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How impurity atoms move through a crystal is a fundamental and renewed issue in condensed matter physics and materials science. Diffusion of oxygen (O) in titanium (Ti) affects the formation of titanium-oxides and the design of Tibased alloys. Moreover, the kinetics of initial growth of titania-nanotubes via anodization of a titanium metal substrate also involves the diffusion of oxygen. Therefore, the understanding of the migration mechanism of oxygen atoms in -Ti is extremely important for controlling oxygen diffusion in Ti alloys. In this work, we show how the diffusion coefficient can be predicted directly from first-principles studies without any empirical fitting parameters. By performing the first-principles calculations based on the density functional theory (DFT) through using the Vienna ab initio Simulation Package (VASP), we obtain three locally stable interstitial oxygen sites in the hexagonal closed-packed (hcp) lattice of titanium. These sites are octahedral center (OC) site, hexahedral center (HE) site, and TiTi bond center crowdion (CR) site with interstitial energies of -2.83, -1.61, and -1.48 eV, respectively. From the interstitial energies it follows that oxygen atom prefers to occupy the octahedral site. From electronic structure analysis, it is found that the TiO bonds possess some covalent characteristics and are strong and stable. Using the three stable O sites from our calculations, we propose seven migration pathways for oxygen diffusion in hcp Ti and quantitatively determine the transition state and diffusion barrier with the saddle point along the minimum energy diffusion path by the climbing image nudged elastic band (CI-NEB) method. The microscopic diffusion barriers (E) from the first-principles calculations are important for quantitatively describing the temperature dependent diffusion coefficients D from Arrhenius formula D = L2v* exp(-((E)/(kBT)), where v* is the jumping frequency and L is the atomic displacement of each jump. The jumping frequency v* is determined from where vi and vj are the vibration frequency of oxygen atom at the initial state and the transition state respectively. This analysis leads to the formula for calculating the temperature dependent diffusion coefficient by using the microscopic parameters (vi and E) from first-principles calculations without any fitting parameters. Using the above formula and the vibration frequencies and diffusion barriers from first-principles calculations, we calculate the diffusion coefficients among different interstitial sites. It is found that the diffusion coefficient from the octahedral center site to the available site nearby is in good agreement with the experimental result, i.e., the diffusion rate D is 1.046510-6 m2s-1 with E of 0.5310 eV. The jump from the crowdion site to the octahedral interstitial site prevails over all the other jumps, as a result of its low energy barrier and thus leading to markedly higher diffusivity values. The diffusion of oxygen atoms is mainly controlled by the jump occurring between OC and CR sites, resulting in high diffusion anisotropy. This finding of oxygen diffusion behavior in Ti provides a useful insight into the kinetics at initial stage of oxidation in Ti which is very relevant to many technological applications of Ti-based materials.
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Keywords:
- first-principles /
- titanium /
- diffusion
[1] Leea T C, Koshyb P, Abdullaha P H Z, Idrisa M I 2016 Surf. Coat. Technol. 301 20
[2] Chen S H, Ho S C, Chang C H, Chen C C 2016 Surf. Coat. Technol. 302 215
[3] Li N B, Xiao G Y, Liu B, Wang Z, Zhu R F 2016 Surf. Coat. Technol. 301 121
[4] Hung W C, Chang F M, Yang T S, Ou K L 2016 Mater. Sci. Eng. C 68 523
[5] Anioek K, Kupka M, Barylski A 2016 Wear 356-357 23
[6] Shokouhfar M, Allahkaram S R 2016 Surf. Coat. Technol. 291 396
[7] Li X, Chen T, Hu J, Li S J, Zou Q, Li Y F, Jiang N, Li H, Li J H 2016 Colloids Surf. B 144 265
[8] Zhou Y, Wen F, Song B, Zhou X, Teng Q, Wei Q S, Shi Y S 2016 Mater. Des. 89 1199
[9] Kang D S, Lee K J, Kwon E P, Tsuchiyama T 2015 Mater. Sci. Eng. A 623 120
[10] Hang W, Chen W Z, Sun J Y, Jiang Z Y 2013 Chin. Phys. B 22 016601
[11] Satko D P, Shaffer B J, Tiley S J, Semiatin S L 2016 Acta Mater. 107 377
[12] Oh J M, Lee B G, Cho S, Lee S W, Choi G, Lim J W 2011 Met. Mater. Int. 17 733
[13] Santhanam A T, Reedhill R E 1971 Metall. Trans. B 2 2619
[14] Shang S L, Zhou B C, Wang W Y, Ross A J, Liu X L, Hu Y J, Fang H Z, Wang Y, Liu Z K 2016 Acta Mater. 109 128
[15] Qu J, Blau P J, Howe J Y 2009 Scripta Mater. 60 10
[16] Bailey R, Sun Y 2015 Surf. Coat. Technol. 28 34
[17] Kresse G, Furthmueller J 1996 Phys. Rev. B Condens. Matter. 54 11169
[18] Joubert D P 1999 Phys. Rev. B Condens. Matter. 1758 1775
[19] Henkelman G, Jónsson H 2000 J. Chem. Phys. 113 9901
[20] Scotti L, Mottura A 2016 J. Chem. Phys. 144 084701
[21] Mantina M, Wang Y, Chen L Q 2009 Acta Mater. 57 4102
[22] Vineyard G H 1957 J. Phys. Chem. Solids 3 121
[23] Wu H H, Trinkle D R 2011 Phys. Rev. Lett. 107 4
[24] Scotti L, Mottura A 2016 J. Chem. Phys. 144 8
[25] Bregolin F L, Behar M, Dyment F 2007 Appl. Phys. A 83 37
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[1] Leea T C, Koshyb P, Abdullaha P H Z, Idrisa M I 2016 Surf. Coat. Technol. 301 20
[2] Chen S H, Ho S C, Chang C H, Chen C C 2016 Surf. Coat. Technol. 302 215
[3] Li N B, Xiao G Y, Liu B, Wang Z, Zhu R F 2016 Surf. Coat. Technol. 301 121
[4] Hung W C, Chang F M, Yang T S, Ou K L 2016 Mater. Sci. Eng. C 68 523
[5] Anioek K, Kupka M, Barylski A 2016 Wear 356-357 23
[6] Shokouhfar M, Allahkaram S R 2016 Surf. Coat. Technol. 291 396
[7] Li X, Chen T, Hu J, Li S J, Zou Q, Li Y F, Jiang N, Li H, Li J H 2016 Colloids Surf. B 144 265
[8] Zhou Y, Wen F, Song B, Zhou X, Teng Q, Wei Q S, Shi Y S 2016 Mater. Des. 89 1199
[9] Kang D S, Lee K J, Kwon E P, Tsuchiyama T 2015 Mater. Sci. Eng. A 623 120
[10] Hang W, Chen W Z, Sun J Y, Jiang Z Y 2013 Chin. Phys. B 22 016601
[11] Satko D P, Shaffer B J, Tiley S J, Semiatin S L 2016 Acta Mater. 107 377
[12] Oh J M, Lee B G, Cho S, Lee S W, Choi G, Lim J W 2011 Met. Mater. Int. 17 733
[13] Santhanam A T, Reedhill R E 1971 Metall. Trans. B 2 2619
[14] Shang S L, Zhou B C, Wang W Y, Ross A J, Liu X L, Hu Y J, Fang H Z, Wang Y, Liu Z K 2016 Acta Mater. 109 128
[15] Qu J, Blau P J, Howe J Y 2009 Scripta Mater. 60 10
[16] Bailey R, Sun Y 2015 Surf. Coat. Technol. 28 34
[17] Kresse G, Furthmueller J 1996 Phys. Rev. B Condens. Matter. 54 11169
[18] Joubert D P 1999 Phys. Rev. B Condens. Matter. 1758 1775
[19] Henkelman G, Jónsson H 2000 J. Chem. Phys. 113 9901
[20] Scotti L, Mottura A 2016 J. Chem. Phys. 144 084701
[21] Mantina M, Wang Y, Chen L Q 2009 Acta Mater. 57 4102
[22] Vineyard G H 1957 J. Phys. Chem. Solids 3 121
[23] Wu H H, Trinkle D R 2011 Phys. Rev. Lett. 107 4
[24] Scotti L, Mottura A 2016 J. Chem. Phys. 144 8
[25] Bregolin F L, Behar M, Dyment F 2007 Appl. Phys. A 83 37
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