derive Eq. (54) given in page 446 (410 in 8th Ed), through the following procedure. Consider an one-dimensional ionic di

[answerhappygod]

derive Eq. (54) given in page 446 (410 in 8th Ed), through the
following procedure. Consider an one-dimensional ionic diatomic
crystal, in which the two types of atoms in the unit cell have
masses M₁, M₂ and the effective charges +q,-q. (Hint: See Fig. 9 in
Ch. 4.)

Derive Eq 54 Given In Page 446 410 In 8th Ed Through The Following Procedure Consider An One Dimensional Ionic Di 1 (410.35 KiB) Viewed 47 times

procedure 1) In general, the magnitude of q is different from
the formal charge. For example, in NaCl, q' is 0.74e instead of e.
Explain the reason.
procedure 2) Write the equations of motion for each atom,
when an alternating electric field is applied to the crystal.
(Hint: like Eq. (18) in upper picture)
procedure 3) Use a plane wave for the electric field and
displacements and the fact that in the long wavelength limit all
similar atoms have the same displacement. Find the following
equation.

Derive Eq 54 Given In Page 446 410 In 8th Ed Through The Following Procedure Consider An One Dimensional Ionic Di 2 (17.68 KiB) Viewed 47 times

where M: the effective mass and wt: transverse frequency at the
long wavelength limit.
procedure 4) Using the definition of the ionic polarization
P = Nq', find the Eq. (54).
-w²P + w/P = (Nq²/M)E Ug-1 Us-1 fig9 yo M₁ d'us dt² d²v, dt² M₂ = = Bu, Pus C(vs+vs-1-2us) 28 C(us+1+us-2v) ; M₁ (54) 3U₁+1 M₂ K 31 (18) 407 (polarization mode) o 22/2/28 소리길래
- w?u = -w?uo + q'E M