Chapter 13: Oscillation Frequency

Oscillation Frequency

Frequency =

and wave vector Assume time harmonic solution.

Then

 

A&B constants

Substituting

 

 

 

2 equations 2 unknowns,

or

For nontrivial A & B

                                                               

                                                              

Dispersion relation between

Solving for

 

 

where,

 

Two values of for any wave number q.

 

 

 

 

 

Fig.5.5

 

Solving for constants.

When The ratio of amplitude

 

 

for lower branch.

 

Vibrations of neighboring atoms are in phase Similar to those when an acoustic wave propagation in the crystal, optical mode lower frequency.

 

3-D crystal: 2 distinct modes of transverse vibration also along with optical or acoustic longitudinal mode