There are couple of issues I want to address with the very last diagram at 22:27 , 1) He consider the situation k→0. I believe that means larger wavelength for the mode of lattice vibrations according to the phonon dispersion curve. So the Blue and red waves in the picture should show small curvature; meaning a wavelength like 5000Å (not a wavelength like 2 times lattice constant or 2a). Then it can match the wavelength of incident light ~ 5000Å. 2)at k=0, Both heavy and light atoms are moving opposite directions and at k=π/a, the heavy atom is not moving at all and the light atom shows harmonic oscillation alone. I see larger displacement for Heavy atom in this diagram. But it should have smaller amplitude (in the Optical mode) than the lighter atom at any k from 0 to π/a 3) I see both atoms are moving downward from the atomic array (not the opposite direction.). One can assume equilibrium position or atomic line is at the middle to fix this. Please correct me if I am wrong. Thank You
There are couple of issues I want to address with the very last diagram at 22:27 ,
1) He consider the situation k→0. I believe that means larger wavelength for the mode of lattice vibrations according to the phonon dispersion curve. So the Blue and red waves in the picture should show small curvature; meaning a wavelength like 5000Å (not a wavelength like 2 times lattice constant or 2a). Then it can match the wavelength of incident light ~ 5000Å.
2)at k=0, Both heavy and light atoms are moving opposite directions and at k=π/a, the heavy atom is not moving at all and the light atom shows harmonic oscillation alone. I see larger displacement for Heavy atom in this diagram. But it should have smaller amplitude (in the Optical mode) than the lighter atom at any k from 0 to π/a
3) I see both atoms are moving downward from the atomic array (not the opposite direction.). One can assume equilibrium position or atomic line is at the middle to fix this.
Please correct me if I am wrong. Thank You