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氧原子在钛晶体中扩散的第一性原理研究

杨亮 王才壮 林仕伟 曹阳

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氧原子在钛晶体中扩散的第一性原理研究

杨亮, 王才壮, 林仕伟, 曹阳

First-principles investigation of oxygen diffusion mechanism in -titanium crystals

Yang Liang, Wang Cai-Zhuang, Lin Shi-Wei, Cao Yang
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  • 在材料领域杂质原子的迁移是一个基础而永恒的主题.采用基于密度泛函理论的第一性原理方法,研究了氧原子在钛(-Ti)晶体中的间隙占位情况,并计算了氧原子稳定占位点间隙能、电子态密度、电荷差分密度及其邻近钛原子的位移情况.采用基于过渡态搜索理论的CI-NEB(climbing image nudged elastic band)方法预测了稳定态氧原子在-Ti晶体中的扩散路径、扩散势垒及相应的跳转频率,并由此推算出氧原子在不同位点之间跳转的扩散系数.研究结果表明,间隙氧原子在六角密排钛晶体结构中共有七种占位,但仅存在三个可稳定占据的间隙位点:八面体中心位点、六面体中心位点及0.28 nm钛-钛键中心位点.各稳定间隙位点之间的扩散具有不对称性,因此可确定三种稳定间隙氧原子位点间存在七条独立扩散路径.获取计算不同路径扩散系数所需要的微观参数,包括扩散势垒、扩散长度、不同扩散路径上鞍点氧原子的跳转频率,最终预测了不同间隙位点之间氧原子的扩散系数值,其中八面体中心扩散到邻近键位的扩散系数与实验值相符合.通过对间隙氧原子扩散行为的深入了解,希望能对控制钛合金中氧的扩散、提高钛金属中氧的含量及相关研究提供基础理论支持.
    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.
      通信作者: 王才壮, czwang@msn.com;cy507@hainu.edu.cn ; 曹阳, czwang@msn.com;cy507@hainu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:51361009)、海南大学青年基金(批准号:qnjj1239)和海南省自然科学基金(批准号:20155216)资助的课题.
      Corresponding author: Wang Cai-Zhuang, czwang@msn.com;cy507@hainu.edu.cn ; Cao Yang, czwang@msn.com;cy507@hainu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51361009), the Foundation for Young Scientist of Hainan University, China (Grant No. qnjj1239), and the Natural Science Foundation of Hainan Province, China (Grant No. 20155216).
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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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出版历程
  • 收稿日期:  2016-12-27
  • 修回日期:  2017-01-16
  • 刊出日期:  2017-06-05

氧原子在钛晶体中扩散的第一性原理研究

    基金项目: 国家自然科学基金(批准号:51361009)、海南大学青年基金(批准号:qnjj1239)和海南省自然科学基金(批准号:20155216)资助的课题.

摘要: 在材料领域杂质原子的迁移是一个基础而永恒的主题.采用基于密度泛函理论的第一性原理方法,研究了氧原子在钛(-Ti)晶体中的间隙占位情况,并计算了氧原子稳定占位点间隙能、电子态密度、电荷差分密度及其邻近钛原子的位移情况.采用基于过渡态搜索理论的CI-NEB(climbing image nudged elastic band)方法预测了稳定态氧原子在-Ti晶体中的扩散路径、扩散势垒及相应的跳转频率,并由此推算出氧原子在不同位点之间跳转的扩散系数.研究结果表明,间隙氧原子在六角密排钛晶体结构中共有七种占位,但仅存在三个可稳定占据的间隙位点:八面体中心位点、六面体中心位点及0.28 nm钛-钛键中心位点.各稳定间隙位点之间的扩散具有不对称性,因此可确定三种稳定间隙氧原子位点间存在七条独立扩散路径.获取计算不同路径扩散系数所需要的微观参数,包括扩散势垒、扩散长度、不同扩散路径上鞍点氧原子的跳转频率,最终预测了不同间隙位点之间氧原子的扩散系数值,其中八面体中心扩散到邻近键位的扩散系数与实验值相符合.通过对间隙氧原子扩散行为的深入了解,希望能对控制钛合金中氧的扩散、提高钛金属中氧的含量及相关研究提供基础理论支持.

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