Coupling of Optic and Acoustic Modes of Vibration in Crystals #249098

In the present case of a diatomic lattice9 the secular equation is a 2 x 2 determinant9 having two solutions (qqeps) for each of the EN values of k lying in the first Brillouin zone; these two solutions correspond to s a opt09 acousto The problem of solving (6) to give the functional form of w(§9s) and of the frs= quency spectrum of the lattice vibrations was first discussed by Born and von Karman£xj§ for any specific case it generally leads to very lengthy calculationso Here we shall use the simplest possible approximaticn9 of the debyeceinsteinfl form (cfo Figo l)