PHZ6426: Fall 2012 Midterm

PHZ6426: Fall 2012
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 .