PHZ6426: Fall 2012 Midterm October 23, 2012 P1 (a) Construct one of the possible unit cells for a simple hexagonal lattice (Fig. 1) and specify the basis vectors. (b) Find the volume of the unit cell. (c) Find the basis vectors of the reciprocal lattice. Sketch the reciprocal lattice. FIG. 1: Simple hexagonal lattice. P2 (a) Find the contribution to the specific heat from an optical phonon mode, described by the Einstein model: ωq = const ≡ ω0 for q ≤ qD , where qD is the Debye wavenumber. (b) Comment on the similarities and differences between the contributions to the specific heat from optical and acoustic phonon modes in two different temperature regimes: kB T ~ω0 and kB T ~ω0 .