利用密度泛函理论研究锯齿型单、双壁碳纳米管从核到管状团簇直至纳米管的逐层结构衍生.研究结果表明五边形结构在管状团簇生长中发挥关键作用.此外,基于管状团簇的研究,运用周期性边界条件得到锯齿型单、双壁碳纳米管,并通过计算能带和态密度研究其电子特性.对单壁(n,0)和双壁(n,0)@(2n,0)碳纳米管,当n=3q(q为整数)时,具有金属或窄带隙半导体特性;n=3q时,具有较宽带隙半导体特性,且带隙随管径的增加而减小.然而,小管径碳纳米管受曲率效应的明显影响,n?=3q的(4,0),(4,0)@(8,0)和(5,0)@(10,0)均呈现金属性;n=3q的(6,0)@(12,0)则表现出明显的半导体特性.%It is well known that carbon nanotubes (CNTs) have received much attention since they were discovered. With the rapid development of carbon-based electronics and quantum computers, CNTs are required to have their unique physical and chemical properties in many fields. However, due to their uncertain mechanism of growth, it is difficult to achieve high production of CNTs with certain controlled structures. In this paper, we construct the nuclei of specific single-and double-walled zigzag CNTs and study their structural derivatives and electronic properties by using the density functional theory. According to the study of carbon clusters, we find some stable cage-like clusters containing zigzag structure which can be used as the nucleus of the corresponding single-walled CNTs. The nucleus of the double-walled CNTs is composed of the corresponding nucleus of single-walled CNTs.It is possible to obtain a tubular cluster by optimizing the structure of the nucleus with accumulating carbon atoms at one end. The results show that the pentagonal structure plays a key role in the growing of tubular clusters. We find that the tubular clusters are grown in the form of global reconstruction when the clusters are short, but grown by local reconstruction when the clusters are longer. It can provide a theoretical reference to realize numerous CNTs with certain structures. Furthermore, the average binding energy (Eb) of tubular clusters is studied, and we find that their Eb is more and more stable and then close to the corresponding CNTs. At the same time, the study of the thermodynamic quantities of tubular clusters shows that their structures are thermodynamically stable.In addition, the infinite zigzag CNTs can be obtained by using the periodic boundary conditions. Furthermore, the energy bands and density of states are calculated to study their electronic properties. The results show that the energy band structures of zigzag CNTs are closely related to the chiral index n. For zigzag CNTs (n, 0) and (n, 0)@(2n, 0), they show a metal property or narrow band gap semiconductor when n = 3q (q is an integer); when n = 3q, they show a wide band gap semiconductor, and the band gap decreases with the diameter increasing. It is interesting that the two metallic single-walled CNTs (SWCNTs) are nested to obtain metallic double-walled (CNTs) DWCNTs, while the two semiconducting SWCNTs are nested to obtain semiconducting DWCNTs. However, due to the obvious curvature effect, small-diameter CNTs (4, 0), (4, 0)@(8, 0) and (5, 0)@(10, 0) show the metal properties but CNT (6, 0)@(12, 0) shows the obvious semiconductor property.
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