Debye temperature

The Debye temperature (after Peter Debye ) is a material -dependent parameter in solid-state physics . It is a measure of the size of the phonon frequencies occurring in a material. It describes the temperature at which all possible states are currently occupied. ${\displaystyle \Theta _{\mathrm {D} }}$

Typical Debye temperatures

material	Debye temperature in K ${\displaystyle \Theta _{\mathrm {D} }}$
diamond	1860
Si	645
Cr	610
Fe	470
Mon	450
Al	428
Ge	374
Cu	345
Ag	215
Au	165
N / A	160
Pb	95
Ar	92
Se	90
Rb	56

According to the Debye model , only states with the lowest frequencies occur in a crystalline solid body made up of oscillators . The largest occurring frequency is the Debye cutoff frequency . This in turn defines the Debye temperature : ${\displaystyle N}$ ${\displaystyle 3N}$ ${\displaystyle \omega _{\mathrm {D} }}$

${\displaystyle \Theta _{\mathrm {D} }={\frac {\hbar \cdot \omega _{\mathrm {D} }}{k_{\mathrm {B} }}}={\frac {\hbar \cdot v_{\mathrm {D} }}{k_{\mathrm {B} }}}\cdot {\sqrt[{3}]{\frac {6\cdot \pi ^{2}\cdot N}{V}}}}$.

Designate

• ${\displaystyle \hbar }$the Planck constant divided by ${\displaystyle 2\pi }$
• ${\displaystyle k_{\mathrm {B} }}$the Boltzmann constant
• ${\displaystyle v_{\mathrm {D} }}$the speed of sound and
• ${\displaystyle V}$the volume of the crystal.

The Debye temperature defines the specific heat for all temperatures within the framework of the Debye model . ${\displaystyle c_{\mathrm {V} }}$

literature

• Charles Kittel: Introduction to Solid State Physics . Oldenbourg Wissenschaftsverlag, 2005, ISBN 3-486-57723-9 , p. 133 ff . ( limited preview in Google Book search).