Direct Energy, 2018a

186 8.6 Thermoelectric Eects
conductivity is given by
κ = C v | −→ v |l (8.35)
The symbol C v represents the specic heat at constant volume in
g·K J , and
the symbol | −→ v | represents the magnitude of the transport velocity in m s .
The scattering length is represented by l in m.
Regardless of whether electrons, phonons, or something else transports
heat through a material, the ability of that heat to get from one end to
the other without being scattered or blocked inuences the thermal conductivity.
Thus, crystals typically have higher thermal conductivity than
amorphous materials [113]. The thermal conductivity of a crystal can be
lowered by exposing the material to radiation which destroys the crystallinity
and increases the likelihood that the heat carrier will be scattered
[110]. For glasses, scattering length is roughly the interatomic spacing [112].
Also, thermal conductivity of glasses is less temperature dependent than
crystals because high temperatures distort the perfect crystallinity, thereby
lowering the thermal conductivity for crystals but not glasses [113].
All the contributing factors, C v , −→ |v |, and scattering length l, are temperature
dependent, so the thermal conductivity is a function of temperature.
The temperature dependence of the factors is discussed in reference [110].
Thermal conductivity, like electrical conductivity, is low at low temperatures
then rises to a maximum before decreasing again at higher temperatures
[112].
8.6.4 Figure of Merit
The gure of merit of a thermoelectric device, Z, is a single measure that
summarizes how good a material is for making thermoelectric devices. It
is dened as
Z = $2 σ
κ , (8.36)
and it has units K −1 . It depends on the Seebeck coecient $, electrical
conductivity σ, and thermal conductivity κ. A large value of Z indicates
that the material is a good choice for use in construction of a thermoelectric
device.
The gure of merit depends on temperature because the parameters
$, σ,and κ are strong functions of temperature. Thus, the best choice material
for a thermoelectric device operating near room temperature may not
be the best choice for a device operating at other temperatures. Sometimes
ZT is used as a measure instead of just Z to account for the temperature
dependence.