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Illustration Monatomic Longitudinal Lattice Vibration (1d)

Single-Atom Longitudinal Lattice Vibration (1d)
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A two-dimensional crystal lattice consists of one-dimensional chains (lattice planes) on which atoms are located at the same distance from each other. In the undeflected state (faded chains), the chains have the distance \( a \) from each other. This distance is called the lattice constant.

For example, if the chain \( n \) is deflected by the amount \( u_n \), then it has an effect on all the other chains - they experience a force and are then deflected as well. For example, the chain \(n+1\) is deflected by \( u_{n+1}\).

Wird nun die Kette losgelassen, bildet sich eine longitudinale Schwingung im Kristallgitter aus.