Grüneisen parameter

The green iron parameters γ ( green by Edward iron) describes the dependence of the frequency of lattice vibrations ( phonons) in a crystal of the relative change in volume, which in turn depends on the temperature. He serves as description of anharmonic effects in crystals, which are neither electrically conductive nor magnetic.

Description

In a simple model, it is assumed that all the interactions are harmoniously in a crystal. This describes real solid insufficient as these, for example, a volume expansion as the temperature rises to show, which is not considered by such a harmonic model. That's why higher-order terms is introduced into the interaction potential in the solid state and receives new effects.

Thus, the relative frequency of oscillation change δω / ω a phonon pulse, and in a certain particular phonon now depends linearly on the relative volume expansion? V / V from:

Here, the dimensionless Grüneisen parameter γ is defined as:

Typical values ​​are at room temperature 1 to 2 this means that the volume and the phonon frequencies change about equally strong.

Strictly speaking, necessary to make a Grüneisen parameters are defined for each mode. In particular, transverse and longitudinal modes may be different. However, in the Debye and Einstein model scale all frequencies with the so-called Debye and Einstein frequency, and accordingly there is only a Grüneisen constant for all modes.

With the bulk modulus, than the specific heat capacity at constant volume and the linear expansion coefficient α. This is equivalent to the fact that specific heat and coefficient of expansion having a similar temperature dependence. Therefore, the definition of a constant Grüneisen parameter is useful.

A thermodynamic derivation of the Grüneisen parameter

Describes the change of the pressure p with the internal energy U at constant volume V. Thus, the Grüneisen parameter is directly measurable. Can be increased at a constant volume, the internal energy within a range of the crystal, for example, when irradiated with a laser pulse. In this case, a pressure wave is generated, which is then detected at the crystal surface.

Swell

  • Siegfried Hunklinger: solid state physics. 2 edition. Oldenbourg Verlag, Munich 2009, ISBN 978-3-486-59045-6.
  • Solid State Physics
Einstein solid Debye model
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