Download Carbon Nanotubes: Basic Concepts and Physical Properties by Stephanie Reich, Christian Thomsen, Janina Maultzsch PDF

By Stephanie Reich, Christian Thomsen, Janina Maultzsch

Possibly, yet i am not yes this is often it. It comes VERY shut although. My grievance (which prevents me from deciding to buy my very own reproduction) is that some distance too many very important suggestions are pointed out in passing with the reader despatched to the literature for the main points. For $130, a section extra completeness will be great. I discover "serious" staff within the box will name me lazy for in need of a $130 publication to be as self-contained as attainable. So be it...

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Example text

SAAis found in exactly the same way as H M . It is also constant, and we set it equal to one. In other words, we assume the wave runctions V A to be normali~ed( ( ~ /(i r- RA)1 qA( r - R A ) )= I. The matrix element between A and B atoms is given by the formal expression The second sum runs over all three nearest neighbors of a given alom A. The vcctors R I i = R B -~RA ~ (i = I , 2 , 3 ) pointing from A to one of its neighbors Bli can be found from Fig. 2 We insert Eq. 13) into Eq. 12) and sum over the B neighbors and A atoms.

The degenerate eigenmode is obtained from a given eigenvector by a 90" rotation of the displacement pattern around the tube. If C4 is not a symmetry operation of the nanotube the displacement vectors must be extended to the new atomic positions. The resulting eigenvector has its nodes where the atoms are fully displaced in Fig. 14 and vice versa. The pair of projection operators P2(2)and P2(1)project nntcl another degenerate E2g mode, namely, an in-phase displacenlent of the two graphene sublattices.

However, the energies Eiin Eq. 8) depend only on products of the matrix and ovcrlap elcments with a complcx conjugate of thcsc clcments. For example, from Eq. 8) we obtain for E2 Similar cosinc terms appear in all other E, and, also, for the expressions for more distant neighbors. al + 2 c o s k . a 2 + 2 c o s k . ( a l -a2) and f(k) = 3 + u ( k ) . 17) The wave vectors k of graphene are commonly given in units of the reciprocal lattice vectors kl and k2 or in a Cartesian coordinate system in reciprocal space.

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