Linear chain

Representation of a linear chain with two different types of atoms (green and red).
The second and third rows show two different modes of oscillation :
in the second row the two types of atoms vibrate in antiphase, in the third row in phase.

The linear chain is a simple dynamic model of a crystal lattice in solid state physics .

In this model, a crystal is modeled as an infinitely long, one-dimensional chain of mass points that represent the atoms or molecules of the crystal lattice. If one chooses only one kind of atom or molecule, one speaks of the AA chain or A chain , one chooses alternately from two different kinds of atom or molecule, one speaks of an AB chain .

The ground points are connected to their nearest neighbors via springs . The model is linear because the restoring force of the springs is assumed to be a linear function of their elongation or compression ( Hooke's law , spring constant ).

In the rest position the distance between all atoms is identical and they can only vibrate longitudinally . At temperatures above absolute zero , the atoms in the chain can vibrate in certain modes on which their speed of sound depends. The model thus describes simple lattice vibrations .

When considering the linear chain theoretically, it turns out that the vibration energy does not depend continuously on the temperature, but only discrete vibration energies are possible. In analogy to the quantization of the energy of the electric field in a cavity , the smallest energy quanta of which are called photons , the excitable lattice vibrations in a crystal lattice are called phonons . ${\displaystyle E_{n}=n\cdot \hbar \cdot \omega }$

Dispersion relation of the AB chain,
d. H. Angular frequency as a function of the wave number . The unit cell of the crystal lattice has the length and contains an A and a B atom; is the distance between two neighboring atoms . ${\displaystyle \omega }$ ${\displaystyle k}$
${\displaystyle a}$ ${\displaystyle a/2}$

literature

• Wolfgang Demtröder : Experimental Physics 3 . Atoms, molecules, solids. 3. Edition. Springer, 2005, ISBN 3-540-21473-9 , pp. 407 ff .

Individual evidence

1. ↑ Lexicon of Physics. linear chain. Spectrum, accessed March 2, 2014 . 
2. ↑ Lexicon of Physics. AA chain. Spectrum, accessed March 2, 2014 . 
3. ↑ Lexicon of Physics. A chain. Spectrum, accessed March 2, 2014 . 
4. ↑ Lexicon of Physics. AB chain. Spectrum, accessed March 2, 2014 .