NanoStruct_PS1

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SoSe 2015

Room BER/105/H,4thWed 22.04.2015 (Set

TU Dresden, Chair Materials Science and Nanotechnology

Assignments toNanostructured Materials / Nanostrukturierte Materialien

Prof. Dr. G. Cuniberti, Dr. D. Ryndyk (HAL 106)Dr. V. Bezugly (HAL 119), Dipl.-Phys. T. Lehmann

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Problem set: Crystal structures

1,1. Crystal structure

The following picture represents a two-dimensional lattice with two difFerent types ofatoms.

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(a) Explain the following keywords. lf possible, mark them in the picture. Whichone is obvious? r^tlirc

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- basis atoms and basis vecto.s

- crystal structure

Which Bravais lattice suits with the illustrated crystal structure? Explain yourdecision.

Draw a simple cubic lattice and indicate the lattice planes corresponding to thefollowing Miller indices:

(001)(110)

- (020)

- (323)

1,2, Atomic structute of graphene

A graphene sheet is a honeycomb lattice of carbon atoms (see Figure below). Letthe distance between carbon atoms be oe = 0.141 nm.

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A good model for graphene is to consider a single plane in which there is one valenceelectron per carbon atom. The unit cell spanned by al and a, contains tlvo carbonatoms convent;onally labelled as A and B atom. There are several possibilities tochoose a unit cell, the dotted lines indicate one in real space which has the shape ofa rhombus, as shown in the Figure.

(a) Determine the three Cartesian components ofthe lattice vectors al and a2 interms of the C-C bond len6h oa 6.

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