Interface scattering

Interface scattering limits the thermal conductivity of non-metallic crystalline solids at very low temperatures.

In an insulating crystal , the conduction of heat takes place through phonons , which is indicated by the equation

${\displaystyle \kappa ={\frac {1}{3}}cv\ell }$

is described. Here the thermal conductivity denotes the volume-related specific heat capacity , the speed of sound and the mean free path of the phonons. In general, it is limited by different scattering processes . At very low temperatures, however, the mean free path is determined solely by the scattering at the crystal interfaces; H. . This clearly means that the phonons run from one end of the crystal to the other without being scattered. Other scattering processes such as flip-over scattering or defect scattering can be neglected at sufficiently low temperatures. ${\displaystyle \kappa }$ ${\displaystyle c}$ ${\displaystyle v}$ ${\displaystyle \ell }$ ${\displaystyle \ell }$ ${\displaystyle \ell =L}$

In combination with the Debye model for the specific heat, the thermal conductivity can be achieved at very low temperatures

${\displaystyle \kappa ={\frac {2}{15}}\pi ^{2}k_{B}\left({\frac {k_{B}T}{\hbar }}\right)^{3}{\frac {L}{v^{2}}}}$

to be discribed. This results in a -dependence of the thermal conductivity, which also corresponds to the experimental observation. The absolute value of in this case is only determined by the speed of sound and the crystal dimension. ${\displaystyle T^{3}}$ ${\displaystyle \kappa }$ ${\displaystyle v}$ ${\displaystyle L}$

literature

• R. Bermann: Thermal conduction in solids. Clarendon Press, Oxford 1976, ISBN 0-19-851429-8 .