5.2 Lattice Vibrations
117
(a)
(b)
(c)
(d)
Fig. 5.26 a Eigenvalues of a diatomic chain with N = 32 unit cells (64 atoms) as a function of the ratio C 2 /C 1
(M 1 = M 2 ). The frequency is normalized (to ω max from (5.18)). The abzissa is logarithmic. b Same calculation as for
panel (a) but M 1 /M 2 = 1.5 (would look the same for M 2 /M 1 = 1.5). c Same calculation as for panel (a) but as a
function of M 2 /M 1 (for C 2 /C 1 = 2). d Same calculation as for panel (c) but for C 2 /C 1 = 0.5
(a)
(b)
Fig. 5.27 Mode patterns for two states of the diatomic linear chain (N = 32 unit cells, M 1 = M 2 ) a within the gap for
C 2 /C 1 = 1/2 and b closest to the gap for C 2 /C 1 = 2. The amplitudes of A-sites (B-sites) are shown in red (blue)