*2.2. Electron Thermal Conductivity*

The first process that influences the electron thermal conductivity is the electronphonon scatter. The process is described by the thermal resistance *W*e−<sup>p</sup> [10]:

$$\mathcal{W}\_{\text{e}-\text{P}}(\theta) = \frac{\rho\_{\text{el}|\text{F}\text{g}}(\theta)}{L(\theta) \cdot \theta}. \tag{10}$$

The ideal electric resistivity is the electric resistivity of pure iron *ρ*elFe(*ϑ*) in this application. The value can be calculated utilizing the following [8,13]:

$$\rho\_{\rm elFe}(\theta) = (-2.4 + 3.65 \times 10^{-2}/\text{K} \cdot \theta + 64 \times 10^{-9}/\text{K}^3 \cdot \theta^3) \text{μ}\Omega \,\text{cm.} \tag{11}$$

Please note that there seems to be a typo in the original source in [13] because the values do not match the measurement data presented in the publication. This typo is corrected in [8]. The values of [8] are used in this study and presented in Equation (11). The Lorenz number *<sup>L</sup>*<sup>0</sup> = 2.443 × <sup>10</sup>−<sup>8</sup> <sup>W</sup>Ω/K2 is modified by a temperature-dependent therm [10] in Equation (10):

$$L(\theta) = L\_0 \cdot \left(1 - e^{-\theta/159.3 \text{ K}}\right). \tag{12}$$

The second considered electron scattering process is the electron–impurity scatter that is represented by *W*e−i:

$$\mathcal{W}\_{\text{e}-\text{i}}(\theta) = \frac{\rho\_{\text{el}\_0}(\theta)}{L\_0 \cdot \theta},\tag{13}$$

with the residual electrical resistivity *ρ*el0(*ϑ*) = *ρ*el(*ϑ*) − *ρ*elFe(*ϑ*) as a difference between the electric resistivity of the alloy *ρ*el(*ϑ*) and the electric resistivity of pure iron *ρ*elFe(*ϑ*). The electric resistivity of an alloy can be calculated utilizing Matthiessen's rule as follows:

$$\rho\_{\rm el}(\theta) = \rho\_{\rm el\_{\rm Fe}}(\theta) + \sum\_{i} \rho\_{\rm elj} \varepsilon\_{\rm a,i} \tag{14}$$

The calculated values utilizing this formula deviate from measurement results as discussed in [10], due to the independency of the electric resistivity *ρ*eli from the temperature. The authors [10] propose an improved formulation:

$$
\rho\_{\rm el}(\theta) = \rho\_{\rm el\_{\rm Fe}}(\theta) + \sum\_{i} \rho\_{\rm elj}(\theta) c\_{\rm a,i} \tag{15}
$$

The estimation of the necessity of utilizing the improved equation in comparison to the Matthiessen's rule is not possible for this application. The error estimation in [10] is based on values of the electric resistivity of the alloy at 4 K and based on Cr and Ni alloys. While Equation (14) is preferred, due to the simple availability of the electric resistivity of the alloy components *ρ*eli , Equation (15) seems to give more accurate results. Within this study, the electric resistivity of the alloys is measured over the temperature range and compared to the simplified equation. The final value of the electron thermal conductivity *k*e(*ϑ*) can be calculated with:

$$k\_{\rm c}(\vartheta) = \left(\frac{\rho\_{\rm el\,Fe}(\vartheta)}{L(\vartheta)\cdot\vartheta} + \frac{\rho\_{\rm el\,l\_0}(\vartheta)}{L\_0\cdot\vartheta}\right)^{-1}.\tag{16}$$
