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Micro- and Macro- Mechanical Properties of Thermoelectric Lead Chalcogenides
Abstract
Both n- and p-type lead telluride (PbTe) based thermoelectric (TE) materials display high thermoelectric efficiency, but the low fracture strength may limit their commercial applications. In order to find ways to improve these macroscopic mechanical properties we report here the ideal strength and deformation mechanism of PbTe using density functional theory (DFT) calculations. This provides structure-property relationships at the atomic scale that can be applied to estimate macroscopic mechanical properties such as fracture toughness. Among all the shear and tensile paths that examined here, we find the lowest ideal strength of PbTe is 3.46 GPa along the (001)/<100> slip system. This leads to an estimated fracture toughness of 0.28 MPa m1/2 based on its ideal stress-strain relation, which is in good agreement with our experimental measurement of 0.59 MPa m1/2. We find that softening and breaking of the ionic Pb–Te bond leads to the structural collapse. To improve the mechanical strength of PbTe, we suggest strengthening the structural stiffness of the ionic Pb–Te framework through an alloying strategy, such as alloying PbTe with isotypic PbSe or PbS. This point defect strategy has a great potential to develop high-performance PbTe based materials with robust mechanical properties, which may also be applied to other materials and applications.
... All calculations used the Γ-centered Monkhorst-Pack scheme with a fine resolution of 2π × 1/40Å −1 in the k-point reciprocal space sampling. The detailed quasi-static mechanical loading setup of TiC and TiN is similar to our previous calculations on thermoelectric materials [30,31,32]. ...
... stress-strain curves for the other compounds can be found elsewhere [33,34,35,36,31,32,37,30,38,39,40,41,42]. A detailed procedure for converting the stress-strain curve to a stress-displacement curve can be found in Supplemental Note 1. ...
... Using the integral stress-displacement method (Fig.1) along the weakest crystallographic direction, we estimated the fracture energy (per unit area) G from both our TiC and TiN calculations and from several previously reported ideal strength calculations [33,34,35,36,31,32,37,30,38,39,40,41,42] were used in Eq. 1 or 2 (depending on the mode of fracture) to calculate lower-limit fracture toughness values. Comparisons to experimental results are tabulated in Table S2. ...
Fracture mechanics is a fundamental topic to materials science. Fracture toughness, in particular, is a material property of great technological importance for device design. The relatively low fracture toughness of many semiconductor materials, including electronic and energy materials, handicaps their use in applications involving large external stresses. Here, it is shown that quantum-mechanical density functional theory calculations of ideal strength, in conjunction with an integral stress-displacement method, can be used to estimate the fracture energy needed to calculate fracture toughness. Using the fracture energy associated with the weakest crystallographic direction provides an estimation for the lower-limit of the fracture toughness of a material. The lower-limit values are in good agreement with experimental single crystal measurements across several orders-of-magnitude of fracture toughness. Furthermore, the proposed methodology is useful for benchmarking experimental measurements of fracture toughness in polycrystalline materials and can serve as a starting point for the construction of more detailed fracture models and the computational design of new materials and devices.
... (b) Schematic of ion-blocking electrically conducting interfaces that allow the concentration profile to be reset at each interface so that the ion concentration does not ever reach the upper limit. (c) Relative resistance variation (R/R 0 ) as a function of current density [48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66] to fracture toughness values calculated using fracture energies estimated from the integral stress-displacement method. This calculated fracture toughness is an estimate of the experimental fracture toughness in bulk materials using the idealized case where fracture occurs in the weakest crystallographic direction and without consideration of any additional toughening mechanisms. ...
... ), we estimated the fracture energy G from the weakest crystallographic direction for both our TiC and TiN calculations and several previously reported ideal strength calculations[305,306,307,308,53,309,310,311,312,313,314,315,316,317]. From the estimate of G, and the bulk elastic properties also found from DFT, fracture toughness values were calculated using Eq. ...
... Bond length as a function of tensile strain for TiC and TiN along the [100] direction in tension.Figure 8.4: Calculated fracture toughness compared to experimental values. Specifically, the comparison of experimental fracture toughness values[48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66] to fracture toughness values calculated using fracture energies estimated from the integral stress-displacement method. This calculated fracture toughness is an estimate of the experimental fracture toughness in bulk materials using the idealized case where fracture occurs in the weakest crystallographic direction and without consideration of any additional toughening mechanisms. ...
Given directives such as the UN Global Goals targeting sustainable development, the
research presented herein makes but a small contribution to the advancement of alternative energy technologies. Nevertheless, the present work was largely motivated to
address specific points of intrigue within the thermoelectrics community. The general
principles demonstrated, however, may be directly applicable to other areas of solid-state
research.
Thermoelectric materials, which can convert heat to electricity through the Seebeck effect, require a complex optimization of their electronic and thermal properties. For the
past 2 decades, great strides have been made to improve their energy conversion efficiency—and many successes in doing so can be attributed to reductions in the thermal
conductivity. In the long-standing phonon gas model of thermal transport, where atomic
vibrations carry heat in a manner analogous to gas particles, the strategy has been to
introduce scattering mechanisms that impede transport. This works well in many materials. Recently, however, we have demonstrated that the thermal conductivity of materials like lead telluride may be engineered by controlling their bulk elastic properties, effectively controlling the speed of the phonons, which is a fundamentally different mechanism than scattering.
Another proposed method of reducing thermal conductivity was to utilize phase transitions, with the hope of introducing additional phonon scattering. In fact, there are many reports of reduced thermal conductivity (and improved thermoelectric performance) through both solid-solid and solid-liquid (analogous to ice melting) phase transitions. Here, a reassessment of the underlying thermodynamic relationship between thermal conductivity and thermal diffusivity demonstrates that thermal conductivity is likely underestimated from thermal diffusivity measurements when latent heats from phase transformations are not taken into account. In several well-characterized material systems it is shown that thermal conductivity is not greatly impacted by phase transitions, whereas thermal diffusivity is. This relates to a need for the accurate characterization of the heat capacity of materials at high temperature. For materials not undergoing a phase transition a simple equation was developed to describe high temperature heat capacity that is likely more accurate than experiments in many cases.
Although phase transitions may not result in ultralow thermal conductivity, there are
materials (and materials still to be discovered) with intrinsically high anharmonicity that
results in high phonon scattering rates and low thermal conductivity. Here, anharmonicity is an aspect of bonding in materials that deviates from Hooke’s Law, i.e. there are
non-linear interactions between atoms. Anharmonicity is also used to explain thermal
expansion. Thus, characterizing anharmonicity has widespread repercussions. Here, it
is proposed that the harmonic (e.g. elastic) properties of solids can be thermodynamically
related to higher order anharmonic effects of bonding. Specifically, a physical model of
thermal expansion is developed by considering that harmonic phonons produce a pressure pushing the solid outwards, while the elasticity of the atomic bonds compensates the phonon pressure to achieve mechanical equilibrium. Besides fundamentally reconsidering the nature of anharmonic behaviors in solids, this simple model provides accessible estimates of thermal expansion and the thermodynamic Grüneisen parameter that may be used for thermodynamic modeling and high-throughput screening of anharmonicity, both necessary for next-generation computational materials design.
The desire to reduce thermal conductivity for improved thermoelectric efficiency is summarized well by the "phonon-glass electron-crystal" mantra. Here, the thermal properties of the material are desired to be glass-like (amorphous-like) since glasses are known to exhibit some of the lowest thermal conductivities of all solids. However, glasses are not typically good electronic conductors, and so crystallinity is desirable for this aspect of thermoelectrics optimization. Indeed, this concept has been demonstrated in some solids like semiconducting clathrates, zinc antimonide and skutterudites. Nevertheless, the atomic vibrations in crystals are often only discussed in terms of the phonon gas model. Only recently has it has it been shown that vibrations in crystals and those in glasses can be described in the same mathematical framework, and that crystalline materials can transition to more glass-like behavior under certain circumstances. In this work, a phenomenological model of thermal transport by diffusons (the primary mechanism of heat transport in glasses) is developed for applications to crystalline materials. This study was one of the first to promote a reclassification of vibrations in crystals and gives an estimate of the so-called "minimum" thermal conductivity that can be used to benchmark experimental observations. Specifically, the model gives an estimate for thermal conductivity in the case where all vibrations in the material behave as diffusons. Again, characterizing the fundamental nature of vibrations in solids has far reaching implications for energy materials beyond thermoelectrics.
So far, both thermodynamic analysis and microscopic models have been used to characterize the thermal properties of solids. In this work, they were also utilized to assess the stability of materials for device-level operation. In one case, it is shown that there are thermodynamic stability criteria in a subclass of thermoelectric materials called mixed ionic-electronic conductors. Their stability depends on the atomic chemical potential of the mobile atom. Importantly, this means that there is a critical voltage above which the material can decompose. This is related to, but not the same as, the prevalent idea that these materials cannot sustain high current densities. In fact, it is shown experimentally that the superionic material copper sulfide can sustain high current densities when the voltage is kept below the thermodynamic critical voltage of the material.
Lastly, an estimate for the fracture toughness of solids is proposed that is based on
ideal-strength calculations. Modern computational methods in materials science provide
a unique opportunity to investigate fracture at the level of local atomic structures.
The integral of the ideal stress-displacement curve is used to approximate the work of
fracture. That is, to estimate the total energy required to make new surfaces. This computational method is shown to reproduce the magnitude of experimental results quite
well, indicating that the relevant physics of fracture are being captured. This method is
easily generalized to defect structures in materials and may be useful for atomic scale
materials design.
Although this body of work is but a humble offering to the scientific community, when research is coupled with international collaboration and education outreach, great strides
can be made in small steps. It is my passion to explore material properties, to build the
energy sciences community and to share knowledge with others.
ProQuest Link: https://search.proquest.com/openview/e0e9c10d9d62a1e0d16ef0e5c4eaa1d5/1?pq-origsite=gscholar&cbl=18750&diss=y
... Therefore, studying such precipitation is crucial as local compositional changes of the matrix during the precipitation can affect the semiconducting properties [41,42]. Furthermore, the growth direction of the precipitate can induce anisotropic strains in the matrix, affecting its mechanical properties [43][44][45]. The PbTe-Ni joints were created using the diffusion bonding technique, where the bulk alloy discs were ground and polished flat, clamped together, and annealed at 600 • C for varying holding times. ...
... However, no significant alterations in hardness values (within standard experimental deviations) were observed with varying bonding times. Previous literature reports have highlighted changes in microhardness values for doped PbTe, typically attributed to changes in carrier concentrations [44,57,58]. Heavily doped p-type PbTe alloys tend to exhibit higher hardness values compared to n-type PbTe. ...
Establishing dependable interconnects within thermoelectric (TE) modules is of utmost signifcance in ensuring
the longevity and functionality of these solid-state devices. PbTe-based devices are used in mid-temperature
range applications, with Ni being the most preferred interconnect. The available literature has focused primarily on optimizing the joining parameters. However, fne microstructural features have not been reported that
can affect the local semiconducting and mechanical properties. This research paper presents novel fndings
regarding the formation of previously undiscovered fne (Ni3-xTe2) β2 precipitates resembling Widmanstatten ¨
morphology within the PbTe matrix during joining processes. PbTe and Ni discs are diffusion bonded at 600 ◦C
for various holding times. The precipitation is studied through advanced analytical TEM/STEM techniques. The
current study leads to two noteworthy observations: 1) specifc orientation relationships were discovered between the two phases: [001] PbTe ‖ [001] β2, (020) PbTe ‖ (210) β2 and growth directions were along 〈100〉 in
PbTe matrix phase. 2) Formation of near-coincidence site lattice (NCSL) structures occurring periodically at the
growing fronts of these precipitates. Atomic scale lattice strain mapping indicates a cyclic state of compression
and tension at these interfaces. These fndings shed light on local composition changes and strain felds within
the PbTe matrix during fne β2 precipitation, which has the potential to impact interface reliability
... Following the Griffith-Irwin formulation (also known as linear elastic fracture mechanics), 57 the fracture toughness (K c ) of FAB can be predicted using the stress-strain curves shown in Figure 2. Recently, this method has been used for several materials. 39,56,58 The curves for the weakest direction (i.e., [010]) and slip system (i.e., (010)[100]) of FAB are converted into the engineering stress-engineering displacement curves (Figures S2-S4). The most vulnerable direction/plane represents the most favorable crack propagation direction/plane. ...
... The detailed procedure is provided in the Supporting information. 39,58 The stress intensity factor (K Ic ) for mode I loading is defined as ...
The thermal and magnetic cycling of a magnetocaloric material degrades its mechanical properties and device performance. We used ab initio tensile and shear simulations to investigate the mechanical properties such as ideal strength, fracture toughness and deformation and failure mechanisms of Fe2AlB2 at finite strain. The weakest direction of Fe2AlB2 is [010], and the weakest slip system is (010)[100]. The ideal tensile strength (σm = 12.51 GPa) of Fe2AlB2 is less than its ideal shear strength (τm = 13.32 GPa). The strain energy difference (ΔE = −13 eV/f.u.) of Fe2AlB2 confirms cleavage fracture as its most plausible failure mode. The concomitant changes in the c‐lattice parameter and Al–Al bond along the c‐axis determine the ideal tensile strength of Fe2AlB2. Likewise, the subtle changes in the a‐lattice parameter and Al–Al bond along the a‐axis specify its ideal shear strength. The tensile strain induces a magnetic to nonmagnetic transition in Fe2AlB2 at the critical tensile strain (εc = 0.08). A similar transition occurs at the critical fracture strain (εcf = 0.48) due to shear deformation. The brittle nature of Fe2AlB2 is predicted by its anisotropic Poisson's ratios, strength ratio, and failure mode. The fracture toughness of Fe2AlB2 for mode I fracture is (KIc = 2.17 MPa m1/2), mode II fracture is (KIIc = 1.33 MPa m1/2), and mode III fracture is (KIIIc = 1.16 MPa m1/2). The failure mechanism of Fe2AlB2 due to the tensile deformation is marked by the sharp and appreciable changes in the lattice parameters, bonding characteristics, and magnetic moment of Fe at the critical fracture strain (εcf = 0.44). This study provides a fundamental understanding of the mechanical behavior of Fe2AlB2 at the finite strain relevant to the cycling stability of the magnetocaloric Fe2AlB2.
... 24 Other than the introduction of various defects and external conditions, the welltailored deformability should be related to the layered HBS especially VdW. According to our previous researches, though weak VdW is mainly responsible for large deformation and fracture of Bi2Te3 lattice [25][26][27][28] as the cumulative disadvantage of structure softening with applied loads found in other TE semiconductors, [29][30][31][32][33] it can also be greatly strengthened to form a new covalent Te1-Te1 bond and triple the shear strength via nanotwinning. 34 Moreover, inspired by some peculiar behaviors dominated by weak but reversible dynamic bonding, namely the dislocation-controlled deformation of extraordinarily ductile α-Ag2S semiconductor 15,35 and the reversible interlayer separation of flexible MoS2 sheet, 36 this intramolecular dispersion force should belong to the concept of sacrificial bonds (SB) concerned in artificial polymeric and natural materials with excellent mechanical properties. ...
... It seems to be a sophisticated evolution against the stated cumulative disadvantage of structure softening that could easily lead to strain localization and brittle failure of TE semiconductors under loads, i.e. bond weakening (in local configurations), structural softening, …, further weakening and breakage of bonds, further structural softening, …, fracture. [29][30][31][32][33] However, for better understanding of the micromechanics in Bi2Te3 HBS, the combined information of configuration, energy and stress is necessary. ...
Bismuth telluride (Bi₂Te₃) based semiconductor is one of the typical inorganic thermoelectric (TE) materials with excellent energy conversion efficiency, but the intrinsic brittleness severely limits its mechanical performance for further application of long-term reliability and wearable devices. To understand the recent mechanical improvement of the ductile and flexible inorganic TE materials at atomic scales, here we use molecular dynamics simulations to intuitively illuminate the enhanced shear deformability and performance stability of brittle Bi₂Te₃ crystal through the tailored effects of surfaces. We reveal that the peculiar micro-behavior origins from the layered hierarchical bonding structure with weak but reversible Van der Waals force, namely a sacrificial bond, between Te1-Te1 adjacent layers. The synergetic evolution of local structures including sacrificial bonds and strain-induced defects tends to partly compensate for the mechanical degradation caused by structure softening during shearing, achieving a relatively large strain before cleavage. The inspired engineering strategy on synergistically optimizing bonds and defects opens a pathway for designing multi-scale hierarchical inorganic TE materials with excellent overall performance.
... The shear simulations were realized by imposing the shear strain on a particular slip system while the five other strain components were allowed to be relaxed 11,17,20,[29][30][31][32][33][34] . The calculation models for the shear simulations are employed on the supercell including 96, 48, 72, 72, and 72 atoms along the (001)/<100>, (001)/<110>, (111)/<-110>, (111)/ <-1-12>, and (111)/<11-2> slip systems, respectively. ...
Half Heusler materials exhibit excellent thermoelectric and mechanical properties, rendering them potential candidates for advanced thermoelectric devices. Currently, the developments on interrelated devices are impeded by their inherent brittleness and limited ductility. Nevertheless, it exists the potential ductility on half Heusler materials with face-centered cubic sub-lattices through the expectation of the occurrence of shear-induced ‘catching bonds’ which can result in excellent ductility on other face-centered cubic materials. This work focuses on half Heusler thermoelectric materials XFeSb (X = Nb, Ta) and SnNiY (Y = Ti, Zr, Hf), the shear deformation failure processes are deeply investigated through the first principle calculations. Shear-induced ‘catching bonds’ are found on XFeSb (X = Nb, Ta) along the (111)/<-1-12> slip system, which releases the internal stress and exactly resulting in the potential ductility. According to the thermodynamic criterion based on generalized stacking fault energy, the essence of shear-induced ‘catching bonds’ are interpreted as the (111)/<-110> slips formed by several 1/3(111)/<-1-12> partial dislocations motions. During the (111)/<-1-12> shear on SnNiY (Y = Ti, Zr, Hf), the structural integrity is maintained without inducing ‘catching bonds’. Different deformation processes occurring in the identical crystal structure are elucidated through the energy explanation, revealing that shear-induced ‘catching bonds’ originate from the crystal plane cleavage on the (111) plane. The present works offer significant advantages for the assessment and comprehension of shear-induced ‘catching bonds’ in other materials and facilitate the development of XFeSb (X = Nb, Ta)-based thermoelectric devices with excellent ductility.
... It might be a key for understanding the brittle behavior of n-type and p-type doped PbTe. [52][53][54][55][56] To understand the influence of dopants on the mechanical properties of the PbTe structure, we employed the local vibrational theory for local stretching force constants. As shown in Fig. 3, we virtually cut the 3D cell of the doped PbTe structure into two regions, namely A and B. Region A included the first atomic layer from the dopant in each direction. ...
Finding new efficient thermoelectric materials is a significant challenge for materials science. It is crucial to have a comprehensive understanding of material-property relationships to develop new materials successfully, given that minor structural or compositional changes can result in significant property changes. This paper extensively utilizes advanced theoretical approaches and investigates the impact of n- and p-type impurities on the mechanical characteristics of PbTe thermoelectric materials. n- and p-type doping of PbTe were studied using various techniques, including elastic tensor calculations, crystal orbital Hamilton population method, and local vibrational theory. Our findings reveal the specific ways in which doping type affects the material's mechanical properties. This information can aid researchers in optimizing PbTe doping strategies.
... 9 Despite this, PbTebased materials are rarely used in modern TE devices due to the high brittleness and sublimation rates of p-type PbTe. 7 In recent years, Snyder and Dunand et al. [3][4][5][6][7]10,11 performed a series of investigations on the mechanical properties of TE materials, including PbTe-based materials. It has been established in their studies that R band bonding, grain boundaries, and dopant size mismatch have little effect on the embrittlement of p-type PbTe. ...
High brittleness observed in p-type PbTe is a significant obstacle in the commercial use of PbTe-based thermoelectric materials. An in-depth study of dislocations in PbTe is crucial due to their significant impact on material plasticity. In this work, the properties of 12[011](0 1¯ 1) edge dislocation in PbTe are investigated by using the local misfit energy of a shear model within the framework of the Peierls–Nabarro theory. By incorporating a moderate strain region size, a smooth and gradual transition of Pb–Te bonds during the shear process can be facilitated while balancing the elastic and inelastic components of the local misfit energy. The average misfit energy and the Peierls stress of the dislocation are calculated and compared with those of SrTiO3, a material that has demonstrated unexpected plasticity in its single crystal form. The findings indicate that undoped PbTe exhibits reasonably good plasticity. This work presents a theoretical approach to investigate dislocation properties in PbTe, laying the foundation for further research on the mechanical aspects of p-type dopant-induced issues in PbTe-based materials.
... Because crack propagation in brittle materials is caused by the breaking of a single bond at the crack tip 48 and the stress on the breaking of a bond at the crack tip corresponds to the ideal tensile strength 10 , the fracture toughness is considered to be related to the ideal tensile strength, which in turn corresponds to the bond strength. In fact, some studies have attempted to estimate fracture toughness from the stress-strain relationship of ideal strength calculations 49,50 . Based on the relationship between ideal tensile strength and fracture toughness, the increase in ideal tensile strength of hole doped Si is qualitatively consistent with the increase in fracture toughness of hole doped Si in the experiment. ...
Brittle fracture of a covalent material is ultimately governed by the strength of the electronic bonds. Recently, attempts have been made to alter the mechanical properties including fracture strength by excess electron/hole doping. However, the underlying mechanics/mechanism of how these doped electrons/holes interact with the bond and changes its strength is yet to be revealed. Here, we perform first-principles density-functional theory calculations to clarify the effect of excess electrons/holes on the bonding strength of covalent Si. We demonstrate that the bond strength of Si decreases or increases monotonically in correspondence with the doping concentration. Surprisingly, change to the extent of 30–40% at the maximum feasible doping concentration could be observed. Furthermore, we demonstrated that the change in the covalent bond strength is determined by the bonding/antibonding state of the doped excess electrons/holes. In summary, this work explains the electronic strengthening mechanism of covalent Si from a quantum mechanical point of view and provides valuable insights into the electronic-level design of strength in covalent materials.
... However, for viable commercial applications, good mechanical properties and machinability are also of significant importance, beside the excellent thermoelectric properties, since the majority of practical devices in service are often exposed to harmful environments typified by strong mechanical vibrations, thermal and mechanical cycling, and corrosive atmospheres [16][17][18]. Moreover, the application of thermoelectric modules in self-micro-power supply systems and wearable devices requires the modules to have excellent flexibility and foldability [19]. ...
... Good thermoelectric materials are often too expensive and brittleand their synthesis too arduousto achieve the form factor and quantity required for standardized mechanical property tests like tensile tests and notched three-point bend tests. Instead, initial forays into quantifying mechanical performance in thermoelectric materials tend to rely on computational models or cheaper experiments like Vickers hardness tests [14,[20][21][22][23][24]. Vickers microhardness measurements and fracture toughness estimated from Vickers indentation cracks were reported in La 2.74 Te 4 (x near the optimum for high-temperature performance) by Ma et al. [14], who later measured reduced spalling from indentation tests and increased strength when compositing La 2.74 Te 4 with metallic Ni or Co [25,26]. ...
... As a result of the layered nature, KMgX can be easily cleaved along the a-b plane. Furthermore, KMgX family compounds have a lower bulk modulus than the popular layered thermoelectric materials PbTe and PbSe [39], indicating their low strength. In Table I, the optimized lattice constants, band gap (E g ), and bulk modulus of KMgX members are listed. ...
Through a combined first-principles and Boltzmann transport theory, we systematically investigate the thermal and electrical transport properties of the unexplored ternary quasi two-dimensional KMgSb system of KMgX (X = P, As, Sb, and Bi) family. Herein, the transport properties of KMgSb under the application of hydrostatic pressure and alloy engineering are reported. At a carrier concentration of ∼8×1019 cm−3, the figure of merit zT (∼0.75) for both the n-type and p-type of KMgSb closely matched, making it an attractive option for engineering both legs of a thermoelectric device using the same material. This is particularly desirable for high-performance thermoelectric applications. Furthermore, the zT value increases as pressure decreases, further enhancing its potential for use in thermoelectric devices. In the case of substitutional doping (replacing 50 \% Sb by Bi atom), we observed ∼49 % (in-plane) increase in the peak thermoelectric figure of merit (zT). The maximum zT value obtained after alloy engineering is ∼1.45 at 900~K temperature. Hydrostatic pressure is observed to be a great tool to tune the lattice thermal conductivity (κL). We observed that the negative pressure-like effects could be achieved by chemically doping bigger-size atoms, especially when κL is a property under investigation. Through our computational investigation, we explain that hydrostatic pressure and alloy engineering may improve thermoelectric performance dramatically.
... We could see that annealing treatment did not degrade the hardness, and the corresponding HV value of ∼2.5 GPa for YbCd 2 Sb 2 -dense/ porous was better than that of other famous thermoelectric materials, such as Bi 2 Te 3 , 40 PbQ (Q = S, Se, Te), 41−45 or Mg 3 Sb 2 (Table S3). 46 Furthermore, the relevant K IC of ∼0.37 and 0.38 MPa·m 1/2 for YbCd 2 Sb 2 -dense and -porous, respectively, were close to those of PbQ, 45 revealing a great potential of practical applications for YbCd 2 Sb 2 . ...
... Besides, the mechanical and dynamical behavior of materials provide very important information such as stability and stiffness of the materials, micro cracks and plastic deformations etc. which are crucial for the technological applications of the materials. Also, there are limited studies about the elastic properties of some thermoelastic materials such as thallium-tellurium based compounds [22], lead chalcogenides [23], etc. Moreover, there is hardly any study about the anisotropic elastic properties of the experimentally existing Tl 4 Ag 18 Te 11 thermoelectric material [21]. ...
The anisotropic mechanical properties of Tl4Ag18Te11 compound was investigated elaborately for the first time by using Density Functional Theory calculations with the Vienna Ab-initio Simulation Package in this work. Tl4Ag18Te11 compound was optimized in the I4mm space group and the formation energy was determined as a negative value that is the indication of the experimental synthesizability of this compound. The optimized crystal structure was employed for the calculations of the elastic constants and the obtained values revealed the mechanical stability of Tl 4 Ag 18 Te 11 compound. The polycrystalline properties were determined such as shear modulus, Poisson's ratio, etc. In addition, the anisotropic elastic properties were presented. The direction dependent sound waves velocities, polarization of the sound waves, enhancement factor and the power flow angle were determined. The thermal conductivity studies were performed and the minimum thermal conductivity (0.259 W m −1 K −1) and the diffusion thermal conductivity (0.202 W m −1 K −1) were calculated. This study illustrates the capability of this compound for the thermoelectric materials.
... The engineering application of TE materials requires mechanical robustness that can undergo cycling thermal stress in a temperature gradient and can resist crack opening or failure of devices from vibrations. Unfortunately, thermo-mechanical loadings can cause the degeneration of the mechanical properties, leading to the failure of TE devices [24][25][26][27]. Thus, it is essential to obtain an in-depth understanding of how mechanical properties of these TE materials behave in engineering applications. ...
In₄Se_(3-δ) semiconductors exhibit high zT as an n-type TE material, making them promising materials for thermoelectric (TE) applications. However, their commercial applications have been limited by the degradation of their mechanical properties upon cyclic thermal loading, making it important to understand their stress response under external loadings. Thus we applied molecular dynamics (MD) simulations using a density functional theory (DFT) derived force field to investigate the stress response and failure mechanism of In₄Se_(3-δ) under shear loading as a function of strain rates and temperatures. We considered the most plausible slip system (001)/<100> based on the calculations. We find that shear slippage among In/Se layered structures dominates the shear failure of In₄Se_(3-δ). Particularly, Se vacancies promote disorder of the In atoms in the shear band, which accelerates the shear failure. With increasing temperature, the critical failure strength of In4Se3 and the fracture strain of In₄Se₃ decrease gradually. In contrast, the fracture strain of In₄Se_(2.75) is improved although the ultimate strength decreases as temperature increases, suggesting that the Se vacancies enhance the ductility at high temperature. In addition, the ultimate strength and the fracture strain for In₄Se_(2.75) increase slightly with the strain rate. This strain rate effect is more significant at low temperature for In₄Se_(2.75) because of the Se vacancies. These findings provide new perspectives of intrinsic failure of In₄Se_(3-δ) and theory basis for developing robust In₄Se_(3-δ) TE devices.
... 20 In addition, PbSe has higher toughness and melting point than PbTe. 21 Substantial progress 22−26 has been made in the p-type PbSe system mostly through valence band convergence. However, achieving convergence of the conduction bands in the PbSe system is more difficult because they are far apart from each other in energy. ...
As an inexpensive and earth abundant analogue of PbTe, PbSe has aroused growing attention recently as advanced thermoelectric materials. In the present report, the effect of PbTe and PbS co-alloying on the thermoelectric properties of n-type Pb0.99Sb0.01Se was systematically studied. PbTe and PbS are completely soluble in PbSe matrix, rendering strong phonon scattering because of reinforced lattice disorder. A minimal lattice thermal conductivity of ∼0.5 W m–1 K–1 at 823 K was successfully obtained for Pb0.99Sb0.01Se0.84Te0.08S0.08, which is ∼25% less than that of the Pb0.99Sb0.01Se control sample. Moreover, PbTe and PbS co-alloying leads to a reduced electron carrier concentration of Pb0.99Sb0.01Se, probably arising from the amphoteric dopant nature of Sb in PbTe. As a result, the Seebeck coefficient of Pb0.99Sb0.01Se is notably enhanced by co-alloying with PbTe and PbS, partly compensating the loss the carrier mobilities due to point defect scattering. Altogether, a maximal thermoelectric figure of merit ZT ∼ 0.9 at 823 K is attained in the Pb0.99Sb0.01Se0.68Te0.16S0.16 compound, which is nearly a 40% improvement over the control sample of Pb0.99Sb0.01Se.
... [15] Meanwhile, several methodologies have been applied to reduce the lattice thermal conductivity, such as strengthening the phonon scattering. [16][17][18][19][20][21] Phonon scattering, produced by point defects in Ref. [16] and accommodation of metal cations in Ref. [17], is responsible for having a reduced lattice thermal conductivity. The mass and strain fluctuations between host and guest atoms, which produces strong phonon scattering, could also be maximized by vacancies as demonstrated in Ref. [18]. ...
We have reported a first principles study of structural, mechanical, electronic, and thermoelectric properties of the monoclinic ternary thallium chalcogenes Tl 2 MQ 3 ( M =Zr, Hf; Q =S, Se, Te). The electronic band structure calculations confirm that all compounds exhibit semiconductor character. Especially, Tl 2 ZrTe 3 and Tl 2 HfTe 3 can be good candidates for thermoelectric materials, having narrow band gaps of 0.169 eV and 0.21 eV, respectively. All of the compounds are soft and brittle according to the second-order elastic constant calculations. Low Debye temperatures also support the softness. We have obtained the transport properties of the compounds by using rigid band and constant relaxation time approximations in the context of Boltzmann transport theory. The results show that the compounds could be considered for room temperature thermoelectric applications ( ZT ∼ 0.9 ).
Wearable thermoelectric applications require materials with both high energy conversion efficiency and excellent flexibility/deformability. Inorganic thermoelectric materials have shown high conversion efficiency, but they are usually brittle and have poor mechanical flexibility, which makes their integration into flexible devices a challenging task. GeAs is a group IV-V binary compound with a van der Waals layered structure, and its thermoelectric response has been reported. Herein, we investigate the mechanical and thermoelectric properties of GeAs crystal by a combination of density functional theory and density functional perturbation theory methods. Our results show that GeAs features a moderately dispersive valence band and multivalley convergence, which give rise to a large Seebeck coefficient and power factor when it is properly p-doped. Remarkably, its electrical transport in the out-of-plane direction even outperforms that in the in-plane direction, while phonon transport is suppressed, leading to a predominant thermoelectric response in the vertical direction. More interestingly, GeAs demonstrates a structural stiffness higher than thermoelectric CuInTe2 and PbTe, and a ductility ratio comparable to a recently discovered plastic semiconductor, InSe. The stress-strain curve simulation reveals that GeAs can withstand deformations up to 20%. These findings showcase GeAs as a ductile thermoelectric material suitable for wearable devices and energy conversion.
Most thermoelectric (TE) materials are brittle and exhibit high coefficient of thermal expansion (CTE), both of which are undesirable considering their service conditions. In this context, invar 36 is known to be a ductile material with a very low CTE feature. However, its TE performance is yet to be reported. Accordingly, the present work involves preparation of invar 36 and investigation of its TE performance. The CTE and mechanical properties of invar 36 were also measured to calculate its thermal shock resistance parameter (R’) and to comment on its thermal shock resistance. Further, we calculated R’ of state-of-the-art TE materials using literature data for a detailed comparison. The results show that Seebeck coefficient of invar 36 is -14.4 μV/K at RT and its carrier type is changing from n- to p-type at ~550 K. This is an unusual behavior, observed in some well-known TE materials like PbTe and CoSb3, and might suggest a mixed conduction in plain invar 36. Also, we report that invar 36 exhibits a PF of ~2.6 μW/cmK² at RT, which is comparable to some TE materials. On the other hand, the ZT of invar 36 (~0.007) was found to be 10-100 times lower than common TE materials at RT. However, considering a possible minority carrier compensation and as-measured thermal conductivity (~11.9 W/mK), ZT might be improved through careful doping and/or grain size reduction strategies in the future. Besides, unlike most TE materials, invar 36 is ductile with excellent mechanical properties (Elongation: 39%, YS: 436 MPa, UTS: 583 MPa, E: 146 GPa, υ: 0.28, Toughness: 200 MJ/m³). Importantly, invar 36 exhibits 10 times lower CTE (1.7 ×10-6 K⁻¹ between RT – 473 K) and 75 to 1000 times higher R’ (20125 W/m) than state-of-the-art TE materials, thus, it might attract interest in applications where durability is equally important.
Twin boundaries (TBs) have been found to be an effective strategy in enhancing mechanical properties of semiconductors. Our previous first principles study proved that TBs can raise the ideal strength of thermoelectric semiconducting InSb. In order to further optimize the mechanical properties of InSb, here we studied the role of TB orientation α, spacing λ, and doping in the strength and toughness of InSb. TB orientation behaves with three different deformation modes, including the stacking, slippage cross TBs, and slippage along TBs. When the deformation mode is the slippage cross TBs, TB spacing can enhance the ideal strength corresponding to the Hall-Petch effect. We found that the ideal strength of nano-twinned InSb with α = 43.31° and λ = 1.12 nm can be optimized to be 56.2% higher than its single crystal. These findings will be helpful in guiding the TB design for better mechanical properties of InSb.
Coherent twin boundaries (CTBs) with the lowest interfacial energy provide a strong phonon-CTB scattering source to suppress the lattice thermal conductivity needed for thermoelectric properties, but the impact on mechanical properties of PbTe remains unexplored. We construct nanotwinned structures with Pb- or Te-terminated CTB (Pb- or Te-CTB) along (111) plane and employ molecular dynamics simulations to examine structural evolution. We find that Pb-CTBs weaken ionic Pb-Te bonds to generate an easy dislocation source at CTBs. Due to nucleation and motion of partial dislocations on each Pb-CTB plane driven by shear load, Pb-CTBs gradually migrate to Te-CTBs, which is accompanied by breaking and re-forming of Pb-Te bonds. This “catching bond” maintains structural integrity while dramatically enhancing deformability of nanotwinned PbTe. Dislocations move from Te-CTBs toward twin lamellae, resulting in the structural slippage and fracture. These findings provide a theoretical strategy to improve the ductility of PbTe-based semiconductors through TB engineering.
The intrinsic shear strength (1.25 GPa) of In4Se3 remarkably lower than those of classic thermoelectric (TE) materials such as CoSb3 (7.17 GPa), PbTe (3.46 GPa), TiNiSn (10.52 GPa), which limits the commercial applications of In4Se3 based TE materials. To improve the shear strength of single-crystalline In4Se3, we used density functional theory to study the influence of point defects on the mechanical behavior of In4Se3 under the pure shear loading. We found that doping with Ca, Ag, Yb, Pb, Zn, I, and Br can improve the shear strength of In4Se3. In particular, Ca-doped In4Se3 obtained the highest shear strength (1.43 GPa), an increase of 14.4%. These point defects can improve the van der Waals interaction between In/Se layers significantly, hence enhancing the shear strength, while the slippage between the In/Se layers is still predominating its deformation and failure. Our work offers a possibility in strengthening layered materials with robust mechanical properties.
Thermoelectric materials enable the direct conversion between waste heat and electric energy, playing an important role in alleviating energy crisis. Many excellent thermoelectrics developed so far contain expensive and scarce Te element, largely limiting their applications. Therefore, exploring Te-free compounds with extraordinary thermoelectric performance becomes a vital topic in thermoelectric community in recent years. PbSe is an ideal candidate that meets above criteria and has advanced rapidly in the last decade with reported peak ZTs close to 2.0. Herein we review the recent research progress of PbSe-based thermoelectric materials. This review article starts with a general introduction of the properties of IV-VI semiconductors as advanced thermoelectric materials by comparing their cost, crustal abundance, mechanical strength and chemical bonding. Following that, phase diagram, crystal and electronic band structures of PbSe are comprehensively summarized. Then we discuss how the frequently used dopants regulate its carrier concentrations. Subsequently, electronic band structure engineering (including resonant levels, band flattening, band convergence, band inversion, etc.) and microstructural architecturing (including atomic arrangements, dislocation arrays, nanoscale precipitates, etc.) approaches and their impacts on charge and phonon transport properties of PbSe are elaborated. Finally, we summarize the typical production processes of PbSe and comment on their scalability. The future directions for how to further improve the thermoelectric properties of PbSe and promote its applications are discussed at the end of this article.
Thermoelectric materials can be potentially employed in solid-state devices that harvest waste heat and convert it to electrical power, thereby improving the efficiency of fuel utilization. The spectacular increases in the efficiencies of these materials achieved over the past decade have raised expectations regarding the use of thermoelectric generators in various energy saving and energy management applications, especially at mid to high temperature (400–900 °C). However, several important issues that prevent successful thermoelectric generator commercialization remain unresolved, in good part because of the lack of a research roadmap.
Dislocations and the residual strain they produce are instrumental for the high thermoelectric figure of merit, zT ≈ 2, in lead chalcogenides. However, these materials tend to be brittle, barring them from practical green energy and deep space applications. Nonetheless, the bulk of thermoelectrics research focuses on increasing zT without considering mechanical performance. Optimized thermoelectric materials always involve high point defect concentrations for doping and solid solution alloying. Brittle materials show limited plasticity (dislocation motion), yet clear links between crystallographic defects and embrittlement are hitherto unestablished in PbTe. This study identifies connections between dislocations, point defects, and the brittleness (correlated with Vickers hardness) in single crystal and polycrystalline PbTe with various n‐ and p‐type dopants. Speed of sound measurements show a lack of electronic bond stiffening in p‐type PbTe, contrary to the previous speculation. Instead, varied routes of point defect–dislocation interaction restrict dislocation motion and drive embrittlement: dopants with low doping efficiency cause high defect concentrations, interstitial n‐type dopants (Ag and Cu) create highly strained obstacles to dislocation motion, and highly mobile dopants can distribute inhomogeneously or segregate to dislocations. These results illustrate the consequences of excessive defect engineering and the necessity to consider both mechanical and thermoelectric performance when researching thermoelectric materials for practical applications. High concentrations of crystalline point defects and dislocations limit plasticity and increase brittleness in some of the highest efficiency PbTe thermoelectric materials through microscopy and mechanical testing. The need for a balance between mechanical and thermoelectric properties when subjecting PbTe to extensive defect engineering is highlighted.
For performance stability and wearable application of Bi2Te3 thermoelectric (TE) semiconductors, it is necessary to enhance its deformability at the operating temperature. Given Van der Waals sacrificial bond (SB) behavior in Bi2Te3 crystals, temperature-dependent anharmonic effects on the structural evolution and mechanical performance during shearing is studied through molecular dynamics simulations. With increasing temperature, in addition to larger difference of initial bond strength, the synergy between SB and defect during slipping tends to be suppressed, resulting in strain localization with less crystal deformability. The temperature-induced change of nanocrystal deformation modes is clearly identified by the growth trend difference of deformation heterogeneity parameter (F) that is defined according to configurational energy distribution. This simulation work provides new insights into the role of sacrificial bonds and substructures on synergistically deformability tuning, likely improving defect engineering strategy for designing advanced multi-scale hierarchical TE semiconductors.
Intensive studies have been carried out over the past decade to identify nanostructured thermoelectric materials that allow the efficient conversion of waste heat to electrical power. However, less attention has...
The engineering applications of thermoelectric (TE) devices require TE materials possessing high TE performance and robust mechanical properties. Research on thermal and electrical transport properties of TE materials has made significant progress during the last two decades, developing TE materials on the threshold of commercial applications. However, research on mechanical strength and toughness has lagged behind, restricting application of TE materials. Mechanical failure in these materials involves multi-scale processes spanning from atomistic scale to macro scale. We have proposed an integral stress-displacement method to estimate fracture toughness from intrinsic mechanical behavior. In this review, we summarize our recent progress on fracture toughness of TE materials. This is in three parts:
(1) Predicting fracture toughness of TE materials from intrinsic mechanical behavior;
(2) Intrinsic mechanical behavior and underlying failure mechanism of TE materials; and
(3) Nanotwin and nanocomposite strategies for enhancing the mechanical strength and fracture toughness of TE materials.
These findings provide essential comprehensive understanding of fracture behavior from micro to the macro scale, laying the foundation for developing reliable TE devices for engineering applications.
This chapter discusses new strategies leading to significant improvements in the thermoelectric figure of merit (ZT) and examines recent advances in module fabrication of lead telluride (PbTe)-based materials. PbTe is a traditional thermoelectric material for high-temperature use (600–900 K); its ZT value continues to increase with the application of new strategies and have exceeded ~ 2.5 for p-type PbTe and ~ 1.8 for n-type PbTe. The reduction in lattice thermal conductivity by nanostructuring/hierarchical architecturing has been intensively studied in PbTe-based materials. The improvement of thermoelectric power factor by electronic band engineering has also been extensively developed in PbTe. The technology transfer between material development and module fabrication has already begun with the newly developed high-ZT PbTe. An efficiency of ~ 12% has been demonstrated in a cascade-type module made of nanostructured PbTe and Bi2Te3 for a hot-side temperature of 873 K and a cold-side temperature of 283 K.
Flexibly modulating thermal conductivity is of great significance to improve the application potential of materials. PbTe and PbSe are promising thermoelectric materials with pressure-induced phase transitions. Herein, the lattice thermal conductivities of PbTe and PbSe are investigated as a function of hydrostatic pressure by first-principles calculations. The thermal conductivities of both PbTe and PbSe in NaCl phase and Pnma phase exhibit complex pressure-dependence, which is mainly ascribed to the nonmonotonic variation of a phonon lifetime. In addition, the thermal transport properties of the Pnma phase behave anisotropically. The thermal conductivity of Pnma-PbTe is reduced below 1.1 W/m·K along the c-axis direction at 7–12 GPa. The mean free path for 50% cumulative thermal conductivity increases from 7 nm for NaCl-PbSe at 0 GPa to 47 nm for the Pnma-PbSe in the a-axis direction at 7 GPa, making it convenient for further thermal conductivity reduction by nanostructuring. The thermal conductivities of Pnma-PbTe in the c-axis direction and Pnma-PbSe in the a-axis direction are extremely low and hypersensitive to the nanostructure, showing important potential in thermoelectric applications. This work provides a comprehensive understanding of phonon behaviors to tune the thermal conductivity of PbTe and PbSe by hydrostatic pressure.
In the last decade, high-performance Cu2Se thermoelectric materials and devices are attracting increasing research interest. In this review, we firstly summarize fundamentals of Cu2Se, including crystal structure, band structure, phase transition, and intrinsic thermoelectric performance. Then, we compare and overview the effectiveness of enhancing electrical transports and reducing lattice thermal conductivity on boosting figure of merit, zT of Cu2Se and found that zT enhancement of Cu2Se should be mainly attributed to reduced lattice thermal conductivity. After that, we highlight the chemical stability and mechanical properties of Cu2Se and its thermoelectric modules. In the end, we point out future research directions in the field of Cu2Se thermoelectrics. This review fills the gap of overview on the progress and challenge of Cu2Se thermoelectrics, and provide a new perspective to achieve Cu2Se-based thermoelectric materials with high thermoelectric performance.
Due to the advantages of environment-friendly constituent elements, relatively large Seebeck coefficient, and low thermal conductivity, multicomponent diamond-like chalcogenides (MDLCs), such as CuInTe2, Cu2SnSe3, Cu3SbSe4 and Cu2ZnSnSe4, have attracted intensive attention for energy conversion as promising thermoelectric (TE) materials in recent years. This chapter provides an overview of research on MDLCs in TE field. Commencing with the crystal structure and phase transition of MDLCs, we will introduce electronic structure and lattice dynamics of MDLCs through some typical TE compounds. We then discuss new methods (i.e., band engineering, entropy engineering, in situ displacement reaction, and mosaic nanostructure) developed in MDLCs for optimizing TE performance. Finally, in addition to the performance of TE device, investigations on stability and mechanical properties of MDLCs are also presented. For future practical applications of this potential material system, the problems needed to be solved and possible directions to further promote TE performance are also explored in the outlook part.
The layered In4Se3 based material is recognized as a state-of-the-art n-type thermoelectric material for the middle temperature range of 500 K to 900 K. Despite excellent thermoelectric properties, its inferior mechanical properties restrict its commercial possibilities. In this work, we use Quantum Mechanics (density functional theory) to investigate the ideal strength and failure mechanisms of ideal and Se deficient In4Se3 under pure shear and biaxial shear loads. We found that the lowest ideal shear strength of ideal In4Se3 is 1.25 GPa along the (100)/<001> slip system. Slippage between the In/Se layer dominates its deformation and failure. With Se vacancies, the ideal strength of In4Se2.75 drops to 1.00 GPa while the failure mechanism remains almost the same as that of ideal In4Se3. Moreover, under biaxial shear loads (as in nano-indentation experiments) the ideal strength of In4Se3 increases to 1.50 GPa, with compression now accounting for the failure. Even so, In4Se3 shows poorer mechanical properties under biaxial shear loads. These insights into the deformation and failure mechanism of In4Se3 compounds should help suggest designing modifications to improve mechanical properties.
Lead telluride (PbTe) is one of the best thermoelectric materials in the intermediate temperature range, which shows great potential for waste heat recycling. However, its low strength and high brittleness limits its large-scale application, since the thermoelectric device usually undergoes mechanical vibration, mechanical and/or thermal cycling, and thermal shock in service. In this study, the enhanced mechanical properties and thermoelectric properties of PbTe are realized simultaneously through introducing dispersive transition metal dichalcogenide MoTe2 (Molybdenum Telluride). The in situ formed MoTe2 precipitations with the size in the range from 2 μm to 5 μm and the tight and smooth interface between the PbTe matrix and precipitates contribute to the obvious crack deflection, crack bridging, and pull-out of long grains, dissipating more energy during the crack propagation and resulting in a tortuous propagation path. Due to the toughening and the dispersion strengthening effect, the compressive strength, bending strength and fracture toughness of the sample with a composite amount of 1% are 109 MPa, 50 MPa and 0.65 MPa·m1/2, respectively, which are increased by about 37%, 117% and 67% compared with the Na0.02Pb0.98Te matrix. Additionally, the in-situ MoTe2 precipitates intensify the interface phonon scattering and thus decrease the lattice thermal conductivity. As a result, Na0.02Pb0.98Te-1%MoTe2 sample achieves the maximum ZT value of 1.46 at 700K, which is 11% higher than that of Na0.02Pb0.98Te without any MoTe2 nano-precipitation.
The eutectic Te–SnTe composites with self-organized rod and lamellar structure were synthesized using the directional solidification technology. The experiments show that the volume fraction and shape-tunable morphology of the SnTe phase vary with the alloy compositions. The thermoelectric properties of the composites are dependent on the volume fraction of SnTe phase and exhibit obvious anisotropy in different growth directions. The composites perpendicular to the growth direction possess much larger S and lower κL than that in the parallel direction. High resolution transmission electron microscopy (HRTEM) results illustrate that there are a given amount of dislocations and atomic mismatch stress field around the Te–SnTe eutectic interface areas, which effectively scatter the heat-carrying phonons, leading to an ultralow lattice thermal conductivity of 0.64 Wm−1K−1 for Sn-80at%Te eutectic alloy. The obtained maximum figure of merit is 0.40 for Sn-90at%Te alloy which is 1.5–1.9 times higher than that of pure SnTe and Te, respectively. It demonstrates that introducing large amounts of eutectic interfaces in Te–SnTe composites is an effective way to enhance the thermoelectric performance.
The Bi2Te3−xSex family has constituted n‐type state‐of‐the‐art thermoelectric materials near room temperature (RT) for more than half a century, which dominates the active cooling and novel heat harvesting application near RT. However, the drawbacks of a brittle nature and Te‐content restricts the possibility for exploring potential applications. Here, it is shown that the Mg3+δSbxBi2−x family ((ZT)avg = 1.05) could be a promising substitute for the Bi2Te3−xSex family ((ZT)avg = 0.9–1.0) in the temperature range of 50–250 °C based on the comparable thermoelectric performance through a synergistic effect from the tunable bandgap using the alloy effect and the suppressible Mg‐vacancy formation using an interstitial Mn dopant. The former is to shift the optimal thermoelectric performance to near RT, and the latter is helpful to partially decouple the electrical transport and thermal transport in order to get an optimal RT power factor. The positive temperature dependence of the bandgap suggests this family is also a superior medium‐temperature thermoelectric material for the significantly suppressed bipolar effect. Furthermore, a two times higher mechanical toughness, compared with the Bi2Te3−xSex family, allows for a promising substitute for state‐of‐the‐art n‐type thermoelectric materials near RT.
Thermoelectric generators can convert heat directly into usable electric power but suffer from low efficiencies and high costs, which has hindered wide-scale applications. Accordingly, an important goal in the field of thermoelectricity is to develop new high performance materials that are composed of more earth-abundant elements. The best systems for mid-temperature power generation rely on heavily doped PbTe, but the Te in these materials is scarce in the Earth’s crust. PbSe is emerging as a less expensive alternative to PbTe, although it displays inferior performance due to a considerably smaller power factor S2σ, where S is the Seebeck coefficient and σ is electrical conductivity. Here, we present a new p-type PbSe system, Pb0.98Na0.02Se-x%HgSe, which yields a very high power factor of ~ 20 µW⋅cm-1⋅K-2 at 963 K when x = 2, a 15 % improvement over the best performing PbSe-x%MSe materials. The enhancement is attributed to a combination of high carrier mobility and the early onset of band convergence in the Hg-alloyed samples (~ 550 K), which results in a significant increase in the Seebeck coefficient. Interestingly, we find that the Hg2+ cations sit at an off-centered position within the PbSe lattice, and we dub the displaced Hg atoms ‘discordant’. DFT calculations indicate that this feature plays a role in lowering thermal conductivity, and we believe that this insight may inspire new design criteria for engineering high performance thermoelectric materials. The high power factor combined with a decrease in thermal conductivity gives a high figure of merit ZT of 1.7 at 970 K, the highest value reported for PbSe to date.
Thermoelectricity offers a sustainable path to recover and convert waste heat into readily available electric energy, and has been studied for more than two centuries. From the controversy between Galvani and Volta on the Animal Electricity, dating back to the end of the XVIII century and anticipating Seebeck’s observations, the understanding of the physical mechanisms evolved along with the development of the technology. In the XIX century Ørsted clarified some of the earliest observations of the thermoelectric phenomenon and proposed the first thermoelectric pile, while it was only after the studies on thermodynamics by Thomson, and Rayleigh’s suggestion to exploit the Seebeck effect for power generation, that a diverse set of thermoelectric generators was developed. From such pioneering endeavors, technology evolved from massive, and sometimes unreliable, thermopiles to very reliable devices for sophisticated niche applications in the XX century, when Radioisotope Thermoelectric Generators for space missions and nuclear batteries for cardiac pacemakers were introduced. While some of the materials adopted to realize the first thermoelectric generators are still investigated nowadays, novel concepts and improved understanding of materials growth, processing, and characterization developed during the last 30 years have provided new avenues for the enhancement of the thermoelectric conversion efficiency, for example through nanostructuration, and favored the development of new classes of thermoelectric materials. With increasing demand for sustainable energy conversion technologies, the latter aspect has become crucial for developing thermoelectrics based on abundant and non-toxic materials, which can be processed at economically viable scales, tailored for different ranges of temperature. This includes high temperature applications where a substantial amount of waste energy can be retrieved, as well as room temperature applications where small and local temperature differences offer the possibility of energy scavenging, as in micro harvesters meant for distributed electronics such as sensor networks. While large scale applications have yet to make it to the market, the richness of available and emerging thermoelectric technologies presents a scenario where thermoelectrics is poised to contribute to a future of sustainable future energy harvesting and management.
This work reviews the broad field of thermoelectrics. Progress in thermoelectrics and milestones that led to the current state-of-the-art are presented by adopting an historical footprint. The review begins with an historical excursus on the major steps in the history of thermoelectrics, from the very early discovery to present technology. A panel on the theory of thermoelectric transport in the solid state reviews the transport theory in complex crystal structures and nanostructured materials. Then, the most promising thermoelectric material classes are discussed one by one in dedicated sections and subsections, carefully highlighting the technological solutions on materials growth that have represented a turning point in the research on thermoelectrics. Finally, perspectives and the future of the technology are discussed in the framework of sustainability and environmental compatibility.
Nanotwinning exhibits strengthening effects in many metals, semiconductors, and ceramics. However, we show from ab-initio calculations that nanotwins significantly decrease the strength of thermoelectric semiconductor Mg2Si. The theoretical shear strength of nanotwinned Mg2Si is found to be 0.93 GPa, much lower than that (6.88 GPa) of flawless Mg2Si. Stretching the Mg-Si bond under deformation leads to the structural softening and failure of flawless Mg2Si. While in nanotwinned Mg2Si, the Mg-Si bond at the twin boundary (TB) is expanded to accommodate the structural misfit, weakening the TB rigidity and leading to the low ideal shear strength.
The study of thermoelectric materials spans condensed matter physics, materials science and engineering, and solid-state chemistry. The diversity of the participants and the inherent complexity of the topic mean that it is difficult, if not impossible, for a researcher to be fluent in all aspects of the field. This review, which grew out of a one-week summer school for graduate students, aims to provide an introduction and practical guidance for selected conceptual, synthetic, and characterization approaches and to craft a common umbrella of language, theory, and experimental practice for those engaged in the field of thermoelectric materials. This review does not attempt to cover all major aspects of thermoelectric materials research or review state-of-the-art thermoelectric materials. Rather, the topics discussed herein reflect the expertise and experience of the authors. We begin by discussing a universal approach to modeling electronic transport using Landauer theory. The core sections of the review are focused on bulk inorganic materials and include a discussion of effective strategies for powder and single crystal synthesis, the use of national synchrotron sources to characterize crystalline materials, error analysis, and modeling of transport data using an effective mass model, and characterization of phonon behavior using inelastic neutron scattering and ultrasonic speed of sound measurements. The final core section discusses the challenges faced when synthesizing carbon-based samples and the measuring or interpretation of their transport properties. We conclude this review with a brief discussion of some of the grand challenges and opportunities that remain to be addressed in the study of thermoelectrics.
CuInTe2 is recognized as a promising thermoelectric material in the mediate temperature range, but its mechanical properties important for its engineering applications remain unexplored so far. Here, we apply quantum mechanics (QM) to investigate such intrinsic mechanical properties as ideal strength and failure mechanism along pure shear, uniaxial tension, and biaxial shear deformations, respectively. We find that the ideal shear strength of CuInTe2 is 2.43 GPa along (221)[11-1] slip system, which is much lower than its ideal tensile strength of 4.88 GPa along [1-10] in tension, suggesting that slipping along (221)[11-1] is the most likely activated failure mode under pressure. The shear induced failure of CuInTe2 arises from the softening and breakage of the covalent In–Te bond. However, the tensile failure arises from the breakage of Cu–Te bond. Under biaxial shear load, compression leads to the shrinking the In–Te bond and hence the buckling of the In-Te hexagonal framework. We also find that the ideal strength of CuInTe2 is relatively low among important thermoelectric materials, indicating that it is necessary to enhance the mechanical properties for the commercial applications of CuInTe2.
Bismuth telluride (Bi2Te3) based thermoelectric (TE) materials have been commercialized successfully as solid-state power generators, but their low mechanical strength suggests that these materials may not be reliable for long-term use in TE devices. Here we use density functional theory to show that the ideal shear strength of Bi2Te3 can be significantly enhanced up to 215% by imposing nanoscale twins. We reveal that the origin of the low strength in single crystalline Bi2Te3 is the weak van der Waals interaction between the Te1 coupling two Te1─Bi─Te2─Bi─Te1 five-layer quint substructures. However, we demonstrate here a surprising result that forming twin boundaries between the Te1 atoms of adjacent quints greatly strengthens the interaction between them, leading to a tripling of the ideal shear strength in nanotwinned Bi2Te3 (0.6 GPa) compared to that in the single crystalline material (0.19 GPa). This grain boundary engineering strategy opens a new pathway for designing robust Bi2Te3 TE semiconductors for high-performance TE devices.
Recent experiments have uncovered n-type Zintl compounds including layered Mg3Sb2 with high thermoelectric efficiency. However, until now the mechanics of Mg3Sb2, which is important to understand for its widespread applications, has not been investigated. Here we used density functional theory (DFT) to determine the deformation and failure mechanism of Mg3Sb2, and compared with isostructural CaMg2Sb2 and CaZn2Sb2 crystals. Mg3Sb2 is found to have a very low ideal shear strength of 1.95 GPa. The weakly ionic Mg−Sb bond, which links the Mg2+ sheet structure and the [Mg2Sb2]2- substructure, breaks and creates pathways to slip between different [Mg2Sb2]2- substructures under pure shear deformation in Mg3Sb2. The substitution of
the Mg2+ sheet structure by more electropositive Ca2+ leads to a much higher ideal shear strength of 4.07 GPa in isostructural CaMg2Sb2 compared with that in Mg3Sb2. The substitution of the [Mg2Sb2]2- substructure by [Zn2Sb2]2- in CaMg2Sb2 has little influence on the mechanical strength, leading to similar ideal shear strength for the CaZn2Sb2 and CaMg2Sb2. To enhance the mechanical strength of Mg3Sb2, we suggest that the weakly ionic Mg−Sb bond should be strengthened to improve the interaction between the Mg2+ sheet structure and the [Mg2Sb2]2- substructure by proper doping strategies such as partial substitution of Mg by more electropositive cations of Ca or Sr. These deformation modes are essential to understand the intrinsic mechanical process of this novel class of thermoelectric materials, which provides an insightful guidance for designing high-performance layered Zintl compounds with improved strength and ductility.
Grain or phase boundaries play a critical role in the carrier and phonon transport in bulk thermoelectric materials. Previous investigations about controlling boundaries primarily focused on the reducing grain size or forming nanoinclusions. Herein, liquid phase compaction method is first used to fabricate the Yb-filled CoSb3 with excess Sb content, which shows the typical feature of low-angle grain boundaries with dense dislocation arrays. Seebeck coefficients show a dramatic increase via energy filtering effect through dislocation arrays with little deterioration on the carrier mobility, which significantly enhances the power factor over a broad temperature range with a high room-temperature value around 47 μW cm−2 K−1. Simultaneously, the lattice thermal conductivity could be further suppressed via scattering phonons via dense dislocation scattering. As a result, the highest average figure of merit ZT of ≈1.08 from 300 to 850 K could be realized, comparable to the best reported result of single or triple-filled Skutterudites. This work clearly points out that low-angle grain boundaries fabricated by liquid phase compaction method could concurrently optimize the electrical and thermal transport properties leading to an obvious enhancement of both power factor and ZT.
To minimize the lattice thermal conductivity in thermoelectrics, strategies typically focus on the scattering of low-frequency phonons by interfaces and high-frequency phonons by point defects. In addition, scattering of mid-frequency phonons by dense dislocations, localized at the grain boundaries, has been shown to reduce the lattice thermal conductivity and improve the thermoelectric performance. Here we propose a vacancy engineering strategy to create dense dislocations in the grains. In Pb1-xSb2x/3Se solid solutions, cation vacancies are intentionally introduced, where after thermal annealing the vacancies can annihilate through a number of mechanisms creating the desired dislocations homogeneously distributed within the grains. This leads to a lattice thermal conductivity as low as 0.4[thinsp]Wm-1[thinsp]K-1 and a high thermoelectric figure of merit, which can be explained by a dislocation scattering model. The vacancy engineering strategy used here should be equally applicable for solid solution thermoelectrics and provides a strategy for improving zT.
TiNiSn based half-Heusler (HH) compounds exhibit excellent thermoelectric (TE) performance. In realistic thermoelectric applications, high strength, high toughness TiNiSn based TE devices are required. To illustrate the failure mechanism of TiNiSn, we applied density functional theory to investigate the response along various tensile and shear deformations. We find that shearing along the (111)/〈110〉 slip system has the lowest ideal shear strength of 10.52 GPa, indicating that it is the most plausible slip system under pressure. The Ni–Sn covalent bond is more rigid than the Ni–Ti and Ti–Sn ionic bonds. The TiSn framework resists external deformation until the maximum shear stress. The softening of the Ti–Sn ionic bond leads to the decreased rigidity of the TiSn framework in TiNiSn, resulting in reversible plastic deformation before failure. Further shear deformation leads to the breakage of the Ti–Sn bond, hence resulting in the collapse of the TiSn framework and structural failure of TiNiSn. To improve the ideal strength, we suggest a sub-structure engineering approach leading to improved rigidity of the TiSn framework. Here, we find that the substitution of Ti by Hf and Zr can enhance the ideal shear strength to 12.17 GPa in Hf_(0.5)Zr_(0.5)NiSn, which is attributed to a more rigid XSn (X = Hf and Zr) framework compared to TiSn.
Half-Heusler compounds based on XNiSn and XCoSb (X = Ti, Zr or Hf) have rapidly become important thermoelectric materials for converting waste heat into electricity. In this Review, we provide an overview on the electronic properties of half-Heusler compounds in an attempt to understand their basic structural chemistry and physical properties, and to guide their further development. Half-Heusler compounds can exhibit semiconducting transport behaviour even though they are described as ‘intermetallic’ compounds. Therefore, it is most useful to consider these systems as rigid-band semiconductors within the framework of Zintl (or valence-precise) compounds. These considerations aid our understanding of their properties, such as the bandgap and low hole mobility because of interstitial Ni defects in XNiSn. Understanding the structural and bonding characteristics, including the presence of defects, will help to develop different strategies to improve and design better half-Heusler thermoelectric materials.
CoSb3-based filled skutterudite has emerged as one of the most viable candidates for thermoelectric applications in automotive industry. However, the scale-up commercialization of such materials is still a challenge due to the scarcity and cost of constituent elements. Here we study Ce, the most earth abundant and low-cost rare earth element as a single-filling element and demonstrate that, by solubility design using a phase diagram approach, the filling fraction limit (FFL) x in CexCo4Sb12 can be increased more than twice the amount reported previously (x=0.09). This ultra-high FFL (x=0.20) enables the optimization of carrier concentration such that no additional filling elements are needed to produce a state of the art n-type skutterudite material with a zT value of 1.3 at 850 K before nano-structuring. The earth abundance and low cost of Ce would potentially facilitate a widespread application of skutterudites.
The elastic constant tensor of an inorganic compound provides a complete description of the response of the material to external stresses in the elastic limit. It thus provides fundamental insight into the nature of the bonding in the material, and it is known to correlate with many mechanical properties. Despite the importance of the elastic constant tensor, it has been measured for a very small fraction of all known inorganic compounds, a situation that limits the ability of materials scientists to develop new materials with targeted mechanical responses. To address this deficiency, we present here the largest database of calculated elastic properties for inorganic compounds to date. The database currently contains full elastic information for 1,181 inorganic compounds, and this number is growing steadily. The methods used to develop the database are described, as are results of tests that establish the accuracy of the data. In addition, we document the database format and describe the different ways it can be accessed and analyzed in efforts related to materials discovery and design.
Recent experiments reported a substantial strengthening of cubic boron nitride by nanotwinning. This discovery raises fundamental questions about new atomistic mechanisms governing incipient plasticity in nanostructured strong covalent solids. Here we reveal an unusual twin-boundary dominated indentation strain-stiffening mechanism that produces a large strength enhancement at nanometer-scale twinning size where a strength reduction is normally expected due to the reverse Hall-Petch effect. First-principles calculations unveil significantly enhanced indentation shear strength in nanotwinned cubic boron nitride by bond rearrangement at the twin boundary under indentation compression and shear strains that produces especially strong stress response. This remarkable strain-stiffening mechanism offers fundamental insights for understanding the stress response of nanotwinned covalent solids under indentation.
Lead telluride-based materials demonstrate the highest thermoelectric performance in the temperature range from 200°C to 400°C, and they are of interest for numerous waste heat recovery applications. Unfortunately, these conventionally grown materials are usually very brittle, which results in significant material loss during module manufacturing and a decrease in module reliability when subjected to continuous vibrations common for automotive applications. We present a hot extrusion process developed for the first time for PbTe which yields polycrystalline materials with strong mechanical properties combined with high thermoelectric performance. n-Type lead telluride was extruded from conventionally synthesized and powdered material at temperatures in the range of 450°C to 520°C depending on material stoichiometry. The extruded rods were of cylindrical shape with 2.54 cm diameter and lengths up to 40 cm. Young’s modulus measured using mechanical spectroscopy varied from 59 GPa to 51 GPa for temperatures in the range of 20°C to 300°C. Slicing and dicing of extruded rods to obtain cubical samples with 2 mm side demonstrated no difficulties, illustrating the material homogeneity and its potential for manufacturing module legs. The microstructure of the material was studied by scanning electron microscopy. Doping with antimony iodide during the milling process controls the conduction electron concentration in the range from 1 × 1019 cm−3 to 6 × 1019 cm−3. For optimized doping of 0.08 wt.% SbI3, the maximum thermoelectric figure of merit (ZT) reaches a value of 0.99 at 380°C, as measured by the Harman method. The combination of high thermoelectric performance and improved fracture toughness makes this novel hot-extruded polycrystalline PbTe material highly competitive for many applications.
This paper is concerned with the mechanical properties of PbTe and Pb1-xSnxTe compounds and their correlation with the respective charge carrier concentrations. Single-crystals and samples prepared by powder metallurgy display similar general trends. It was found that although there is a similar electronic behavior (constant scattering factor of -0.5) for the various compositions examined, the mechanical properties of the compounds are completely different. (c) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Mg(2)Si and Mg(2)Sn are indirect band gap semiconductors with two low-lying conduction bands (the lower mass and higher mass bands) that have their respective band edges reversed in the two compounds. Consequently, for some composition x, Mg(2)Si(1-x)Sn(x) solid solutions must display a convergence in energy of the two conduction bands. Since Mg(2)Si(1-x)Sn(x) solid solutions are among the most prospective of the novel thermoelectric materials, we aim on exploring the influence of such a band convergence (valley degeneracy) on the Seebeck coefficient and thermoelectric properties in a series of Mg(2)Si(1-x)Sn(x) solid solutions uniformly doped with Sb. Transport measurements carried out from 4 to 800 K reveal a progressively increasing Seebeck coefficient that peaks at x=0.7. At this concentration the thermoelectric figure of merit ZT reaches exceptionally large values of 1.3 near 700 K. Our first principles calculations confirm that at the Sn content x≈0.7 the two conduction bands coincide in energy. We explain the high Seebeck coefficient and ZT values as originating from an enhanced density-of-states effective mass brought about by the increased valley degeneracy as the two conduction bands cross over. We corroborate the increase in the density-of-states effective mass by measurements of the low temperature specific heat. The research suggests that striving to achieve band degeneracy by means of compositional variations is an effective strategy for enhancing the thermoelectric properties of these materials.
We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order N-atoms(3) operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ''metric'' and a special ''preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order N-atoms(2) scaling is found for systems up to 100 electrons. If we take into account that the number of k points can be implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
The search for alternative energy sources is nowadays at the forefront of applied research. In this context, thermoelectricity for direct energy conversion from thermal to electrical energy plays an important role, in particular, for the exploitation of waste heat [G. J. Snyder and E. S. Toberer, Nat. Mater. 7, 105 (2008); M. S. Dresselhaus etal, Adv. Mater. (Weinheim, Ger.) 19, 1043 (2007)]. Materials for such applications should exhibit thermoelectric potential as well as mechanical stability. PbTe based alloys have been considered for many years as state of the art thermoelectric materials for mid-temperature power generation (500–900 K), with efficiency values that are still being improved by both alloying [P. F. P. Poudeu etal, Chem., Int. Ed. 45, 1 (2006); J. R. Sootsman etal, Chem. Mater. 18, 4993 (2006); P. F. P. Poudeu etal, Chem. Soc. 126, 14347 (2006); J. Androulakis etal, Adv. Mater. (Weinheim, Ger.) 18, 1170 (2006); K. F. Hsu etal, Science 303, 818 (2004)] and doping [Y. Gelbstein etal, Physica B (Amsterdam) 363, 196 (2005); Y. Gelbstein etal, Physica B (Amsterdam) 396, 16 (2007)] optimizations. However, the mechanical properties of PbTe based materials are highly dependent on the conductivity type ( n or p ) and carrier concentrations [Y. Gelbstein etal, Scr. Mater. 58, 251 (2008)]. This paper puts forward the mechanical durability of thermoelectric materials and, in particular, of PbTe as a dominant factor that is nondetachable from the transport properties, which should be considered in the search for high quality thermoelectric materials. Here we discuss the microhardness enhancement of p -type PbTe alloys with hole concentrations higher than 5×10<sup>18</sup> cm <sup>-3</sup> . This anomaly is obtained while all the other investigated n -type (up to 10<sup>20</sup> cm <sup>-3</sup> ) a-
nd p -type (up to 10<sup>18</sup> cm <sup>-3</sup> ) compositions maintained a constant microhardness value of ∼30 H <sub>V</sub> . The origin of this microhardness enhancement is not yet understood on a fundamental level, however two possible mechanisms are discussed. One deals with the elastic interaction between dislocations and impurities with higher covalent radius than the sublattice vacancy. The other is correlated with the existence of a second valence band of heavy holes in PbTe, which begins to fill up at the same concentration where a hardness enhancement was observed. These mechanisms correlating between mechanical end electronic properties of PbTe based alloys can serve as guidelines for the search for potential candidates, obtaining both thermoelectric potential and mechanical stability for thermoelectric applications.
Dislocation nucleation from a stressed crack tip is analyzed based on the Peierls concept. A periodic relation between shear stress and atomic shear displacement is assumed to hold along the most highly stressed slip plane emanating from a crack tip. This allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack. An exact solution for the loading at that nucleation instability is developed via the J-integral for the case when the crack and slip planes coincide, and an approximate solution is given when they do not. Solutions are also given for emission of dissociated dislocations, especially partial dislocation pairs in fcc crystals. The level of applied stress intensity factors required for dislocation nucleation is shown to be proportional to √γus, where γus, the unstable stacking energy, is a new solid state parameter identified by the analysis. It is the maximum energy encountered in the block-like sliding along a slip plane, in the Burgers vector direction, of one half of a crystal relative to the other. Approximate estimates of γus are summarized and the results are used to evaluate brittle vs ductile response in fcc and bcc metals in terms of the competition between dislocation nucleation and Griffith cleavage at a crack tip. The predictions seem compatible with known behavior and also show that in many cases solids which are predicted to first cleave under pure mode I loading should instead first emit dislocations when that loading includes very small amounts of mode II and III shear. The analysis in this paper also reveals a feature of the near-tip slip distribution corresponding to the saddle point energy configuration for cracks that are loaded below the nucleation threshold, as is of interest for thermal activation.
The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blöchl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
Although aluminum has a smaller modulus in {111}〈112̄〉 shear than that of copper, we find by first-principles calculation
that its ideal shear strength is larger because of a more extended deformation range before softening. This fundamental behavior,
along with an abnormally high intrinsic stacking fault energy and a different orientation dependence on pressure hardening,
are traced to the directional nature of its bonding. By a comparative analysis of ion relaxations and valence charge redistributions
in aluminum and copper, we arrive at contrasting descriptions of bonding characteristics in these two metals that can explain
their relative strength and deformation behavior.
Thermoelectric materials, which can generate electricity from waste heat or be used as solid-state Peltier coolers, could play an important role in a global sustainable energy solution. Such a development is contingent on identifying materials with higher thermoelectric efficiency than available at present, which is a challenge owing to the conflicting combination of material traits that are required. Nevertheless, because of modern synthesis and characterization techniques, particularly for nanoscale materials, a new era of complex thermoelectric materials is approaching. We review recent advances in the field, highlighting the strategies used to improve the thermopower and reduce the thermal conductivity.
Creep deformation is of concern in PbTe thermoelectric modules operating for years at high homologous temperatures while being subjected to internal or external stresses. The creep strain rates of hot-pressed PbTe are measured at 400 °C; a power-law is found, with a stress exponent n = 1.7 at low stresses (2–7 MPa) and n = 4.4 at high stresses (7–35 MPa). Creep rates measured at low stresses (4–6 MPa) between 350 and 500 °C provide a creep activation energy Q = 181 ± 18 kJ/mol. The creep parameters and the good hot ductility of PbTe are compared to those for cast Bi2Te3 reported in the literature.
Thermoelectrics directly converts waste heat into electricity and is considered a promising means of sustainable energy generation. While most of the recent advances in the enhancement of the thermoelectric figure of merit (ZT) resulted from a decrease in lattice thermal conductivity by nanostructuring, there have been very few attempts to enhance electrical transport properties, i.e., the power factor. Here we use nanochemistry to stabilize bulk bismuth telluride (Bi2Te3) that violates phase equilibrium, namely, phase-pure n-type K0.06Bi2Te3.18. Incorporated potassium and tellurium in Bi2Te3 far exceed their solubility limit, inducing simultaneous increase in the electrical conductivity and the Seebeck coefficient along with decrease in the thermal conductivity. Consequently, a high power factor of ∼43 μW cm(-1) K(-2) and a high ZT > 1.1 at 323 K are achieved. Our current synthetic method can be used to produce a new family of materials with novel physical and chemical characteristics for various applications.
In this work, we demonstrate the use of high performance nanostructured PbTe-based materials in high conversion efficiency thermoelectric modules. We fabricated the samples of PbTe–2% MgTe doped with 4% Na and PbTe doped with 0.2% PbI2 with high thermoelectric figure of merit (ZT) and sintered them with Co–Fe diffusion barriers for use as p- and n-type thermoelectric legs, respectively. Transmission electron microscopy of the PbTe legs reveals two shapes of nanostructures, disk-like and spherical. The reduction in lattice thermal conductivity through nanostructuring gives a ZT of ∼1.8 at 810 K for p-type PbTe and ∼1.4 at 750 K for n-type PbTe. Nanostructured PbTe-based module and segmented-leg module using Bi2Te3 and nanostructured PbTe were fabricated and tested with hot-side temperatures up to 873 K in a vacuum. The maximum conversion efficiency of ∼8.8% for a temperature difference (ΔT) of 570 K and ∼11% for a ΔT of 590 K have been demonstrated in the nanostructured PbTe-based module and segmented Bi2Te3/nanostructured PbTe module, respectively. Three-dimensional finite-element simulations predict that the maximum conversion efficiency of the nanostructured PbTe-based module and segmented Bi2Te3/nanostructured PbTe module reaches 12.2% for a ΔT of 570 K and 15.6% for a ΔT of 590 K respectively, which could be achieved if the electrical and thermal contact between the nanostructured PbTe legs and Cu interconnecting electrodes is further improved.
Filled skutterudites RxCo4Sb12 are excellent n-type thermoelectric materials owing to their high electronic mobility and high effective mass, combined with low thermal conductivity associated with the addition of filler atoms into the void site. The favourable electronic band structure in n-type CoSb3 is typically attributed to threefold degeneracy at the conduction band minimum accompanied by linear band behaviour at higher carrier concentrations, which is thought to be related to the increase in effective mass as the doping level increases. Using combined experimental and computational studies, we show instead that a secondary conduction band with 12 conducting carrier pockets (which converges with the primary band at high temperatures) is responsible for the extraordinary thermoelectric performance of n-type CoSb3 skutterudites. A theoretical explanation is also provided as to why the linear (or Kane-type) band feature is not beneficial for thermoelectrics.
Skutterudites based on CoSb3 have high thermoelectric efficiency, but the low fracture strength is a serious consideration for commercial applications. To understand the origin of the brittleness in CoSb3, we examine the response along various shear and tensile deformations using density functional theory. We find that the Co-Sb bond dominates the ideal strength. Among all the shear and tensile deformation paths, shearing along the (001)/〉100〉 slip system has the lowest ideal strength, indicating it is the most likely slip system to be activated under pressure. We also find that, because the Sb-Sb covalent bond is softer than the Co-Sb bond, the Sb-rings are less rigid than the Co-Sb frameworks, which leads to the Sb-rings softening before the Co-Sb frameworks. Further deformation leads to deconstruction of Sb-rings and collapse of Co-Sb frameworks, resulting in structural failure. Moreover, we find that filling of the CoSb3 void spaces with such typical fillers as Na, Ba, or Yb has little effect on the ideal strength and failure mode, which can be understood because they have little effect on the Sb-rings.
The different modifications of elementary boron and the related boron-rich borides exhibit complex structures, which are essentially composed of nearly regular B12 icosahedra and of structural elements consisting of fragments or condensed systems of icosahedra. These structure elements are bonded directly to one another or via single boron or foreign atoms thus forming rigid comparably open three-dimensional frameworks with a large variety of structures. In the open structures of all the icosahedral boron-rich solids there are voids of sufficient size to accommodate foreign atoms. This interstitial doping is very important to modify the semiconductor properties of these solids. Only the rhombohedral phases of boron show semiconducting properties.
All phosphides, arsenides and antimonides of boron, aluminum, gallium and antimony (BP, BAs, BSb, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb) crystallize under normal conditions in the (cubic) zincblende lattice (space group \( T_{d^2 } - F\bar 4 3m \) ).
Squeezing out efficient thermoelectrics
Thermoelectric materials hold the promise of converting waste heat into electricity. The challenge is to develop high-efficiency materials that are not too expensive. Kim et al. suggest a pathway for developing inexpensive thermoelectrics. They show a dramatic improvement of efficiency in bismuth telluride samples by quickly squeezing out excess liquid during compaction. This method introduces grain boundary dislocations in a way that avoids degrading electrical conductivity, which makes a better thermoelectric material. With the potential for scale-up and application to cheaper materials, this discovery presents an attractive path forward for thermoelectrics.
Science , this issue p. 109
This review discusses recent developments and current research in high performance bulk thermoelectric materials, comprising nanostructuring, mesostructuring, band alignment, band engineering and synergistically defining key strategies for boosting the thermoelectric performance. To date, the dramatic enhancements in the figure of merit achieved in bulk thermoelectric materials have come either from the reduction in lattice thermal conductivity or improvement in power factors, or both of them. Here, we summarize these relationships between very large reduction of the lattice thermal conductivity with all-scale hierarchical architecturing, large enhanced Seebeck coefficients with intra-matrix electronic structure engineering, and control of the carrier mobility with matrix/inclusion band alignment, which enhance the power factor and reduce the lattice thermal conductivity. The new concept of hierarchical compositionally alloyed nanostructures to achieve these effects is presented. Systems based on PbTe, PbSe and PbS in which spectacular advances have been demonstrated are given particular emphasis. A discussion of future possible strategies is aimed at enhancing the thermoelectric figure of merit of these materials.
The following values have no corresponding Zotero field:
number: 3
Lead chalcogenides (PbQ, Q = Te, Se, S) have proved to possess high thermoelectric efficiency for both n-type and p-type compounds. Recent success in tuning of electronic band structure, including manipulating the band gap, multiple bands or introducing resonant states have led to a significant improvement in the thermoelectric performance of p-type lead chalcogenides compared to the n-type ones. Here, the n-type quaternary composites of (PbTe)0.75(PbS)0.15(PbSe)0.1 are studied to evaluate the effects of nanostructuring on lattice thermal conductivity, carrier mobility and effective mass variation. The results are compared with the similar ternary systems of (PbTe)1-x(PbSe)x, (PbSe)1-x(PbS)x and (PbS)1-x(PbTe)x. The reduction in the lattice thermal conductivity owing to phonon scattering at the defects and interfaces was found to be compensated by reduced carrier mobility. This results in a maximum figure of merit, zT, of ~ 1.1 at 800 K similar to the performance of the single phase alloys of PbTe, PbSe and (PbTe)1-x(PbSe)x.
Lead chalcogenides, most notably lead selenide (PbSe) and lead telluride (PbTe), have become an active area of research due to their thermoelectric (TE) properties. The high figure of merit of these materials has brought much attention to them, due to their ability to convert waste heat into electricity. Recent efforts, such as applying pressure or doping, have shown an increase in TE efficiency. Variation in application and synthesis conditions gives rise to a need for analysis of mechanical properties of these materials. In addition to the rocksalt (NaCl) structure at ambient conditions, lead chalcogenides have an orthorhombic (Pnma) intermediate pressure phase and a higher pressure CsCl phase. By using first-principles calculations, performed within density functional theory, we study the structural, elastic and mechanical properties of PbTe and PbSe in their three phases. For each phase, elastic constants, bulk modulus, shear modulus, and Young's modulus are calculated, and the NaCl phase is studied with typical dopants, both n-type (Bi and I) and p-type (Na, In, and Tl). Pugh's ratio is employed to give insight on the brittleness of the materials and phase studied. The results presented here will be useful to guide future experiments toward the search for structurally stable TE materials.
A point defect chemistry approach to improving thermoelectric (TE) properties is introduced, and its effectiveness in the emerging mid-temperature TE material Mg2(Si,Sn) is demonstrated. The TE properties of Mg2(Si,Sn) are enhanced via the synergistical implementation of three types of point defects, that is, Sb dopants, Mg vacancies, and Mg interstitials in Mg2Si0.4Sn0.6-xSbx with high Sb content (x > 0.1), and it is found that i) Sb doping at low ratios tunes the carrier concentration while it facilitates the formation of Mg vacancies at high doping ratios (x > 0.1). Mg vacancies act as acceptors and phonon scatters; ii) the concentration of Mg vacancies is effectively controlled by the Sb doping ratio; iii) excess Mg facilitates the formation of Mg interstitials that also tunes the carrier concentration; vi) at the optimal Sb-doping ratio near x ≈ 0.10 the lattice thermal conductivity is significantly reduced, and a state-of-the-art figure of merit ZT > 1.1 is attained at 750 K in 2 at% Zn doped Mg2Si0.4Sn0.5Sb0.1 specimen. These results demonstrate the significance of point defects in thermoelectrics, and the promise of point defect chemistry as a new approach in optimizing TE properties.
The skutterudite/electrode thermoelectric joints were fabricated with the insertion of Ti foil by spark plasma sintering. The interfacial microstructure and reliability of joints were studied during thermal duration test. A multilayer structure, which was composed of intermetallic compounds, was observed at the CoSb3/Ti interface after thermal aging of 20 days. The interfacial reactions and diffusion path between CoSb3 and Ti were discussed. The contact resistance of CoSb3/electrode junction was measured through four-probe method and the thermal contact resistance was calculated based on multilayer mode measurement. Effects of the contact resistivity on the performance of CoSb3-based device were discussed.
This volume contains basic data of semiconductors. All data were compiled from the 17 volumes of the New Series of the Landolt-Börnstein data handbook, dealing with semiconductors. They comprise the information a scientist working an semiconductors is needing in his every-day work.
The slip systems observed in a number of crystal structures common among
metals and simple ceramic materials are examined to see whether they allow the
crystal to undergo an arbitrary strain without change of volume. For most
materials, other than f.c.c. and b.c.c. metals, there are insufficient
independent slip systems. The condition under which cross slip can give rise to
extra independent systems is stated. The results explain in a natural way recent
experimental findings on the ductility of polycrystals with the sodium chloride
structure. (auth)
The elastic moduli of both single crystal and polycrystalline magnesia were determined in the kcps frequency range by a Forster-type resonance method. The values obtained at 25°C for single crystal are: c11 = 28•92c12 = 8•79 and c44 = 15•46 × 10 dynes per cm. The calculated isotropic elastic moduli for polycrystalline MgO obtained from the single crystal compliances are in good agreement with experimental values measured on theoretical density (glass-free) MgO. The measured Young's modulus and shear modulus at zero per cent porosity are 30•50 and 12•90 × 10 dynes per cm, respectively. The results of the present work are compared with the earlier work in the mcps frequency range.
The pseudo-binary alloys (PbTe)1−x–(SnTe)x in the whole composition range were prepared by pressureless sintering. It was found that the electrical conductivities increased with mole fraction x (x≤0.6), and then decreased. A transition from extrinsic to intrinsic state for the carriers occurred while temperature was elevated to 573 K. The temperature, corresponding to the maximum Seebeck coefficients for the alloys which decreased with mole fraction x, shifted to higher temperature region when x≤0.6, and then remained constant. In addition, thermal conductivities were observed to be very low, especially for the alloys with smaller x values, mainly attributed to the low densities and phonon-grain boundary scattering for the compacts. Higher Z values were observed in the higher temperature region, especially for the alloy with x=0.4. Higher compression strengths (310–330 MPa) and hardness (HV95) were obtained for the alloys with mole fraction x ranging from 0.2 to 0.6, which is closely related to the higher densities of the alloys.
A substantial fraction of the mysteries associated with crack extension might be eliminated if the description of fracture experiments could include some reasonable estimate of the stress conditions near the leading edge of a crack particularly at points of onset of rapid fracture and at points of fracture arrest. It is pointed out that for somewhat brittle tensile fractures in situations such that a generalized plane-stress or a plane-strain analysis is appropriate, the influence of the test configuration, loads, and crack length upon the stresses near an end of the crack may be expressed in terms of two parameters. One of these is an adjustable uniform stress parallel to the direction of a crack extension. It is shown that the other parameter, called the stress-intensity factor, is proportional to the square root of the force tending to cause crack extension. Both factors have a clear interpretation and field of usefulness in investigations of brittle-fracture mechanics.
We report on an analysis of strain and crystallite size effects in mechanically alloyed PbTe. The evolution of the microstructure was monitored by Rietveld refinements of the neutron powder diffraction data collected at room temperature. For milling times shorter than 6h, the synthesis is not completed and the samples are clearly multi-phase with high concentrations of unreacted starting constituents. For longer milling times, the diffraction patterns are consistent with a single-phase PbTe. Within the range of reaction times studied, the crystallite size decreases with an exponential decay law and saturates to a value of 26nm. However, the strain parameter does not show such a monotonic behavior. Indeed, it first increases and reaches a maximum when the synthesis is achieved and then drops for longer milling time as a result of the thermal activated annealing induced by additional mechanical shocks.
The 18-electron ternary intermetallic systems TiNiSn and TiCoSb are promising for applications as high-temperature thermoelectrics and comprise earth-abundant, and relatively nontoxic elements. Heusler and half-Heusler compounds are usually prepared by conventional solid state methods involving arc-melting and annealing at high temperatures for an extended period of time. Here, we report an energy-saving preparation route using a domestic microwave oven, reducing the reaction time significantly from more than a week to one minute. A microwave susceptor material rapidly heats the elemental starting materials inside an evacuated quartz tube resulting in near single phase compounds. The initial preparation is followed by a densification step involving hot-pressing, which reduces the amount of secondary phases, as verified by synchrotron X-ray diffraction, leading to the desired half-Heusler compounds, demonstrating that hot-pressing should be treated as part of the preparative process. For TiNiSn, high thermoelectric power factors of 2 mW/mK{sup 2} at temperatures in the 700 to 800 K range, and zT values of around 0.4 are found, with the microwave-prepared sample displaying somewhat superior properties to conventionally prepared half-Heuslers due to lower thermal conductivity. The TiCoSb sample shows a lower thermoelectric figure of merit when prepared using microwave methods because of a metallic second phase.
THE definitions currently used to classify chemical bonds (in terms of
bond order, covalency versus ionicity and so forth) are derived from
approximate theories1 3 and are often imprecise. Here we
outline a first step towards a more rigorous means of classification
based on topological analysis of local quantum-mechanical functions
related to the Pauli exclusion principle. The local maxima of these
functions define 'localization attractors', of which there are only
three basic types: bonding, non-bonding and core. Bonding attractors lie
between the core attractors (which themselves surround the atomic
nuclei) and characterize the shared-electron interactions. The number of
bond attractors is related to the bond multiplicity. The spatial
organization of localization attractors provides a basis for a
well-defined classification of bonds, allowing an absolute
characterization of covalency versus ionicity to be obtained from
observable properties such as electron densities.
Two-phase PbTe–PbS materials, in which PbS is a nanostructured phase, are promising thermoelectric materials for the direct conversion of heat energy into electricity. In this study, a Vickers indentation mean hardness of 1.18 ± 0.09 GPa was measured for hot pressed specimens Pb0.95Sn0.05Te–PbS 8% while the mean hardness of cast specimens was 0.68 ± 0.07 GPa. The mean fracture toughness of the not pressed specimens was estimated as 0.35 ± 0.04 MPa m1/2 via Vickers indentation. Resonant Ultrasound Spectroscopy (RUS) measurements on hot pressed specimens gave mean values of Young's modulus, shear modulus and Poisson's ratio of 53.1 GPa, 21.4 GPa and 0.245, respectively while for the cast specimens the Young's and shear moduli were about 10% lower than for the hot pressed, with a mean value of Poisson's ratio of 0.245. The differences between the hardness and elastic moduli values for the cast and hot pressed specimens are discussed.
Skutterudite based thermoelectric unicouples are being considered for use in Advanced Radioisotope Power Systems (ARPSs) to support NASA’s planetary exploration missions. For these systems, which would be much lighter than state of the art Radioisotope Thermoelectric Generators (RTGs), it is important to ensure minimal degradation in the performance of unicouples that may be caused by material sublimation. In this work, two unicouples, JAN-04 with a thin metallic coating on the legs near the hot junction to suppress antimony sublimation and SEP-03 without coating, are tested for >1000 and 3600 h, respectively. The legs in the two unicouples are of almost the same dimensions and compositions; the p-legs are made of CeFe3.5Co0.5Sb12 and Bi0.4Sb1.6Te3 segments and the n-legs are made of CoSb3 and Bi2Te2.95Se0.05 segments. SEP-03 is tested at average hot and cold junction temperatures of 961.5 ± 22.0 and 296.3 ± 5.7 K, respectively, in argon gas at ∼0.068 MPa, and JAN-04 is tested at 962.8 ± 20.5 and 294.5 ± 3.3 K, respectively, initially in argon gas at the same pressure for ∼26.5 h then in vacuum ∼9.0 × 10−7 Torr for >973.5 h. The measured open circuit voltage Voc (240 mV) and peak electrical power (1.64 We) for SEP-03 at the beginning of test (BOT) are higher than those for JAN-04 (188 mV and 0.84 We, respectively). Although the argon gas effectively decreased the antimony loss from the legs of SEP-03, marked degradations in performance occurred. The estimated peak efficiency for SEP-03 decreased from 13.8% at BOT to 5.8% at end of test (EOT), and the peak power decreased from 1.64 We at BOT to 0.48 We at EOT, however, Voc decreased by ∼14%. The latter for JAN-04 decreased only by ∼3%, the estimated peak efficiency (∼12%) changed very little and the peak power decreased by ∼20%. Unlike SEP-03, the measured total and contact resistances of the legs in JAN-04 changed very little.
Although the formalism that allows the calculation of alloy thermodynamic properties from
first-principles has been known for decades, its practical implementation has so far remained a tedious
process. The Alloy Theoretic Automated Toolkit (ATAT) drastically simplifies this procedure by implementing
decision rules based on formal statistical analysis that frees the researchers from a constant
monitoring during the calculation process and automatically “glues” together the input and the output of
various codes, in order to provide a high-level interface to the calculation of alloy thermodynamic properties
from first-principles. ATAT implements the Structure Inversion Method (SIM), also known as the
Connolly-Williams method, in combination with semi-grand-canonical Monte Carlo simulations. In order
to make this powerful toolkit available to the wide community of researchers who could benefit from it,
this article present a concise user guide outlining the steps required to obtain thermodynamic information
from ab initio calculations.
Pb1−xGdxTe single crystals, doped with x = 0.001–0.04, were grown by using a Bridgeman method. The influence of doping element Gd on microstructure and creating of defects into materials were investigated. The experimental results from recent studies of microhardness and structural measurements (X-ray, SEM), are shown. Powder X-ray diffractograms have shown that the cubic-phase NaCl, with a lattice parameter a = 6.46 Å, was obtained for all samples with different compositions. To determine the sample's microhardness, the Vickers indentor has been used consecutively loaded by 50 g. The substitutional site of the Gd3+ ions and the influence of the concentration of defects, as vacancies and impurity atoms, on structural parameters are discussed. Here we investigate the concentration dependence of impurity ion sites into host lattice of PbTe, and a model of formation of a three-dimensional superlattice of ionized impurities is presented.
We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N-atoms(2) scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special 'preconditioning' optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package), The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
A recent report of highly unusual ferroelectric fluctuations in PbTe by E. S. Božin et al. [Science 330, 1660 (2010)] raises fundamental questions about the nature of underlying lattice dynamics. We show by first-principles calculations that the reported results can be attributed to abnormally large-amplitude thermal vibrations that stem from a delicate competition of dual ionicity and covalency, which puts PbTe near ferroelectric instability. It produces anomalous properties such as partially localized low-frequency phonon modes, a soft transverse optical phonon mode, and a positive temperature coefficient for the band gap. These results account for experimental findings and resolve the underlying atomistic mechanisms, which have broad implications for materials near dynamic instabilities.
Thermoelectric generators, which directly convert heat into electricity, have long been relegated to use in space-based or other niche applications, but are now being actively considered for a variety of practical waste heat recovery systems-such as the conversion of car exhaust heat into electricity. Although these devices can be very reliable and compact, the thermoelectric materials themselves are relatively inefficient: to facilitate widespread application, it will be desirable to identify or develop materials that have an intensive thermoelectric materials figure of merit, zT, above 1.5 (ref. 1). Many different concepts have been used in the search for new materials with high thermoelectric efficiency, such as the use of nanostructuring to reduce phonon thermal conductivity, which has led to the investigation of a variety of complex material systems. In this vein, it is well known that a high valley degeneracy (typically ≤6 for known thermoelectrics) in the electronic bands is conducive to high zT, and this in turn has stimulated attempts to engineer such degeneracy by adopting low-dimensional nanostructures. Here we demonstrate that it is possible to direct the convergence of many valleys in a bulk material by tuning the doping and composition. By this route, we achieve a convergence of at least 12 valleys in doped PbTe(1-x)Se(x) alloys, leading to an extraordinary zT value of 1.8 at about 850 kelvin. Band engineering to converge the valence (or conduction) bands to achieve high valley degeneracy should be a general strategy in the search for and improvement of bulk thermoelectric materials, because it simultaneously leads to a high Seebeck coefficient and high electrical conductivity.
Thermoelectric materials are solid-state energy converters whose combination of thermal, electrical, and semiconducting properties
allows them to be used to convert waste heat into electricity or electrical power directly into cooling and heating. These
materials can be competitive with fluid-based systems, such as two-phase air-conditioning compressors or heat pumps, or used
in smaller-scale applications such as in automobile seats, night-vision systems, and electrical-enclosure cooling. More widespread
use of thermoelectrics requires not only improving the intrinsic energy-conversion efficiency of the materials but also implementing
recent advancements in system architecture. These principles are illustrated with several proven and potential applications
of thermoelectrics.