Bending Coordinates Application to the Linear Chain

Consider the monoatomic linear chain illustrated in Fig.4.30. The potential 

For q TT/a, one obtains o)(q) q This starting result indicates that such a system is dispersive even at infinite wavelength  

In three-dimensional crystals, this result is important for layer compounds such as graphite the transverse out-of-plane vibrations with q parallel to the layers can be adequately described by bending coordinates 

Transverse modes of the linear chain described by bending coordinates a 

---