Briefly describe how the Tight-Binding Model may be used to model the electronic structure of graphene close to the Fermi energy. Draw an E-k diagram of the band dispersion at the K point of the Brillouin zone, indicate the band filling, and mark the position of the Dirac point. Indicate the position of the Fermi energy for the three cases of perfect undoped graphene, n-type doping and p-type doping. 15:30(1) Draw diagrams to show how a single-crystal sample of graphite must be orientated with respect to the incident and scattered beams in order to make each of these measurements. [2 marks] (i) The wavelength of the X-rays is 1.54 A, and peaks are found at scattering angles of 42.4 and 26.6 in first order. Calculate the nearest-neighbour distance 1n the sheet, and the distance between the sheets. [4 marks] (111) State the effects that give rise to the binding in the sheets, and to the binding between the sheets in graphite. [2 marks] d) Briefly describe how the Tight-Binding Model may be used to model the electronic structure of graphene close to the Fermi energy. Draw an F-k diagram of the band dispersion at the K-point of the Brillouin zone, indicate the band filling, and mark the position of the Dirac point. Indicate the position of the Fermi energy for the three cases of perfect undoped graphene, n-type doping and p-type doping. [7 marks]