Coupling of Optic and Acoustic Modes of Vibration in Crystals

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. 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 KarmanGBPxj 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)