1. Graphene MATERIALS SCIENCE &ENGINEERING Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh AN INTRODUCTORY E-BOOK Part of http://home.iitk.ac.in/~anandh/E-book.htm A Learner’s Guide

2.  Carbon is perhaps the most fascinating element in nature  The principal forms of carbon are:  Graphite  Diamond  Fullerene, nanotubes and related structures Graphene  A single sheet of graphite is called graphene  It is sp 2 hybridized  covalently bonded  The bonding between the graphene sheets in graphite is of van der Walls type  In this set of slides we consider crystallographic concepts related to graphene  It is a hexagonal array of Carbon atoms, which is NOT a lattice

3. Part of the hexagonal array of C atoms which forms the Graphene structure Not all carbon positions form a lattice

4. As atoms A & B do not have identical surrounding both cannot be lattice points

5. Crystal = Lattice + Motif Grey atoms sit on the lattice positions Motif = 1 grey + 1 green (in positions as shown) Structure of single graphene sheet  Either the green or the grey carbon atoms can be considered to be located at lattice points (but not both)  In plane motif consists of two C atoms  The unit cell is as marked