Debye Temperature

Debye temperature

[də′bī ′tem·prə·chər]
(solid-state physics)
The temperature θ arising in the computation of the Debye specific heat, defined by 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
MetalθpSemiconductoθDDielectricθo
Hg...............60–90...............Sn (gray)...............212AgBr150
Pb...............94.5...............Ge...............366NaCI320
Na...............160...............Si...............658Diamond1,850
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

θD = h vD/k

where k is Boltzmann’s constant, h is Planck’s constant, and vD 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 ≫ θD the specific heat of a crystal consisting of atoms of one type at constant volume is Cr = 6 cal (°C. mole)-1, which agrees with Dulong and Petit’s law. At T ≪ θD the specific heat is proportional to (Γ/θp,)3 (the Debye T3 approximation).

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

References in periodicals archive ?
The factors which determine superconducting behaviour in alkali halides are electron-phonon mass enhancement factor [lambda], electron-electron interaction parameter [[mu].sup.*], Debye temperature Od, s, p [right arrow] d electron transfer and the d electron delocalization.
Figure 6 shows that in the present ACDM this temperature is the Debye temperature ([[theta].sub.D] = 334 K for Cu and 376 K for Ni) while such temperature for ACEM is the Einstein temperature [9] because from this temperature the ratio reaches the classical value of 1/2 [9, 10, 14] and classical limit is applicable.
However, the coefficient of thermal expansion [beta](T) slightly depends on the temperature above the Debye temperature, and this is the reason of nonlinearity of the deformation.
Where [[theta].sub.D] is the Debye temperature of the solid, T is the absolute temperature, and R is the universal gas constant (8.31434 J/mol*K).
Furthermore, when the simulated temperature is lower than the Debye temperature, the BTE will be invalid for the exchange between classical statistics and quantum statistics, and the results should be revised by quantum corrections.
Concerning the successive development of this novel analytical apparatus for Debye temperatures, we would still like to note that some partial results in form of asymptotic (approximate) Debye temperature expressions had already been published in two preceding papers, namely, in [13] for the low-temperature region (T < [[THETA].sub.D](T)/12),
As a result, Debye temperature would increase due to localization of heat energy in the Brillouin zone, and the calculated specific heat capacities showed almost no changes after cation exchange.
Moreover, a material's electronic structure and elastic modulus can be used to estimate its Debye temperature (0D), which is commonly employed to identify the high- and low-temperature areas of a solid.
If instead the S(r) on the ordinate axis we assume the heat for various substances temperatures T (which values are debugged on the abscissa), than instead [L.sub.0] we should indicate the Debye temperature [[theta].sub.D].
In this context, we remark that the new characteristic temperature [[THETA].sub.B] almost coincide with the Debye temperature [[THETA].sub.D].