5.1.1 Lattice Constant, Thermal Expansion, and Mass Density

Lattice constants for both PbTe and SnTe crystallized in the rock salt structure at $300\,\ensuremath{\mathrm{K}}$ are collected in Table 5.1. Their temperature dependence is expressed by the thermal expansion coefficient, which is rather large compared to other semiconductors. For lead telluride, values of $1.98\times10^{-5}\,\ensuremath{\mathrm{K}}^{-1}$ [192] and $2.04\times10^{-5}\,\ensuremath{\mathrm{K}}^{-1}$ [193] were reported, while the values are significantly smaller at very low temperatures [192]. A good approximation for the thermal expansion coefficient for PbTe and SnTe above $250\,\ensuremath{\mathrm{K}}$ is $2\times10^{-5}\,\ensuremath{\mathrm{K}}^{-1}$ [191].

Table 5.1: Lattice constants for PbTe and SnTe in the rock-salt crystal structure at 300K.

PbTe		SnTe
$a\,[\ensuremath{\mathrm{\AA}}]$	Ref.	$a\,[\ensuremath{\mathrm{\AA}}]$	Ref.
6.462	[194]	6.327	[188]
6.443	[190]	6.303	[190]

Reported mass densities for PbTe and SnTe at room temperature are collected in Table 5.2.

The mass density for alloys can be interpolated linearly between the ones of the constituents

$$\rho^{\ensuremath{\mathrm{AB}}} = (1-x) \rho^{\ensuremath{\mathrm{A}}} + x \rho^{\ensuremath{\mathrm{B}}}$$ (5.1)

with $1-x$ and $x$ as the PbTe and SnTe content, respectively.

Table 5.2: Mass densities for PbTe and SnTe at 300K.

PbTe		SnTe
$\rho\,[\ensuremath{\mathrm{kg m^{-3}}}]$	Ref.	$\rho\,[\ensuremath{\mathrm{kg m^{-3}}}]$	Ref.
8160	[188]	6410	[195]
8219	[196]	6383	[196]
8241	[193]	6454	[197]

M. Wagner: Simulation of Thermoelectric Devices