# Debye Temperature

## Debye temperature

[də′bī ′tem·prə·chər]*k*θ =

*h*ν, where

*k*is the Boltzmann constant,

*h*is Planck's constant, and ν is the Debye frequency. Also known as characteristic temperature.

## Debye Temperature

a physical constant of matter that characterizes numerous properties of solids, such as specific heat, electric conductivity, thermal conductivity, broadening

Table 1 | |||||
---|---|---|---|---|---|

Metal | θ_{p} | Semiconducto | θ_{D} | Dielectric | θ_{o} |

Hg............... | 60–90............... | Sn (gray)............... | 212 | AgBr | 150 |

Pb............... | 94.5............... | Ge............... | 366 | NaCI | 320 |

Na............... | 160............... | Si............... | 658 | Diamond | 1,850 |

Ag............... | 225............... | ||||

W............... | 270............... | ||||

Cu............... | 339............... | ||||

Fe............... | 467............... | ||||

Be............... | 1,160............... |

of X-ray spectral lines, and elastic properties. The concept was first introduced by P. Debye in his theory of specific heat. The Debye temperature is defined by the equation

*θ _{D}* =

*h v*

_{D}/kwhere *k* is Boltzmann’s constant, *h* is Planck’s constant, and v_{D} is the maximum frequency of the vibrations of a solid’s atoms. The Debye temperature indicates the approximate temperature limit below which quantum effects may be observed. At temperatures T ≫ θ_{D} the specific heat of a crystal consisting of atoms of one type at constant volume is C_{r} = 6 cal (^{°}C. mole)^{-1}, which agrees with Dulong and Petit’s law. At T ≪ θ_{D} the specific heat is proportional to (Γ/θ_{p},)^{3} (the Debye T^{3} approximation).

Typical values of the Debye temperature for some substances are given in degrees Kelvin in Table 1.