Effect of doped elements X (B, Al, Sn, Co) on binding performance of IDB-X/Diamond interface
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摘要: 基于量子力学第一性原理，建立了IDB-B/Diamond、IDB-Al/Diamond、IDB-Sn/Diamond和IDB-Co/Diamond 4种膜基界面模型，计算了膜基界面结合能、差分电荷密度和布居数，以探究孕镶金刚石钻头（impregnated diamond bits， IDB）基体中的常用元素X（X = B、Al、Sn、Co）对 IDB-X/Diamond膜基结合强度的影响机制。计算结果表明：膜基界面结合能大小为Wad-B > Wad-Al > Wad-Co > Wad-Sn；B、Al是增强膜基结合强度的有益元素，因为B、Al原子的电荷主要转移到掺杂位点附近的C1~C3原子，其与C1~C3原子的键合作用强；Sn、Co会削弱膜基结合强度，这是由于Sn、Co原子与C1~C3原子的键合作用弱，同时膜基界面间的其他C原子因俘获电荷而相斥。压痕对比的实验结果与仿真结论相符。Abstract:
Objectives At present, resource exploration and mining continue to expand to deep underground. Impregnated diamond bits (IDB) with excellent performance have become the main tool for deep underground drilling. Our research group has found that depositing a layer of CVD diamond coating in situ on the surface of IDB can achieve homogeneous epitaxial growth and heterogeneous epitaxial growth of diamond coatings, which can improve the working life of IDB. This article is based on the first principles of quantum mechanics and uses the CASTEP computational tool to study the influence mechanism of X (X = B, Al, Sn, Co) elements commonly used in the IDB on the interfacial bonding performance of CVD diamond coatings on IDB from a microscopic perspective. It provides a theoretical reference and basis for further optimizing the formulation of drill bit substrates and improving the interfacial bonding strength between the film and substrate. Methods This article uses the CASTEP module of the quantum mechanics computing software Materials Studio to study the influence mechanism of X (X = B, Al, Sn, Co) elements commonly used in IDB on the interfacial bonding performance of CVD diamond coatings on IDB from a microscopic perspective. Firstly, establish [100] crystal orientation, 3×3 size IDB, and CVD diamond coating supercell models, with dimensions of 7.54 Å × 7.54 Å × 3.56 Å along the X, Y, and Z directions. After adding a vacuum layer with a thickness of 12 Å, the IDB model and CVD diamond coating model are obtained. Then, replace the C atoms at specific locations on the surface of the IDB model with X (X = B, Al, Sn, Co) atoms. Afterwards, the IDB-X substrate is combined with the CVD diamond coating model along the [100] crystal plane to establish an IDB-X/Diamond film substrate interface model. After testing, the film-substrate interface spacing is set to 2 Å. Next, the CASTEP module is used to optimize the IDB-X/Diamond film-substrate interface model doped with X (X = B, Al, Sn, Co) atoms. The properties of the four film-substrate interface models are analyzed from the aspects of film-substrate interface binding energy, differential charge density, and Mulliken population. Finally, verification is conducted with indentation experiments. Results (1) From the perspective of film-substrate interface binding energy, the binding energies of B, Al, Co, and Sn atom doping are 11.68, 9.94, 7.38, and 6.85 J/m2, respectively. Based on the weakening phase Co of the film-substrate interface binding energy, the film-substrate interface binding energy doped with B and Al atoms is significantly higher than that of Co atoms, indicating that the B and Al elements in the substrate are beneficial for improving the film-substrate interface binding energy. The film-substrate interface binding energy doped with Sn atoms is similar to that of Co atoms, indicating that the Sn element in the substrate also weakens the bonding strength between the film and substrate. (2) From the perspective of differential charge density, the charges of B, Al, Sn, and Co atoms all tend to transfer to the surrounding C atoms, especially to the C1−C3 atoms in CVD diamond coatings, and the tendency to transfer charges to C1 atoms is more pronounced. This indicates that the four doped atoms have a stronger effect on the charges generated by the C atoms in the film. The density of charge transfer from B atom to C1−C3 atom is relatively high, which reflects the strong charge interaction between B atom and C1−C3 atom. The tendency of Al atoms to transfer charges is mainly concentrated in C1 and C2 atoms, and the tendency to transfer charges to C3 atoms is not obvious, indicating that the bonding between Al atoms and C1 and C2 atoms may be stronger. The tendency of Sn atoms to transfer charges to C1 atoms is obvious, but the tendency to transfer charges to C2 and C3 atoms is slightly weaker, indicating that the charge interaction force between Sn atoms and C atoms in the substrate is weak. Co atoms have a weak tendency to transfer charges to C1 and C3 atoms, while their tendency to transfer charges to C2 atoms is not significant, indicating that the charge interaction between Co atoms and the film and substrate is weak. (3) From the perspective of atomic and chemical bond Mulliken population, B, Al, Sn, and Co all lose electrons and carry positive charges, with charge loss numbers of 0.59e, 1.89e, 2.06e, and 1.71e, respectively. Meanwhile, the C1−C3 atoms near the four doping elements all receive negative charges, indicating significant charge transfer between the four doped atoms and C1−C3 atoms. This suggests the existence of four types of bonding interactions between the film-substrate interface interface: C—B, C—Al, C—Sn, and C—Co. The effective utilization rates of the lost charges of B, Al, Sn, and Co atoms by C1~C3 atoms are 98%, 58%, 43%, and 39%, respectively. The Mulliken population of the C—B bond is the largest and the bond length is the smallest, followed by the Mulliken population of the C—Al bond. The Mulliken populations of the C—Sn bond and C—Co bond are relatively small. (4) From the indentation experiment, it can be seen that the indentation of diamond films pretreated with B and Al elements is shallow and the pit area is small, indicating that the film-substrate interface binding strength of IDB-B/Diamond and IDB-Al/Diamond is high. Among them, the indentation pit area of diamond films pretreated with B element is the smallest, indicating that B element is most conducive to enhancing the film-substrate interface binding strength, followed by Al element. The diamond coatings pretreated with Sn and Co elements have deeper indentation and a larger indentation pit area, indicating poor film-substrate interface effect of IDB-Sn/Diamond and IDB-Co/Diamond. Conclusions (1) From the perspective of energy, the binding energy of the film-substrate interface doped with four elements is Wad-B (11.68 J/m2)>Wad-Al (9.94 J/m2)>Wad-Co (7.38 J/m2)>Wad-Sn (6.85 J/m2). Based on the weakening phase of the film-substrate interface binding energy of the Co element, the doping of B and Al elements are conducive to improving the film-substrate interface bonding strength. The film-substrate interface binding energy of Sn element doped is similar to that of Co element, indicating that Sn element doped also weakens the film-substrate interface bonding strength. (2) From the perspective of charge, the charges of B and Al atoms mainly transfer to the C1−C3 atoms near the doping site, with effective charge utilization rates of 98% and 58%, respectively. In addition, the Mulliken populations of C−B and C−Al bonds are relatively high, indicating that the bonding between B and Al atoms and C1−C3 atoms is strong, playing the role of film substrate connection nodes and improving the film substrate interface binding strength. The effective charge utilization rates of Sn and Co atoms are both less than 50%, indicating that a large amount of charge is transferred to other C atoms at the film substrate interface except for C1−C3 atoms, resulting in weak bonding between Sn and Co atoms and C1−C3 atoms. At the same time, other C atoms repel each other due to the charge obtained, weakening the film substrate interface binding strength. (3) From the indentation experiment, it can be seen that the film-substrate interface bonding strength of B element-induced crystal pretreatment is the highest, followed by Al element, while Sn and Co elements are relatively poor. -
当前，地表资源接近枯竭，资源勘探和开采持续向地下深层扩张[1]，孕镶金刚石钻头（impregnated diamond bits， IDB）以其优异的切削性能和对高温高压环境优良的耐受力，成为地下深层钻进的主要工具[2]。
IDB一般是将金属粉料与金刚石颗粒混合均匀后，采用粉末冶金的方法热压烧结而成[3]。Sn和Co是IDB基体中常用的金属黏结剂[2,4]，可增强基体对金刚石颗粒的把持力；在IDB基体配方中添加B元素可以提高金刚石颗粒的抗氧化性和IDB整体的耐磨性[2,5]，加强金刚石颗粒和基体之间的结合力[6]；添加Al 元素可以提高基体强度[2]和致密度[4]，降低基体界面张力和表面张力[7]。
本课题组提出在IDB表面原位沉积一层CVD 金刚石涂层，实现金刚石涂层的同质外延生长和异质外延生长，进一步提高IDB的工作寿命。大量宏观实验研究指出，在金刚石涂层与基底界面间引入B元素[8-9]或者在过渡层中引入Al元素[10-11] ，有利于提高膜基结合力。关于Sn元素对膜基界面性能影响的研究较少。由于Co是IDB中综合性能良好的金属黏结剂，且会削弱膜基结合强度[12]，故本文引入Co元素作为对照。
基于量子力学第一性原理，借助CASTEP计算工具，从微观角度研究IDB基体中常用的X（X = B、Al、Sn、Co）元素对孕镶金刚石基底与CVD金刚石涂层膜基界面结合性能的影响机制，为优化IDB基体配方和提高膜基界面结合强度提供理论参考与依据。
1. 模型建立与计算方法
1.1 几何模型
借助量子力学计算软件Materials Studio，以IDB表层的金刚石颗粒为基底[13]，采用基底表层原子替代的方式[14]，建立含X（X = B、Al、Sn、Co）原子的IDB-X/Diamond膜基界面模型。其中，基底表层原子替代指在建立好孕镶金刚石基底后，分别用B、Al、Sn、Co原子替代基底表层特定位点的C原子。
参考文献[13]的建模方法，首先，分别建立孕镶金刚石基底和CVD金刚石涂层的单晶胞模型；其次，分别进行[100]晶向的切晶胞处理，因为在结构优化过程中膜基界面模型的原子相对位置变化主要集中于最外3层原子，为保证模型的稳定性，经表面能收敛性测试，切取C原子厚度定为5层；接着，建立3 × 3的孕镶金刚石基底和CVD金刚石涂层超晶胞模型，其沿X、Y、Z方向的尺寸均为7.54 Å × 7.54 Å × 3.56 Å，分别添加厚度为12 Å的真空层后得到孕镶金刚石基底模型和CVD金刚石涂层模型；然后，将孕镶金刚石基底模型表面特定位点的C原子用X（X = B、Al、Sn、Co）原子进行替代，替代位点如图1所示；最后，将X（X = B、Al、Sn、Co）原子替代后的IDB-X基底与CVD金刚石涂层模型沿[100]晶面结合，建立IDB-X/Diamond膜基界面模型，测试后，设置膜基界面间距为2 Å，如图2所示。由于所建膜基界面模型中基底与涂层为同种晶胞构建而来，且基底晶面和涂层晶面尺寸相同，故两晶面之间的结合稳定性优异，界面适配度好。
图 2 IDB-X/Diamond膜基界面模型图Figure 2. IDB-X/Diamond membrane-based interface model diagram1.2 计算方法
基于密度泛函理论的CASTEP第一性原理计算方法，广泛应用于研究包括金刚石材料在内的陶瓷、金属、半导体等各种晶体材料及其表界面性质[15]。
本文采用Materials Studio的CASTEP模块优化X（X = B、Al、Sn、Co）原子掺杂的IDB-X/Diamond膜基界面模型，进而从膜基界面结合能、差分电荷密度、原子和化学键重叠布居数方面来分析4种膜基界面模型的性质。选用广义梯度近似下的交换关联泛函GGA-PBE，平面波截断能设置为400 eV，采用超软赝势（ultrasoft pseudopotential），布里渊区k点取样精度为3 × 3 × 1，能量计算收敛判据为1 × 10−5 eV/atom，原子最大受力不超过0.3 eV/nm，原子最大位移不超过1 × 10−4 nm，原子最大应力为0.05 GPa，结构优化算法采用BFGS。结构优化后的IDB-X/Diamond膜基界面模型如图3所示。
图 3 结构优化后的IDB-X/Diamond膜基界面模型Figure 3. Optimized structure of IDB-X/Diamond membrane-based interface model2. 计算结果与分析
2.1 膜基界面结合能
膜基界面结合能可以反映涂层和基底的黏附效果，通常膜基界面结合能越大，膜基的黏附效果越好，其计算公式[16]为：
$$ {{W}}_{\mathrm{a}\mathrm{d}-\mathrm{X}}=\frac{{{E}}_{\mathrm{I}\mathrm{D}\mathrm{B}-\mathrm{X}} + {{E}}_{\mathrm{D}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{d}}-{{E}}_{\mathrm{I}\mathrm{D}\mathrm{B}-\mathrm{X}/\mathrm{D}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{d}}}{{A}} $$ 其中，Wad-X为X（X = B、Al、Sn、Co）原子掺杂的膜基界面结合能，EIDB-X、EDiamond、EIDB-X/Diamond分别为结构优化后的IDB-X基底、CVD金刚石涂层和IDB-X/Diamond膜基界面模型的能量，A为优化后膜基界面的面积。膜基界面结合能计算结果如表1所示。
表 1 IDB-X/Diamond膜基界面结合能Table 1. IDB-X/Diamond membrane-based interface binding energy掺杂元素 X EIDB-X / eV EDiamond / eV EIDB-X/Diamond / eV A / Å Wad-X /（J·m−2） B − 6773.67 − 6913.28 − 13728.42 56.90 11.68 Al − 6738.01 − 13686.58 9.94 Co − 8709.79 − 15649.28 7.38 Sn − 6812.62 − 13750.23 6.85 由表1 可知，B、Al、Co、Sn原子掺杂的膜基界面结合能分别为11.68 、9.94 、7.38 、6.85 J/m2。以膜基界面结合能的削弱相Co[13]为基准，则B、Al原子掺杂的IDB-B和IDB-Al基底与CVD金刚石涂层的膜基界面结合能明显高于Co原子的，说明基底中的B、Al元素对于膜基结合强度的提高是有利的；而Sn原子掺杂的IDB-Sn基底与CVD金刚石涂层的膜基界面结合能与Co原子掺杂的相近，说明基底中的Sn元素同样对膜基结合强度有削弱作用。
2.2 电荷分析
2.2.1 差分电荷密度分析
差分电荷密度能反映膜基界面间电荷转移以及原子间成键情况，从电子云的相互作用入手，进一步揭示膜基界面结合的机理。由于每个膜基界面模型中2个掺杂原子呈对称结构，故取其中一个掺杂原子及其附近的C1~C3原子展开电荷分析，电荷取样点位如图4所示。图5展示了B、Al、Sn、Co原子掺杂的膜基界面模型的差分电荷分布图。
图 5 IDB-X/Diamond膜基界面差分电荷分布图Figure 5. Differential charge distribution at IDB-X/Diamond membrane-based interface由图5可知：B、Al、Sn、Co原子的电荷均有向周围的C原子，尤其是向C1~C3原子转移的倾向，且向C1原子转移电荷的倾向更明显，这表明4种掺杂原子与涂层中的C原子产生的电荷作用更强。从图5a可以明显看出B原子的电荷向C1~C3原子转移，并且转移的电荷密度均较高，这反映了B原子与C1~C3原子的电荷作用均较强，形成了紧密的键合作用，有利于膜基结合强度的提高。图5b中Al原子转移电荷的倾向主要集中于C1和C2原子，向C3原子转移电荷的倾向不明显，表明Al原子与C1和C2原子的键合作用可能更强，能有效黏结涂层和基底。图5c中Sn原子向C1原子转移电荷的倾向明显，但是向C2和C3原子转移电荷的倾向略弱，表明Sn原子与基底C原子的电荷作用力较弱，不利于提高膜基结合强度。图5d中Co原子向C1和C3原子有较弱的电荷转移倾向，向C2原子转移电荷倾向不明显，表明Co原子与涂层和基底的电荷作用均较弱，不能有效黏结涂层和基底。
2.2.2 布居数分析
原子布居数可以反映各原子的得失电子情况，化学键重叠布居数可以反映原子间键合作用的强弱，其越大则原子间成键越稳定[17]。本文按图4所示点位，计算了X（X=B、Al、Sn、Co）掺杂原子与C1~C3原子的原子布居数（见表2）和化学键重叠布居数（见表3）。
表 2 原子布居数Table 2. Mulliken atomic population掺杂元素X 原子种类 原子布居数 失电荷数 φ 有效电荷利用率 λ / % s p d 总电子数 n B C1 1.13 3.08 0.00 4.21 −0.21e 98 B 0.70 1.71 0.00 2.41 0.59e C2 1.16 3.02 0.00 4.18 −0.18e C3 1.16 3.03 0.00 4.19 −0.19e Al C1 1.21 3.22 0.00 4.43 −0.43e 58 Al 0.57 0.54 0.00 1.11 1.89e C2 1.17 3.19 0.00 4.36 −0.36e C3 1.16 3.15 0.00 4.31 −0.31e Sn C1 1.16 3.18 0.00 4.34 −0.34e 43 Sn 0.48 1.46 0.00 1.94 2.06e C2 1.16 3.11 0.00 4.27 −0.27e C3 1.15 3.13 0.00 4.28 −0.28e Co C1 1.23 3.00 0.00 4.23 −0.23e 39 Co 0.10 −0.60 7.79 7.29 1.71e C2 1.19 3.03 0.00 4.22 −0.22e C3 1.16 3.05 0.00 4.21 −0.21e 注：有效电荷利用率 = [−(φC1 + φC2 + φC3) / φX] ×100%，X = B、Al、Sn、Co。 表 3 化学键重叠布居数Table 3. Overlapping population of chemical bonds掺杂元素X 键 重叠布居数 键长 / Å B C1—B 1.07 1.490 C2—B 0.87 1.550 C3—B 0.87 1.540 Al C1—Al 0.60 1.822 C2—Al 0.57 1.858 C3—Al 0.03 1.955 Sn C1—Sn 0.53 1.923 C2—Sn 0.38 1.995 C3—Sn 0.36 1.989 Co C1—Co 0.26 1.882 C2—Co −0.17 1.886 C3—Co 0.24 1.907 由表2可知：B、Al、Sn、Co原子掺杂的膜基界面模型中，B、Al、Sn、Co均失去电子带正电，其失电荷数分别为0.59e、1.89e、2.06e和1.71e，而4种掺杂原子附近的C1~C3原子均得到电子带负电，4种掺杂原子与C1~C3原子之间存在明显的电荷转移，表明膜基界面间存在C—B、C—Al、C—Sn和C—Co 4种键合作用。C1~C3原子对B、Al、Sn、Co原子失去电荷的有效利用率分别为98%、58%、43%和39%，其中C1~C3原子对B原子失去电荷的有效利用率接近100%，表明B原子贡献的电荷几乎都用于和C1~C3原子成键，B原子起到膜基连接节点的作用，有利于膜基结合；C1~C3原子对Al原子失去电荷的有效利用率高于50%，表明Al原子与C1~C3原子成键的同时还与其他C原子成键，导致这一部分C原子因得电子而带同种电荷产生斥力，然而Al原子用于产生引力的电荷数大于产生斥力的电荷数，故Al原子掺杂仍有益于膜基结合；C1~C3原子对Sn、Co原子失去电荷的有效利用率均低于50%，表明Sn、Co原子失去电荷中的大部分电荷被界面间其他C原子俘获，导致膜基界面间C原子产生的斥力较多，既不利于Sn、Co原子与C1~C3成键，又会进一步削弱膜基结合强度。
从表3可以发现，C1与4种掺杂原子之间的化学键重叠布居数均大于C2、C3的，表明基底表层掺杂的B、Al、Sn、Co原子均更倾向于向金刚石涂层移动，与涂层中的C原子成键，这一点也与上文的差分电荷密度分析一致。C—B键的重叠布居数最大且键长最小，说明C—B键的键能更大，成键更稳定，同时C—B键的长度最接近金刚石中C—C键的长度1.54 Å，表明B原子掺杂引起的晶格畸变很小，有利于维持金刚石构型。C—Al键的重叠布居数次之，虽然C3—Al的重叠布居数小，但C1—Al与C2—Al的重叠布居数较大且比较接近，表明Al原子与涂层和基底中的C原子成键较为对称，成键稳定性较高，是连接涂层和基底的有益元素，同时C—Al键的键长较小，键能较大，有利于膜基结合。C—Sn键与C—Co键的重叠布居数均较小，就Sn元素而言，虽然C1—Sn的重叠布居数略大，但是C2—Sn与C3—Sn的重叠布居数均较小，表明Sn原子与基底的连接较弱，不利于膜基结合；对于Co元素来说，C—Co键的重叠布居数均较小，且C2—Co成反键，最能削弱膜基结合强度。
3. 压痕实验及结果
压痕实验可以直接表现涂层化合物的界面结合性能[18]，裂纹越多，压痕凹坑越深，凹坑面积越大，则认为膜基结合强度越差。本文采用B、Al、Sn、Co元素引晶预处理的方式[19]将4种元素掺入膜基界面，进而使用微波等离子体化学气相沉积（MPCVD）设备在孕镶金刚石颗粒硬质合金基底上沉积金刚石涂层，采用相同的实验参数：CH4流量4 sccm，H2流量200 sccm，CO2流量6 sccm，Ar流量15 sccm，压强7 kPa，温度800 ℃，沉积时间9 h。然后使用HR-150A洛氏硬度仪，采用天然金刚石压头，施加588 N的试验压力进行压痕实验，进而使用VHX-2000超景深显微镜拍摄压痕形貌来对比分析4种掺杂元素对膜基结合强度的影响。图6展示了4种压痕形貌。
从图6a、图6b可以发现，B、Al元素引晶预处理的金刚石涂层压痕较浅，凹坑面积较小，表明IDB-B/Diamond和IDB-Al/Diamond的膜基结合强度高，其中B元素引晶预处理的金刚石涂层压痕凹坑面积最小，表明B元素最利于增强膜基结合强度，Al元素次之。图6c、图6d中Sn、Co元素引晶预处理的金刚石涂层压痕较深且压痕凹坑面积较大，图6d中凹坑面积最大，表明IDB-Sn/Diamond和IDB-Co/Diamond的膜基结合效果较差，膜基界面间引入Sn、Co元素会削弱膜基结合强度。
4. 结论
基于第一性原理探究了IDB基体中的常用元素X（X = B、Al、Sn、Co）对IDB-X/Diamond膜基界面结合性能的影响，计算了膜基界面结合能、差分电荷密度和布居数，揭示了能量和电荷的变化情况，并采用MPCVD设备沉积金刚石涂层开展压痕实验，得到以下结论：
（1）从能量方面来看，4种元素掺杂的膜基界面结合能大小为Wad-B（11.68 J/m2）>Wad-Al（9.94 J/m2）>Wad-Co（7.38 J/m2）>Wad-Sn（6.85 J/m2）。以膜基界面结合能的削弱相Co元素为基准，则B、Al元素掺杂有利于提高膜基结合强度，Sn元素掺杂的膜基界面结合能与Co元素相近，表明Sn元素掺杂同样会削弱膜基结合强度。
（2）从电荷方面来看，B、Al原子的电荷主要转移到掺杂位点附近的C1~C3原子，其有效电荷利用率分别为98%和58%，C—B、C—Al键的重叠布居数均较高，表明B、Al原子与C1~C3原子的成键较强，起到了膜基连接节点的作用，能提高膜基结合强度；Sn、Co原子的有效电荷利用率均﹤50%，表明大量电荷转移到膜基界面间除C1~C3原子之外的其他C原子，导致Sn、Co原子与C1~C3原子的成键较弱，同时其他C原子由于得电荷而相斥，削弱膜基结合强度。
（3）从压痕实验来看，B元素引晶预处理的金刚石涂层与孕镶金刚石基底的结合强度最高，Al元素次之，Sn、Co元素较差。
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图 2 IDB-X/Diamond膜基界面模型图
Figure 2. IDB-X/Diamond membrane-based interface model diagram
图 3 结构优化后的IDB-X/Diamond膜基界面模型
Figure 3. Optimized structure of IDB-X/Diamond membrane-based interface model
图 5 IDB-X/Diamond膜基界面差分电荷分布图
Figure 5. Differential charge distribution at IDB-X/Diamond membrane-based interface
表 1 IDB-X/Diamond膜基界面结合能
Table 1. IDB-X/Diamond membrane-based interface binding energy
掺杂元素 X EIDB-X / eV EDiamond / eV EIDB-X/Diamond / eV A / Å Wad-X /（J·m−2） B − 6773.67 − 6913.28 − 13728.42 56.90 11.68 Al − 6738.01 − 13686.58 9.94 Co − 8709.79 − 15649.28 7.38 Sn − 6812.62 − 13750.23 6.85 
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表 2 原子布居数
Table 2. Mulliken atomic population
掺杂元素X 原子种类 原子布居数 失电荷数 φ 有效电荷利用率 λ / % s p d 总电子数 n B C1 1.13 3.08 0.00 4.21 −0.21e 98 B 0.70 1.71 0.00 2.41 0.59e C2 1.16 3.02 0.00 4.18 −0.18e C3 1.16 3.03 0.00 4.19 −0.19e Al C1 1.21 3.22 0.00 4.43 −0.43e 58 Al 0.57 0.54 0.00 1.11 1.89e C2 1.17 3.19 0.00 4.36 −0.36e C3 1.16 3.15 0.00 4.31 −0.31e Sn C1 1.16 3.18 0.00 4.34 −0.34e 43 Sn 0.48 1.46 0.00 1.94 2.06e C2 1.16 3.11 0.00 4.27 −0.27e C3 1.15 3.13 0.00 4.28 −0.28e Co C1 1.23 3.00 0.00 4.23 −0.23e 39 Co 0.10 −0.60 7.79 7.29 1.71e C2 1.19 3.03 0.00 4.22 −0.22e C3 1.16 3.05 0.00 4.21 −0.21e 注：有效电荷利用率 = [−(φC1 + φC2 + φC3) / φX] ×100%，X = B、Al、Sn、Co。
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表 3 化学键重叠布居数
Table 3. Overlapping population of chemical bonds
掺杂元素X 键 重叠布居数 键长 / Å B C1—B 1.07 1.490 C2—B 0.87 1.550 C3—B 0.87 1.540 Al C1—Al 0.60 1.822 C2—Al 0.57 1.858 C3—Al 0.03 1.955 Sn C1—Sn 0.53 1.923 C2—Sn 0.38 1.995 C3—Sn 0.36 1.989 Co C1—Co 0.26 1.882 C2—Co −0.17 1.886 C3—Co 0.24 1.907
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