The effect of texture degree on the anisotropic thermoelectric properties of (Bi,Sb)₂(Te,Se)₃ based solid solutions

Abstract

Structural anisotropy plays an important role in the thermoelectric properties of the widely used (Bi,Sb)₂(Te,Se)₃ based materials. In this work, (Bi,Sb)₂(Te,Se)₃ based alloys have been fabricated by various methods to produce samples with different orientation factors, F. It is demonstrated that the n-type alloys are much easier to (001) texture than the p-type ones. After hot deformation, the F values decrease by about 20% and 75% for n- and p-type zone-melted samples, and increase by about 60% and 80% for n- and p-type hot-pressed samples, respectively. It is found the in-plane to out-of-plane ratio of thermal and electrical conductivity increases from 1.2–2.2, and 1.1–2.5 respectively, when the F values range from 0.1 to 1, while the Seebeck coefficient is almost isotropic.

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1. Introduction

Thermoelectric (TE) materials, which can directly convert waste heat into usable electricity, have been widely studied in recent decades due to their potential use in power generation and solid-state refrigeration. The performance of TE materials is represented by the dimensionless figure of merit zT = (α²σ/κ)/T, where α is the Seebeck coefficient, σ the electrical conductivity, κ the thermal conductivity, and T the absolute temperature.^1–3

Bismuth telluride based alloys are well known as the most efficient commercial TE materials operated near room temperature. These compounds are composed of atomic layers in the order of –Te⁽¹⁾ –Bi–Te⁽²⁾ –Bi–Te⁽¹⁾ – along the c-axis, and the Te⁽¹⁾–Te⁽¹⁾ layers are weakly bound with van der Waals force. The structural anisotropy results in corresponding anisotropy in TE and mechanical properties.^4–9 Previous work have demonstrated that the electrical conductivity and thermal conductivity perpendicular to the c-axis are about 3–4 and 2–2.5 as large as those along the c-axis, respectively, in single crystal Bi₂Te₃ alloys.¹⁰ However, the Seebeck coefficient is nearly isotopic regardless of the grain orientation.^10,11 Therefore, the formation of (00l) texture in polycrystalline counterparts is favourable for improving zT, due to the increased the ratio of electrical conductivity to thermal conductivity along the in-plane direction. However, measuring the thermal and electrical conductivities along out-of-plane and in-plane directions respectively would lead to an overestimate of zT.^12,13 On the other hand, to improve their poor mechanical properties, resulting from the easy cleavage along basal planes, the texture should be destroyed properly by grain refinement. Recently, powder metallurgical methods and deformation processing, such as hot pressing (HP),^5,14 mechanical alloying (MA), and hot deformation (HD),^3,11,15,16 have been investigated extensively for Bi₂Te₃ based polycrystalline alloys. For example, it has been found that the hot-pressed samples have about 2.5 times higher bending resistance strength than the directionally solidified ones.⁴ However the figures of merit z of polycrystalline (Bi,Sb)₂Te₃ materials (2.1–3.2 × 10⁻³ K⁻¹) are lower than those of single crystals (3.4–3.6 × 10⁻³ K⁻¹) at ambient temperature.^3,4,17–19 As the texture has opposite impact on TE and mechanical properties, it is necessary to study the effect factors of texture formation. Though the anisotropy was firstly discovered in single crystals, it can also be induced under the pressure during powder processing.^14,20–23 The degree of orientation or texture is influenced by many factors, such as powder size, alloying component and preparation technology. Therefore, it is vital to investigate how these factors affect the anisotropy of properties in (Bi,Sb)₂(Te,Se)₃ based bulk materials.

In this work, we investigate the anisotropy of both n-type and p-type (Bi,Sb)₂(Te,Se)₃ based bulk materials with the different fabrication methods, and the relationship between anisotropy and processing methods of (Bi,Sb)₂(Te,Se)₃ based bulk materials prepared by zone-melting (ZM), direct hot-deforming (DHD), hot-pressing (HP), and hot deformation after hot-pressing (HD). The TE properties σ, α and κ of the samples are evaluated along different directions, in order to clarify the texture related TE anisotropy in (Bi,Sb)₂(Te,Se)₃ based alloys. And the relationship between the degree of preferred orientation and the TE properties has been proposed.

2. Experimental section

In this study, commercial zone-melted n-type Bi₂Te_2.7Se_0.3 doped with I and p-type Bi_0.5Sb_1.5Te₃ ingots (named ZM hereafter) were provided by Ferrotec Co. The bars of 2 × 2 × 10 mm and the disks of Φ 10 × 2 mm were cut along in-plane (parallel to the growth direction or perpendicular to the pressing direction) and out-of-plane directions (perpendicular to the growth direction or parallel to the pressing direction) of each bulk samples prepared by different methods, named as n/p (n- or p-type)-fabrication methods-direction. For example, the in-plane properties of n-type zone-melted ingots were named as n-ZM-I.

The cylinders of Φ 16 × 24 was cut from the zone-melted ingots. Then directly hot deforming the ZM samples with 80 MPa at 723 K for 30 minutes in a larger graphite die with an inner diameter of 20 mm. The obtained samples were named as n/p-DHD-I/O.

The zone-melted ingots were ball-milled for 20 min at 20 Hz to yield fine powers. These powders were firstly hot pressed (HP) in Φ 16 mm graphite dies at 723 K for 30 min under the uniaxial pressure of 80 MPa. The obtained Φ 16 mm samples were named as n/p-HP-I/O. Subsequently, hot deformation (HD) was performed by repressing the HP samples of Φ 16 mm in a larger graphite die with an inner diameter of Φ 20 mm at 823 K for 30 min at the same pressure. The obtained samples were named as n/p-HD-I/O. More details for HP and HD processing can be found elsewhere.²⁴

The phase structure of all bulk samples were investigated by X-ray powder diffraction (XRD) on a Rigaku D/MAX-2550P. The in-plane and out-plane electrical conductivity σ and the Seebeck coefficient α were measured on a commercial Linseis LSR-3 system. The specific heat C_P and the in-plane and out of plane thermal diffusivity D measurement were performed on a Netzsch LFA 457 laser flash apparatus with a Pyroceram standard. The density ρ_D was estimated by an ordinary dimension and weight measurement procedure. The thermal conductivity was then calculated using the relation κ = Dρ_DC_P.

3. Results and discussion

3.1. Effect of alloying constituent on anisotropy

Fig. 1 shows the XRD patterns of the HD samples of p-type and n-type materials with compositions Bi₂Te_2.7Se_0.3 and Bi_0.5Sb_1.5Te₃ respectively. XRD analysis was performed on the planes both parallel and perpendicular to the pressing direction to investigate the grain orientation, named as n-I, n-O, p-I, p-O, respectively. All the characteristic peaks can be indexed into the rhombohedral (Bi,Sb)₂(Te,Se)₃ structure. For both p-type and n-type samples, the diffraction intensities of the (00l) peaks along in-plane direction are much stronger than those along out-of-plane direction. This proved that the samples tend to be (001) oriented after the hot-pressing and hot-deformation. The orientation factor F of (00l) diffractions was calculated by the following formulae:

Fig. 1 In-/out-plane XRD patterns of HD bulk samples.

The value of F = 0.26 and F = 0.14 were obtained for the sample n-I, p-I respectively, comparable with the previous work.¹¹ The results implied that the n-type alloys have a larger F value and are much easier to be (001) textured than the p-type one under the same fabrication conditions. The different degree of texture can affect TE properties significantly.^15,16,25,26

The electrical conductivity (σ) and thermal conductivity (κ) along in-plane (I) and out-plane (O) direction for both p-type and n-type samples are shown in Fig. 2a and b, respectively. σ_I and κ_I are much higher than σ_O and κ_O for both n-type and p-type samples due to the higher in-plane carrier mobility caused by preferred orientation, or texture. Obviously, the ratios of σ_I/σ_O and κ_I/κ_O are 1.47 and 1.45 respectively at room temperature for n-type samples, higher than 1.3 and 1.27 of p-type samples. Thus, it can be concluded that n-type samples are easier to evolve strong texture than p-type ones under the same fabricating process.

Fig. 2 In/out-plane electrical conductivity (a) and thermal conductivity (b) of HD samples.

Unlike σ and κ, the Seebeck coefficients (α) of the n-type and p-type samples along two different directions are very similar, as shown in Fig. 3a, consistent with the previous results.^11,14 The Seebeck coefficient is sensitive to the band structure near Fermi level E_F and carrier concentration, and independent of the grain orientation. Therefore, the texture should have negligible impact on the Seebeck coefficient.^11,14 Fig. 3b shows the calculated zT of HD samples. In spite of the obvious anisotropy of the electrical and thermal conductivities, no obvious difference was observed in the zT along the two different directions, due to the negligible change of ratio σ/κ in the two directions. However, if σ_I and κ_O were used to calculate the zT, the maximum zT values can be ≈25% and 60% overestimated for the p-type and n-type alloys, respectively. Such results clearly demonstrate that the texture has a significant effect on zT calculation of (Bi,Sb)₂(Te,Se)₃ based alloys, and the σ and κ should be measured along the same direction in the samples.^27–29

Fig. 3 In/out-plane Seebeck coefficient (a) and zT (b) of HD samples.

As stated above, the n-type Bi₂Te_2.7Se_0.3 based materials are easier to form texture than p-type. Then how will the TE properties be influenced if p-type and n-type samples have the same original orientation factor (F). The commercial n/p-type (Bi,Sb)₂(Te,Se)₃ based ingots were produced by unidirectional crystal-growth method of zone-melting. Both p-type and n-type samples have uniform orientation theoretically, supposing their (orientation factors) F = 1. Thus, in this part, the TE properties of the pristine ZM ingots were measured to investigate anisotropy. As shown in Fig. 4, near room temperature the ratios of σ_I/σ_O and κ_I/κ_O are about 2.5 and 2.2, respectively, for n-type samples, higher than p-type samples of 2.2 and 1.8. Thus n-type (Bi,Sb)₂(Te,Se)₃ based material still has stronger anisotropy than p-type one.

Fig. 4 In/out-plane electrical conductivity (a) and thermal conductivity (b) of ZM samples.

As shown in Fig. 5a, the α_I and α_O of ZM samples reveal negligible difference before intrinsic excitation. However, a different temperature dependence of zT was observed and the maximum zT was obtained along the in-plane direction, inconsistent with the result of HD samples analyzed above. It can be understood because different crystal structures of in-plane and out-plane direction would influence carrier and phonon scatterings. Carriers and phonons can transfer more effectively along in-plane direction. As a result, zT along two different directions exhibits considerable anisotropy in the pristine ZM samples.

Fig. 5 In/out-plane Seebeck coefficient (a) and zT (b) of zone-melted p/n bulk samples.

3.2. Effects of different fabrication methods on anisotropy

The F values of all n- and p-type samples were calculated and are shown in Fig. 6. The F values decrease to 0.8 and 0.2 for n- and p-type DHD samples (hot deforming the ZM ingots), respectively, and to 0.16 and 0.1 for the HP samples, and then increase to 0.26 and 0.14 for the HD samples after hot deforming the HP bulks.

Fig. 6 F of n-type (a) and p-type (b) samples prepared by different kinds of methods.

The F values of all n- and p-type samples were calculated and are shown in Fig. 6. The F values decrease to 0.8 and 0.2 for n- and p-type DHD samples (hot deforming the ZM ingots), respectively, and to 0.16 and 0.1 for the HP samples, and then increase to 0.26 and 0.14 for the HD samples after hot deforming the HP bulks.

Fig. 7 shows the in-plane and out-plane TE properties of n-type ZM, DHD, HP and HD samples. Compared with the pristine ZM ingots, the electrical conductivity of DHD samples decreased slightly due to the weaker texture and reduced grain sizes.

Fig. 7 Temperature dependences of in-plane electrical conductivity (a), Seebeck coefficient (b), power factor (c), in-plane thermal conductivity (d), in-plane lattice thermal conductivity (e), and the in-plane zT (f) of different samples.

The HP samples have the lowest electrical conductivity because the texture was almost destroyed during ball milling. The enhanced grain boundary scattering of carriers further reduces μ_H. Though the donor-like effect caused by grinding can increase the electron concentration,³⁰ it cannot compensate for the loss of μ_H. As a result, the electrical conductivity decreases compared with that of the pristine ZM ingots. Compared with the HP samples, the mobility of HD counterparts is higher, due to the texture enhancement and grain growth, although the HD samples also have the higher carrier concentration introduced by donor-like effect.^31,32,44

Fig. 7b displays the temperature dependence of Seebeck coefficient (α). When measured along different directions, the α_I and α_O of samples prepared by different methods are very similar, consistent with the previous result.^14,31 The α is strongly dependent on the carrier concentration and sensitive to the point defects generated during the fabrication processing.^31,33,42 The Seebeck coefficient of HD samples increases slightly due to the recovery effect.^31,34,35 The obvious drop in absolute α of HP and HD samples results from significant donor-like effect, revealing the unfavourable impact of powder processing on the electrical properties of n-type (Bi,Sb)₂(Te,Se)₃ alloys.^36,44 The plot of the calculated power factors PF = σα² is shown in Fig. 7c. The pristine ZM and DHD samples have higher PF around the room temperature than the HP samples. The PF of HD samples increases compared with HP samples, even surpassing the pristine ZM samples at high temperature.

The in-plane thermal conductivity is also much higher than the out-plane one. At room temperature, κ_I/κ_O is 1.87 in DHD samples, lower than ZM samples (κ_I/κ_O = 2.2) due to the weakened texture. The in-plane total thermal conductivity κ of all samples is plotted as a function of temperature in Fig. 7d. The κ variation of samples fabricated by different methods is consistent with the variation of σ, because the contribution of κ_el is higher when σ is larger. The κ_ph of all samples in Fig. 7e was estimated by subtracting κ_el from the total κ, where κ_el was calculated using the Wiedeman–Franz relationship κ_el = L₀σT with L₀ = 2.0 × 10⁻⁸ V² K⁻².^24,37 The lattice thermal conductivity of DHD samples is close to that of the pristine ZM ingots. After ball milling, the texture destruction and grain refining result in a lower lattice thermal conductivity of HP samples than ZM samples. During the hot deformation, textures and grain size both undergo noticeable changes. Though the textures could lead to increase in in-plane lattice thermal conductivity, the HD samples have the lowest lattice thermal conductivity than all samples, which mainly results from the in situ nanostructures and high-density lattice defects generated during the hot deformation process.^31,34 Besides, the turning-point of κ for the HP and HD samples is shifted toward higher temperature, demonstrating that the bipolar contribution to the thermal conductivity is suppressed due to the increase of majority concentration.³⁴

As shown in Fig. 7f, zT of pristine ZM has a slight improvement after hot deformation. Through ball milling and hot pressing, the optimal service temperature has been pushed to higher temperature, and TE properties have been further improved by hot deformation. The results demonstrate that we can improve TE properties and tune the optimal temperature by changing fabrication methods and make (Bi,Sb)₂(Te,Se)₃ material suitable for higher temperature TE power generation. The electrical conductivity of p-type ZM, DHD, HP and HD samples decreases successively because the donor-like effect induced during these processes can increase electron concentration and decrease the majority carrier concentration in p-type samples (Fig. 8).^30,31,35,38 On the other hand, the mobility decrease caused by the weakened texture also contributes to σ reduction. The variation of thermal conductivity of samples prepared by different methods is consistent with their σ variation.³⁹ And the zT is the combined effects of electrical transport properties and thermal conductivity.

Fig. 8 Temperature dependences of in-plane electrical conductivity (a), Seebeck coefficient (b), power factor (c), in-plane thermal conductivity (d), in-plane lattice thermal conductivity (e), and the in-plane zT (f) of different samples.

3.3. Effects of F on (Bi,Sb)₂(Te,Se)₃ alloys properties

As demonstrated in this work and previous works,^{11,14,33,40,41,43} the anisotropic TE properties are relevant to the structural anisotropy of the samples. The correlation between F and TE properties at 300 K is shown in Fig. 9. The ratios of σ_I/σ_O and κ_I/κ_O reveal a rising trend with the increment of F, while α is insensitive to the grain orientation with the ratio α_I/α_O ≈ 1. As a result, zT of two directions have no obvious difference and regular change with F value, but the value along in plane direction is slightly higher than out-plane.

Fig. 9 F dependences of in-plane electrical conductivity (a), Seebeck coefficient (b), in-plane thermal conductivity (c) and the in-plane zT (d).

Fig. 10 shows the in-plane and out-plane bending strength and compressive strength of all p- and n-type samples. The bending strength and compressive strength along the same direction of ZM and DHD samples exhibited completely opposite trend. For ZM samples, the in-plane bending strength for both p- and n-type samples are very low, less than 10 MPa, due to the weak van der Waals bond between Te⁽¹⁾–Te⁽¹⁾ layers in the crystal structure.¹ While the in-plane compressive strength is nearly three and two times as much as bending strength for p- and n-type material respectively. It can be understood because the compressive direction is parallel to cleavage plane, and it is difficult to slip under in-plane compressive stress. In contrast, along the out-plane direction, bending strength is much higher than compressive strength owing to the pressure direction perpendicular to the cleavage plane.⁴¹

Fig. 10 Bending (a) and compressive (b) strength of samples prepared by different methods.

In comparison with the ZM and DHD samples, the compressive strength and bending strength along two directions of HP and HD specimens have high values and present inconspicuous anisotropy resulting from the grain refinement and random distribution.

4. Conclusions

In this work, we compared the effects of different processing methods on F value and material properties. When prepared by the same processing, n-type Bi₂Te_2.7Se_0.3 alloys have higher F and stronger anisotropy than p-type Bi_0.5Sb_1.5Te₃ alloys. Unlike the isotropic Seebeck coefficient, the anisotropy of TE performance displayed a strong dependence on F. The ratios of σ_I/σ_O and κ_I/κ_O reveal a rising trend with the increment of F. Ball milling and hot pressing can increase the optimal service temperature, and further improve TE properties by hot deformation. Therefore TE performance and mechanical properties can be optimized by changing fabrication method to adjust microstructure and texture degree.

Acknowledgements

This work was supported by the National Basic Research Program of China (No. 2013CB632503), National Natural Science Foundation of China (No. 61534001 and 51271165)

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