Brillouin zones of graphite

The unit cell of a graphite crystal is analyzed by using the basic principle of the harmonic oscillator. For this purpose, we consider the atoms that conform the hexagonal unit cell, connected by small springs. The equation of motion of such cell is established in order to obtain the vibration natural frequency of the system (w) in terms of the wave vector (k) and the interatomic distance. With these data the Brillouin zones are generated and the seat points in the energy contours, which are a characteristic of a periodic system, are determined. By means of a simple model, the Brillouin zones and the patterns of the energy contours have been reproduced for a graphite sheet, without losing generalities or crystal properties. This analysis was carried out in a simple way with high grade of efficiency in comparison with other more elaborated theories.