polymer compositeband theory-2

1 a 1 , x a 2 , y Γ X M X a 2 *, k y a 1 *, k x k x = 0 , k y = 0 Γ k x = 0 . 5 a 1 * , k y = 0 X k x = 0 , k y = 0 . 5 a 2 * X k x = 0 . 5 a 1 * , k y = 0 . 5 a 2 * M k x = 0 . 2 5 a 1 * , k y = 0 k x = 0 , k y = 0 . 2 5 a 2 * k x = 0 . 2 5 a 1 * , k y = 0 . 2 5 a 2 * Two-dimensional lattice 2 ∑ =Ψ sr srsr yxcyx , ,, ),(),( χ Crystal orbitals ( ) aiskairkc yxsr += exp , 3 ( ) 2/1 22 /2/2 yx kkk +== ππλ k = (k x ,k y ) the wave vector of electron showing the direction and length of the wave For square array with N atoms in each direction (k x ,k y ) = (2π/Na) (p,q), p, q are integers -π/a = k x , k y < + π/a E(k) = α + 2β{cos(k x a + cos(k y a)} Two-dimensional lattice 4 5 6 7 Graphite 8 9 10 (a) Molecular orbitals of C 60 . (b) Band structure of K 3 C 60 . (c) Corresponding density-of –states curves.