**1. Introduction**

The demand for clean and reliable energy-harvesting technologies over the past few decades has led researchers to focus much on thermoelectric power generation (TEG) techniques. The thermoelectric effects (namely Peltier and Seebeck effects) exhibit the ability of a material

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

subjected to temperature gradient, to mobilize charge carriers within its volume. The right connection of two such materials can be used for building a TEG module which is reliable, quiet (due to no moving parts), and most importantly scalable. Such TEG modules had been used for the past 40 or so years as reliable power generators in top-edge technology systems at remote terrestrial and extra-terrestrial locations in NASA's systems. Furthermore, one can take advantage of the thermoelectric (TE) effects and tailor other types of modules for different applications, in a wide range of operating temperatures, such as cooling systems in cars (enhancing the coefficient of performance, COP, of the entire cooling system and car performance), harvesting residual heat from solar systems and photo-voltaic conversion cells, and harvesting residual heat from heat exchangers and converting it to useful electricity at industry, power supply modules for onsite sensor systems, and even wearable devices (if incorporated in organic films).

of the material including Young's modulus to other physical properties and therefore interlinking the material transport and electric properties with the mechanical ones on the atomic

Mechanical Properties of Thermoelectric Materials for Practical Applications

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The above long list of different suggested applications for TEGs is to show the wide range of service conditions that these generators will need to withstand. Such applications may vary from static operating conditions with a low number of thermal cycles and low operating temperatures, via higher temperature amplitudes and frequencies and up to dynamic applications with a high number of cycles, high thermal amplitudes, and occasional mechanical impacts. Furthermore, the TEG service conditions necessarily subject the materials to wide temperature ranges and gradients within the materials themselves, so any mechanical characterization of TE materials should also concern the temperature dependence of the property. One such work was conducted measuring Young's modulus temperature dependence of LAST (Pb-Sb-Ag-Te) [4] between room temperature and 823 K and found an inverse relation

In order to advance the development of thermoelectric modules for approaching practical applications, the design of future modules must take into account the mechanical properties of the involved materials for assuring adherence to the service conditions. Such design approaches based on finite element analysis, carried out for different applications, were reported [5–8]. Such analyses are essential while designing a specific TE device and give the ability to play with different parameters without the need of physical construction—saving money, time, man power, and materials in the process. Any simulation of the mechanical performance most definitely requires the values of the material's elastic constants (Young's,

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 usage will be much easier and efficient. Therefore, in order to achieve optimal operational TEGs, further evaluation and maximization of the following mechanical properties—elastic modulus, strength, hardness, fracture toughness, fatigue resistance (fatigue limit), and thermal fatigue resistance—are required at the entire operational temperature range (depending on the application). These are not the only mechanical properties at question but are the major ones that will provide both scientists and manufacturers with sufficient data to improve and further proceed to practical TEGs. As it will be clarified in detail, characterizing these few mechanical properties is handful enough

All the mechanical property results for most of the currently investigated TE materials

reported in this chapter are summarized in **Table 1** for convenience.

level.

for the time being.

**2. Mechanical properties**

between Young's modulus and the temperature.

bulk, shear, Poisson's ratio) and strengths for the very least.

The energy conversion efficiency is a fraction of the Carnot efficiency and determined by the dimensionless figure of merit (*ZT*), which is defined as *ZT = α<sup>2</sup> T/ρκ*, where *α*, *T*, *ρ,* and *κ* are the Seebeck coefficient, absolute temperature, electrical resistivity, and thermal conductivity, respectively. While most of the research in the past 15 years was focused on improving the *ZT* of materials (and hence the efficiency), a little focus was given to the mechanical evaluation and reliability of these materials. Therefore, much work of evaluating the material properties in the mechanical, thermomechanical, and fatigue fields is still to be done while paying attention to the TEG whole-module integrity challenges such as thermal stability and metalized contact layer durability [1, 2].

From the physics standpoint both transport and mechanical properties originate at the atomic level. The mechanical response of the material mainly depends on the atomic bonding between the atoms from which it is constructed. An atomic bond is basically the sharing of electron(s) between two or more adjacent particles (nonmetals for covalent bond, ions for ionic bond, or atom nucleus for metals). The cohesive energy (*E*C) between two particles is a measure of the work required for their separation and is a result of the repulsive and attractive forces between the two, which depend on the particle masses (the same force law as in gravity). The distance between two particles where the potential energy is minimal defines the cohesive energy of the two. The stronger the cohesive energy, the stronger the bond between the particles and more work is required for breaking the bonds. The gradient of force per small change of distance between the particles is defined as Young's modulus. The material strength is the force required to break atomic bonds and forcing a plastic and constant change in the material volume. The material compressibility, better known for its reciprocal—bulk modulus (*B*), is a measure for the material's resistance to hydrostatic compression. Many researchers tried over the years to find relations between the cohesive energy and bulk modulus to other various physical properties of the material (such as melting temperature, atomic volume, lattice constants, Debye temperature, etc.). Such specific connections will undoubtedly be restricted to a group of materials with similar structure, bond type, or other physicochemical property. Recently, after the examination of a large reported database on the physical properties of about 30 metals, it was realized that a correlation between the bulk modulus and the cohesive energy density (the atomic cohesive energy divided over the atomic volume—*E*C/*V*) can be made [3]. Such a correlation opens the possibilities of correlating the other elastic constants of the material including Young's modulus to other physical properties and therefore interlinking the material transport and electric properties with the mechanical ones on the atomic level.

The above long list of different suggested applications for TEGs is to show the wide range of service conditions that these generators will need to withstand. Such applications may vary from static operating conditions with a low number of thermal cycles and low operating temperatures, via higher temperature amplitudes and frequencies and up to dynamic applications with a high number of cycles, high thermal amplitudes, and occasional mechanical impacts.

Furthermore, the TEG service conditions necessarily subject the materials to wide temperature ranges and gradients within the materials themselves, so any mechanical characterization of TE materials should also concern the temperature dependence of the property. One such work was conducted measuring Young's modulus temperature dependence of LAST (Pb-Sb-Ag-Te) [4] between room temperature and 823 K and found an inverse relation between Young's modulus and the temperature.

In order to advance the development of thermoelectric modules for approaching practical applications, the design of future modules must take into account the mechanical properties of the involved materials for assuring adherence to the service conditions. Such design approaches based on finite element analysis, carried out for different applications, were reported [5–8]. Such analyses are essential while designing a specific TE device and give the ability to play with different parameters without the need of physical construction—saving money, time, man power, and materials in the process. Any simulation of the mechanical performance most definitely requires the values of the material's elastic constants (Young's, bulk, shear, Poisson's ratio) and strengths for the very least.

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 usage will be much easier and efficient.

Therefore, in order to achieve optimal operational TEGs, further evaluation and maximization of the following mechanical properties—elastic modulus, strength, hardness, fracture toughness, fatigue resistance (fatigue limit), and thermal fatigue resistance—are required at the entire operational temperature range (depending on the application). These are not the only mechanical properties at question but are the major ones that will provide both scientists and manufacturers with sufficient data to improve and further proceed to practical TEGs. As it will be clarified in detail, characterizing these few mechanical properties is handful enough for the time being.
