Elastic waves in carbon 2D supracrystals

Young’s modulus and the Poisson’s ratio of planar and nanotubular supracrystalline structures

“…(4) into Eqs. (2) and (3) gives the expressions for the two dimensional Young's modulus and the Poisson's ratio as follows: (6) Two dimensional (C) 44 type supracrystals belong to the 4mm class of symmetry and differ in elastic anisot ropy [12]. Their arrangement with respect to the crys tallographic axes is shown in Fig.…”

“…Like graphene, two dimensional supracrystals of the 6mm class exhibit an elastic anisotropy [12]. For them, substituting s 11 and s 12 from Eq.…”

“…For the (C) 44 structure, the left val ues correspond to the 〈11〉 direction, and the right val ues correspond to the 〈10〉 direction. The values of the elastic rigidities c 11 , c 12 , and c 13 are taken from [12]. We call attention that both the Young's modulus and elas tic rigidities of a two dimensional structure have the dimension of a force divided by a length.…”

“…For the graphene like two dimensional supracrystalline sheets of various classes of symmetry ( Fig. 1), the components of the tensors of two dimen sional elastic rigidities were calculated in [11,12] through the constants of central and noncentral inter atomic interaction. These constants were calculated Abstract-A method has been proposed for calculating the two dimensional Young's modulus and the Pois son's ratio for planar and nanotubular structures through the components of the two dimensional elastic rigidity tensor obtained by numerical methods.…”

“…Supracrystalline structures under study as com pared with graphene. The notation corresponds to that used in [12]. using a modified Davydov's method [13]; and, then, the components of the elastic rigidity tensor were found using the scheme proposed by Davydov [14] on the basis of the Keating model [15].…”