**Figure 7.** 3ω method for extracting thermal conductivity of commercial p-type Bi2Te3 at room temperature, with frequency-dependent third harmonic voltage, V3ω (full symbols), and its phase shift (empty symbols) and with respect to

We calculated the electronic density of states based on the experimentally determined unit cells in generalized gradient approximation (GGA) DFT scheme with Perdue-Burke-Emzerhof

w

*V V d V i*

0 0 ln 2 ln 2 ln 2 , 8 4 16

*l R l R* (9)

 w  b

k

3

w

conductivity can be determined.

logarithmic frequency (inset).

**2.5. DFT calculations**

PPMS.

w

p k

b

194 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Pristine Bi2Te3 was successfully prepared by arc-melting as reported in Ref. [20]. Bi2Te3 both n-type and p-type presents the best thermoelectric properties for applications near room temperature. Consequently, preparation of these compounds by arc-melting and verification of their thermoelectric properties was an interesting milestone. We found, that samples present high electrical conductivity, while they retain low thermal conductivity, which is strongly affected by morphology. On the other hand, Seebeck coefficient values are similar to previously reported results.

As shown in **Figure 8**, typical microstructure of samples can be described as piles of stacked sheets parallel to plane defined by **b** and **c** crystallographic axis, providing easy cleavage of materials. Thickness of individual sheets is well below 0.1 μm (typically 20–40 nm). Thermoelectric properties of these materials are strongly influenced by this micro- or nanostructuration, involving many surface boundaries (interfaces) that are responsible for scattering of both charge carriers and phonons.

**Figure 8.** Typical microstructure of Bi2Te3 prepared by arc-melting, showing nanostructuration in sheets perpendicular to crystallographic c axis. Magnification (a) 7000×, (b) 25,000×, (c) 50,000×, and (d) 80,000×.

Transport properties in pure Bi2Te3 were measured in PPMS device [20] and high-temperature device (described in Section 2.4.3) on cold-pressed pellets. In the temperature range between 300 and 540 K, absolute value of Seebeck coefficient increases continuously until a maximum of −93 μV K−1, as shown in **Figure 9a**. These measurements were repeated in different samples.

**Figure 9.** Temperature dependences of (a) Seebeck coefficient and (b) electrical resistivity of Bi2Te3 prepared by arcmelting.

Published data for undoped Bi2Te3 offer a wide range of Seebeck coefficient values from −50 to −260 μV K−1 [15, 34–36] depending on material's nature and charge carriers concentration. Compounds prepared by wet chemical methods demonstrate similar Seebeck coefficient values [18, 34], whereas for samples prepared by ball-milling and hot-pressing technique, this coefficient is as high as −190 μV K−1 [37]. In bismuth telluride samples, charge carriers concentration is strongly affected by antisite BiTe and TeBi defects, which are randomly created during synthesis process. This feature yields a wide range of Seebeck coefficient values measured in samples prepared by different methods [15, 34–39].

Electrical resistivity (**Figure 9b**) suggests semimetallic behavior, and, thus, we observe an increase in electrical resistivity with temperature. As temperature increases, charge carrier' scattering is augmented. We found resistivity values of 2 μOhm m at 320 K, whereas for samples prepared by mechanical alloying and SPS or hot pressing, they display higher values of 30 and 7 μOhm m, respectively [37, 38]. Samples synthesized by chemical processes show resistivity values between 13 and 5 μOhm m [34, 39]. These results indicate improvement compared to other preparation procedures. The number of thermally excited charge carriers increases with temperature, as shown by Hall concentration measurements. Charge carriers' density at 310 K is equal to 7.46 × 1018 cm−3, similar to other literature values [35]. Hall mobility of charge carriers is calculated by *μH* = *RH σ*, resulting in 4514 cm2 V−1 s−1, which is an extremely high value due to low resistivity. Preferred orientation of sheets might be the main cause of this great electron mobility along measurement direction, resulting from the exceptionally anisotropic nature of Bi2Te3, with in-plane conductivity [40] over double that of out of plane.

Low thermal conductivity is critical for good thermoelectric performance. Thermal conductivity vs temperature is displayed in **Figure 10a** for Bi2Te3. At 365 K, thermal conductivity reaches its minimum value of 1.2 W m−1 K−1 after decreasing along the whole temperature range. This is an excellent value for Bi2Te3 bulk material, comparable to one of the lowest values presented in literature of 0.9 W m−1 K−1, Ref. [15]. It implies good compromise with excellent electrical resistivity and its electronic contribution to thermal conductivity. Layered nanostructured morphology of pellets is probably playing important role in reducing thermal conductivity, where abundant grain boundaries along phonon path (between layers or block of layers) increase phonon scattering. This effect compensates for improved electrical resistivity. Other procedures leading to nanostructured samples, i.e., ball-milling and hot pressing, yield thermal conductivity value of 1.2 W m−1 K−1 at 330 K [37], while for chemical synthesis values of 0.8 W m−1 K−1 at 380 K are obtained [34], however, in alloys with higher electrical resistivity. Eventually, then, our arc-melting technique produces Bi2Te3 with ZT approaching 0.3 (**Figure 10b**).

**Figure 9.** Temperature dependences of (a) Seebeck coefficient and (b) electrical resistivity of Bi2Te3 prepared by arc-

Published data for undoped Bi2Te3 offer a wide range of Seebeck coefficient values from −50 to −260 μV K−1 [15, 34–36] depending on material's nature and charge carriers concentration. Compounds prepared by wet chemical methods demonstrate similar Seebeck coefficient values [18, 34], whereas for samples prepared by ball-milling and hot-pressing technique, this coefficient is as high as −190 μV K−1 [37]. In bismuth telluride samples, charge carriers concentration is strongly affected by antisite BiTe and TeBi defects, which are randomly created during synthesis process. This feature yields a wide range of Seebeck coefficient values measured in

Electrical resistivity (**Figure 9b**) suggests semimetallic behavior, and, thus, we observe an increase in electrical resistivity with temperature. As temperature increases, charge carrier' scattering is augmented. We found resistivity values of 2 μOhm m at 320 K, whereas for samples prepared by mechanical alloying and SPS or hot pressing, they display higher values of 30 and 7 μOhm m, respectively [37, 38]. Samples synthesized by chemical processes show resistivity values between 13 and 5 μOhm m [34, 39]. These results indicate improvement compared to other preparation procedures. The number of thermally excited charge carriers increases with temperature, as shown by Hall concentration measurements. Charge carriers' density at 310 K is equal to 7.46 × 1018 cm−3, similar to other literature values [35]. Hall mobility

high value due to low resistivity. Preferred orientation of sheets might be the main cause of

V−1 s−1, which is an extremely

samples prepared by different methods [15, 34–39].

196 Thermoelectrics for Power Generation - A Look at Trends in the Technology

of charge carriers is calculated by *μH* = *RH σ*, resulting in 4514 cm2

melting.

**Figure 10.** (a) Thermal conductivity measured in PPMS device; inset shows pellet used with TTO setup and (b) figure of merit of Bi2Te3 prepared by arc-melting.

## **3.2. Bi2Te3 based alloys: Bi2(Te1−xSex)3**

Preparation of Bi2Te3-Bi2Se3 solid solutions by alloying Bi2Se3 with Bi2Te3, where stronger Se-Bi interactions are created, enlarges band-gap energy and forms new donor levels. This may lead to enhanced electrical conductivity [41–43] and improve thermoelectric performance. Besides, decrease in lattice thermal conductivity is expected due to point defects induced by alloying. On the other hand, Bi2(Te1−xSex)3 alloys are extremely susceptible to anisotropic effects, which have been notable disadvantages in preparation of bulk samples that have not been able to keep high electrical resistivity. Attempts for preparation of oriented grains in bulk samples have been made to overcome this issue [44].

We prepared Bi2(Te0.8Se0.2)3 pellets by arc-melting. NPD study was essential to investigate structural details of this doped sample. Neutrons are particularly suitable to study these intermetallic alloys having texturized nature of powder, which gives XRD patterns with large and untreatable preferred orientation effects. Neutrons provide bulk analysis, with good penetration; also the way of filling sample holders, (vanadium cylinders), helps to reduce unwanted preferred orientation, which is additionally minimized by rotation of sample holders. Moreover, lack of form factors for neutrons as diffraction probe enables accessing remote regions of reciprocal space, thus yielding accurate anisotropic displacement factors, which may give hints of the origin of phonon propagation across these materials, characterized by low thermal conductivity.

For Bi2(Te0.8Se0.2)3, NPD data were collected at RT at HRPT diffractometer of SINQ spallation source at PSI with *λ* = 1.494 Å. Crystal structure refinement was carried out in Bi2Te3-type model [45] in hexagonal setting of rhombohedral R-3m space group (no. 166), *Z* = 3, with Bi located at 6*c* (00z) Wyckoff site and Te/Se distributed at random over two different crystallographic sites, (Te,Se)1 at 3*a* positions and (Te,Se)2 at 6*c*. There was excellent agreement between observed and calculated profiles, as shown in **Figure 11**; minor preferred orientation correction was effective in improving refinement for all reflections in the whole angular range, reaching low Bragg discrepancy factors of 5.15%. **Tables 1** and **2** include lattice and atomic parameters and anisotropic displacements factors, as well as discrepancy factors after refinement. Unitcell parameters are **a** = 4.3315(1) Å and **c** = 30.208(7) Å. Unit-cell size is substantially smaller than that of parent Bi2Te3 compound (with unit-cell parameters: **a** = 4.385915 (6) Å, **c** = 30.495497 (1) Å, upon incorporation of smaller Se atoms.

**Figure 12** shows two views of refined crystal structure of Bi2(Te0.8Se0.2)3, along c axis (left panel) and perpendicular to c axis (right panel). It consists of hexagonal close-packed sheets, each layer being composed of fivefold stacking sequence of covalently bonded (Te,Se)2-Bi-(Te,Se)1- Bi-(Te,Se)2 atoms, whereas interatomic forces between adjacent layers ((Te,Se)2-(Te,Se)2 interactions) are mainly van der Waals type. As a consequence, crystals of these alloys are easily cleaved perpendicular to **c**-direction. Bi atoms are coordinated to 3 (Te,Se)1 at distances of 3.129(7) Å and 3 (Te,Se)2 at 3.102(9) Å in distorted octahedral configuration. Distance between terminal (Te,Se)2 of adjacent layers is 3.634(9) Å. It is noteworthy that anisotropic displacement ellipsoids are strongly flattened with short axis perpendicular to bonding directions, i.e., along [110] directions as shown in the left panel in **Figure 12**.

**Figure 11.** NPD profiles for Bi2(Te0.8Se0.2)3. Crosses are experimental points, solid line is calculated fit and difference is at the bottom. Vertical marks correspond to allowed Bragg reflections.

Unit-cell parameters: a = 4.3315 (4) Å, c = 30.208 (5) Å, 490.83 (10) Å3 , Z = 3. Ueq and Uij are, respectively, the equivalent and anisotropic atomic displacement parameters. Discrepancy factors after refinement are also included.

**Table 1.** Structural parameters for Bi2(Te0.8Se0.2)3 refined in R-3m space group (hexagonal setting) from NPD data collected at RT with λ = 1.494 Å.

**Table 2.** Anisotropic displacement parameters (Å2 ).

**3.2. Bi2Te3 based alloys: Bi2(Te1−xSex)3**

198 Thermoelectrics for Power Generation - A Look at Trends in the Technology

have been made to overcome this issue [44].

(1) Å, upon incorporation of smaller Se atoms.

[110] directions as shown in the left panel in **Figure 12**.

by low thermal conductivity.

Preparation of Bi2Te3-Bi2Se3 solid solutions by alloying Bi2Se3 with Bi2Te3, where stronger Se-Bi interactions are created, enlarges band-gap energy and forms new donor levels. This may lead to enhanced electrical conductivity [41–43] and improve thermoelectric performance. Besides, decrease in lattice thermal conductivity is expected due to point defects induced by alloying. On the other hand, Bi2(Te1−xSex)3 alloys are extremely susceptible to anisotropic effects, which have been notable disadvantages in preparation of bulk samples that have not been able to keep high electrical resistivity. Attempts for preparation of oriented grains in bulk samples

We prepared Bi2(Te0.8Se0.2)3 pellets by arc-melting. NPD study was essential to investigate structural details of this doped sample. Neutrons are particularly suitable to study these intermetallic alloys having texturized nature of powder, which gives XRD patterns with large and untreatable preferred orientation effects. Neutrons provide bulk analysis, with good penetration; also the way of filling sample holders, (vanadium cylinders), helps to reduce unwanted preferred orientation, which is additionally minimized by rotation of sample holders. Moreover, lack of form factors for neutrons as diffraction probe enables accessing remote regions of reciprocal space, thus yielding accurate anisotropic displacement factors, which may give hints of the origin of phonon propagation across these materials, characterized

For Bi2(Te0.8Se0.2)3, NPD data were collected at RT at HRPT diffractometer of SINQ spallation source at PSI with *λ* = 1.494 Å. Crystal structure refinement was carried out in Bi2Te3-type model [45] in hexagonal setting of rhombohedral R-3m space group (no. 166), *Z* = 3, with Bi located at 6*c* (00z) Wyckoff site and Te/Se distributed at random over two different crystallographic sites, (Te,Se)1 at 3*a* positions and (Te,Se)2 at 6*c*. There was excellent agreement between observed and calculated profiles, as shown in **Figure 11**; minor preferred orientation correction was effective in improving refinement for all reflections in the whole angular range, reaching low Bragg discrepancy factors of 5.15%. **Tables 1** and **2** include lattice and atomic parameters and anisotropic displacements factors, as well as discrepancy factors after refinement. Unitcell parameters are **a** = 4.3315(1) Å and **c** = 30.208(7) Å. Unit-cell size is substantially smaller than that of parent Bi2Te3 compound (with unit-cell parameters: **a** = 4.385915 (6) Å, **c** = 30.495497

**Figure 12** shows two views of refined crystal structure of Bi2(Te0.8Se0.2)3, along c axis (left panel) and perpendicular to c axis (right panel). It consists of hexagonal close-packed sheets, each layer being composed of fivefold stacking sequence of covalently bonded (Te,Se)2-Bi-(Te,Se)1- Bi-(Te,Se)2 atoms, whereas interatomic forces between adjacent layers ((Te,Se)2-(Te,Se)2 interactions) are mainly van der Waals type. As a consequence, crystals of these alloys are easily cleaved perpendicular to **c**-direction. Bi atoms are coordinated to 3 (Te,Se)1 at distances of 3.129(7) Å and 3 (Te,Se)2 at 3.102(9) Å in distorted octahedral configuration. Distance between terminal (Te,Se)2 of adjacent layers is 3.634(9) Å. It is noteworthy that anisotropic displacement ellipsoids are strongly flattened with short axis perpendicular to bonding directions, i.e., along

**Figure 12.** Two projections of crystal structure, along c axis (left panel) and perpendicular to c axis (right panel). Strongly anisotropic displacement ellipsoids (95% probability), with the short axis along [110] direction are illustrated.

Transport properties were evaluated in our homemade apparatus (Section 2.4.5). Seebeck coefficient vs temperature curve is plotted in **Figure 13a**.

Slow decrease in S is observed between 300 and 550 K, where average value is −75 μV K−1. There is small improvement in thermopower regarding pure Bi2Te3 samples, but it is still low in contrast to other Bi2(Te1−xSex)3 alloys, where values of −190 μV K−1 are reported [46] or even −259 μV K−1 at room temperature in samples with optimized composition [47]. Hall concentration of charge carriers is determined as 3.1 × 1019 cm−3 at 300 K (inset in **Figure 13a**), which is somewhat higher than in pure Bi2Te3 [20, 35], as a result of donor feature of Bi2(Te1−xSex)3 alloys.

As expected, temperature dependence of electrical resistivity (**Figure 13b**) exhibits the same semimetallic behavior as pure compound, but abrupt reduction in resistivity is observed at 530 K, until minimum value of 55 μOhm m is reached. Compared with pure compound (Section 3.1), with extremely low electrical resistivity (2 μOhm m at 300 K) prepared by arcmelting, these results indicate deterioration of thermoelectric performance. The drop in electrical conduction is possibly a consequence of the enormous anisotropy of this alloy, meaning that orientations of layered structures are not aligned for improved electron mobility. Analogous relationship between charge carriers scattering, doping and electrical conductivity is reported by Ajay Soni et al. [47] for Bi2Te2.2Se0.8 nanocomposite, which shows metallic and semiconductor behavior throughout their measurement range with values around 75 μOhm m at room temperature.

**Figure 12.** Two projections of crystal structure, along c axis (left panel) and perpendicular to c axis (right panel). Strongly anisotropic displacement ellipsoids (95% probability), with the short axis along [110] direction are illustrated.

Transport properties were evaluated in our homemade apparatus (Section 2.4.5). Seebeck

Slow decrease in S is observed between 300 and 550 K, where average value is −75 μV K−1. There is small improvement in thermopower regarding pure Bi2Te3 samples, but it is still low in contrast to other Bi2(Te1−xSex)3 alloys, where values of −190 μV K−1 are reported [46] or even −259 μV K−1 at room temperature in samples with optimized composition [47]. Hall concentration of charge carriers is determined as 3.1 × 1019 cm−3 at 300 K (inset in **Figure 13a**), which is somewhat higher than in pure Bi2Te3 [20, 35], as a result of donor feature of Bi2(Te1−xSex)3

As expected, temperature dependence of electrical resistivity (**Figure 13b**) exhibits the same semimetallic behavior as pure compound, but abrupt reduction in resistivity is observed at 530 K, until minimum value of 55 μOhm m is reached. Compared with pure compound (Section 3.1), with extremely low electrical resistivity (2 μOhm m at 300 K) prepared by arcmelting, these results indicate deterioration of thermoelectric performance. The drop in electrical conduction is possibly a consequence of the enormous anisotropy of this alloy, meaning that orientations of layered structures are not aligned for improved electron mobility. Analogous relationship between charge carriers scattering, doping and electrical conductivity is reported by Ajay Soni et al. [47] for Bi2Te2.2Se0.8 nanocomposite, which shows metallic and semiconductor behavior throughout their measurement range with values around 75 μOhm m

coefficient vs temperature curve is plotted in **Figure 13a**.

200 Thermoelectrics for Power Generation - A Look at Trends in the Technology

alloys.

at room temperature.

**Figure 13.** Temperature dependences of (a) Seebeck coefficient and (b) electrical resistivity for Bi2(Te0.8Se0.2)3 measured in homemade apparatus.

**Figure 14** shows dependence of total thermal conductivity on temperature determined in PPMS device.

Expected Umklapp maximum at low temperature appears with subsequent decrease over the whole measurement range until minimum value of 0.8 W m−1 K−1 is reached at 300 K. This is better (lower) thermal conductivity than reported for pristine nanostructured Bi2Te3 obtained by arc-melting, reaching 1.2 W m−1 K−1 at 365 K [20]. Excellent present values could be related to stronger anisotropy, higher electrical resistivity and point defects induced by alloying. In Bi2Te3-Bi2Se3 alloys produced by encapsulated melting and hot pressing, the best thermal conductivity value was equal to 1.04 W m−1 K−1 at 323 K [46], while for samples made by largescale zone melting, values of 1.2 W m−1 K−1 at 323 K are observed [48].

In samples prepared by polyol method followed by SPS, which leads to nanocomposite materials, low values of thermal conductivity are found: 0.9 W m−1 K−1 at 300 K for Bi2Te2.2Se0.8 and 0.7 W m−1 K−1 at 300 K for Bi2Te2.7Se0.3 nanocomposites [47]. The literature survey shows, that our thermal conductivity values are among the best reported, which is probably related to the nanostructuration effects, that we describe for arc-melted samples, with advantage of the simplicity of our one-step straightforward method.

**Figure 14.** Temperature dependence of thermal conductivity of Bi2(Te0.8Se0.2)3 measured in PPMS device. Extremely low thermal conductivity of 0.8 W m−1 K−1 is observed at 300 K.

#### **3.3. SnSe and related alloys**

Tin selenide and its various alloys show good thermoelectric performance at temperatures well above the maximum attainable in PPMS. Therefore, the main use of these results, measured with PPMS, is to guide us in search for candidate compositions. However, as we show, we found surprisingly high values of Seebeck coefficient, whereas thermal conductivity of tin selenide produced by arc-melting is considerably lower than that of single crystals. Both are highly promising results for thermoelectric materials.

#### *3.3.1. Structural characterization*

We have prepared by simple and straightforward arc-melting technique highly textured SnSe samples with record Seebeck coefficient values and extremely low thermal conductivity [19]. Test NPD study was essential to investigate structural details of SnSe, since this bulk study is by far much less sensitive to the preferred orientation effects. Not only pristine SnSe, but other several novel series of SnSe-based alloys, namely Sn1−xMxSe (M = Sb, Ge) prepared by arcmelting, have been investigated by neutron diffraction. We will illustrate these studies with description of *in situ* structural evolution of Sn0.8Ge0.2Se in the temperature range of maximum thermoelectric efficiency. NPD data were collected in diffractometer D2B. Measurements were taken at 25, 200, 420 and 580°C*.*

conductivity value was equal to 1.04 W m−1 K−1 at 323 K [46], while for samples made by large-

In samples prepared by polyol method followed by SPS, which leads to nanocomposite materials, low values of thermal conductivity are found: 0.9 W m−1 K−1 at 300 K for Bi2Te2.2Se0.8 and 0.7 W m−1 K−1 at 300 K for Bi2Te2.7Se0.3 nanocomposites [47]. The literature survey shows, that our thermal conductivity values are among the best reported, which is probably related to the nanostructuration effects, that we describe for arc-melted samples, with advantage of

**Figure 14.** Temperature dependence of thermal conductivity of Bi2(Te0.8Se0.2)3 measured in PPMS device. Extremely low

Tin selenide and its various alloys show good thermoelectric performance at temperatures well above the maximum attainable in PPMS. Therefore, the main use of these results, measured with PPMS, is to guide us in search for candidate compositions. However, as we show, we found surprisingly high values of Seebeck coefficient, whereas thermal conductivity of tin selenide produced by arc-melting is considerably lower than that of single crystals. Both are

We have prepared by simple and straightforward arc-melting technique highly textured SnSe samples with record Seebeck coefficient values and extremely low thermal conductivity [19]. Test NPD study was essential to investigate structural details of SnSe, since this bulk study is by far much less sensitive to the preferred orientation effects. Not only pristine SnSe, but other

scale zone melting, values of 1.2 W m−1 K−1 at 323 K are observed [48].

the simplicity of our one-step straightforward method.

202 Thermoelectrics for Power Generation - A Look at Trends in the Technology

thermal conductivity of 0.8 W m−1 K−1 is observed at 300 K.

highly promising results for thermoelectric materials.

**3.3. SnSe and related alloys**

*3.3.1. Structural characterization*

**Figure 15** illustrates NPD patterns of Sn0.8Ge0.2Se at 420 and 580°C*.* Crystal structure can be Rietveld-refined in orthorhombic *Pnma* space group below 420°C. At this temperature, an orthorhombic (*Pnma*) to orthorhombic (*Cmcm*) phase transition takes place. **Figure 16** shows phase diagram displaying temperature dependence of unit-cell parameters of both orthorhombic phases. A dramatic rearrangement of atoms is observed along with phase transitions, bearing a more ordered structure. **Figure 17** displays crystal structures at room temperature, 200, 420 and 580°C. It is noteworthy, that change in displacement ellipsoids directions with temperature presents its largest axis along **c** direction in *Pnma* space group, while at high temperature it is oriented along **b** axis in *Cmcm* space group. In *Pnma*, structure consists of trigonal pyramids SnSn3 forming layers perpendicular to [100] direction, with thermal ellipsoids oriented within the layers, whereas across the transition to *Cmcm* the coordination environment changes to tetragonal pyramid, where large Sn ellipsoids in the basal squareplane adopt a configuration with the longest axis perpendicular to four closer chemical bonds, oriented along **b** axis of orthorhombic structure. Such high thermal displacements indicate strong rattling effect of Sn in a pentacoordinated cage, accounting for the observed decrease in thermal conductivity and good thermoelectric performance of this material.

**Figure 15.** Observed (crosses), calculated (full line) and difference (at the bottom) NPD profiles for Sn0.8Ge0.2Se at 420 °C, just below the phase transition. Vertical markers correspond to allowed Bragg reflections.

**Figure 16.** Phase diagram showing thermal evolution of unit-cell parameters.

**Figure 17.** Crystal structures of orthorhombic phases at 25 (upper left), 200 (upper right), 420 (bottom left) and 580°C (bottom right).

#### *3.3.2. Thermoelectric characterization*

**Figure 16.** Phase diagram showing thermal evolution of unit-cell parameters.

204 Thermoelectrics for Power Generation - A Look at Trends in the Technology

(bottom right).

**Figure 17.** Crystal structures of orthorhombic phases at 25 (upper left), 200 (upper right), 420 (bottom left) and 580°C

We first discuss our results on pure (i.e., unalloyed) SnSe, produced by arc-melting. The barshaped sample was cut directly from as-produced ingot as described above. **Figure 18** shows transport properties obtained in PPMS between 2 and 380 K. Seebeck coefficient (in middle panel) exhibits monotonic increase in positive (i.e., p-type) values reaching a maximum of 668 μV K−1 [19]. At the time, this was the highest Seebeck coefficient value reported in SnSe. We have observed this behavior in various samples on repeated measurements, consistently. While preliminary studies reported values only around 50 μV K−1 [49], the ground-breaking single crystal results of Zhao et al. [50] reach around 580 μV K−1, quite independent of crystallographic direction [50]. Meanwhile, other reported values of polycrystalline samples are close to this value [51–53]. Uncontrolled differences in hole concentration may play a role in these variations. Zhao et al. [50] found, that Seebeck coefficient value reaches its maximum in SnSe around 525 K. When we extrapolate our results (limited below 400 K in PPMS), we could expect as much as 800 μV K−1, and as we show below, indeed, we do find such high values with MMR device (described in Section 2.4.2).

Temperature dependence of electrical resistivity is shown in the bottom panel of **Figure 18**; Hall concentration of charge carriers at 300 K is 7.95 × 1015 cm-3 [19]. Resistivity decreases exponentially with temperature, as expected for a semiconductor. We consistently find, that resistivity of SnSe and its alloys produced by arc-melting is rather high. This is a persistent problem of the technique, which we must address in the future. Nevertheless, we must also bear in mind, that these results from PPMS are limited to a temperature range well below that, where SnSe functions as a good thermoelectric. For comparison, our arc-melting produced pellet has bulk resistivity at room temperature (295 K) of around 64 mOhm m, significantly higher than expected: the single crystals of Zhao et al. [50] have 1 mOhm m within bc plane and 5 mOhm m along a-direction, whereas Sassi et al. [52] report 11 mOhm m along the pressing direction in polycrystals and 5 mOhm m perpendicular to it. Hall effect measurements at 300 K yields p-type hole concentration of 7.95 × 1015 cm−3. This is much lower than that of typical thermoelectrics and, indeed, of other SnSe reports (e.g., 4 × 1017 cm−3 by Zhao et al. [50]). Again, this is a persistent finding in our SnSe alloys: free charge carriers' concentration is much lower than expected, indicating the presence of strong traps for charge carriers. It also explains large electrical resistivity along with strong nanostructuration, producing abundant grain boundaries. Surprisingly, large Seebeck coefficient value is also related to low charge density, through Pisarenko relation [54].

Thermal conductivity of SnSe is shown in the top panel of **Figure 18**. It is overwhelmingly dominated by lattice contribution, due to low charge carriers' concentration.

Thermal conductivity peaks around 25 K due to UmKlapp scattering and then starts to decrease monotonically throughout the measurement range, reaching a value as low as 0.2 W m−1 K−1 at 395 K. This is a strikingly low value. Admittedly, direct heat-flow technique employed by PPMS is strongly affected by heat loss problems discussed above and these become acute above room temperature. Nevertheless, values are highly reliable below 100 K, and they are consistently very low there, too, in several samples. The intrinsic lattice thermal conductivity of SnSe is very low, probably an outcome of anharmonicity of chemical bonds. High Grüneisen parameters and strong phonon-phonon interactions are expected as a result of the presence of lone-electron pairs of both Se2− and Sn2+ ions [49, 55]. In fact, lone pairs of p-block elements play an important role deforming lattice vibration, which results in strong anharmonicity; significantly, anisotropic vibrations of both Sn and Se atoms are determined by NPD, with the main ellipsoid axes directed along chemical bonds (**Figure 17**), which is also indicative of such anharmonicity, as vibrations are hindered out of bonding direction by voluminous electron pairs filling empty space in the crystal structure. Moreover, thermal conductivity is significantly lower than those reported in single crystals (1.8 W m−1 K−1) [50, 56] and even lower compared to those recently reported for polycrystalline samples [52]. Extremely small values measured in the present material are most likely related to strong texture obtained during synthesis process, that leads to layered nanostructuration along **a** axis (**Figure 17**). This is particularly effective to boost phonon scattering at nanoscale, thus resulting in record low thermal conductivity for this polycrystalline material.

**Figure 18.** Temperature dependence of (top) thermal conductivity, (middle) Seebeck coefficient, (bottom) electrical resistivity of stoichiometric SnSe.

A second set of measurements of Seebeck coefficient at high temperature were carried out at MMR device, by comparing Seebeck effect of SnSe material with that of constantan wire, as described in Section 2.4.2. Seebeck coefficient was measured using 1 × 1 × 8 mm3 bar-shaped SnSe samples and reference constantan wire of 0.125 mm diameter. Reproducibility of measurements was confirmed by repeating them after making new contacts both on the sample and on reference constantan wire. This procedure warrants accuracy better than 5% over the whole temperature range.

**Figure 19** shows Seebeck coefficient as function of temperature *S*(*T*) measured using the method described above for SnSe. Initially, *S*(*T*) increases with *T* from room temperature up to 400 K, where it reaches about 840 μV K−1. Between 400 and 500 K, Seebeck coefficient is almost temperature independent, and above 500 K *S*(*T*) decreases monotonically up to the maximum experimental temperature, which is lower than temperature corresponding to structural transition from *Pnma* to *Cmcm*, described above from NPD data. These values are slightly higher than those reported by Zhao et al. [50] on single-crystalline samples. This enhancement can be related to nanostructuration of the sample and presence of high density of boundaries.

parameters and strong phonon-phonon interactions are expected as a result of the presence of lone-electron pairs of both Se2− and Sn2+ ions [49, 55]. In fact, lone pairs of p-block elements play an important role deforming lattice vibration, which results in strong anharmonicity; significantly, anisotropic vibrations of both Sn and Se atoms are determined by NPD, with the main ellipsoid axes directed along chemical bonds (**Figure 17**), which is also indicative of such anharmonicity, as vibrations are hindered out of bonding direction by voluminous electron pairs filling empty space in the crystal structure. Moreover, thermal conductivity is significantly lower than those reported in single crystals (1.8 W m−1 K−1) [50, 56] and even lower compared to those recently reported for polycrystalline samples [52]. Extremely small values measured in the present material are most likely related to strong texture obtained during synthesis process, that leads to layered nanostructuration along **a** axis (**Figure 17**). This is particularly effective to boost phonon scattering at nanoscale, thus resulting in record low

**Figure 18.** Temperature dependence of (top) thermal conductivity, (middle) Seebeck coefficient, (bottom) electrical re-

A second set of measurements of Seebeck coefficient at high temperature were carried out at MMR device, by comparing Seebeck effect of SnSe material with that of constantan wire, as

SnSe samples and reference constantan wire of 0.125 mm diameter. Reproducibility of measurements was confirmed by repeating them after making new contacts both on the sample and on reference constantan wire. This procedure warrants accuracy better than 5% over the

bar-shaped

described in Section 2.4.2. Seebeck coefficient was measured using 1 × 1 × 8 mm3

thermal conductivity for this polycrystalline material.

206 Thermoelectrics for Power Generation - A Look at Trends in the Technology

sistivity of stoichiometric SnSe.

whole temperature range.

**Figure 19.** High-temperature Seebeck coefficient as function of temperature for SnSe measured in MMR device.

Morphology of the material produced by arc-melting is highly granular, nanostructured. This raises obvious concern about transport measurements. Do we measure intrinsic properties of the materials or are the data heavily distorted by grain-boundary effects? We can get an idea about this by comparing the three transport properties for the same material in two measurements. First, the sample is cut directly from the arc-molten ingot with a diamond saw and measured. Second, the material is directly cold-pressed after arc-melting and then measured. In both cases, the crystal structure, the platelet-like nanostructure and bulk bar-shaped form of samples are the same. What changes is the microstructure. The cold-pressed sample is denser with better grain-to-grain contacts. This is expected to raise both electrical and thermal conductivities. We use Sb-alloyed SnSe as an example. Thermal conductivity of SnSe and its alloys is not affected by the changed morphology. We also found that above room temperature, value of electrical resistivity has been improved by an order of magnitude, and Seebeck coefficient remains unchanged (not shown). This experiment demonstrates, that we are looking at the intrinsic thermal properties, whereas electrical connectivity of the material is in need of improving: measurements do not reflect the intrinsic electrical properties for tin selenide alloys.

Why would electrical and thermal conductivities respond differently to cold-pressing? Electrical conductivity is improved upon increasing grain-to-grain contacts and contact area. However, thermal conductivity is not affected. The reason is related to the nature of phonon scattering and the phonon mean-free path. We can estimate this by comparing low-temperature thermal conductivity (below UmKlapp peak) and specific heat (inset in the top panel of **Figure 20**), using phenomenological relation for phonon diffusion: = 1 3 ××, that relates thermal conductivity to specific heat at constant volume *CV*, sound velocity (*v*) and phonon mean-free path (*l*). By ignoring the rather complex phonon dispersion of SnSe and using

phonon velocities as given by Zhao et al. [50], we can estimate phonon mean-free path to be between 2 and 10 nm; effectively at low temperature, it is limited by the nanostructured grainsize, but at higher temperatures intrinsic properties dominate.

**Figure 20.** Temperature dependence of (top) thermal conductivity, (middle) Seebeck coefficient and (bottom) electrical resistivity and (inset) specific heat and thermal conductivity comparison at low temperature of Sb0.2Sn0.8Se alloy.

The idea to study alloys of SnSe with SbSe is to control Fermi level and concentration of free charge carriers. To our dismay, we found, that SnSbSe alloys display very high resistivity, higher even, than nominally stoichiometric SnSe, with very low Hall concentration of charge carriers. We did manage to achieve n-type, negative, Seebeck coefficient. Indeed, absolute value of negative Seebeck coefficient reaches 100–200 μV K−1, depending on composition and temperature. These results are summarized for Sb0.2Sn0.8Se in **Figure 20**. Furthermore, for this composition, Hall effect measurements resulted in p-type, with hole concentration 3 × 1016 cm−3 at room temperature. Expected free electron concentration, from *ab initio* calculations of electronic density of states (**Figure 21**), is around 3 × 1021 cm−3 and obviously n-type for this level of Sb fraction in the compound. In order to resolve the apparent contradiction between measured and calculated free electron concentration and measured signs of Hall and Seebeck coefficients, we reconsidered the electronic structure calculation in view of strong Sn deficiency revealed by Rietveld refinement of NPD data. In our calculations, we use 1 × 2 × 2 minimal supercells with 16 Sn and 16 Se sites. Of these, we replace up to 3 Sn with Sb to approximate experimental alloying and remove one Sn to represent observed Sn site deficiency. Resulting band structure shows a striking narrow band in the gap above the valence band, appearing as a sharp peak in the density of states (DOS). This acts as shallow energy charge trap that localizes electrons transferred from Sb substitutes. Thus, Fermi level remains stuck in this band for a wide range of Sb concentration, invalidating our expectation of simple rigid-band charge transfer model. The complicated band structure is then responsible for different signs of Hall and Seebeck coefficients, too.

Why would electrical and thermal conductivities respond differently to cold-pressing? Electrical conductivity is improved upon increasing grain-to-grain contacts and contact area. However, thermal conductivity is not affected. The reason is related to the nature of phonon scattering and the phonon mean-free path. We can estimate this by comparing low-temperature thermal conductivity (below UmKlapp peak) and specific heat (inset in the top panel of

thermal conductivity to specific heat at constant volume *CV*, sound velocity (*v*) and phonon mean-free path (*l*). By ignoring the rather complex phonon dispersion of SnSe and using phonon velocities as given by Zhao et al. [50], we can estimate phonon mean-free path to be between 2 and 10 nm; effectively at low temperature, it is limited by the nanostructured grain-

**Figure 20.** Temperature dependence of (top) thermal conductivity, (middle) Seebeck coefficient and (bottom) electrical resistivity and (inset) specific heat and thermal conductivity comparison at low temperature of Sb0.2Sn0.8Se alloy.

The idea to study alloys of SnSe with SbSe is to control Fermi level and concentration of free charge carriers. To our dismay, we found, that SnSbSe alloys display very high resistivity, higher even, than nominally stoichiometric SnSe, with very low Hall concentration of charge

1

3 ××, that relates

**Figure 20**), using phenomenological relation for phonon diffusion: =

size, but at higher temperatures intrinsic properties dominate.

208 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**Figure 21.** Electronic density of states of stoichiometric and Sn-deficient SnSe and Sb-SnSe with compositions indicated in labels. Fermi level is placed at E = 0, and thus band structures shift around with doping level.

The great advantage of arc-melting synthesis is that it affords a way to rapidly assay various compositions for thermoelectric properties. By introducing atoms of different radii, we can modify electronic structure, even without obvious charge transfer, this is so-called band engineering, for example, modification of bandwidth. Obvious candidates to do this are columnar neighbors of tin, lead and germanium. In the following we present results first on SnPbSe alloys and then on SnGeSe alloys. In both series, we found p-type Seebeck coefficient values.

Studying three different SnPbSe alloy compositions with up to 30% Pb substitution on Sn site has shown no improvement on any of thermoelectric properties (**Figure 22**). Electrical resistivity increases by several orders of magnitude, as we have seen for SnSbSe alloys, too. Indeed, it is so high, that resistance of samples surpasses few MOhm limit of PPMS electronics at low temperature. The Seebeck coefficient value reaches up to 600 μV K−1 at 400 K, which is high, but no higher, than in stoichiometric SnSe produced by arc-melting. Finally, thermal conductivity shows the same UmKlapp peak at low temperature as SnSe and Sb0.2Sn0.8Se with no overall reduction.

**Figure 22.** Temperature dependences of (top) thermal conductivity, (middle) Seebeck coefficient and (bottom) electrical resistivity of SnSe alloyed with Pb.

In contrast, by going to smaller ionic radius, SnGeSe alloy has several beneficial effects, although electrical resistivity is still too high. Most importantly, as shown in **Figure 23**, Seebeck coefficient value surpasses 1000 μV K−1 for low GeSe fraction. Curious, nonmonotonic change of Seebeck coefficient with increase in GeSe fraction is supported by electronic structure calculations, based on experimentally determined crystal structures. These reveal, that semiconducting gap also varies nonmonotonously with Ge substitution, first increasing with respect to the gap of SnSe and then decreasing with more Ge (**Figure 24**). Large Seebeck coefficient value is caused partly by low charge carriers concentration, as indicated by resistivity, that is 1–2 orders of magnitude above that of stoichiometric SnSe, following Pisarenko relation.

Nanostructured State-of-the-Art Thermoelectric Materials Prepared by Straight-Forward Arc-Melting Method http://dx.doi.org/10.5772/65115 211

SnPbSe alloys and then on SnGeSe alloys. In both series, we found p-type Seebeck coefficient

210 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Studying three different SnPbSe alloy compositions with up to 30% Pb substitution on Sn site has shown no improvement on any of thermoelectric properties (**Figure 22**). Electrical resistivity increases by several orders of magnitude, as we have seen for SnSbSe alloys, too. Indeed, it is so high, that resistance of samples surpasses few MOhm limit of PPMS electronics at low temperature. The Seebeck coefficient value reaches up to 600 μV K−1 at 400 K, which is high, but no higher, than in stoichiometric SnSe produced by arc-melting. Finally, thermal conductivity shows the same UmKlapp peak at low temperature as SnSe and Sb0.2Sn0.8Se with

**Figure 22.** Temperature dependences of (top) thermal conductivity, (middle) Seebeck coefficient and (bottom) electrical

In contrast, by going to smaller ionic radius, SnGeSe alloy has several beneficial effects, although electrical resistivity is still too high. Most importantly, as shown in **Figure 23**, Seebeck coefficient value surpasses 1000 μV K−1 for low GeSe fraction. Curious, nonmonotonic change of Seebeck coefficient with increase in GeSe fraction is supported by electronic structure calculations, based on experimentally determined crystal structures. These reveal, that semiconducting gap also varies nonmonotonously with Ge substitution, first increasing with respect to the gap of SnSe and then decreasing with more Ge (**Figure 24**). Large Seebeck coefficient value is caused partly by low charge carriers concentration, as indicated by resistivity, that is 1–2 orders of magnitude above that of stoichiometric SnSe, following

values.

no overall reduction.

resistivity of SnSe alloyed with Pb.

Pisarenko relation.

**Figure 23.** Sn1−xGexSe (x = 0, 0.1, 0.2, 0.3) temperature dependences (top) thermal conductivity, (middle) Seebeck coeffi‐ cient and (bottom) electrical resistivity—exhibiting characteristic semiconducting behavior. Two independent measure‐ ments are shown for x = 0.1 and 0.3. Below 150–200 K electrical resistance of Ge‐doped SnSe samples increases beyond the limits (few MOhm) of the electronics of PPMS, and this influences Seebeck voltage, too (from Ref. [21]).

**Figure 24.** Calculated electronic density of states (DOS) of SnSe, black solid line, Sn0.88Ge0.12Se, red dashed line, and Sn0.81Ge0.19Se, blue dotted line (from Ref. [21]).

#### *3.3.3. Thermal conductivity results from laser flash thermal diffusivity method*

**Figure 25** shows total thermal conductivity (κ) obtained by laser flash diffusivity method for different thermoelectric compounds: SnSe, Sn0.8Ge0.2Se and Sn0.8Sb0.2Se; PbTe is used as a reference.

**Figure 25.** Thermal conductivity values of SnSe, Sn0.8Ge0.2Se, Sn0.8Sb0.2Se and PbTe obtained by laser flash diffusivity method.

Lead telluride, PbTe, is a well-known thermoelectric material, that, due to its band gap of about 0.3 eV, is useful in intermediate temperature range of operation. Its thermal conductivity falls from room temperature with a 1/T dependence, which is a fingerprint of the enhancement of phonon-phonon interactions with increasing temperature. This behavior, together with its band-gap value, makes PbTe one of the most competitive thermoelectric materials for generators above 500 K. However, several efforts are being made to enhance its efficiency. The main ways to drive this goal are enhancement of thermoelectric properties by nanostructuring and modifications in the density of states to create resonant states in the conduction band [57].

The pure SnSe and related alloys (Sn0.8Ge0.2Se, Sn0.8Sb0.2Se) display significantly lower thermal conductivities in the high-temperature region. At room temperature, values of total thermal conductivity are 0.89 and 0.7 W m−1 K−1 for SnSe and Sn0.8Sb0.2Se compounds, respectively. These values are further reduced with increasing temperature, reaching 0.4 W m−1 K−1 at 675 K. It is noteworthy, that above-described thermal conductivities determined in PPMS are considerably lower than values obtained by an indirect procedure, from thermal diffusivity.

Total thermal conductivity has two contributions, lattice thermal conductivity (κ*lat*), due to phonon transport, and charge carriers' thermal conductivity (κ*ch*), due to thermal transport of charge carriers (electrons and/or holes). As a first approximation, Wiedemann-Franz law [26] allows reasonable estimation of charge carriers thermal conductivity as a function of temperature, *κch* = (*L*0*T*) ⁄ *ρ*, where *L0* is the Lorentz number and *ρ* is the electrical resistivity. For the case of SnSe family, total thermal conductivity is almost fully dominated by lattice thermal conductivity. In fact, ratio of thermal conductivity due to charge carriers to total thermal conductivity is approximately 10−4. The different anisotropic direction of both measurements might be related to the differences in the magnitude of determined thermal conductivity with respect to the direct measure provided by PPMS.

## **4. Conclusions**

*3.3.3. Thermal conductivity results from laser flash thermal diffusivity method*

212 Thermoelectrics for Power Generation - A Look at Trends in the Technology

reference.

method.

**Figure 25** shows total thermal conductivity (κ) obtained by laser flash diffusivity method for different thermoelectric compounds: SnSe, Sn0.8Ge0.2Se and Sn0.8Sb0.2Se; PbTe is used as a

**Figure 25.** Thermal conductivity values of SnSe, Sn0.8Ge0.2Se, Sn0.8Sb0.2Se and PbTe obtained by laser flash diffusivity

Lead telluride, PbTe, is a well-known thermoelectric material, that, due to its band gap of about 0.3 eV, is useful in intermediate temperature range of operation. Its thermal conductivity falls from room temperature with a 1/T dependence, which is a fingerprint of the enhancement of phonon-phonon interactions with increasing temperature. This behavior, together with its band-gap value, makes PbTe one of the most competitive thermoelectric materials for generators above 500 K. However, several efforts are being made to enhance its efficiency. The main ways to drive this goal are enhancement of thermoelectric properties by nanostructuring and modifications in the density of states to create resonant states in the conduction band [57].

The pure SnSe and related alloys (Sn0.8Ge0.2Se, Sn0.8Sb0.2Se) display significantly lower thermal conductivities in the high-temperature region. At room temperature, values of total thermal conductivity are 0.89 and 0.7 W m−1 K−1 for SnSe and Sn0.8Sb0.2Se compounds, respectively. These values are further reduced with increasing temperature, reaching 0.4 W m−1 K−1 at 675 K. It is noteworthy, that above-described thermal conductivities determined in PPMS are considera-

Total thermal conductivity has two contributions, lattice thermal conductivity (κ*lat*), due to phonon transport, and charge carriers' thermal conductivity (κ*ch*), due to thermal transport of charge carriers (electrons and/or holes). As a first approximation, Wiedemann-Franz law [26] allows reasonable estimation of charge carriers thermal conductivity as a function of temperature, *κch* = (*L*0*T*) ⁄ *ρ*, where *L0* is the Lorentz number and *ρ* is the electrical resistivity. For the case of SnSe family, total thermal conductivity is almost fully dominated by lattice thermal conductivity. In fact, ratio of thermal conductivity due to charge carriers to total thermal conductivity is approximately 10−4. The different anisotropic direction of both measurements

bly lower than values obtained by an indirect procedure, from thermal diffusivity.

We have described a fast one-step procedure to prepare nanostructured intermetallic alloys belonging to the families of well-known Bi2Te3 and recently described SnSe, all of them showing similar nanostructure consisting of stacks of nanosheets, that perturb propagation of phonons and provide extremely low thermal conductivity. Crystal structure studies from NPD data reveal anisotropic displacement parameters, probably due to the presence of lone-electron pairs of the p-block elements (Bi, Te, Sn, Se…) also contributing to low lattice thermal conductivity. Seebeck coefficient values are enhanced in SnSe system, reaching extraordinary high values close to 1000 μV K−1 in SnGeSe alloys. As a drawback of nanostructuration, electrical resistivity values are much higher in this system than those described in single crystalline samples, probably arising from many grain boundaries, which perturb charge carriers path. We describe also a simple apparatus for the measurement of high-temperature transport properties, ideally conceived to determine *S* and *σ* in disk-shaped pellets directly obtained from the intermetallic ingots. The use of Nb pistons, chemically inert to reactive p elements like Bi, Te or Se, is particularly suitable given the weak S factor for Nb, yielding reproducible results for known materials like Cu or Al.

#### **Abbreviations**

## **Acknowledgements**

We thank the financial support of the Spanish Ministry of Science and Innovation to the project MAT2013-41099-R and by JCCM through Project PPII-2014-019-P. We thank the Institut Laue-Langevin (ILL) and Paul Scherrer Institut (PSI) for providing the neutron beam time.

## **Author details**

Federico Serrano-Sánchez1 , Mouna Gharsallah1,2, Julián Bermúdez1 , Félix Carrascoso1 , Norbert M. Nemes1 , Oscar J. Dura3 , Marco A. López de la Torre3 , José L. Martínez1 , María T. Fernández-Díaz4 and José A. Alonso1\*

\*Address all correspondence to<EMAIL_ADDRESS>
1 Institute of Materials Science of Madrid, Madrid, Spain

2 National School of Engineers, Sfax University, Tunisia

3 Department of Applied Physics and INEI, University of Castilla La Mancha, Ciudad Real, Spain

4 Institut Laue Langevin, Grenoble, France

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**Acknowledgements**

**Author details**

Norbert M. Nemes1

Spain

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Federico Serrano-Sánchez1

María T. Fernández-Díaz4

, Oscar J. Dura3

214 Thermoelectrics for Power Generation - A Look at Trends in the Technology

\*Address all correspondence to<EMAIL_ADDRESS>
1 Institute of Materials Science of Madrid, Madrid, Spain

2 National School of Engineers, Sfax University, Tunisia

4 Institut Laue Langevin, Grenoble, France

10.1007/978-1-4899-5723-8

Florida; 2012.

and José A. Alonso1\*

We thank the financial support of the Spanish Ministry of Science and Innovation to the project MAT2013-41099-R and by JCCM through Project PPII-2014-019-P. We thank the Institut Laue-

, Mouna Gharsallah1,2, Julián Bermúdez1

3 Department of Applied Physics and INEI, University of Castilla La Mancha, Ciudad Real,

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#### **Nanometer Structured Epitaxial Films and Foliated Layers Based on Bismuth and Antimony Chalcogenides with Topological Surface States Nanometer Structured Epitaxial Films and Foliated Layers Based on Bismuth and Antimony Chalcogenides with Topological Surface States**

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The thermoelectric and galvanomagnetic properties of nanometer structured epitaxial films and foliated layers based on bismuth and antimony chalcogenides were investi‐ gated, and an increase in the figure of merit Z up to 3.85 × 10‐3 K‐1 was observed in the Bi0.5Sb1.5Te3 films over the temperature range of 180–200 K. It is shown that an increase in the Seebeck coefficient and the change in the slope on temperature, associated with changes in the effective scattering parameter of charge carriers and strong anisotropy of scattering in the films, lead to enhance power factor due to the growth of the effective mass of the density of states. These features are consistent with the results of research of oscillation effects in strong magnetic fields at low temperatures and research of Raman scattering at normal and high pressures in the foliated layers of solid solutions (Bi, Sb)2(Te, Se)3, in which the topological Dirac surface states were observed. The unique properties of topological surface states in the investigated films and layers make topological insulators promising material for innovation nanostructured thermoelec‐ trics.

**Keywords:** thermoelectric films, topological surface states, power factor, scattering on interphase, block boundaries

## **1. Introduction**

Thermoelectrics based on bismuth and antimony chalcogenides are well known and have been extensively studied for their excellent thermoelectric properties [1–3]. Recently, the nanostruc‐

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

tured (Bi,Sb)2(Te,Se)3 epitaxial films were shown to possess an enhanced thermoelectric figure of merit Z compared to corresponding bulk crystals due to mechanical stresses and intensive phonon scattering at the grain boundaries. Lattice thermal conductivity of heteroepitaxial nanostructured films may be substantially diminished, as compared to corresponding bulk crystals, due to acoustic phonon scattering by grain and interface boundaries. Boundaries and strain may be easily induced in thin Bi2Te3‐based films grown on mismatched substrates. In contrast to point defects, which suppress heat transfer by short wave phonons, grain and interface boundaries are efficient in scattering of long wave ones. That is why, investigation of thin films with different structure and level of mechanical stresses looks quite important for development of thermoelectric materials with enhanced performance.

At the current stage, a new property of these materials, known as topological insulator, became one of the important subjects of the investigations [4–6]. These novel quantum states are the result of the electronic band inversion due to strong spin‐orbit interaction, so the bulk becomes insulating and the surface displays an unusual metallic electronic surface state of Dirac fermions with linear dispersion and spin texture that ensures high mobility of charge carriers due to the lack of backscattering on defects. The nanostructured films of topological materials [7, 8] theoretically proved the possibility of formation of topological excitons that can condense in a wide temperature range with the appearance of superfluidity and thus a significant increase in the mobility of the charge carriers. Currently, there is only a preliminary report on the pilot study of the heterostructure Sb2Te3/Bi2Te3, which assumes the realization of exciton condensation [9]. The theoretical model [10] for topological thermoelectrics based on the Landauer transport theory shows that the value of the Seebeck coefficient and thermoelectric efficiency is determined by the ratio of the mean free path of Dirac fermions to the mean free path of bulk electrons. According to the proposed model, an increase in the contribution of the surface states and the energy dependence of the lifetime of the electronic states provide the maximum amount of the Seebeck coefficient and the increase in the thermoelectric efficiency. Experimental research of transport of thin films (Bi1‐xSbx)2Te3 [11] carried out in a wide range of compositions, and temperatures have confirmed validity of this model. It follows that the study of surface states of Dirac fermions is promising for thermoelectricity to improve the energy conversion efficiency of nanostructured thermoelectrics. This chapter includes the thermoelectric properties under normal conditions and under high pressure, galvanomagnetic and optical properties of nanostructured films based on Bi2Te3, obtained by different methods, in order to determine the possible effect of the topological surface states of Dirac fermions depending on the composition, the Seebeck coefficient and temperature.

## **2. Features of formation and structure of the grown (Bi,Sb)2Te3 films**

Because of incongruent evaporation/sublimation of (Bi,Sb)2Te3 solid solutions and pronounced volatility of tellurium at temperatures higher than 400°C, formation of stoichiometric epitaxial films of bismuth and antimony chalcogenides is a nontrivial task. Hot wall technique [12, 13] was used to grow stoichiometric Bi0.5Sb1.5Te3 layers with a thickness of 30–500 nm.

Structure of the grown thermoelectric films was investigated by X‐ray (Philips X'pert MRD, CuKα1, ω/2Θ‐ and φ‐scans). Surface morphology of the grown (Bi,Sb)2Te3 films was studied by atomic force microscopy (Nanoscope IIIa, tipping mode). Nanostructured epitaxial thermo‐ electric films of (Bi,Sb)2Te3 were grown by hot wall technique on mica (muscovite) substrates. Usage of a mica substrate promotes small in‐plane misorientation of the blocks in the BST film, but relatively high deposition temperature is in a favor of low density of defects in their volume. Thickness of the grown thermoelectric layers was in the range of 30–500 nm. Substrate temperature during thermoelectric film formation was roughly 70°C less then temperature of sublimating stoichiometric Bi0.5Sb1.5Te3 burden. X‐ray ω/2Θ scans were traced for the grown Bi0.5Sb1.5Te3 films when plane including incident and reflected Roentgen beams was in plane normal to (000.1) of mica or (101.5) of the thermoelectric layer (see **Figures 1** and **2**). From obtained scans follow that c‐axis in the (Bi,Sb)2Te3 films grown on mica by hot wall technique was normal to substrate plane. Driving force for preferential orientation of c‐axis in the grown films along normal to a substrate plane was substantial anisotropy of a surface free energy of the bismuth and antimony chalcogenides. From X‐ray, φ*‐*scan traced for a (101.5) Bi0.5Sb1.5Te3 reflex, see insert in **Figure 1**, follows that thermoelectric films grown on mica were well in‐ plane preferentially oriented as well. In‐plane disorientation of blocks in the films was ∼0.3°. (The estimation obtained from full width at half of a maximum of a peak on the φ**‐**scan. Roughly, equidistant system of growth steps was clear detectable at the film surface (see **Figure 2**), at AFM image of free surface of the (Bi,Sb)2Te3 film grow on mica. Height of the growth steps was about 1 nm.

tured (Bi,Sb)2(Te,Se)3 epitaxial films were shown to possess an enhanced thermoelectric figure of merit Z compared to corresponding bulk crystals due to mechanical stresses and intensive phonon scattering at the grain boundaries. Lattice thermal conductivity of heteroepitaxial nanostructured films may be substantially diminished, as compared to corresponding bulk crystals, due to acoustic phonon scattering by grain and interface boundaries. Boundaries and strain may be easily induced in thin Bi2Te3‐based films grown on mismatched substrates. In contrast to point defects, which suppress heat transfer by short wave phonons, grain and interface boundaries are efficient in scattering of long wave ones. That is why, investigation of thin films with different structure and level of mechanical stresses looks quite important for

At the current stage, a new property of these materials, known as topological insulator, became one of the important subjects of the investigations [4–6]. These novel quantum states are the result of the electronic band inversion due to strong spin‐orbit interaction, so the bulk becomes insulating and the surface displays an unusual metallic electronic surface state of Dirac fermions with linear dispersion and spin texture that ensures high mobility of charge carriers due to the lack of backscattering on defects. The nanostructured films of topological materials [7, 8] theoretically proved the possibility of formation of topological excitons that can condense in a wide temperature range with the appearance of superfluidity and thus a significant increase in the mobility of the charge carriers. Currently, there is only a preliminary report on the pilot study of the heterostructure Sb2Te3/Bi2Te3, which assumes the realization of exciton condensation [9]. The theoretical model [10] for topological thermoelectrics based on the Landauer transport theory shows that the value of the Seebeck coefficient and thermoelectric efficiency is determined by the ratio of the mean free path of Dirac fermions to the mean free path of bulk electrons. According to the proposed model, an increase in the contribution of the surface states and the energy dependence of the lifetime of the electronic states provide the maximum amount of the Seebeck coefficient and the increase in the thermoelectric efficiency. Experimental research of transport of thin films (Bi1‐xSbx)2Te3 [11] carried out in a wide range of compositions, and temperatures have confirmed validity of this model. It follows that the study of surface states of Dirac fermions is promising for thermoelectricity to improve the energy conversion efficiency of nanostructured thermoelectrics. This chapter includes the thermoelectric properties under normal conditions and under high pressure, galvanomagnetic and optical properties of nanostructured films based on Bi2Te3, obtained by different methods, in order to determine the possible effect of the topological surface states of Dirac fermions

development of thermoelectric materials with enhanced performance.

220 Thermoelectrics for Power Generation - A Look at Trends in the Technology

depending on the composition, the Seebeck coefficient and temperature.

**2. Features of formation and structure of the grown (Bi,Sb)2Te3 films**

was used to grow stoichiometric Bi0.5Sb1.5Te3 layers with a thickness of 30–500 nm.

Because of incongruent evaporation/sublimation of (Bi,Sb)2Te3 solid solutions and pronounced volatility of tellurium at temperatures higher than 400°C, formation of stoichiometric epitaxial films of bismuth and antimony chalcogenides is a nontrivial task. Hot wall technique [12, 13]

**Figure 1.** X‐ray ω/2Θ scan traced for the grown Bi0.5Sb1.5Te3 film when plane including incident and reflected Roentgen beams was in plane normal to (000.1) plane of substrate. Insert plots φ‐scan of a (101.5) reflex from the same film.

**Figure 2.** X‐ray ω/2Θ scan traced for the grown Bi0.5Sb1.5Te3 film when plane including incident and reflected Roentgen beams was normal to (101.5) plane of the thermoelectric layer. AFM image of free surface of the grown thermoelectric layer is shown on insert.

#### **3. Thermoelectric properties**

Efficiency of thermoelectric energy conversion is dependent on figure of merit (*Z*) of the used materials (Z = *S*2  σ*/κ*, where S—Seebeck coefficient, σ—electrical conductivity, and *κ*—thermal conductivity) with electron and hole conductance. Thermoelectric properties of bismuth telluride and related solid solution Bi0.5Sb1.5Te3 heteroepitaxial nanostructured films were investigated below room temperature. The temperature dependences of the Seebeck coefficient S and the electroconductivity σ of the Bi2Te3 and Bi0.5Sb1.5Te3 films are shown in **Figure 3**. The electrical conductivity of bulk samples grows more sharply with temperature decrease for both Bi2Te3 and Bi0.5Sb1.5Te3 solid solution than for films (**Figure 3**, curves 6, 8 and 5, 7). The observed decrease in electrical conductivity in the films is related to the influence of scattering on interphase and intercrystallite grain boundaries.

The temperature dependences of the Seebeck coefficient (**Figure 3**), unlike such electrical conductivity dependences, are located higher for films than for bulk Bi2Te3 (curves 1, 2) and Bi0.5Sb1.5Te3 (curves 3, 4). The highest power factor values were obtained in submicrometer Bi0.5Sb1.5Te3 film at S = 242 μV K‐1 over the temperature range of 80–300 K and in the Bi0.5Sb1.5Te3 film at S = 234 μV K‐1 over the range of 130–260 K (**Figure 4**, curves 5, 3). An enhancement of the Seebeck coefficient and change in its temperature dependence slope both indicate the changes of charge carrier scattering mechanisms in grown films [14, 15] compared those to the bulk thermoelectric materials (**Figure 4**, curves 1–5 and curves 6–9).

**Figure 3.** Temperature dependences of the Seebeck coefficient S (1–9), electroconductivity σ (10–18) in heteroepitaxial films (1–5, 10–14), and bulk samples (6–9 and 15–18) of Bi0.5Sb1.5Te3 (1–3, 6–9, 10–12, 16–18) and Bi2Te3 (4, 5, 13, 14).

**Figure 2.** X‐ray ω/2Θ scan traced for the grown Bi0.5Sb1.5Te3 film when plane including incident and reflected Roentgen beams was normal to (101.5) plane of the thermoelectric layer. AFM image of free surface of the grown thermoelectric

Efficiency of thermoelectric energy conversion is dependent on figure of merit (*Z*) of the used

conductivity) with electron and hole conductance. Thermoelectric properties of bismuth telluride and related solid solution Bi0.5Sb1.5Te3 heteroepitaxial nanostructured films were investigated below room temperature. The temperature dependences of the Seebeck coefficient S and the electroconductivity σ of the Bi2Te3 and Bi0.5Sb1.5Te3 films are shown in **Figure 3**. The electrical conductivity of bulk samples grows more sharply with temperature decrease for both Bi2Te3 and Bi0.5Sb1.5Te3 solid solution than for films (**Figure 3**, curves 6, 8 and 5, 7). The observed decrease in electrical conductivity in the films is related to the influence of scattering

The temperature dependences of the Seebeck coefficient (**Figure 3**), unlike such electrical conductivity dependences, are located higher for films than for bulk Bi2Te3 (curves 1, 2) and Bi0.5Sb1.5Te3 (curves 3, 4). The highest power factor values were obtained in submicrometer Bi0.5Sb1.5Te3 film at S = 242 μV K‐1 over the temperature range of 80–300 K and in the Bi0.5Sb1.5Te3 film at S = 234 μV K‐1 over the range of 130–260 K (**Figure 4**, curves 5, 3). An

 σ*/κ*, where S—Seebeck coefficient, σ—electrical conductivity, and *κ*—thermal

layer is shown on insert.

materials (Z = *S*2

**3. Thermoelectric properties**

on interphase and intercrystallite grain boundaries.

222 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**Figure 4.** Temperature dependences of power factor S2 σ for heteroepitaxial films (1–5) and bulk samples (6–9) of Bi0.5Sb1.5Te3 (1–3, 6–9) and Bi2Te3 (4, 5) for S (μV K‐1) at room temperatures: 1—214, 2—224, 3—242, 4—203, 5—234, 6— 214, 7—207, 8—233, 9—221.

The results of the study of galvanomagnetic and thermoelectric properties in epitaxial films have been used to determine the average effective mass of the density of states m/m0 and mobility μ0 of charge carriers taking into account the effective scattering parameter in the model with an isotropic relaxation time similar to the bulk thermoelectrics [14, 16, 17]. Calculations of the effective mass m/m0 and mobility m0 have showed that the effective mass of the films is higher than in the bulk samples (**Figure 5**, curves 1–5 and 6, 7) with slight reduction of the mobility in the films (**Figure 5**, curves 13, 14). From the study of the galvano‐ magnetic properties, the behavior of the effective mass and mobility in the films was found to depend on the scattering mechanism of charge carriers and the parameters of the ellipsoidal constant energy surfaces [13, 18].

**Figure 5.** Temperature dependences of the density‐of‐states effective mass m/m0 (1–7) and charge carrier mobilitym0 (8–14) for films (1–5, 8–12) and bulk samples (6, 7, 13, 14) of Bi0.5Sb1.5Te3 (1–3, 6–7, 8–10, 13–14) and Bi2Te3 (4, 5, 11, 12).

The product (m/m0) 3/2μ0, proportional to the figure of merit Z, is higher for films than bulk thermoelectrics due to growth of the effective mass of the density states, which determines an increase in power factor of the films (**Figure 6**). At temperatures below 200 K, an increase in the (m/m0) 3/2μ0 was observed in the solid solution Bi0.5Sb1.5Te3 at a value of the Seebeck coefficient S = 242 μV K‐1 at room temperature (**Figure 6**, curve 3).

An estimated value of the figure of merit Z in heteroepitaxial Bi0.5Sb1.5Te3 film increases to 3.85 × 10‐3 K‐1 over the temperature range of 180–200 K. Such increase in Z is approximately by 60% compared to conventional bulk materials and by 20% compared with multicomponent bulk thermoelectrics optimized for temperatures below 200 K [19, 20]. Reduction in thermal conductivity in the Bi0.5Sb1.5Te3 films can reach 20–30% due to additional scattering of charge carriers in the intercrystallite and interphase boundaries [3, 21] that give an additional rise in the figure of merit.

Nanometer Structured Epitaxial Films and Foliated Layers Based on Bismuth and Antimony Chalcogenides... http://dx.doi.org/10.5772/65750 225

**Figure 6.** Temperature dependence of the (m/m0) 3/2 μ0 parameter for films (1–5) and bulk samples (6, 7) of Bi0.5Sb1.5Te3 (1–3, 5–7) and Bi2Te3 (4).

#### **4. Mechanisms of charge carriers scattering**

The results of the study of galvanomagnetic and thermoelectric properties in epitaxial films have been used to determine the average effective mass of the density of states m/m0 and mobility μ0 of charge carriers taking into account the effective scattering parameter in the model with an isotropic relaxation time similar to the bulk thermoelectrics [14, 16, 17]. Calculations of the effective mass m/m0 and mobility m0 have showed that the effective mass of the films is higher than in the bulk samples (**Figure 5**, curves 1–5 and 6, 7) with slight reduction of the mobility in the films (**Figure 5**, curves 13, 14). From the study of the galvano‐ magnetic properties, the behavior of the effective mass and mobility in the films was found to depend on the scattering mechanism of charge carriers and the parameters of the ellipsoidal

**Figure 5.** Temperature dependences of the density‐of‐states effective mass m/m0 (1–7) and charge carrier mobilitym0 (8–14) for films (1–5, 8–12) and bulk samples (6, 7, 13, 14) of Bi0.5Sb1.5Te3 (1–3, 6–7, 8–10, 13–14) and Bi2Te3 (4, 5, 11, 12).

thermoelectrics due to growth of the effective mass of the density states, which determines an increase in power factor of the films (**Figure 6**). At temperatures below 200 K, an increase in

An estimated value of the figure of merit Z in heteroepitaxial Bi0.5Sb1.5Te3 film increases to 3.85 × 10‐3 K‐1 over the temperature range of 180–200 K. Such increase in Z is approximately by 60% compared to conventional bulk materials and by 20% compared with multicomponent bulk thermoelectrics optimized for temperatures below 200 K [19, 20]. Reduction in thermal conductivity in the Bi0.5Sb1.5Te3 films can reach 20–30% due to additional scattering of charge carriers in the intercrystallite and interphase boundaries [3, 21] that give an additional rise in

coefficient S = 242 μV K‐1 at room temperature (**Figure 6**, curve 3).

3/2μ0, proportional to the figure of merit Z, is higher for films than bulk

3/2μ0 was observed in the solid solution Bi0.5Sb1.5Te3 at a value of the Seebeck

constant energy surfaces [13, 18].

224 Thermoelectrics for Power Generation - A Look at Trends in the Technology

The product (m/m0)

the figure of merit.

the (m/m0)

The charge carrier scattering mechanisms of Bi2Te3 and solid solution Bi0.5Sb1.5Te3 films were investigated from analysis of the galvanomagnetic coefficients including transverse and longitudinal components of magnetoresistivity tensor rijkl, electroresistivity rij, and Hall coefficient rijk within many‐valley model of energy spectrum for isotropic scattering mecha‐ nism [14, 18, 22]. A relaxation time for isotropic carrier scattering depends on energy E by power law: τ = τ0 Er , where τ0 is an energy independent factor and r is the scattering parameter. The least square analysis of experimental galvanomagnetic coefficients for isotropic scattering mechanism permits to determine the degeneracy parameter βd [13, 15]. The dependence of βd on temperature obtained in magnetic field at B = 10 T is in agreement with that at B = 14 T (**Figure 7**, curves 1, 2).

The parameter βd depends on temperature more sharply in the film than in the bulk Bi2‐xSbxTe3 solid solutions (**Figure 7**, points 3, 4). The temperature dependence of the βd of the films is supposed to be explained by an additional charge carrier scattering on interphase and inter‐ crystallite boundaries of monocrystalline grains of the films. As shown in **Figure 8**, the depend‐ ence of the degeneracy parameter βd on the reduced Fermi level η shows that the βd values in films are less than in bulk materials. Therefore, the degeneracy of films is smaller than bulk thermoelectrics [13].

The effective scattering parameter reff and the reduced Fermi level η were calculated by Nelder‐ Mead least square method from the temperature dependences of the degeneracy parameter βd and the Seebeck coefficient S [14, 24]. As compared to bulk materials, the values of the parameter reff are considerably different from the value r = ‐0.5, specific for an acoustic phonon scattering mechanism due to sharper energy dependence of electron relaxation time in the films, that is, explained by an additional charge carriers scattering on interphase and inter‐ crystallite boundaries of epitaxial films (**Figure 8**).

**Figure 7.** Temperature dependence of the degeneracy parameter βd (1–2) in the Bi0.5Sb1.5Te3 film. βd is (1) 10 T and (2) 14  T. Points for bulk solid solutions: 3 [23], 4 [14].

**Figure 8.** The degeneracy parameter βd (1–6) and the effective scattering parameter reff (7–12) on reduced Fermi level η in Bi2Te3 (1, 7), Bi0.5Sb1.5Te3 (2, 8) films, and Bi2‐xSbxTe3‐ySey (x = 1.2, y = 0.09), (3, 4, 9, 10); Bi2‐xSbxTe3‐ySey (x = 1.3, y = 0.07), (5, 11); Bi2‐xSbxTe3 (x = 1.6), (6, 12) bulk solid solutions.

The materials under study exhibit both anisotropy of the transport properties and anisotropy of charge carrier scattering. In a six‐valley model of the energy spectrum with anisotropic scattering of charge carriers, the components of the relaxation time tensor () can be presented as = ϕ() where ϕ(ε) is an isotropic function depending on μ and τij is an anisotropic multiplier that is independent on energy. The ratios of the () tensor components were determined in the temperature interval from 10 to 300 K [15, 17, 25, 26]. The relation between the τ (ε) components was found as follows: τ22 > τ11 > τ33, and charge carrier scattering along bisector directions was dominant in the film as in the bulk thermoelectrics at low temperatures [17, 25, 27]. The ratio τ22/τ11 in the Bi2‐xSbxTe3 film is increased along bisector axes, but the ratio τ33/τ11 is diminished along the trigonal direction in contrast to corresponding bulk thermoelectrics at low [17, 25] and room [27] temperatures. The value τ23 is near the same as τ11 for the films, while for bulk materials τ23 is less than τ11. These specific features of charge carriers scattering lead to increase in the slope of the Seebeck coefficient dependence on temperature (**Figure 3**) and to enhance the thermoelectric power factor for films. Optimization of structure and charge state of the grains and/or interface boundaries might be in favor of a large thermoelectric power factor and figure of merit.

## **5. Thermoelectric properties under high pressure**

**Figure 7.** Temperature dependence of the degeneracy parameter βd (1–2) in the Bi0.5Sb1.5Te3 film. βd is (1) 10 T and (2) 14

**Figure 8.** The degeneracy parameter βd (1–6) and the effective scattering parameter reff (7–12) on reduced Fermi level η in Bi2Te3 (1, 7), Bi0.5Sb1.5Te3 (2, 8) films, and Bi2‐xSbxTe3‐ySey (x = 1.2, y = 0.09), (3, 4, 9, 10); Bi2‐xSbxTe3‐ySey (x = 1.3, y = 0.07),

The materials under study exhibit both anisotropy of the transport properties and anisotropy of charge carrier scattering. In a six‐valley model of the energy spectrum with anisotropic scattering of charge carriers, the components of the relaxation time tensor () can be presented as = ϕ() where ϕ(ε) is an isotropic function depending on μ and τij is an anisotropic multiplier that is independent on energy. The ratios of the () tensor components

T. Points for bulk solid solutions: 3 [23], 4 [14].

226 Thermoelectrics for Power Generation - A Look at Trends in the Technology

(5, 11); Bi2‐xSbxTe3 (x = 1.6), (6, 12) bulk solid solutions.

The thermoelectric properties of *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solutions with atomic substitutions in the tellurium sublattice at (*x* = 0.27, 0.3, *y* = 0, and *x* = *y* = 0.09) and p‐Bi2Te3 were studied under pressure of 8 GPa on submicron layer samples at room temperature using the technique described in Ref. [28–30]. It was found that the Seebeck coefficient decreases and the electro‐ conductivity increases with increasein pressure, but the power factor S2 σ increases for all compositions, and becomes maximum at pressures of 3–4 GPa (**Figure 9**). The effective mass m/m0 and mobility μ0 in the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* and p‐Bi2Te3 films were obtained taking into account of the change in the scattering mechanism depending on the solid solution composi‐ tion and carrier density [14, 31]. With increasing pressure *P*, the effective mass m/m0 [29] in the n‐ and p‐type compositions decreases (**Figure 10**). For *p‐*Bi2Te3 and for composition at x =  y = 0.09, the dependence of m/m0 and μ0 on *P* has an inflection at pressures about 3–4 GPa [29, 30]. These inflections in the dependences of m/m0 and μ0 on *P*, observed at nearly the same pressure as for the maximum value of power factor S2 σ, were explained by the influence of topological phase transition at room temperature (**Figure 10**, curves 3, 7).

The existence of the topological transition in Bi2Te3 is confirmed by precise diffraction studies of the pressure dependence of lattice parameters [32], abrupt change in the elasticity modulus and its derivative [33], and the change in the Fermi surface section from study of de Haas‐van Alphen [32, 34]. This topological transition in Bi2Te3 was also confirmed by study of Raman spectroscopy under high pressure [35]. The maximum of the product (m/m0) 3/2μ0, proportional to the figure of merit, was observed at about the same pressure range as for the topological transition (**Figure 11**). The estimations of the thermal conductivity κ in the *n*‐ and *p*‐type materials show that increase in κ in the pressure range ∼3–4 GPa is not higher than 50% [36]. But the power factor of *n‐*Bi2Te3‐x‐ySexSy solid solutions and the p‐type compositions Bi2‐*x*Sb*x*Te3 [29] increases under pressure more significantly, and thus, enhancement of the figure of merit values can reach 50–70% taking into account the influence of topological transition at room temperature.

**Figure 9.** Pressure dependences of power factor of the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solution layers; *x*, *y* are (1) 0.27, 0; (2) 0.3, 0; (3) 0.09, 0.09 and p‐Bi2Te3 (4).

**Figure 10.** Pressure dependences of the effective mass m/m0 and the mobility μ0 of the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solutions; *x*, *y* are (1, 5) 0.27, 0; (2, 6) 0.3, 0; (3, 7) 0.09, 0.09 and p‐Bi2Te3 (4, 8).

**Figure 11.** Pressure dependences of the product (m/m0) 3/2μ0 of the *n*‐Bi2Te3‐*x‐y*Se*x*S*y* solid solutions; *x*, *y* are (1) 0.27, 0; (2) 0.3, 0; (3) 0.09, 0.09 and p‐Bi2Te3 (4).

## **6. Quantum oscillations of magnetoresistance**

**Figure 9.** Pressure dependences of power factor of the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solution layers; *x*, *y* are (1) 0.27, 0; (2) 0.3, 0;

**Figure 10.** Pressure dependences of the effective mass m/m0 and the mobility μ0 of the *n‐*Bi2Te3‐*x‐y*Se*x*S*y* solid solutions; *x*,

3/2μ0 of the *n*‐Bi2Te3‐*x‐y*Se*x*S*y* solid solutions; *x*, *y* are (1) 0.27, 0; (2)

*y* are (1, 5) 0.27, 0; (2, 6) 0.3, 0; (3, 7) 0.09, 0.09 and p‐Bi2Te3 (4, 8).

228 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**Figure 11.** Pressure dependences of the product (m/m0)

0.3, 0; (3) 0.09, 0.09 and p‐Bi2Te3 (4).

(3) 0.09, 0.09 and p‐Bi2Te3 (4).

Quantum oscillations of the magnetoresistance associated with surface electronic states in three‐dimensional topological insulators have been studied in *p‐*type Bi2Te3 films [37] in strong magnetic fields from 6 to 14 T at low temperatures (**Figure 12**). The main parameters of surface charge carriers in the films (**Tables 1** and **2**) were determined by analyzing the temperature dependences of normalized amplitude of magnetoresistance oscillations [38]. The phase shift of oscillation period, evaluated by extrapolation of dependence of the Landau level indexes (n = 2, 3, 4, 5) (**Figure 12**) on inverse magnetic field in the limit of 1/B = 0, was found to be consistent with the value of π Berry phase, which is characteristic of surface states of Dirac fermions with linear dispersion [37]. The obtained parameters of the surface states of charge carriers in the nanostructured materials under consideration are important for the develop‐ ment of new high‐performance thermoelectrics. The parameters of the surface states of Dirac fermions, such as the mean free path and the energy dependence of lifetime of the charge carriers at the surface, the Fermi energy and respective position of the Fermi level, have a specific influence on the Seebeck coefficient and power factor.

**Figure 12.** Magnetoresistance dependence ρxx (1–3) on magnetic field B and quantum oscillations Δρxx(4–6) dependence on inverse magnetic field 1/B; ρxx at the temperatures: 1, 4–1.6 K, 2, 5–4.2 K, 3, 6–10 K and the Landau level index (*n* = 2, 3, 4, 5) corresponding to the minimum amplitudes of the oscillations.

**Table 1.** Cyclotron resonance frequency *ν*, Fermi velocity *v*F, Fermi energy *EF*, charge carrier mobility *μ*, mean free path of charge carriers *lF*, the relaxation time *τ*, and Dingle temperature *TD* of the Bi2Te3 films.

**Table 2.** Frequency of quantum oscillations of the magnetoresistance *F*, cross section of the Fermi surface *S*(*kF*), Fermi wave vector *kF*, and surface concentration of charge carriers *nFs* in the Bi2Te3 films.

#### **7. Raman spectra**

The resonance Raman scattering and morphology of an interlayer van der Waals surface (0001) in thin layer films of chalcogenides based on bismuth and antimony were studied in depend‐ ence on the composition, the Seebeck coefficient, and the thickness of the samples. Raman spectra of optical phonons Eg 2 , A1u2 , and A1g2 in thin layers of binary compound *n*‐Bi2Te3 and alloys Bi2Te3‐ySey, Bi2‐xSbxTe3‐ySey, in heteroepitaxial films of *p*‐Bi2Te3 and chemically foliated solid solutions Bi2‐xSbxTe3‐ySey are shown in **Figures 13** and **14**. The morphology of the interlayer surfaces (0001) of these samples was studied by atomic force microscopy.

**Figure 13.** Raman spectra of mechanically split thin layers of n‐Bi2Te3 (1‐1, 1‐2), n‐Bi2Te2.88Se0.12 (2‐1, 2‐2) and n‐ Bi2Te2.7Se0.3 (3‐1, 3‐2, 4‐1, 4‐2). (1‐1, 1‐2): S = ‐270 μV K‐1, Rq = 0.45 nm, Ha = 1.75 nm. (2‐1, 2‐2): S = ‐285 μV K‐1, Rq = 3.8 nm, Ha = 8 nm. (3‐1, 3‐2): S = ‐305 μV K‐1, Rq = 4.6 nm, Ha = 15 nm. (4‐1, 4‐2): S = ‐315 μV K‐1, Rq = 2.9 nm, Ha = 2.3 nm.

Nanometer Structured Epitaxial Films and Foliated Layers Based on Bismuth and Antimony Chalcogenides... http://dx.doi.org/10.5772/65750 231

*F***, T** *S(kF)***, nm‐2** *kF***, nm** *nFs***× 1012, cm‐2**

**Table 2.** Frequency of quantum oscillations of the magnetoresistance *F*, cross section of the Fermi surface *S*(*kF*), Fermi

The resonance Raman scattering and morphology of an interlayer van der Waals surface (0001) in thin layer films of chalcogenides based on bismuth and antimony were studied in depend‐ ence on the composition, the Seebeck coefficient, and the thickness of the samples. Raman

alloys Bi2Te3‐ySey, Bi2‐xSbxTe3‐ySey, in heteroepitaxial films of *p*‐Bi2Te3 and chemically foliated solid solutions Bi2‐xSbxTe3‐ySey are shown in **Figures 13** and **14**. The morphology of the

**Figure 13.** Raman spectra of mechanically split thin layers of n‐Bi2Te3 (1‐1, 1‐2), n‐Bi2Te2.88Se0.12 (2‐1, 2‐2) and n‐ Bi2Te2.7Se0.3 (3‐1, 3‐2, 4‐1, 4‐2). (1‐1, 1‐2): S = ‐270 μV K‐1, Rq = 0.45 nm, Ha = 1.75 nm. (2‐1, 2‐2): S = ‐285 μV K‐1, Rq = 3.8 nm,

Ha = 8 nm. (3‐1, 3‐2): S = ‐305 μV K‐1, Rq = 4.6 nm, Ha = 15 nm. (4‐1, 4‐2): S = ‐315 μV K‐1, Rq = 2.9 nm, Ha = 2.3 nm.

in thin layers of binary compound *n*‐Bi2Te3 and

, and A1g2

interlayer surfaces (0001) of these samples was studied by atomic force microscopy.

24 0.23 0.27 0.58 30 [39] 0.29 0.30 0.72 41.7 [40] 0.40 0.36 1.0 50 [39] 0.48 0.39 1.21

230 Thermoelectrics for Power Generation - A Look at Trends in the Technology

wave vector *kF*, and surface concentration of charge carriers *nFs* in the Bi2Te3 films.

2 , A1u2

**7. Raman spectra**

spectra of optical phonons Eg

**Figure 14.** Raman spectra of the thin films of n‐Bi1.6Sb0.4Te2.91Se0.09 (5‐1, 5‐2), p‐Bi2Te3 (6‐1, 6‐2) and foliated Bi0.9Sb1.1Te2.94Se0.06 (7‐1, 7‐2) solid solution. (5‐1, 5‐2): S = ‐280 μV K‐1, Rq = 0.36 nm, Ha = 1.55 nm. (6‐1, 6‐2): Rq = 0.56 nm, Ha = 1.8 nm. (7‐1, 7‐2): S = ‐280 μV K‐1. (7‐1) dissolution time t = 150 h, Rq = 36 nm, Ha = 180 nm. (7‐2) t = 200 h, Rq = 26 nm, Ha = 80 nm.

The roughness Rq and Ha corresponding to the maximum of the distribution function of nanofragment heights on the surface of samples [41] are indicated in the captions of **Figures 13** and **14**.

The appearance of the inactive phonons A1u2 in the Raman spectra, caused by a violation of the inversion symmetry of the crystal, was revealed at decreasing sample thickness and also at high pressure for which topological phase transition in Bi2Te3 [35] was observed. Therefore, the occurrence of the A1u2 was explained by the behavior of surface electronic states of Dirac fermions [42, 43]. The relative intensities I(A1u2 )/I(Eg 2 ) have maximal values in the most thin layers of solid solutions of n‐Bi2Te2.7Se0.3, n‐Bi1.6Sb0.4Te2.91Se0.09, and epitaxial film of the p‐B2Te3 with high Seebeck coefficients (**Figure 15**) with high quality of the interlayer (0001) surface with small roughness Rq and Ha values (**Figures 13** and **14**). In the samples n‐Bi2Te2.88Se0.12, prepared by the Czochralski technique and by the chemical foliated p‐Bi0.9Sb1.1Te2.94S0.06 the ratio I(A1u2 )/I(Eg2), is quite lower (**Figure 15**, curves 2, 7). So the ratio I(A1u2 )/I(Eg2) is strongly affected by the used technology, composition and thickness of the samples. The analysis of the Raman spectra of bismuth telluride and its solid solutions allows to optimize the Seebeck coefficients, composition, sample thickness, and morphology of the surface, which provide the significant role of surface states of Dirac fermions at room temperature.

**Figure 15.** The dependence of the relative intensities I(A1u2 )/I(Eg 2 ) on the thickness of the layers of n‐Bi2Te3 (1), n‐ Bi2Te2.88Se0.12 (2), n‐Bi2Te2.7Se0.3 (3, 4), n‐Bi1.6Sb0.4Te2.91Se0.09 (5), p‐Bi2Te3 (6), and p‐Bi0.9Sb1.1Te2.94Se0.06 (7).

#### **8. Conclusion**

The thermoelectric and galvanomagnetic properties of heteroepitaxial films based on bismuth telluride, grown by the hot wall epitaxy method, were investigated. The highest power factor was obtained in the Bi0.5Sb1.5Te3 films. An enhancement of the Seebeck coefficient and change in its temperature dependence slope both indicate the variation in the charge carrier scattering mechanisms compared to the bulk thermoelectric materials. The increase in the power factor and (m/m0) 3/2μ0, associated with the increase in the effective mass of density of states m/m0, and the reduction in thermal conductivity lead to an increase in the figure of merit Z in the Bi0.5Sb1.5Te3 films up to 3.85 × 10‐3 K‐1 over the temperature range of 180–200 K. Such increase in Z is approximately more by 60% compared to similar bulk materials. The charge carrier scattering mechanisms of the Bi0.5Sb1.5Te3 films were investigated from the data on galvano‐ magnetic properties for isotropic and anisotropic scattering within many‐valley model of energy spectrum. For isotropic scattering, the degeneracy parameter βd, the effective scattering parameter reff**,** and the reduced Fermi level η were calculated. As compared to bulk materials, the values of the parameter reff are considerably different from r = ‐0.5, specific for an acoustic phonon scattering in the epitaxial films. The difference of the reff values is related to an additional charge carriers scattering on interphase and intercrystallite boundaries in the films.

The account of anisotropy of the carrier scattering mechanism has shown that scattering along bisector crystallographic axes is main as compared with corresponding bulk thermoelectrics. Revealed charge carrier scattering peculiarities affect transport properties of the films and might be in favor of a large thermoelectric power factor and the figure of merit.

The studies of the thermoelectric properties of the n‐Bi2Te3‐x‐ySexSy solid solutions under pressure have shown the increase in power factor and product (m/m0) 3/2μ0, which is determined by the growth of the effective mass m/m0. In the composition *n‐*Bi2Te3‐*x‐y*Se*x*S*y* (x = y = 0.09) and p‐Bi2Te3, the change in the slopes of the pressure dependence of the effective mass and the mobility in the range of 3–4 GPa are coincident with maximum of power factor and explained by an influence of the topological transition. An increase in the thermoelectric figure of merit, as compared to normal conditions, was estimated as 50–70% under pressure due to effect of the topological transitions.

Quantum oscillations of the magnetoresistance were revealed at low temperatures T below 10 K in the range of magnetic field from 6 to 14 T in nanostructured submicron Bi2Te3 films grown by hot wall technique. From the analysis of the magnetoresistance oscillations, the cyclotron resonance frequency, cross‐sectional Fermi surface, Landau level indexes and π Berry phase, effective cyclotron mass, Fermi wave vector, velocity and Fermi energy, surface charge carrier concentration, lifetime, and mobility of charge carriers were evaluated. The estimated parameters of topological electronic surface states of nanostructured chalcogenides of bismuth and antimony are of special interest for development of new high‐performance thermoelec‐ trics, because the Seebeck coefficient and hence power factor are significantly determined by the basic parameters such as charge carriers lifetime, the mean free path of charge carriers, and Fermi energy level position.

The resonance Raman scattering and morphology of the interlayer surface (0001) of bismuth and antimony chalcogenides were studied at room temperature depending on the composi‐ tion, the Seebeck coefficient, and the thickness of the layers. Raman shifts and the relative intensities of phonon modes were studied in mechanical and chemical foliated thin layers and epitaxial films of bismuth telluride and its solid solutions. The increase in relative intensity ratio of Raman inactive phonons I(A1u2 )/I(Eg 2 ), sensitive to the topological surface states, was observed for thin layers of n‐Bi2Te2.7Se0.3 and n‐Bi1.6Sb0.4Te2.91Se0.09 solid solutions at low carrier density with Seebeck coefficient values more than ‐280 μV K‐1 and in epitaxial p‐B2Te3 film grown by the hot wall method on mica with perfect interlayer surface. Thus, the resonance Raman spectra analysis allows to optimize the composition, thickness, Seebeck coefficient values, and morphology of the layers and films with enhanced contribution of the topological surface states at room temperature, which increases the prospects of application of these thermoelectrics.

## **Author details**

**Figure 15.** The dependence of the relative intensities I(A1u2

232 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**8. Conclusion**

and (m/m0)

)/I(Eg 2

The thermoelectric and galvanomagnetic properties of heteroepitaxial films based on bismuth telluride, grown by the hot wall epitaxy method, were investigated. The highest power factor was obtained in the Bi0.5Sb1.5Te3 films. An enhancement of the Seebeck coefficient and change in its temperature dependence slope both indicate the variation in the charge carrier scattering mechanisms compared to the bulk thermoelectric materials. The increase in the power factor

and the reduction in thermal conductivity lead to an increase in the figure of merit Z in the Bi0.5Sb1.5Te3 films up to 3.85 × 10‐3 K‐1 over the temperature range of 180–200 K. Such increase in Z is approximately more by 60% compared to similar bulk materials. The charge carrier scattering mechanisms of the Bi0.5Sb1.5Te3 films were investigated from the data on galvano‐ magnetic properties for isotropic and anisotropic scattering within many‐valley model of energy spectrum. For isotropic scattering, the degeneracy parameter βd, the effective scattering parameter reff**,** and the reduced Fermi level η were calculated. As compared to bulk materials, the values of the parameter reff are considerably different from r = ‐0.5, specific for an acoustic phonon scattering in the epitaxial films. The difference of the reff values is related to an additional charge carriers scattering on interphase and intercrystallite boundaries in the films. The account of anisotropy of the carrier scattering mechanism has shown that scattering along bisector crystallographic axes is main as compared with corresponding bulk thermoelectrics. Revealed charge carrier scattering peculiarities affect transport properties of the films and

might be in favor of a large thermoelectric power factor and the figure of merit.

3/2μ0, associated with the increase in the effective mass of density of states m/m0,

Bi2Te2.88Se0.12 (2), n‐Bi2Te2.7Se0.3 (3, 4), n‐Bi1.6Sb0.4Te2.91Se0.09 (5), p‐Bi2Te3 (6), and p‐Bi0.9Sb1.1Te2.94Se0.06 (7).

) on the thickness of the layers of n‐Bi2Te3 (1), n‐

Lidia N. Lukyanova\* , Yuri A. Boikov, Oleg A. Usov, Mikhail P. Volkov and Viacheslav A. Danilov

\*Address all correspondence to<EMAIL_ADDRESS>
Ioffe Institute, Saint Petersburg, Russia

## **References**

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236 Thermoelectrics for Power Generation - A Look at Trends in the Technology

#### **Thermoelectric Power Generation by Clathrates Thermoelectric Power Generation by Clathrates**

Andrei V. Shevelkov Andrei V. Shevelkov

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/65600

#### **Abstract**

Clathrate compounds combine aesthetic beauty of their crystal structures with promising thermoelectric properties that have made them one of the most explored family of compounds deemed as base for thermoelectric generators for mid- and hightemperature application. This chapter surveys crystal and electronic structure and structure-related transport properties of selected types of clathrates and discusses their thermoelectric performance and prospects of their future applications.

**Keywords:** thermoelectric materials, thermoelectric power generation, clathrates, phonon glass-electronic crystal, charge carrier transport, heat transport

## **1. Introduction**

No compound is able to outplay properly doped bismuth telluride as material for thermoelectric cooling. Since the pioneer works of A.F. Ioffe in the 1950, this material solely holds the position in the industry [1]. Situation is different, when it comes to thermoelectric power generation, where traditional materials based on Bi2Te3 are giving way to new state-of-the-art materials. Among the latter, there are clathrates; these compounds combine low, glass-like thermal conductivity with high electrical conductivity and Seebeck coefficient and are demanded as perspective thermoelectric materials that convert temperature gradient into electric power [2–4].

Clathrates are different from many other prospective materials for thermoelectric power generators, because they feature the spatial separation of two substructures known as host clathrate framework and rattling guests [4–6]. The framework is based on strong covalent bonds, four for each atom, that ensure effective transport of charge carriers leading to high values of both electrical conductivity and thermopower, whereas the rattling of guests inside oversized cages of the framework causes low thermal conductivity owing to either scattering

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

of heat-carrying phonons or reducing phonon group velocity due to avoided crossing of rattling modes and branches of acoustic phonons. The spatial host-guest separation provides the base for practical utilization of "phonon glass-electron crystal" (PGEC) concept introduced by Slack, according to which decoupling of heat and charge carriers transport enables their independent optimization [7]. But despite the spatial separation, thermal and charge carriers transport properties are not truly independent, which makes optimization of thermoelectric efficiency a very intricate and delicate task. Recent years have witnessed appreciable progress in enhancing thermoelectric efficiency of clathrates at mid- and high-temperature regions. The phonon engineering approaches, including introduction of rare earth guests and formation of complex superstructures, have led to extremely low thermal conductivity for narrow-gap clathrate semiconductors. New synthetic approaches have enabled accurate tuning of charge carriers' concentration by extremely precise doping, as well as providing very high densities of properly consolidated ceramic materials. Finally, new compositions of clathrates have emerged, that allow combination of reasonably high thermoelectric efficiency and utmost chemical and thermal stability. Already now, there are examples of clathrate compounds displaying high values of figure-of-merit, even surpassing unity at T > 470 K, and further progress is highly expected.

This chapter surveys recent progress in developing thermoelectric materials for power generation on the base of inorganic clathrate compounds. We consider crystal and electronic structures of these compounds, the underlying physics of their thermoelectric properties, synthetic methods of their preparation, and, as a central issue, their thermoelectric performance. Current achievements and future prospects are discussed.

## **2. Clathrates as inclusion compounds**

#### **2.1. Crystal structures**

Clathrates belong to plentiful class of inclusion compounds. Their discovery is traced back to the beginning of the nineteenth century, when Sir Davy observed formation of solid chlorine hydrate upon passing gaseous chlorine through water cooled to +5°C. Other hydrates came soon after, and by the middle of the twentieth century, quite a number of hydrates of various gases and liquids were discovered, and their crystal structures were solved. Despite clear differences in their chemical composition and crystal structures, these compounds shared a single common feature, which is complete sequestering of a guest moiety inside cages of framework. Another distinct feature of those compounds is the absence of strong host-guest bonds. In 1965 [8], Kasper, Hagenmuller, and Pouchard reported two new sodium silicides, whose crystal structures were identical to hydrates of various gases, proving that host-guest size matching had the primary role in their formation and stability, rather than the details of chemical bonding. Since then, almost three hundred compounds belonging to ten structure types were documented [3–5, 9]. They involve almost 50 chemical elements constituting more than 50% of all stable chemical elements (**Figure 1**).

**Figure 1.** "Clathrate Periodic Table."

of heat-carrying phonons or reducing phonon group velocity due to avoided crossing of rattling modes and branches of acoustic phonons. The spatial host-guest separation provides the base for practical utilization of "phonon glass-electron crystal" (PGEC) concept introduced by Slack, according to which decoupling of heat and charge carriers transport enables their independent optimization [7]. But despite the spatial separation, thermal and charge carriers transport properties are not truly independent, which makes optimization of thermoelectric efficiency a very intricate and delicate task. Recent years have witnessed appreciable progress in enhancing thermoelectric efficiency of clathrates at mid- and high-temperature regions. The phonon engineering approaches, including introduction of rare earth guests and formation of complex superstructures, have led to extremely low thermal conductivity for narrow-gap clathrate semiconductors. New synthetic approaches have enabled accurate tuning of charge carriers' concentration by extremely precise doping, as well as providing very high densities of properly consolidated ceramic materials. Finally, new compositions of clathrates have emerged, that allow combination of reasonably high thermoelectric efficiency and utmost chemical and thermal stability. Already now, there are examples of clathrate compounds displaying high values of figure-of-merit, even surpassing unity at T > 470 K, and further

This chapter surveys recent progress in developing thermoelectric materials for power generation on the base of inorganic clathrate compounds. We consider crystal and electronic structures of these compounds, the underlying physics of their thermoelectric properties, synthetic methods of their preparation, and, as a central issue, their thermoelectric perform-

Clathrates belong to plentiful class of inclusion compounds. Their discovery is traced back to the beginning of the nineteenth century, when Sir Davy observed formation of solid chlorine hydrate upon passing gaseous chlorine through water cooled to +5°C. Other hydrates came soon after, and by the middle of the twentieth century, quite a number of hydrates of various gases and liquids were discovered, and their crystal structures were solved. Despite clear differences in their chemical composition and crystal structures, these compounds shared a single common feature, which is complete sequestering of a guest moiety inside cages of framework. Another distinct feature of those compounds is the absence of strong host-guest bonds. In 1965 [8], Kasper, Hagenmuller, and Pouchard reported two new sodium silicides, whose crystal structures were identical to hydrates of various gases, proving that host-guest size matching had the primary role in their formation and stability, rather than the details of chemical bonding. Since then, almost three hundred compounds belonging to ten structure types were documented [3–5, 9]. They involve almost 50 chemical elements constituting more

ance. Current achievements and future prospects are discussed.

240 Thermoelectrics for Power Generation - A Look at Trends in the Technology

**2. Clathrates as inclusion compounds**

than 50% of all stable chemical elements (**Figure 1**).

progress is highly expected.

**2.1. Crystal structures**

All clathrate crystal structures are based on closed polyhedra having from 20 to 28 vertices (**Figure 2**). Various combinations of these polyhedra lead to complete filling of the space, which is distinctive feature of clathrates. In this review, we will focus on four clathrates types, known as type-I, type-II, type-III, and type-VIII clathrates, as many of them demonstrate high thermoelectric figure-of-merit, in part stemming from the details of their crystal structure.

**Figure 2.** Clathrate-forming polyhedra: (a) 20-vertex pentagonal dodecahedron; (b) 24-vertex tetrakaidecahedron; (c) 26-vertex pentakaidecahedron; and (d) 28-vertex hexakaidecahedron.

Clathrates of type-I are the most numerous; recent review lists over 100 representatives of this structure type [10]. Their crystal structure consists of two types of polyhedra, 20-vertex dodecahedron and 24-vertex tetrakaidecahedron. The latter polyhedra form three-dimensional cubic array in such a way, that centers of adjacent 6-member rings form close rod packing, as in the crystal structure of Cr3Si, whereas the smaller polyhedra fill the remaining empty space (**Figure 3**). Guest atoms fill the centers of the polyhedra, forming only long, non-covalent contacts with atoms forming polyhedral framework. The resulting crystal structure belongs to cubic space group Pm3n and has general chemical formula E46G8, which emphasizes that there are 46 framework atoms and eight guest atoms per unit cell. Whereas the guest atoms occupy two positions, sixfold inside the larger polyhedral cage and twofold inside the smaller one, and have very large coordination numbers of 24 and 20, respectively, all atoms of the framework (24-fold, 16-fold, and sixfold) have tetrahedron environment.

**Figure 3.** Crystal structure of clathrates: (A) type-I clathrate; (B) two adjacent polyhedra in type-I clathrate; (C) type-II clathrate; (D) type-III clathrate; (E) type-VIII clathrate; and (F) asymmetric cage in type-VIII clathrate.

The nature of chemical elements that form type-I clathrates is quite diverse. In general, type-I clathrates are classified into two groups depending on charge of the framework. The most numerous are anionic clathrates, in which the framework bears negative charge compensated by guest cations. A reverse of the host-guest polarity leads to cationic (also known as inversed) clathrates. As a rule, atoms that form framework come from *p*-block of Mendeleev periodic table; however, inclusion of *d*-metals is also possible. Guest atoms are different depending on charge of the framework. In anionic clathrates, guests are cations of large alkali or alkali earth metals; only a few examples of clathrates hosting rare earth metals are documented [11–13]. In the case of cationic clathrates, halogens and chalcogens of 3–5 periods of Mendeleev table serve as anionic guests.

Type-I clathrates frequently feature deviations from ideal crystal structure described above. This includes mixed occupancy of positions by atoms of different chemical nature, partially vacant positions, splitting of positions into two or three closely lying partial occupied sites, and various types of atom and vacancy ordering that lead to formation of superstructures and reduction in symmetry [10]. In most cases, these crystallographic details affect the electronic structure of clathrates and invoke properties that enhance thermoelectric efficiency.

Other clathrate types are less numerous. Their crystal structures are also built of different highcoordination polyhedra. For instance, type-II clathrate is made of combination of 20-vertex dodecahedra with 28-vertex hexakaidecahedra in such a fashion that cubic face-centered structure is formed (**Figure 3**). Crystal structure of type-III clathrates is the only clathrate structure that contains three types of polyhedra at the time; they are 20-vertex dodecahedra, 24-vertex tetrakaidecahedra, and 26-vertex pentakaidecahedra. They share faces to form a tetragonal crystal structure displayed in **Figure 3**. Type-VIII clathrates are slightly different as they have only one type of polyhedra, which is substantially distorted. It can be viewed as dodecahedron, in which three E–E bonds are broken, and three extra E atoms are inserted instead. The resulting polyhedron has rather low symmetry, but its packing within cubic unit cell brings about clathrate type of the crystal structure. As long as distorted polyhedra cannot fill the entire space, additional 8-vertex polyhedra are left unfilled in this crystal structure (**Figure 3**).

#### **2.2. Application of Zintl scheme and electronic structures**

al cubic array in such a way, that centers of adjacent 6-member rings form close rod packing, as in the crystal structure of Cr3Si, whereas the smaller polyhedra fill the remaining empty space (**Figure 3**). Guest atoms fill the centers of the polyhedra, forming only long, non-covalent contacts with atoms forming polyhedral framework. The resulting crystal structure belongs to cubic space group Pm3n and has general chemical formula E46G8, which emphasizes that there are 46 framework atoms and eight guest atoms per unit cell. Whereas the guest atoms occupy two positions, sixfold inside the larger polyhedral cage and twofold inside the smaller one, and have very large coordination numbers of 24 and 20, respectively, all atoms of the frame-

**Figure 3.** Crystal structure of clathrates: (A) type-I clathrate; (B) two adjacent polyhedra in type-I clathrate; (C) type-II

The nature of chemical elements that form type-I clathrates is quite diverse. In general, type-I clathrates are classified into two groups depending on charge of the framework. The most numerous are anionic clathrates, in which the framework bears negative charge compensated by guest cations. A reverse of the host-guest polarity leads to cationic (also known as inversed) clathrates. As a rule, atoms that form framework come from *p*-block of Mendeleev periodic table; however, inclusion of *d*-metals is also possible. Guest atoms are different depending on charge of the framework. In anionic clathrates, guests are cations of large alkali or alkali earth metals; only a few examples of clathrates hosting rare earth metals are documented [11–13]. In the case of cationic clathrates, halogens and chalcogens of 3–5 periods of Mendeleev table serve

Type-I clathrates frequently feature deviations from ideal crystal structure described above. This includes mixed occupancy of positions by atoms of different chemical nature, partially

clathrate; (D) type-III clathrate; (E) type-VIII clathrate; and (F) asymmetric cage in type-VIII clathrate.

as anionic guests.

work (24-fold, 16-fold, and sixfold) have tetrahedron environment.

242 Thermoelectrics for Power Generation - A Look at Trends in the Technology

Chemical composition of clathrates frequently looks unusual in terms of the stoichiometry of phases. For instance, the following compounds displaying promising thermoelectric properties are formulated as Sr8Ga16Ge30, Ba8Ga16Sn30, K8In8Sn38, and Si30P16Te8. These formulas can be rationalized on the basis of Zintl electron-counting scheme, which, in fact, shows that these compounds should behave as semiconductors [14].