Grüneisen parameters
The Grüneisen parameter or (after Eduard Grüneisen ) describes the dependence of the frequency of lattice vibrations ( phonons ) in a crystal on the relative change in volume , which in turn depends on the temperature . It is used to describe anharmonic effects in crystals that are neither electrically conductive nor magnetic , and is used in the Mie-Grüneisen equation of state .
description
In a simple model one assumes that all interactions in a crystal are harmonious . However, this does not adequately describe real solids , as these e.g. B. show a volume expansion with increasing temperature , which is not taken into account by such a harmonic model. Therefore, terms of higher order are introduced into the interaction potential in the solid and new effects are obtained.
Thus, the relative change δω / ω of the oscillation frequency of a phonon with a certain impulse and in a certain phonon branch depends linearly on the relative volume expansion δ V / V :
The dimensionless Grüneisen parameter is defined as:
Typical values for are between 1 and 2 at room temperature (see here ), i.e. H. the volume and the phonon frequencies change roughly equally.
Strictly speaking, a separate green iron parameter must be defined for each mode ; in particular, transverse and longitudinal modes can differ. However, in the Debye or Einstein model, all frequencies scale with the Debye frequency or with the Einstein frequency . Accordingly, there is only one green iron constant for all modes:
With
- as an isothermal compression module
- as specific heat capacity at constant volume
- the linear thermal expansion coefficient .
This is synonymous with the fact that specific heat and coefficient of expansion have a similar temperature dependence. That is why the definition of a constant Grüneisen parameter makes sense.
A thermodynamic representation of the Grüneisen parameter describes the change of the pressure p with the internal energy U at a constant volume V :
This means that the Grüneisen parameter can be measured directly. One can increase the internal energy in one area of the crystal at constant volume if one z. B. irradiates with a laser pulse . A pressure wave is generated, which is then detected on the crystal surface.
swell
- Siegfried Hunklinger : Solid State Physics . 2nd Edition. Oldenbourg Wissenschaftsverlag, Munich 2009, ISBN 978-3-486-59045-6 .