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Modified pressure of relativistic electrons in a superhigh magnetic field

Dong Ai-Jun ,  Gao Zhi-Fu ,  Yang Xiao-Feng ,  Wang Na ,  Liu Chang ,  Peng Qiu-He

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Yang Hai-Lin, Chen Qi-Li, Gu Xing, Lin Ning. First-principles calculations of O-atom diffusion on fluorinated graphene. Acta Phys. Sin., 2023, 72(1): 016801. doi: 10.7498/aps.72.20221630
Citation: Yang Hai-Lin, Chen Qi-Li, Gu Xing, Lin Ning. First-principles calculations of O-atom diffusion on fluorinated graphene. Acta Phys. Sin., 2023, 72(1): 016801. doi: 10.7498/aps.72.20221630
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Modified pressure of relativistic electrons in a superhigh magnetic field

Dong Ai-Jun, Gao Zhi-Fu, Yang Xiao-Feng, Wang Na, Liu Chang, Peng Qiu-He
Acta Phys. Sin., 2023, 72(3): 030502.
doi: 10.7498/aps.72.20220092
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  • Abstract

    Magnetar is a kind of pulsar powered by magnetic field energy. The study of magnetars is an important hotspot in the field of pulsars. In this paper, according to the work of Zhu Cui, et al. (Zhu C, Gao Z F, Li X D, Wang N, Yuan J P, Peng Q H 2016 Mod. Phys. Lett. A 31 1650070), we reinvestigate the Landau-level stability of electrons in a superhigh magnetic field (SMF), B≫Bcr(Bcr is a quantum critical magnetic field with a value of 4.414×1013 G), and its influence on the pressure of electrons in magnetar. First, we briefly review the pressure of electrons in neutron star (NS) with a weak-magnetic field limit (B≪Bcr). Then, we introduce an electron Landau level stability coefficient gν and a Dirac-δ function to deduce a modified pressure formula for the degenerate and relativistic electrons in an SMF in an application range of matter density ρ ≥ 107 g·cm–3 and Bcr ≪B < 1017 G. By modifying the phase space of relativistic electrons, the SMF can enhance the electron number density ne, and reduce the maximum of electron Landau level number νmax, which results in a redistribution of electrons. As B increases, more and more electrons will occupy higher Landau levels, and the electron Landau level stability coefficient gν will decrease with the augment of Landau energy-level number ν. By modifying the phase space of relativistic electrons, the electron number density ne increases with the MF strength increasing, leading the electron pressure Pe to increase. Utilizing the modified expression of electron pressure, we discuss the phenomena of Fermion spin polarization and electron magnetization in the SMF, and the modification of the equation of state by the SMF. We calculate the baryon number density, magnetization pressure, and the difference between pressures in the direction parallel to and perpendicular to the magnetic field in the frame of the relativistic mean field model. Moreover, we find that the pressure anisotropy due to the strong magnetic field is very small and can be ignored in the present model. We compare our results with the results from other similar studies, and examine their similarities and dissimilarities. The similarities include 1) the abnormal magnetic moments of electrons and the interaction between them are ignored; 2) the electron pressure relate to magnetic field intensity B, electron number density ne and electron Fermi energy EeF, and the latter two are complex functions containing B; 3) with ne and EeF fixed, Pe increases with B rising; 4) as B increases, the pressure-density curves fitted by the results from other similar studies have irregular protrusions or fluctuations, which are caused by the transformation of electron energy state from partial filling to complete filling at the ν-level or the transition of electrons from the ν to the (ν+1)-level. This phenomenon is believed to relate to the behavior of electrons near the Fermi surface in a strong magnetic field, which essentially reflects the Landau level instability. Finally, the future research direction is prospected. The present results provide a reference for future studies of the equation of state and emission mechanism of high-B pulsar, magnetar and strongly magnetized white dwarf.
      PACS:
      68.43.Jk(Diffusion of adsorbates, kinetics of coarsening and aggregation)
      31.15.es(Applications of density-functional theory (e.g., to electronic structure and stability; defect formation; dielectric properties, susceptibilities; viscoelastic coefficients; Rydberg transition frequencies))
      73.20.At(Surface states, band structure, electron density of states)
      68.65.Pq(Graphene films)

    Authors and contacts

    • 1.

      School of Physics and Electronic Science, Guizhou Normal University, Guiyang 550001, China

    • 2.

      Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, China

    • 3.

      School of Astronomy & Space Science, Nanjing University, Nanjing 210000, China

    • 4.

      Guizhou Provincial Key Laboratory of Radio Data Processing, Guiyang 550001, China

      • Corresponding author: Gao Zhi-Fu, zhifugao@xao.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12041304, U1831120), the Natural Science Foundation of Xinjiang Uygur Autonomous Region, China (Grant No. 2022D01A155), the Natural Science Foundation of Guizhou, China (Grant Nos. [2019]1241, KY(2020)003), and the High Level Talent Program support project of Chinese Academy of Sciences, China (Grant No. [2019]085).

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    金属的腐蚀就是金属和腐蚀性介质(如O2, Cl–等)发生氧化还原反应而发生有害的物理化学等变化, 失去原有性能的过程. 金属腐蚀是一种非常常见的现象, 几乎遍及日常生活中所有产业. 2020年中国工程院调查表明, 我国年腐蚀成本高达3万亿元, 占全国GDP的3.34%.

    石墨烯(G)是目前最薄的防腐蚀涂层和填料[1-5], 其几何孔径小, 使得原子、分子都难以通过. 2008年, Bunch等[3]研究了气体分子对G的渗透, 发现G能阻隔所有气体分子. 有研究[6]表明, O2分子、H2O分子穿过G分别需要克服16.34 eV, 42.8 eV的能垒. Topsakal等[7]发现O原子穿过G需要克服5.98 eV的能垒, O原子穿透G的扩散率约为表面扩散率的10–87倍, 可以忽略. G还具有优异的机械性能(杨氏模量约为1.0 TPa, 断裂强度约为130 GPa)[1,2,8]和优异的耐磨性. 单层和多层G薄膜都非常透明(4层G的透射率 > 90%), 因此G涂层不会干扰下层金属的光学特性[9,10].

    但是G也具有优异的导电性(电子迁移率为105—106 cm2/(V·s))[2], 在缺陷和破损处会发生电化学腐蚀, 从而加速金属的腐蚀速度[11-13]. 解决这一问题的方法包括功能化石墨烯[14-18]、多层石墨烯[19]、制备自修复石墨烯涂层[10]和掺杂原子[3]等. 功能化石墨烯是在G表面引入一些特定的官能团(如-F, -H, -O等[20]), 当这些官能团吸附在G表面时, 可以打开G的带隙, 降低其导电性能, 从而抑制电化学腐蚀的发生. 以氟化石墨烯(FG)为例, F原子的吸附使G上C原子的sp2杂化变为sp3杂化, 破坏了G的π键, 达到降低G的导电性, 抑制缺陷处的电化学腐蚀的目的[21]. Shen等[22]采用F2在还原氧化石墨烯上吸附F原子的办法, 制备了氟吸附浓度(氟化浓度)分别为12.56%, 33.98%和43.36%的3种氟化还原氧化石墨烯, 发现随着氟化浓度的增打, 氟化石墨烯的导电率降低. 此外, 还有研究表明, 氟功能化石墨烯材料由于氟的存在, 会导致表面能降低, 在水环境中表现出高度疏水性[23]. 高度疏水性有利于潮湿环境下抑制腐蚀性介质的吸附, 可以用于制备超疏水防腐蚀涂层[21]. 同时, FG继承了G的片状结构, 这种结构被认为产生了“迷宫效应”, 扩展了腐蚀性介质的扩散路径, 有利于涂层的抗腐蚀性能的提高 [18].

    不仅如此, 氟功能化的石墨烯还继承了石墨烯薄膜优异的阻隔性能. Wu等[24]通过实验证实了F元素的引入可以限制腐蚀物种的扩散, 延缓腐蚀产物的形成; 并通过理论计算发现其机制在于: 当G表面吸附F原子后, 石墨烯层对腐蚀性介质, 如Cl原子的吸附更强, 同时Cl原子穿过缺陷的能垒也显著提高. Li等[20]使用密度泛函理论分别计算了O原子在单个-O, -OH, -H和-F吸附的G涂层上的扩散和穿透, 结果表明, 这些吸附介质打破了石墨烯的电子结构, 增强了吸附位置的电子云, 提高了O原子垂直穿透G的能垒, 从而增加了O原子通过石墨烯的阻碍; 但同时O原子在水平方向上的扩散迁移率也有所提高, 这有利于O原子对金属基底的腐蚀. Yao等[25]通过第一性原理计算分析了O原子在G、两个Cl原子吸附的G和单个Cl, F原子共吸附的G表面的扩散, 结果发现Cl原子的引入会降低O原子在G上的扩散能垒, 因此当环境中的Cl原子吸附在G表面时, 会导致O原子的扩散速率增大, 而F原子吸附在Cl原子的对顶位, 增加了O原子的扩散能垒, 能有效抑制O原子的扩散; 该研究说明氟化对含氯环境下的腐蚀防护有利.

    以上研究表明降低腐蚀性物质在水平方向上的扩散迁移率是功能化石墨烯的抗腐蚀研究上需要关注的一个问题. 但以上理论研究都是围绕单个F原子吸附的FG(低于5%)展开的. 对于氟化浓度较高的石墨烯, 如完全氟化石墨烯(CF)和C∶F为4∶1的单面吸附的部分氟化石墨烯(C4F), 它们都是最稳定氟化石墨烯结构[26], 其宽带隙为3 eV左右[21,27-29] , 而且CF的C原子都是sp3C原子, 与纯粹石墨烯相比, 电子结构变化最大; 而C4F上的F原子呈对顶位吸附, 可以将其表面分隔开, 可推测这能抑制O原子的表面扩散. 因此本文采用基于密度泛函理论的第一性原理计算方法, 研究了O原子在CF和C4F上的扩散和穿透, 探讨CF和C4F对腐蚀性物质的阻隔机理. 此外, 与基底界面的结合强度也是涂层抗腐蚀性能的重要指标之一, 本文也对CF和C4F与Cu基底的相互作用进行了研究.

    2.1   计算方法

    本工作使用的是基于密度泛函理论的第一性原理计算软件VASP (vienna ab-initio simulation package)[30], 使用投影缀加平面波(PAW)方法[31]描述电子-离子相互作用, 利用广义梯度近似(GGA)PW91泛函交换关联相互作用[32]. 采用500 eV的平面波截断能, 二维结构和表面的k点网格设置为3 × 3 × 1, 真空层厚度为15 Å, 所有几何结构都进行了全优化, 直到作用在每个原子上的能量和力分别小于10–5 eV和10–2 eV/Å. 还使用DFT-D2方案[33]来修正范德瓦耳斯(vdW)力.

    使用VASP软件的NEB过渡态搜索方法[34]来找到O原子在CF和C4F上的扩散和穿透的路径和能垒. NEB方法只需要知道初态和末态的结构, 就能得到扩散的路径和能垒.

    为了评估FG涂层与基底材料的结合能力, 本文计算了FG涂层与Cu(111)表面的界面结合能, 界面结合能(Eab)的计算公式[35]如下:

    Eab=ECu+El−ECu/l,
    		 (1)

    其中ECu/l表示结合后界面总能量, ECu表示Cu(111)表面能量, El表示吸附的G和FG(包括C4F和CF)层能量, 由于各界面的面积不同, 可以用界面粘附功(Wab)来对比不同界面的结合强度以及界面的稳定性, 粘附功越大, 界面结合力越强, 界面结构越稳定. 其计算公式如下[35]:

    Wab=Eab/ACu/l,
    		 (2)

    其中ACu/l为界面接触面积.

    2.2   计算模型

    首先构建并优化了G, C4F和CF的单层模型, 结构如图1所示. CF中的F原子交替吸附在C原子层两侧, C—F键为1.383 Å, C—C键为1.577 Å, 与文献[36]的1.38 Å和1.58 Å一致. C4F的F原子吸附在C原子层同一侧, 且呈对顶位分布, C—F键长为1.46 Å, 接近文献的1.45 Å, C—C键长为1.508 Å和1.401 Å, 与文献[37]的1.51 Å(Csp3-Csp2)和1.40 Å (Csp2-Csp2)一致.

    图 1 优化后的晶格结构　(a) G; (b) C4F; (c) CF\r\nFig. 1. Optimized lattice structure: (a) G; (b) C4F; (c) CF.
    图 1  优化后的晶格结构　(a) G; (b) C4F; (c) CF
    Fig. 1.  Optimized lattice structure: (a) G; (b) C4F; (c) CF.
    下载: 全尺寸图片 幻灯片

    FG与Cu(111)界面模型如图2所示. 分别选取了4 × 4的单层G (C32, a = b = 9.86 Å), C4F (C32F8, a = b = 9.93 Å)和CF (C32F32, a = b = 10.39 Å)与2 × 2的3层Cu(111)表面结构(Cu48, a = b = 10.26 Å)结合, 晶格失配率分别为3.97%, 3.27%和1.26%, 晶格失配率公式[38]如下:

    图 2 优化前的界面模型　(a) Cu/G界面; (b) Cu/C4F界面; (c) Cu/CF界面\r\nFig. 2. Interface model before optimization: (a) Cu/G interface; (b) Cu/C4F interface; (c) Cu/CF interface.
    图 2  优化前的界面模型　(a) Cu/G界面; (b) Cu/C4F界面; (c) Cu/CF界面
    Fig. 2.  Interface model before optimization: (a) Cu/G interface; (b) Cu/C4F interface; (c) Cu/CF interface.
    下载: 全尺寸图片 幻灯片
    δ=2|a−b|a+b.
    		 (3)

    3.1   O原子在C4F上的扩散与穿透

    研究表明, 桥位是O原子在G上的最佳吸附位[20,7]. 首先计算了O原子在G相邻两个桥位上的扩散, 得到它的最佳扩散路径是桥位(B)-顶位(T)-桥位(B), 与文献[20, 7]一致. 如图3所示, 它的扩散能垒为0.72 eV, 接近文献[20]的0.79 eV. 说明计算方法可取.

    图 3 O原子在G相邻桥位上的扩散的能垒图\r\nFig. 3. The diffusion barrier diagram of diffusion of O atom on the adjacent bridge site of G.
    图 3  O原子在G相邻桥位上的扩散的能垒图
    Fig. 3.  The diffusion barrier diagram of diffusion of O atom on the adjacent bridge site of G.
    下载: 全尺寸图片 幻灯片

    分别计算O原子在C4F 无F面和有F面上的扩散, 首先, 研究发现sp2碳原子(不吸附F的C原子)间的桥位是O原子的最稳定吸附位(见附表A1). 图4(a)展示了O原子在C4F无F面的四条扩散路径, 分别是路径1: B-T-B; 路径2: B-H1(空心位1)-B; 路径3: B-H2(空心位2)-B; 路径4: B-T-T-B. 图4(b)展示了O原子在C4F有F面的3条扩散路径, 分别是路径5: B-T-B; 路径6: B-H1-B; 路径7: B-H2-B.

    图 4 (a) O原子在C4F无F面的扩散路径; (b) O原子在C4F有F面的扩散路径\r\nFig. 4. (a) the diffusion paths of O atom on the F-free surface of C4F; (b) the diffusion paths of O atom on the F adsorbed surface of C4F.
    图 4  (a) O原子在C4F无F面的扩散路径; (b) O原子在C4F有F面的扩散路径
    Fig. 4.  (a) the diffusion paths of O atom on the F-free surface of C4F; (b) the diffusion paths of O atom on the F adsorbed surface of C4F.
    下载: 全尺寸图片 幻灯片

    在C4F无F面上, O原子的最佳扩散路径是B-T-B, 即路径1, 如图5(a)所示, 其能垒为1.44 eV, 相比于在G上的扩散能垒提高了近一倍. O原子沿路径2(通过空心位H1)扩散到sp2碳六边形对桥位的能垒为4.31 eV, 沿路径3(通过空心位H2)扩散到不同sp2碳六边形环上的能垒为3.42 eV, 远高于沿顶位扩散的能垒, O原子难以通过空心位扩散. 在C4F无F面上, O原子还可以通过路径4扩散到不同sp2碳六边形环上, 其能垒如图5(d)所示, 为2.66 eV, 小于沿空心位扩散的能垒, 但相较于路径1而言, 扩散难度大大提升.

    图 5 O原子在C4F无F面上扩散的能垒图　(a) 路径1; (b) 路径2; (c) 路径3; (d) 路径4\r\nFig. 5. Diffusion barrier diagram of O atom diffusion on the F-free surface of C4F: (a) Path 1; (b) path 2; (c) path 3; (d) path 4.
    图 5  O原子在C4F无F面上扩散的能垒图　(a) 路径1; (b) 路径2; (c) 路径3; (d) 路径4
    Fig. 5.  Diffusion barrier diagram of O atom diffusion on the F-free surface of C4F: (a) Path 1; (b) path 2; (c) path 3; (d) path 4.
    下载: 全尺寸图片 幻灯片

    O原子在C4F有F面上的最佳扩散路径也是B-T-B, 即路径5, 如图6(a)所示, 能垒为1.42 eV, 与无F面相近. 图6(b)显示了O原子沿路径6的扩散, 相对于沿顶位的扩散, 沿空心位的能垒更高, 达到了3.36 eV, O原子难以沿空心位扩散. 在不同sp2碳六边形间的扩散, 由于F原子的阻隔, O原子只能通过空心位H2扩散, 如图6(c)所示, 沿路径7的能垒高达4.0 eV, 如此高的能垒将O原子困在sp2碳六边形环上, 几乎无法扩散出F原子的包围, 这有利于涂层的腐蚀防护.

    图 6 O原子在C4F有F面上扩散的能垒图　(a) 路径5; (b) 路径6; (c) 路径7\r\nFig. 6. Diffusion barrier diagram of O atom diffusion on the F adsorbed surface of C4F: (a) Path 5; (b) path 6; (c) path 7
    图 6  O原子在C4F有F面上扩散的能垒图　(a) 路径5; (b) 路径6; (c) 路径7
    Fig. 6.  Diffusion barrier diagram of O atom diffusion on the F adsorbed surface of C4F: (a) Path 5; (b) path 6; (c) path 7
    下载: 全尺寸图片 幻灯片

    O原子垂直穿透G的最佳路径是从桥位穿透[4,7], 如图7(a)所示, 计算得到该路径的能垒为6.16 eV, 与文献[4]的5.5 eV和文献[7]的5.98 eV相差不大. 对于O原子穿透C4F的路径, 同样计算了从桥位穿透的情况, 得到能垒为5.08 eV(见图7(b)), 略小于穿透G的能垒, 但仍然能有效阻隔O原子的穿透. 虽然F的加入破坏了C4F上部分C原子的sp2结构, 但其保留的sp2C原子环的结构仍然很稳定, 因此能有效阻隔O原子的穿透.

    图 7 O原子穿透　(a) G; (b) C4F的能垒图\r\nFig. 7. Diffusion barrier diagram of O atom penetrating: (a) G; (b) C4F.
    图 7  O原子穿透　(a) G; (b) C4F的能垒图
    Fig. 7.  Diffusion barrier diagram of O atom penetrating: (a) G; (b) C4F.
    下载: 全尺寸图片 幻灯片

    以上计算表明C4F上的F原子大大提高了O原子的水平扩散难度, 能有效抑制O原子在其表面的扩散, 有利于阻碍O原子对金属基底的腐蚀. 这与文献[20]中O在单个F原子修饰的G表上扩散能垒降低的情况不同, 而与文献[25]中Cl原子和F原子对顶位吸附在G中时, O原子的扩散能垒增加相似, 说明C4F上F原子的对顶位吸附应该是O原子的扩散能垒提升的主要原因, 有可能是对顶位的F在石墨烯上形成的稳定共轭电子, 从而增大了O原子的扩散能垒.

    C4F中只有单面吸附F原子, 但无论是有F面还是无F面, O原子都倾向于吸附在sp2 C原子环的桥位上, 并沿着桥位-顶位-桥位扩散. F原子的环绕排列, 大大提高了O原子向周边扩散的能垒, F原子将C4F分隔成一个个区块, 每个区块像陷阱一样, 当O原子吸附在上面时, 巨大的能垒使其难以向下或向其他区块扩散, 因此能很好阻止O原子扩散到金属基底.

    3.2   O原子在CF上的扩散和穿透

    在CF上, 所有的C原子都吸附一个F原子, 变为了sp3C原子, C原子间距离变大. O原子需要穿过表面F原子层进入C原子层, 首先讨论了O原子穿透CF的情形. 如图8(a)所示, 首先, 当O原子接近F原子层时, 受到F原子的排斥, 要克服2.82 eV的能垒进入F原子层并替换F原子, 吸附在C原子顶位上, 之后向下运动到C原子间桥位上, 该过程需克服1.84 eV的能垒, 之后O原子再穿过桥位, 需要克服0.81 eV的能垒. 可见, 相比于G, CF的阻隔能力下降, O原子穿透CF的阻力主要来自于F原子层; 但O原子穿透CF的路径更复杂, 对于减缓O原子的穿透有一定作用.

    图 8 (a) O原子穿透CF的F原子层到达C原子层的能垒图; (b) O原子在CF内相邻桥位上的扩散的能垒图; (c) O原子在CF内沿空心位扩散的能垒图\r\nFig. 8. (a) Diffusion barrier diagram of O atom penetrating the F atomic layer of CF to the C atomic layer; (b) diffusion barrier diagram of O atom diffusion on the adjacent bridge site in CF; (c) diffusion barrier diagram of O atom diffusion along the hollow site in CF.
    图 8  (a) O原子穿透CF的F原子层到达C原子层的能垒图; (b) O原子在CF内相邻桥位上的扩散的能垒图; (c) O原子在CF内沿空心位扩散的能垒图
    Fig. 8.  (a) Diffusion barrier diagram of O atom penetrating the F atomic layer of CF to the C atomic layer; (b) diffusion barrier diagram of O atom diffusion on the adjacent bridge site in CF; (c) diffusion barrier diagram of O atom diffusion along the hollow site in CF.
    下载: 全尺寸图片 幻灯片

    O原子穿过F原子层后, O原子取代C—C键连接在两个相邻C原子间. 我们计算了O原子在CF层内的水平扩散, 其中沿空心位扩散需要克服7.60 eV的巨大能垒(见图8(c)), 相比之下, 在相邻桥位间扩散更容易. 其最佳扩散路径的能垒如图8(b)所示, O原子扩散到相邻桥位过程中, 先与两个C原子成键连接, 移动到中间时, 与3个C原子成键连接, 这个过程吸热, 能垒为2.69 eV, 之后再移动到相邻桥位上, 与两个C原子成键连接, 如此高的能垒能有效防止O原子向周围扩散.

    3.3   过渡态电子结构分析

    为了确定F吸附对O扩散的影响, 对表面扩散的几条最佳扩散路径过渡态的电子结构进行了分析, 图9和图10显示了O原子在石墨烯和F化石墨烯上沿最佳路径扩散的初始态及过渡态的态密度. 对比初始态和过渡态的态密度可以发现, 在各个过渡态的费米能级附近都会出现新的杂化峰, 这些杂化峰由C的p轨道和O的p轨道杂化产生. 从初始态到过渡态过程中, 在G和C4F表面, 过渡态的O原子处于顶位, 其中一个C—O键断裂, 体系能量升高, 而在CF内断裂一个C—C键, 生成一个C—O键. O原子吸附在C4F和CF上时, O原子的p轨道与F原子的p轨道在–5 eV附近有重叠峰, 到达过渡态时, 峰值减小, 扩散过程中, 受到F原子的影响, O原子需要更高的能量完成迁移.

    图 9 O原子沿最佳扩散路径扩散的DOS图　(a) G表面初始态和过渡态的DOS图; (b) C4F有F面初始态和过渡态的DOS图; (c) C4F无F面初始态和过渡态的DOS图; (d) CF内初始态和过渡态的DOS图\r\nFig. 9. DOS diagram of O atom diffusion along the optimal diffusion path: (a) DOS diagram of initial state and transition state of G surface; (b) DOS diagram of initial state and transition state on the F adsorbed surface of C4F; (c) DOS diagram of initial state and transition state on the F-free surface of C4F; (d) DOS diagram of initial state and transition state in CF.
    图 9  O原子沿最佳扩散路径扩散的DOS图　(a) G表面初始态和过渡态的DOS图; (b) C4F有F面初始态和过渡态的DOS图; (c) C4F无F面初始态和过渡态的DOS图; (d) CF内初始态和过渡态的DOS图
    Fig. 9.  DOS diagram of O atom diffusion along the optimal diffusion path: (a) DOS diagram of initial state and transition state of G surface; (b) DOS diagram of initial state and transition state on the F adsorbed surface of C4F; (c) DOS diagram of initial state and transition state on the F-free surface of C4F; (d) DOS diagram of initial state and transition state in CF.
    下载: 全尺寸图片 幻灯片

    3.4   涂层与Cu(111)面的结合

    除了涂层的阻隔性能, 还研究了FG与金属Cu(111)面间的相互作用, 并与G与Cu(111)面的相互作用进行比较, 这对于评估涂层材料的使用价值有很大意义. 本文使用的是4 × 4的G, G与Cu(111)面的界面粘附功为2.626 J/m2, 界面距离为2.938 Å (见图10(a)), 根据bader电荷分析, 发现G与Cu表面第一层原子发生电荷交换, 平均单个Cu原子向G层转移0.03个电荷, G与Cu表面通过弱键相连. C4F与Cu(111)面的界面粘附功更高, 粘附功为3.529 J/m2, C4F与Cu基底表面距离为2.045 Å (见图10(b)), 可以看到部分C原子与表面Cu原子间形成较强的键合, bader电荷分析发现, 表面Cu原子与C4F的C原子间的电荷交换增加, 平均单个Cu原子失去0.092个电荷, 界面粘附功的增加与F原子没有直接关系, 主要是F的吸附破坏了石墨烯的电子结构, 使得C原子与表面的Cu原子能形成更强的键合, 这使得C4F与Cu基底的结合更为紧密, 有利于金属的腐蚀防护. CF与Cu(111)面的界面粘附功为3.559 J/m2, 略高于C4F与Cu(111)面的界面粘附功, 底层F原子与表层Cu原子间距离为2.827 Å (见图10(c)). 根据bader电荷分析, 最上层Cu原子平均失去0.042个电荷, 相比Cu/G界面略微增加, 下层F原子与表面Cu原子间形成弱键.

    图11展示了3种界面体系在费米面附近的总态密度以及3种原子(包括Cu原子的3d轨道、C原子的2p轨道和F原子的2p轨道)的分波态密度, 与Cu/G界面一样, Cu/C4F界面的 C原子在费米能级处态密度不为0, 说明C4F与Cu结合后, 复合体系表现出金属性, 对电化学腐蚀 有利.

    图 10 优化后的界面模型　(a) Cu/G界面; (b) Cu/C4F界面; (c) Cu/CF界面\r\nFig. 10. Optimized interface model: (a) Cu/G nterface; (b) Cu/C4F interface; (c) Cu/CF interface.
    图 10  优化后的界面模型　(a) Cu/G界面; (b) Cu/C4F界面; (c) Cu/CF界面
    Fig. 10.  Optimized interface model: (a) Cu/G nterface; (b) Cu/C4F interface; (c) Cu/CF interface.
    下载: 全尺寸图片 幻灯片
    图 11 Cu/G、Cu/C4F和Cu/CF界面的DOS图, 虚线为费米能级\r\nFig. 11. DOS diagram of Cu/G, Cu/C4F and Cu/CF interfaces.
    图 11  Cu/G、Cu/C4F和Cu/CF界面的DOS图, 虚线为费米能级
    Fig. 11.  DOS diagram of Cu/G, Cu/C4F and Cu/CF interfaces.
    下载: 全尺寸图片 幻灯片

    由Cu/G界面的态密度图可以发现, G中C的p轨道与Cu的d轨道共振峰较少, 只在费米能级附近出现, 而且展宽较小, 说明G与Cu基底间相互作用不强. 对于Cu/C4F界面, Cu原子的d轨道主要在0到5 eV以内与C原子的p轨道发生杂化, 共振峰的波峰较为平缓, 重叠区域面积较大, 电子离域性较强, 说明Cu原子和C原子间成键较强, C4F与Cu表面的相互作用较强. 对于Cu/CF界面, F原子和C原子的p轨道在0到5 eV和–3 eV以下有多处共振峰和重叠区域, 说明CF比C4F更稳定, CF在费米能级处态密度为0, 与Cu的结合对CF的电子结构没有受到太大影响. 值得注意的是, 在–5到5 eV范围内, 相比于Cu/G和Cu/C4F界面, Cu/CF界面上Cu原子的d轨道与F原子和C原子的p轨道有更多的重叠区域, 尖峰数量较多, 而且在–5—–3 eV范围内Cu的d轨道与F的p轨道有明显的杂化峰, 且重叠区域面积较大, 说明Cu/CF界面中Cu基底与F原子间的杂化作用更强, 因此Cu/CF界面的粘附功大于Cu/G和Cu/C4F界面, 所以Cu/CF界面结构更稳定. 界面粘附功的提升可能是因为F原子具有高负电性, 与表面Cu原子间的相互作用更强.

    为了更好比较界面原子间的键合强度, 使用Lobster程序[39]计算了表面Cu原子与界面处最近邻的C原子或F原子间的COHP和ICOHP, 如图12展示了界面处原子对的-COHP, -COHP为正表示成键作用, 为负表示反键作用. Cu/G界面的Cu—C键、Cu/C4F界面的Cu—C键和Cu/CF界面的Cu—F键的-ICOHP值分别为0.195, 0.395和0.032, 表明界面间键强由大到小为Cu/C4F界面的Cu—C键 > Cu/G界面的Cu—C键 > Cu/CF界面的Cu—F键. 由图12可以发现Cu/CF界面的Cu—F键在费米能级以下有很大的反键区域, 这使得Cu/CF界面的电荷转移虽高于Cu/G界面, 但Cu/CF界面的Cu—F键的强度却更小.

    图 12 3种界面的轨道哈密顿分布(-COHP), 费米能级位于0 eV\r\nFig. 12. Crystal orbital Hamilton populations (-COHP) of three interfaces, the Fermi level is at 0 eV
    图 12  3种界面的轨道哈密顿分布(-COHP), 费米能级位于0 eV
    Fig. 12.  Crystal orbital Hamilton populations (-COHP) of three interfaces, the Fermi level is at 0 eV
    下载: 全尺寸图片 幻灯片

    本文采用第一性原理计算方法, 研究了O原子在CF和C4F上的扩散和穿透行为. 计算结果表明, 在C4F上, O原子的扩散受到了F原子的阻碍, O原子吸附在相邻sp2C原子间的桥位上, 最佳扩散路径是沿sp2C原子环上的B-T-B, 需要克服1.42 eV的能垒. O原子在CF内的扩散能垒为2.69 eV, 比在G和C4F上的扩散能垒大很多, 扩散难度大.

    研究还发现随着F原子吸附浓度的增大, 石墨烯C原子层的稳定结构被逐渐破坏, C原子层的阻隔能力逐渐减小, CF的C原子层对O原子的阻隔能力大大减小, O原子主要受到F原子层的阻隔, C4F的C原子层的结构没有受到太大的破坏, 依旧有很好的阻隔能力.

    CF和C4F薄膜与Cu基底界面的相互作用研究表明, 石墨烯的F化可以提高薄膜与金属基底的结合强度, 且界面结合强度与稳定性随F化浓度的增大而变强. 3种界面体系中, Cu/CF界面的界面粘附功最大, 说明Cu/CF界面的结构最稳定, Cu原子的电荷转移比Cu/G界面高一些, 相比于Cu/C4F界面则更少, 成键不强, 界面粘附功主要由F原子和Cu原子间的电荷相互作用提供; Cu/C4F界面的界面粘附功略小于Cu/CF界面的界面粘附功, 其界面结构较为稳定, Cu原子的电荷转移最多, 部分Cu原子和C原子间成键较强, C4F上F的吸附导致石墨烯电子结构被破坏, 使得C原子与Cu表面原子间形成强键, 界面粘附功增大; Cu/G界面的界面粘附功最小, 电荷转移也最少, 说明G与Cu基底的结合最不稳定.

    表 A1  O原子在C4F不同位置吸附的能量数据
    Table A1.  Energy data of O atom adsorption at different positions of C4F.
    O原子吸附位置C4F
    有F面/eV无F面/eV
    桥位–325.31–326.67
    顶位–323.89–325.23
    空心位H1–321.96–322.36
    空心位H2–321.92–323.25
    下载: 导出CSV 
    | 显示表格
    表 A2  O原子在CF内不同位置吸附的能量数据
    Table A2.  Energy data of O atom adsorption at different positions in CF.
    O原子吸附位置CF内/eV
    桥位–413.70
    空心位–406.10
    下载: 导出CSV 
    | 显示表格

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  • 图 1  中子星内部弱磁场极限下相对论电子压强Pe随电子数密度ne的变化

    Figure 1.  Relativistic electron pressure Pe with electron number density ne in the limit of weak magnetic field inside a neutron star.

    DownLoad: Full-Size Img PowerPoint

    图 2  不同磁场下中子星内部电子压强Pe随物质密度ρ的变化

    Figure 2.  Relation between electron pressure Pe and matter density ρ in neutron stars with different magnetic fields.

    DownLoad: Full-Size Img PowerPoint

    图 3  本文与其他强磁场中电子数密度和电子压强研究的对比　(a)强磁化白矮星中电子压强Pe随ρ变化关系; (b)中子星壳层电子数密度ne随ρ变化关系; (c)磁化白矮星中(最大电子费米能量EFmax = 20mec2)电子压强Pe随ρ变化关系; (d) 两种不同的理论模型下白矮星中电子压强Pe随ρ变化关系

    Figure 3.  Study of electron number density and electron pressure in strong magnetic fields by other authors and their comparison with this work: (a) Relationship between electron pressure Pe and ρ in a strongly magnetized white dwarf (WD); (b) relationship between the electron number density ne and ρ in the crust of a neutron star; (c) electron pressure Pe as a function of ρ in a magnetized WD with maximum electron Fermi energy EFmax = 20mec2; (d) electron pressure Pe as a function of ρ in a magnetized WD under two different theoretical models.

    DownLoad: Full-Size Img PowerPoint

    图 4  中子星内部费米子完全极化场景下饱和磁场强度Bs随粒子数密度n的变化关系　(a) 质子/电子完全极化下Bs vs. ne/np; (b) 中子完全极化下Bs vs. nB (nB为重子数密度)

    Figure 4.  Relationship between the saturated magnetic field strength Bs and the particle number density n in a fully polarized neutron star fermion matter: (a) Bs vs. ne/np in a fully polarized scenario for proton/electron matter system; (b) Bs vs. nB in a fully polarized scenario for the neutron matter system (nB is the baryon number density).

    DownLoad: Full-Size Img PowerPoint

    图 5  不同磁场下中子星内部相对论电子的磁化率χ与电子数密度ne的变化关系

    Figure 5.  Relation between the magnetic susceptibility χ and number density of relativistic electrons ne in neutron stars with different magnetic field strengths.

    DownLoad: Full-Size Img PowerPoint

    图 6  中子星内部磁场B随物质密度ρ的变化关系

    Figure 6.  Relation of the magnetic field B and matter density ρ in a neutron star.

    DownLoad: Full-Size Img PowerPoint

    表 1  在相对论平均场TMA参数模型下nN, EeF, Pe, P和M的部分计算值

    Table 1.  Partial calculations of nN, EeF, Pe, P and M in a relativistic mean field model with the TMA parameter set.

    B≪B *B > B *
    nN/fm–3EeF/MeVPe/(MeV·fm–3)P/(MeV·fm–3)M/M⊙EeF/MeVPe/(MeV·fm–3)P/(MeV·fm–3)M/M⊙
    0.00132.9244.9×10–103.78×10–60.02893.3518.41×10–103.79×10–60.0311
    0.021123.492.03×10–66.79×10–50.059327.622.88×10–67.36×10–50.0613
    0.077268.581.47×10–40.00210.051781.062.87×10–40.002580.0543
    0.1332107.899.04×10–40.01430.2904128.650.001820.01790.2932
    0.1554120.900.00140.02290.4201145.130.002950.07250.4241
    0.2003143.580.00280.04750.6884175.480.006320.08610.6965
    0.2338158.310.00420.07240.8808183.720.007620.09650.8912
    0.3206190.040.00870.16241.2945251.490.02670.21051.3062
    0.3556200.780.01080.20921.4236273.350.03720.27611.4327
    0.4186218.290.01510.30651.6071312.720.06370.42111.6223
    0.4746231.980.01930.40681.7263347.670.09740.58161.7412
    0.5446247.310.02490.54791.8312391.120.15610.82781.8522
    0.6076259.750.03040.68801.8947 429.700.22641.02721.9132
    0.6846273.650.03740.87371.9444456.800.29051.30921.9675
    0.7266280.730.04140.98091.9621480.230.35511.47821.9853
    0.8396298.230.05281.28451.9830526.730.51351.95212.0061
    0.9156318.400.06551.59251.9916586.650.74782.53162.0342
    DownLoad: CSV

    表 2  相对论平均场模型下nN, ρ, B, ne, |MB|, ΔP和P// 的部分计算值, 这里选择TMA参数组和密度依赖的中子星强磁场模型

    Table 2.  Partial calculations of nN, ρ, B, ne, |MB|, ΔP和P// in a relativistic mean field model. TMA parameter set and a density-dependent magnetic field model for a neutron star are selected.

    nN/fm–3ρ/(g·cm–3)B/Gne/cm–3|M|/G|MB|/(dyn·cm–2)ΔP/(dyn·cm–2)P///(dyn·cm–2)
    0.00132.535×10121.000×10141.051×10324.277×10114.277×10258.385×10261.196×1030
    0.02113.992×10131.003×10145.689×10342.841×10132.845×10273.641×10273.324×1031
    0.07221.014×10141.011×10141.418×10362.428×10142.485×10282.567×10288.147×1031
    0.13322.521×10141.073×10145.520×10366.049×10146.964×10287.055×10285.651×1031
    0.15542.940×10141.116×10147.781×10367.638×10149.508×10289.607×10282.509×1034
    0.20033.789×10141.247×10141.301×10371.089×10151.796×10291.708×10292.719×1034
    0.23384.423×10141.393×10141.744×10371.868×10152.604×10292.619×10293.049×1034
    0.32066.065×10142.011×10143.017×10375.406×10158.143×10298.175×10296.645×1034
    0.35566.727×10142.377×10143.563×10375.406×10151.285×10301.291×10308.716×1034
    0.41857.917×10143.237×10144.572×10377.676×10152.485×10302.493×10301.329×1035
    0.47468.978×10144.244×10144.580×10371.237×10165.203×10305.217×10301.836×1035
    0.54471.031×10155.860×10146.647×10372.249×10161.318×10311.321×10312.613×1035
    0.60761.145×10157.685×10147.704×10373.353×10162.577×10312.583×10313.243×1035
    0.68461.295×10151.042×10159.012×10375.225×10165.445×10315.453×10314.133×1035
    0.72651.375×10151.215×10159.725×10376.533×10167.932×10317.944×10314.675×1035
    0.83861.586×10151.763×10151.160×10381.109×10171.955×10321.958×10326.165×1035
    0.91561.774×10152.347×10151.342×10381.678×10173.938×10323.943×10327.996×1035
    DownLoad: CSV
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  • Received Date:  13 January 2022
  • Accepted Date:  12 October 2022
  • Available Online:  28 November 2022
  • Published Online:  05 February 2023

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