| The carbon nanotubes have rapidly attracted a lot of attention in the domain of material science because of their unique physical, chemical and structure properties, as well as their signification potential on a broad range of applications. Hence, carbon nanotubes have become one of representative and typical nanomaterials. However, when carbon nanotubes have been doped, substituted and decorated, the presence of defects and impurities can give rise to nanotube functionalization and enhance range of applications. Having roughly the same atomic radius as C, nitrogen atom is a natural choice of the dopant and can be easily incorporated into the carbon network through many different techniques. In our work, we study N-doped carbon nanotubes through first principle calculations, and effects of doping nitrogen atoms on the structure and electronic properties are discussed.The fist part in our wok is about the formation energy of N-doped zigzag (n, 0) single-walled carbon nanotube through first principle calculations. The geometry of zigzag (n, 0) carbon nanotubes only depend on the chiral index n, and the number of the hexagon which forms the unit of zigzag is also just n. Hence, their many properties are related with index n. For example, according to their electronic structures, they have been divided into categories of metals (n=3k, k is integer) and semiconductors (n≠3k, k is integer). It is reported by A.V. Krasheninikov and B.C. Pan that the curves of the formation energy vs. diameter for these tubes are of sawtooth-like shapes due to adsorption and interstice atoms, and such periodicity is characterized by the lower formation energies of defected tubes with n being a multiple of 3 as compared to their neighboring tubes. However, these defects are considered only at single site and the reasons why the sawtooth-like shapes appear have not been clarified in detail. In this work, we have investigated whether the formation energy curves of zigzag carbon nanotubes with B/N substitutional impurities atoms are of the same shape as those with interstice and adsorption, and try to answer above question.The (n, 0) tubes with n = 8~19 were chosen. Because the capability of computation was limited and the number of atoms was so large in the supercell, three tube units and aΓsampling point in the Brillouin zone were adopted. The configurations of tubes doped with one substitutional nitrogen/boron atom and three substitutional nitrogen atoms are considered. For the configuration containing three substitutional nitrogen atoms, we choose two kinds of configurations for investigation. One is that nitrogen atoms distribute uniformly so that no two nitrogen atoms are adjacent, while another is opposite to the first configuration, and the nitrogen atoms come together. It is founded that their formation energy curves all exhibit a sawtooth-like feature of periodicity, which is the similar to results for (n, 0) tubes with adsorption and interstice. The periodicity is characterized by the lower formation energies of defected tubes with n being a multiple of 3 as compared to their neighboring tubes, and such variation of sawtooth-like feature are gradually weak with increasing tube diameters. Therefore, it indicates that this sawtooth-like periodicity is not significantly influenced by the number of defects and their distributions.In order to study its microscopic mechanism, we have calculated the average cohesive energies per atom of the perfect (n, 0) tubes. It is founded that the cohesive energy curve also exhibits a periodic feature, and such periodicity is characterized by small protuberances at n = 9, 12, 15, 18 in cohesive energy curve as compared to their neighboring tubes. That is to say that the slopes at n = 9, 12, 15, 18 in cohesive energy curve of (n, 0) tube vary abruptly compared to those at other n values. For (n, 0) tube, the values of the cohesive energies can be classified into two types. One is from (n, 0) tubes with n being a multiple of 3, and another from those with the other n values. Consequently, this periodic feature results from the bonding structures of perfect (n, 0) tubes with different diameters, rather than the defects (substitutional impurity atom N) in the tubes. For (n, 0) tube, when n is a multiple of 3,πelectrons are more delocalized as compared to other tubes. For (n, 0) tube,πelectrons are all gradually delocalized with increasing tube diameters, and theπbonding structures are gradually approach to those of graphene. Through introducing the impurity states by the defects, their bonding structure is destroyed at the sites of the defects and reconstructed. Hence, for the N-doped (n, 0) tubes, the protuberances is relatively weak at n=3k (k is integer) in cohesive energy curve. Consequently, the formation energy, the difference between the cohesive energy for perfect zigzag tubes and that for defect zigzag tubes, should exhibit the same periodic features as theπbonding structures of perfect zigzag tubes. The formation energy curve of zigzag tubes only enlarges this periodic feature.The second part in our wok is about electronic structures of N-doped semiconducting zigzag (n, 0) single-walled carbon nanotube through first principle calculations. It is well known that there is an impurity level near the bottom of the conduction band when nitrogen atoms are incorporated into semiconducting nanotubes. Because nitrogen possesses one electron more than carbon, the excess electron will form local electronic states near the nitrogen impurity. That is to say, when the excess electrons are excited from the bound state of nitrogen to the conduction band, they need much less energy than the case when the electrons are excited from the valence band to conduction band. Hence, nitrogen atom supplying excess electrons is called a donor, and the impurity level near the nitrogen atom is named by donor level, whose energy lie between the band-gap and near the bottom of conduction band. Consequently, the nanotubes are transformed from intrinsic semiconductors to N-type semiconductors. However, when semiconducting tubes are doped with more nitrogen atoms, especially, if nitrogen atoms occupy the sites in the same hexagon for nanotubes, their excess electrons would interact, which will lead to some special characteristics in their electronic structures compared with the tubes doped one nitrogen atom. In this work, we will theoretically investigate the formation energies and the electronic structures for nanotubes doped two nitrogen atoms.We chose the (10, 0) tube as a typical semiconducting tube for investigation and suggest that two nitrogen atoms per five tube units are doped. According to distance between two doped nitrogen atoms, there are two kinds of cases. One case is that two nitrogen atoms are far part, and do not lie in the same hexagon, while the other case is that two nitrogen atoms are near and lie in the same hexagon. For the latter case, there are three types of cases according to distance between two nitrogen atoms. One is opposition configuration, in which nitrogen impurity atoms are the third nearest. Second is interval configuration, in which nitrogen impurity atoms are the second nearest. The other is neighbor configuration, in which nitrogen impurity atoms are adjacent. These three cases each have two configurations. Thus, there are six configurations when two doped nitrogen atoms lie in the same hexagon. The formation energies indicate that neighbor configuration is most unstable and opposition configuration is most energetically favorable among three cases. Furthermore, one of opposition configuration, in which two nitrogen atoms are symmetric along the tube axis, is most likely appear among all configurations. Therefore, the stable configurations for carbon nanotubes doped two nitrogen atoms are sensitive to the symmetry. However, the configuration doped with two nitrogen atoms not in the same hexagon and far apart from each other, the formation energy is two times as configuration doped with one nitrogen atom because the interaction between two nitrogen atoms can be neglected.Afterwards, we have analyzed the electronic structures of semiconducting nanotubes doped with two nitrogen atoms. The electronic density of states indicates that they all have striking impurity states. When two nitrogen atoms are far apart from each other, there are two impurity levels half-occupied at the Fermi level. In contrast, when two nitrogen atoms lie in the same hexagon, the impurity levels spilt up to two levels. One is full-occupied, and another is empty. Especially, for two configurations of them, the occupied impurity states are far apart from the bottom of the conduction band and the empty impurity states are shift up into conduction band, which leads that the conductance for the tubes are reduced. These two configurations are one of neighbor configuration, in which two nitrogen atoms adjacent along circumference, and one of opposition configuration, in which two nitrogen atoms are symmetric along the tube axis, respectively. Through the highest occupied level (highest occupied molecular orbital, HOMO), it is found that the densities of excess electrons in these two configurations are denser than other configurations around the N atoms and the neighboring C atoms. It means that impurity states are more tightly bound near the impurity nitrogen atoms. That is to say, when the excess electrons are excited from the impurity level to the conduction band, they need much more energy than other cases.Through the study of semiconducting nanotubes doped two substitutional nitrogen atoms, it is exhibited that the electronic structures for the semiconducting nanotubes can be tuned through changing the nitrogen doping configurations. The last part in our wok is about geometry structures of N-doped carbon nanotubes through first principle calculations. There are many processes to synthesize the carbon nanotubes doped nitrogen atoms, in which the diverse bonding structures of N atoms have been found, such as molecular N2, triple-bonded, graphite-like structure, and pyridine-like structure. They always exhibit irregular and interlinked corrugated morphologies. In fact, the seamless cylindrical graphitic structure of carbon nanotube yields a high Young's modulus which has been revealed theoretically and experimentally. Hence, this mechanical property also plays an important role in the distribution of nitrogen atoms in N-containing carbon nanotubes, which cannot be neglected. Therefore, in order to clearly understand this important role, in this work, we will study the geometry structures and the formation energies for N-doped carbon nanotubes with different chiralities and diameters Typically, we construct four N-doped carbon nanotubes, (5, 5), (7, 4), (8, 2) and (9, 0) tubes containing two substitutional nitrogen atoms, whose diameters are comparable to one another. According to the bond direction, the bonds should be classified into three types for N-doped carbon nanotubes. It is obvious that, for (5, 5) and (9, 0) tubes, the bonds could be classified into two types due to their high symmetry. The formation energies indicate that substitutional nitrogen atoms tend to be far from each other, while they prefer to be adjacent to each other along the circumference when the N-N bonds have smaller angle between N-N bond axis and tube longitude. The theoretical and experimental results show that carbon nanotubes have extraordinary mechanical properties with high radial modulus. When the N-N bonds have smaller angle between N-N bond axis and tube longitude, they will bear the more radial stress. Since single N-N bonding is weaker than single C-C bonding, when the nearest single C-C bond is replaced by N-N, the strong radial stress will make N-N bond broken. The broken N-N bond significantly releases the radial stress, leading to the final structural stability.The diameter of tube is also an important parameter to determine how two adjacent substitutional nitrogen atoms distribute in N-doped carbon nanotubes. Here, we construct some armchair (n, n) (n=5~8) carbon nanotubes doped two adjacent nitrogen atoms along the circumference. After geometry optimization, it can be seen that the N-N bond distance increase with decreasing tube diameters. When the tube diameter is very small,the chemical bonding between the nitrogen atoms will not be maintained as the radial stress increases with decreasing tube diameter, that is to say, for the thin carbon nanotubes, the N-N bond along the circumference will be broken due to the strong radial stress, and total energy of configuration will descend.Next, we have studied the distribution of impurity nitrogen atoms in N-doped carbon nanotubes when more nitrogen atoms are introduced into carbon nanotubes. Here, for comparison, we select three thin tubes (5, 5), (9, 0) and (10, 0), and three thick tubes (8, 8), (12, 0) and (13, 0). For the zigzag carbon nanotubes, (9, 0) and (12, 0) tubes are metallic, while (10, 0) and (13, 0) tubes are semiconducting. Three kinds of configurations containing six substitutional nitrogen atoms are investigated. First isomer is the case that the substitutional nitrogen atoms distribute uniformly. Second isomer corresponds to the case that there is two pyridine-like structures, which are far apart from each other. Because the bond along the circumference is also the most sensitive to the radial stress in the carbon nanotubes, the third isomer corresponds to the case that six substitutional nitrogen atoms align in two rows parallel to the tube axis. The formation energies indicate that, for thin armchair and semiconducting zigzag nanotubes, nitrogen atoms prefer to be localized, leading to that the broken N-N bond appears and the interstice is formed. Hence, thin N-doped nanotubes are easily subject to opening of the tubular sheets due to the strong radial stress. However, for thick armchair and thin metal zigzag nanotubes, the nitrogen atoms tend to be distributed uniformly. The reason is that the Young's modulus decrease with increasing tube diameter and approached the modulus of a graphene sheet in the limiting case. In addition, for the zigzag tubes, the Young's moduli of metallic carbon tubes are smaller than other semiconducting carbon nanotubes. It is worth noted that the pyridine-like structure will be also popular in the N-doped carbon nanotubes when the carbon nanotubes are synthesized under the existence of a nitrogen source. As the overall N content increase, the number of graphitic walls within the carbon nanotubes decreases and the proportion of pyridine-like N (two-bonded N) also increases. These pyridine-like N"cavities"or"edges"within the predominantly graphitic framework should be responsible for the interlinked morphologies observed in the N-doped carbon nanotubes... |
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