Potential energy per unit cell

We now require that the lattice be in equilibrium under the action of central forces. Let be the potential energy per unit cell. depends on the geometry of the unit cell which is defined by the components a. of the primitive lattice vectors a. . The equilibrium condition at T = 0 is (see also Sect.4.1)... 

Fig.4.1. The solid line shows the Leonard-Jones potential according to (4.2). The dashed line illustrates the static potential energy per unit cell, of the fee lattice according to (4.10)...

We illustrate the procedure by considering the one-dimensional conductor (SN) which consists of parallel zig-zag chains SNSN [4.57] (Fig.4.19). In order to simplify, we consider only the in-plane vibrations of a single chain. According to (4.133), we make the following Ansatz for the potential energy per unit cell ... 

---