In linear diatomic lattice, there are two modes of vibration : The optical mode and the Acoustic mode .
Let the anion has mass m and amplitude of oscillation A and the cation has mass M and amplitude of oscillation B.
Then ,
For optical mode :
The ratio of amplitude comes out to be
( negative sign is indicating that they will oscillate in opposite
direction of each other )
or,
This can be shown as
For acoustic mode :
The ratio of amplitude comes out to be
or,
Hence, the amplitude for both the atom will remain same and they both will oscillate in same direction .
From the above results motion of the atoms can be shown as :
For optical mode :
NOTE : In this diagram amplitude of vibration is not considered. For amplitude please refer to the diagram mentioned earlier.
For any doubt please comment and please give an up vote. Thank you.
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