Question

Q1: Prove that the maximum and minimum frequencies of the acoustic and optical branches of a 10 diatomic lattice are as shown in figure 3.23, page 98. Q2: Derive equation 3.63 from equation 3.59.

fig

Answer 1

Ans 1 - In case of ID diatomic lattice ! let us consider two masses m, and! M . In equilibrium state all the atoms will be (2n-2), (2n-1), 2n62n+1)(20+2) 1 - 2n-2 2n-1 an 2n+ 2n+2 nu w mom momwww tum 29 Uzn-3 U₂n-2 U2n-1 Un Uanti Uanta Uan+3 29 et M let Un be displacement of atom at 24th. site during Vibrating motion of atoms En = m duzn U2n = = cru ( Unt, & uent 2 Uzn) dt? So we have given egn. (3.61 is Iltalt 112_4sin lqa). M, M₂ i optical bronch : - dispersion relation's wted to the team 4 schlsel For lower frequency :- 0 0 M ,

Lat 2 = 0 , W = 0 / 1 / +) At higher Erogesny 1-704= highes, sm?l2a) wrzeln + + all 2a at Sin (29) = 1 sin ga = sint 7 q=1 frequency becomes w22 _ Acautical Branch: – Dispersion relation is JM

at lower frequency 700.7 $70, Sipl-20).se Sinqqa) / At higher frequency 170 & higher We = a/l + 1) = a Jih, n. - A ... 2 ) Thus these are the given frequencies in fig. 3.23. Any 2 :- In this fig. we have not - given the o equation (3-59).