**Acknowledgements**

where *σthermal* is the thermal stress (Pa), *α* is the coefficient of thermal expansion (CTE) (1/k), *E*

For the case where the thermal stress is lower than the yield/fracture stress, then the material will sustain the shock. Therefore, thermal shock could be connected and evaluated via other material's mechanical properties such as Young's modulus, Poisson's ratio, and fracture stress and other thermal properties based on the thermoelastic approach as being expressed in Eq. (7)

(1 <sup>−</sup> <sup>ν</sup>)<sup>κ</sup> \_\_\_\_\_\_\_

Poisson's ratio, and *κ* is the total thermal conductivity (W/m∙k). The higher the *R'* value, the

*Thermal fatigue* is the material's capability to adhere to multiple cycles of heating and cooling. As the material is capable to withstand higher number of cycles, it is said that it has a higher thermal fatigue resistance. The only way to measure this property is currently to subject such

As of the current time, according to our knowledge, there are no references in the study concerning these properties with the actual measured values, and the few that mention them do

Mechanical properties of materials represent the material's responses to different loading conditions and are macroscopic representations of the atomic bonding between the atoms from which they are constructed. It was suggested that the cohesive energy (*E*C) between two particles can be linked to the elastic constants of the materials and other various physical properties (such as melting temperature, atomic volume, lattice constants, and Debye temperature). Such a correlation opens the possibility of interlinking the material's electronic

Measuring or evaluating correctly the mechanical properties of TE materials has the potential to bridge between the atomic (mechanical) and physical (electronic/transport) understanding of these materials to the fully developed working modules that will be optimal from both ends standpoint. That way, the material selection for the proper use will be much easier and efficient. As it was shown in this review, knowing and controlling the mechanical properties of TE materials are paramount necessities for approaching practical TEGs and moving the entire TE technology onward in the Technological Readiness Level (TRL) scale. The material's elastic constants (e.g., Young's modulus and Poisson's ratio), strength, and fracture toughness are the most crucial for the designing practical devices (using finite element analysis). In such an approach, adequate modeling of TEGs could be prepared with lower experimental intervals while saving both money, time, materials, and man power. The elastic constants can provide

a material to thermal cycles and to evaluate its consistency every few cycles.

transport properties with the mechanical ones on the atomic level.

αE (7)

is the material's fracture stress (Pa), *ν* is

is Young's modulus (Pa), and *ΔT* is the temperature difference on the material (k).

<sup>R</sup>′ <sup>=</sup> <sup>σ</sup><sup>f</sup>

so only in a theoretical fashion as stated earlier.

greater the resistance.

76 Bringing Thermoelectricity into Reality

**3. Summary**

where *R'* is the thermal shock resistance (W/m), *σ<sup>f</sup>*

The authors would like to thank the Ministry of National Infrastructures, Energy and Water Resources for granting this project, grant no. 215-11-022.
