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LATTICE VIBRATION IV - Coggle Diagram
LATTICE VIBRATION IV
Real crystal system
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the atoms vibrate in three dimensions with two vibration modes and three vibrational branches, one longitudinal and two transverse
1D case
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eq of motion 
solution
3D case
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first, the monatomic Bravais lattice, in which each unit cell has a single atom
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when substitute, we obtain three simultaneous equations
The roots of this equation lead to three different dispersion relations, or three dispersion curves
The Number Of Branches
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three branches are acoustic, and the remaining (3z − 3) are optical
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Phonons
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phonon momentum
A phonon of wavevector k will interact with particles such as photons, neutrons and electrons as if it had a momentum ħk
However, phonon does not carry physical momentum
The reason is that the center of mass of the crystal does not change it position under vibrations (except k=0).
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