Tham khảo tài liệu 'carbon nanotubes episode 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Dresselhaus et al. armchair the origin to the first lattice point B in the honeycomb lattice. It is convenient to express T in terms of the integers 2 given in Table 1 where it is seen that the length of T is j3L dR and dR is either equal to the highest common divisor of n ni denoted by d or to 3d depending on whether n m 3dr r being an integer or not see Table 1 . The number of carbon atoms per unit cell nc of the ID tubule is 2N as given in Table 1 each hexagon or unit cell of the honeycomb lattice containing two carbon atoms. Figure 3 shows the number of distinct caps that can be formed theoretically from pentagons and hexagons such that each cap fits continuously on to the cylinders of the tubule specified by a given n m pair. Figure 3 shows that the hemispheres of C60 are the smallest caps satisfying these requirements so that the diameter of the smallest carbon nanotube is expected to be 7 A in good agreement with experiment 5 . Figure 3 also shows that the number of possible caps increases rapidly with increasing tubule diameter. Corresponding to selected and representative n m pairs we list in Table 2 values for various parameters enumerated in Table 1 including the tubule diameter d the highest common divisors d and dR the length L of the chiral vector ch in units of a where a is the length of the 2D lattice vector the length of the ID translation vector T of the tubule in units of a and the number of carbon hexagons per ID tubule unit cell N. Also given in Table 2 are various symmetry parameters discussed in section 3. 3. SYMMETRY OF CARBON NANOTUBES In discussing the symmetry of the carbon nanotubes it is assumed that the tubule length is much larger than its diameter so that the tubule caps can be neglected when discussing the physical properties of the nanotubes. The symmetry groups for carbon nanotubes can be either symmorphic such as armchair n n and zigzag the axis of the tubule and with a variety of hemispherical caps. A representative chiral
