# Lattice vibration

Lattice vibration of the wavelength ${\ displaystyle \ lambda}$

The vibrations of the particles that are propagated in crystals are referred to as lattice oscillations , although they are actually waves with respective wave numbers ("lattice" stands for the crystal lattice ). The individual atoms in crystals cannot move independently of one another. The total energy  E can therefore be described as the sum of the energies of sound waves of a certain frequency that permeate the crystal.

Certain thermal properties of solids can be described by assigning properties of particles ( quanta ) to the lattice vibrations . In this case, the lattice vibrations are also called phonons . The basic quantum mechanical equation applies to them :

${\ displaystyle E = h \ cdot \ nu}$

With

On the basis of the phonon concept, Debye was able to explain the temperature dependence of the specific heat capacity of solid bodies ( Debye model ). The electrical resistance in metals and semiconductors is also largely determined by the exchange of energy and momentum between electrons and phonons.

In addition, the phonons proved to be useful for the theory of heat conduction in solids. Thermal conductivity can sometimes be understood as the ability of the vibration to propagate. With higher heat contents, i. H. at higher energies, more lattice vibrations are excited, whereby the energy is quantized : ${\ displaystyle \ epsilon _ {n}}$

${\ displaystyle \ epsilon _ {n} = {h \ cdot \ nu _ {n} \ cdot (n + 1/2)} \ quad {\ text {with}} \; n = 0,1,2 \ dots }$

With

• n is the occupation number of the phonons in the particular modes .${\ displaystyle \ nu _ {n}}$

Part of the energy content of solids is found in the thermal movement of atoms or molecules . As the temperature rises, the mean amplitude of these oscillating movements increases.

## literature

• Neil W. Ashcroft, N. David Mermin: Solid State Physics . 2nd Edition. Oldenbourg, Munich 2005, ISBN 3-486-57720-4 .
• Charles Kittel: Introduction to Solid State Physics . 10th edition. Oldenbourg, Munich 1993, ISBN 3-486-22716-5 .