5.2.1 Specific Heat Capacity

The specific heat capacity $\ensuremath{c_{\mathrm{L}}}$ enters the heat flux equation as a time independent model parameter and is defined as the energy per mass needed to increase the temperature of a specimen by one Kelvin. It is modeled by [209]

$$\ensuremath{c_{\mathrm{L}}}(\ensuremath{T_{\mathrm{L}}}) = \ensur... ...{K}}\right)}^{\ensuremath{\alpha_{c}}}+ c_1/\ensuremath{c_{\mathrm{L,300}}}}\,,$$ (5.13)

where $\ensuremath{c_{\mathrm{L,300}}}$ is the specific heat capacity at $\ensuremath{T_{\mathrm{L}}}= 300\,\ensuremath{\mathrm{K}}$ . Fig. 5.2 shows the temperature dependence of the specific heat capacities for PbTe and SnTe, respectively. Measurement data have been obtained from [210,174,211,121,212] for lead telluride and from [213,214] for tin telluride, where the latter is a review of several collected papers. For the ternary alloys Pb$_{1-x}$ Sn$_x$ Te, the resulting specific heat capacity is expressed as a linear interpolation between the values for the according pure materials

$$\ensuremath{c_{\mathrm{L}}}^{\ensuremath{\mathrm{AB}}} = (1-x) \e... ...math{\mathrm{A}}} + x \ensuremath{c_{\mathrm{L}}}^{\ensuremath{\mathrm{B}}} \,,$$ (5.14)

where A stands for lead telluride, B for tin telluride and $x$ denotes the according atomistic content.

Table 5.5: Parameters for the specific heat capacity models for PbTe and SnTe.

	PbTe	SnTe
$\ensuremath{c_{\mathrm{L,300}}}$	$156\,\mathrm{J/kg K}$	$197.3\,\mathrm{J/kg K}$
$c_1$	$9.5\,\mathrm{J/kg K}$	$115\,\mathrm{J/kg K}$
${\ensuremath{\alpha_{c}}}$	1.15	0.63

Figure 5.2: Temperature dependence of the specific heat capacity of lead telluride and tin telluride including measurement data and model parameter sets.

M. Wagner: Simulation of Thermoelectric Devices