4476 (1970).
- R. A. Andrievskii, Y. F. Khormov, and I. S. Alekseeva, Self-diffusion of carbon and metal atoms in zirconium and niobium carbides, Fiz. Met. Metalloved. 32, 664 (1971).
- F. J. J. Van Loo, W. Wakelkamp, G. F. Bastin, and R. Metselaar, Diffusion of carbon in and , Solid State Ion. 32-33, 824 (1989).
- R. A. Andrievskii, Research into sintering and related phenomena: Personal experience, Powder Metall Met. Ceram 50, 2 (2011).
- L. Hultman, Thermal stability of nitride thin films, Vacuum 57, 1 (2000).
- A. I. Gusev, A. A. Rempel, and A. A. Magerl, Disorder and Order in Strongly Nonstoichiometric Compounds: Transition Metal Carbides, Nitrides and Oxides (Springer, Berlin, 2001).
- D. A. Andersson, P. A. Korzhavyi, and B. Johansson, First-principles based calculation of binary and multicomponent phase diagrams for titanium carbonitride, Calphad 32, 543 (2008).
- D. Watanabe, J. Castles, A. Jostsons, and A. Malin, The ordered structure of TiO, Acta Crystallogr. 23, 307 (1967).
- A. A. Valeeva, A. A. Rempel', and A. I. Gusev, Two-sublattice ordering in titanium monoxide, Jetp Lett. 71, 460 (2000).
- A. A. Valeeva, A. A. Rempel', and A. I. Gusev, Ordering of cubic titanium monoxide into monoclinic , Inorg. Mater. 37, 603 (2001).
- D. A. Andersson, P. A. Korzhavyi, and B. Johansson, Thermodynamics of structural vacancies in titanium monoxide from first-principles calculations, Phys. Rev. B 71, 144101 (2005).
- L. Tsetseris, S. Logothetidis, and S. T. Pantelides, Atomic-scale mechanisms for diffusion of impurities in transition-metal nitrides, Surf. Coat. Technol. 204, 2089 (2010).
- V. I. Razumovskiy, M. N. Popov, H. Ding, and J. Odqvist, Formation and interaction of point defects in group IVb transition metal carbides and nitrides, Comput. Mater. Sci. 104, 147 (2015).
- D. G. Sangiovanni, B. Alling, P. Steneteg, L. Hultman, and I. A. Abrikosov, Nitrogen vacancy, self-interstitial diffusion, and Frenkel-pair formation/dissociation in B1 TiN studied by ab initio and classical molecular dynamics with optimized potentials, Phys. Rev. B 91, 054301 (2015).
- D. Gambino, D. G. Sangiovanni, B. Alling, and I. A. Abrikosov, Nonequilibrium ab initio molecular dynamics determination of Ti monovacancy migration rates in TiN, Phys. Rev. B 96, 104306 (2017).
- L. Tsetseris, S. Logothetidis, and S. T. Pantelides, Vacancies, interstitials and their complexes in titanium carbide, Acta Mater. 56, 2864 (2008).
- H. M. Pinto, J. Coutinho, M. M. D. Ramos, F. Vaz, and L. Marques, First principles study of point defects in titanium oxycarbide, Mat. Sci. Eng. B 165, 194 (2009).
- V. I. Razumovskiy, P. A. Korzhavyi, and A. V. Ruban, Ab initio calculations of kinetic properties in ZrC and TiC carbides, Solid State Phenom. 172-174, 990 (2011).
- X. Tang, R. Salehin, G. B. Thompson, and C. R. Weinberger, Statistical study of vacancy diffusion in TiC and TaC, Phys. Rev. Mater. 4, 093602 (2020).
- R. Salehin, X. Tang, G. B. Thompson, and C. R. Weinberger, Vacancy-cluster and off-lattice metal-atom diffusion mechanisms in transition metal carbides, Comput. Mater. Sci. 199, 110713 (2021).
- V. I. Razumovskiy, A. V. Ruban, J. Odqvist, and P. A. Korzhavyi, Vacancy-cluster mechanism of metal-atom diffusion in substoichiometric carbides, Phys. Rev. B 87, 054203 (2013).
- M. Råsander, H. W. Hugosson, and A. Delin, Density functional study of carbon vacancies in titanium carbide, J. Phys.: Condens. Matter 30, 015702 (2018).
- K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
- W. Sun, H. Ehteshami, and P. A. Korzhavyi, Structure and energy of point defects in TiC: An ab initio study, Phys. Rev. B 91, 134111 (2015).
- W. Sun, H. Ehteshami, P. R. C. Kent, and P. Korzhavyi, Self-diffusion of Ti interstitial based point defects and complexes in TiC, Acta Mater. 165, 381 (2019).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- A. A. Rempel, L. V. Zueva, V. N. Lipatnikov, and H.-E. Schaefer, Positron lifetime in the atomic vacancies of nonstoichiometric titanium and vanadium carbides, Phys. Stat. Solidi A 169, R9 (1998).
- A. A. Valeeva, A. A. Rempel, W. Sprengel, and H.-E. Schaefer, Vacancies on the Ti sublattice in titanium monoxide studied using positron annihilation techniques, Phys. Rev. B 75, 094107 (2007).
- P. A. Korzhavyi, L. V. Pourovskii, H. W. Hugosson, A. V. Ruban, and B. Johansson, Ab Initio study of phase equilibria in , Phys. Rev. Lett. 88, 015505 (2001).
- G. Henkelman, B. P. Uberuaga, and H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys. 113, 9901 (2000).
- C. J. Först, J. Slycke, K. J. Van Vliet, and S. Yip, Point defect concentrations in metastable Fe-C alloys, Phys. Rev. Lett. 96, 175501 (2006).
- A. T. Paxton and C. Elsässer, Analysis of a carbon dimer bound to a vacancy in iron using density functional theory and a tight binding model, Phys. Rev. B 87, 224110 (2013).
- B. C. Guo, K. P. Kerns, and A. W. Castleman, Jr., -metallo-carbohedrenes: A new class of molecular clusters? Science 255, 1411 (1992).
- C. Berkdemir, A. W. Castleman, Jr., and J. O. Sofo, Metal-substituted metallocarbohedrynes: toward less reactive clusters as building blocks of cluster-assembled materials, Phys. Chem. Chem. Phys. 14, 9642 (2012).