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Reduced thermal conductivity of Bi-In-Te thermoelectric alloys in a eutectic lamellar structure
Accepted Manuscript Reduced thermal conductivity of Bi-In-Te thermoelectric alloys in a eutectic lamellar structure Dongmei Liu, Christian Dreβler, Martin Seyring, Steffen Teichert, Markus Rettenmayr PII:
S0925-8388(18)31071-5
DOI:
10.1016/j.jallcom.2018.03.201
Reference:
JALCOM 45431
To appear in:
Journal of Alloys and Compounds
Received Date: 23 January 2018 Revised Date:
14 March 2018
Accepted Date: 15 March 2018
Please cite this article as: D. Liu, C. Dreβler, M. Seyring, S. Teichert, M. Rettenmayr, Reduced thermal conductivity of Bi-In-Te thermoelectric alloys in a eutectic lamellar structure, Journal of Alloys and Compounds (2018), doi: 10.1016/j.jallcom.2018.03.201. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Reduced thermal conductivity of Bi-In-Te thermoelectric alloys in a eutectic lamellar structure Dongmei Liu1,*, Christian Dreβler2, Martin Seyring1, Steffen Teichert2, Markus Rettenmayr1,3† Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Löbdergraben 32, D-07743 Jena, Germany 2
University of Applied Sciences Jena, Carl Zeiss Promenade 2, 07745 Jena, Germany
Center for Energy and Environmental Chemistry, Philosophenweg 7, D-07743 Jena, Germany
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Abstract: Directional solidification of Bi2Te3-In2Te3 eutectic alloys allows for exploiting both crystal anisotropy and internal interface density for the enhancement of thermoelectric properties. A lamellar structure with a spacing of 2 µm was produced for the eutectic alloy Bi-16.5In-60Te (at%). Coherent Bi2Te3-In2Te3 interfaces sharing the same Te atomic layer were found. The Bi2Te3-In2Te3
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composites are n-type thermoelectric materials with lower thermal conductivity than each of the constituent phases. The eutectic alloy with a higher interface density exhibits a lower phonon thermal conductivity than off-eutectic alloys. The disparity between experimentally determined
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values and calculations using composite models concerning the thermoelectric properties demonstrates the enhanced potential of internal interfaces for improving thermoelectric properties.
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Key words: Bi2Te3-In2Te3; thermoelectric material; lamellar eutectic; thermal conductivity.
* †
Corresponding author: Dongmei Liu, E-mail: [email protected] Corresponding author: Markus Rettenmayr, E-mail: [email protected]
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Introduction
Thermoelectric materials have received long standing attention due to their ability of direct conversion of thermal to electrical energy. Thermoelectric composites consisting of two or more different phases exhibit an enhanced figure of merit zT due to the low lattice thermal conductivity.
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The low thermal conductivity of composite materials is generally assumed to be connected with the enhanced phonon scattering by nano/meso-scale interfaces, either grain boundaries or hetero-phase interfaces. This assumption inspired extensive research on understanding the function of nanostructures and the synthesis of nanostructured thermoelectric materials. Among others,
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superlattice/quantum well thin film thermoelectric materials exhibit a particularly high figure of merit zT. However, the production of such materials often involves thin film technologies with a
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limited yield in the order of milligrams, which limits their practical applicability. It is highly desirable to produce materials with similar structures, but via bulk processing that warrants availability in practically applicable large quantities. Lamellar eutectic structures resemble superlattice structures, but of enlarged layer thicknesses/distances and thus are promising candidates. Eutectic thermoelectric materials such as PbTe-Sb2Te3 [1, 2], PbTe-Bi2Te3 [3, 4], PbTe-Si/Ge [5],
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Ag2Te-PbTe-Sb2Te3 [6], PbTe-Te-Ag5Te3 [7], PbTe-MnTe [8], Mn-Si [9], Bi2Te3-Te [10,11], GeTe-Ag8GeTe6 [12], InSb-Sb [13], among others, have been studied especially in the recent five
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years.
Up to present, research on eutectic thermoelectric materials was mainly conducted on randomly
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oriented eutectic structures. Considering that the constituent phases of a composite necessarily have different physical properties, the transport behavior along the hetero-phase interface will be different than that across the interfaces, as e.g. theoretically predicted by models for physical properties of composite materials [14, 15] and shown by experimental observations [16]. This suggests that the thermoelectric properties of isotropic eutectics with randomly distributed interface orientations do not satisfactorily distinguish the influence of the interfaces from other factors. It is highly desirable to study the influence of microstructural features such as length scales, volume fractions and crystallographic orientation distribution separately. Directional solidification with defined orientation of eutectic lamellae is suitable to separate crystal anisotropy from microstructural features. This can further help to optimize the thermoelectric performance of eutectic thermoelectric
ACCEPTED MANUSCRIPT composites. In the present study, we directionally solidified quasi-binary Bi2Te3-In2Te3 near-eutectic alloys, particularly Bi-13.5In-60Te and Bi-16.5In-60Te (at%), for generating an aligned eutectic structure. The quasi-binary Bi2Te3-In2Te3 phase diagram is shown in Fig. 1 based on previously published
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work [17] and our own work [18, 19]. The two constituent phases are a Bi2Te3 solid solution containing In and a stoichiometric In2Te3. The (Bi,In)2Te3 solid solution was reported to be a promising candidate for thermoelectric applications [20, 21], as it exhibits relatively low thermal conductivity at In concentrations around 8 at% [22]. In2Te3 was suggested to be an insulator of wide
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band gap (1.1 eV) [23, 24], which is supposed to act as Bi2Te3/In2Te3 interface raiser. In the present work, thorough characterization of the eutectic structure with respect to the influence of the internal
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interfaces on the thermoelectric conductivity is carried out. Additionally, a comparison between the properties of eutectic Bi2Te3-In2Te3 including the (Bi,In)2Te3 phase with the pure (Bi,In)2Te3 phase of
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the same composition as in the eutectic is presented.
Fig. 1 Quasi-binary Bi2Te3-In2Te3 phase diagram [17-19]. The compositions of the alloys used in the present work are illustrated by dashed lines.
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Experimental
Ingots of compositions Bi-13.5In-60Te and Bi-16.5In-60Te were produced from Bi, In and Te of 99.99% purity supplied by Haines & Maassen Metallhandelsgesellschaft mbH. The loss of Te by evaporation during melting was experimentally determined, and an additional amount of Te (+10%)
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was added to reach the nominal composition. The metallic elements were loaded into quartz tubes of 6 mm in diameter. The quartz tubes were first evacuated to 5×10-6 bar, and then charged with Ar to 0.5 bar. This gas pressure reduces Te evaporation and prevents bursting of the tube because of the pressure increase during heating. The evacuation process was repeated for 3 times, and the tube was
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sealed. The metallic elements were then induction melted. After complete melting of all metallic elements, the melt was held for 10 minutes under strong convection to ensure homogeneity of the
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ingot. By the subsequent directional solidification in a Bridgman type furnace, rod-shaped samples of 6 mm diameter were produced. The samples were prepared metallographically by grinding with a series of SiC papers up to a grit size of 4000, polishing with 3 µm and 1 µm Al2O3 powder and finally polishing with 50 nm colloidal silica. A scanning electron microscope (SEM) equipped with a back-scattered electron (BSE) detector and energy dispersive X-ray (EDX) spectrometry was used
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for microstructural observations. The image analysis software Image J was used to determine the volume fraction of each phase and the lamellar spacing. Transmission electron microscopy (TEM) was used to analyze the crystallographic orientation relationship between Bi2Te3 and In2Te3. TEM
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[25].
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samples were prepared by focused ion beam (FIB). More details can be found in our previous work
Thermoelectric property measurements were performed for all samples. Rectangular parallelepipeds of 3×3×12 mm2 were cut parallel to the orientation of the eutectic lamellae for Seebeck coefficient (S) and electrical conductivity (ߪ) characterization that were performed using a LSR-3 device (Linseis Seebeck and Resistivity) from 50 oC to 300 oC. Disks of ∅6 × 1 mm2 were cut in the direction perpendicular to the growth direction for measuring the thermal diffusivity (α) using a laser flash method (LFA-457). All the properties were characterized in the direction parallel to the growth direction during directional solidification. The thermal conductivity was calculated by ݇ = ߙܥ ߩ, where CP is the heat capacity measured by differential scanning calorimetry (DSC-STA PT1600) and ρ is the density measured by the Archimedes method. CP was determined using a differential
ACCEPTED MANUSCRIPT scanning calorimeter (Netzsch STA-449FA). The electronic contribution to the thermal conductivity (ke) was determined from the electrical conductivity utilizing the Wiedemann-Franz law, ke=LσT, where L is the Lorenz number and L=2.44×10-8 W Ω K-2. Results and discussion
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3.1 Generating an aligned lamellar eutectic of Bi2Te3-In2Te3 by directional solidification
According to the Bi2Te3-In2Te3 pseudo-binary phase diagram (Fig. 1), the eutectic reaction: liquid → Bi2Te3 + In2Te3 occurs at 571 ℃ [17]. The exact In concentration at the eutectic point is not
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precisely known due to disparities in literature [17, 25]. The microstructures of the longitudinal section of directionally solidified Bi-13.5In-60Te and Bi-16.5In-60Te alloys produced at a growth
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rate of 10 ߤm/s and a temperature gradient of 20K/mm are shown in Fig. 2. Based on a series of spot EDX analyses, the bright phase was identified as Bi2Te3 of composition of 32 ±0.5 at%Bi, 8.5±0.15 at%In and 59.5±1 at%Te, and the dark phase as stoichiometric In2Te3 (40±0.5 at%In and 60±0.5 at%Te) with negligible Bi content. Coexistence of primary Bi2Te3 and eutectic colonies consisting of aligned Bi2Te3/In2Te3 layers with an orientation parallel to the growth direction was
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observed for Bi-13.5In-60Te, as shown in Fig. 2(a) and (b). As opposed to that, the composition Bi-16.5In-60Te led to a fully eutectic structure, as shown in Fig. 2(c) and (d). The same microstructure of alternating Bi2Te3 and In2Te3 layers was also observed in the cross sections,
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confirming the lamellar growth of eutectic Bi2Te3-In2Te3 during directional solidification. The statistics of volume fraction of each phase and lamellar spacing was assessed using the
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microstructure of cross sections. The volume fraction of In2Te3 is 16% and ∼22% for the compositions 13.5In and 16.5In, respectively. The eutectic lamellar structure of the two samples exhibits a similar distribution of the lamellar spacing, generally ranging from 0.4 to 3 ߤm, with the majority of spacings between 1 and 2 ߤm. The thickness of In2Te3 ranges from 300 to 600 nm.
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Fig. 2 BSE microstructures in longitudinal sections of directionally solidified Bi-13.5In-60Te (a,b) and Bi-16.5In-60Te (c, d) grown with a temperature gradient of 20K/mm and a growth rate of 10 µm/s. The bright phase represents Bi2Te3 of ~ 8.5±0.15 at%In in solution, and the dark phase represents
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stoichiometric In2Te3 with negligible Bi content.
The interface between the Bi2Te3 and In2Te3 phases was further examined by high resolution
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transmission electron microscopy (HRTEM). Coherency of the Bi2Te3/In2Te3 interface was found, as shown in Fig. 3 (a). This can be attributed to the small lattice mismatch between the two phases in
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the given orientation, only approximately 0.8% using the respective nearest neighbor distance between Te atoms in Bi2Te3 (4.395 Å) and In2Te3 (4.359 Å). The In2Te3 phase exhibits a superstructure accompanied by the diffraction pattern of an orthorhombic crystal structure, as illustrated by arrows in Fig. 3(d). Such a superstructure does not exist for In2Te3 precipitated from a (Bi,In)2Te3 matrix during solid state transformation [19], indicating different crystallographic orientations between the two phases and different influence mechanism of In2Te3 layers on physical properties. The crystallographic relationship between the two phases was determined as (003)Bi2Te3//(031)In2Te3, [010]Bi2Te3//[100]In2Te3. A schematic illustration of the coherent Bi2Te3/In2Te3 interface sharing the same Te layer is shown in Fig. 3 (e).
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Fig. 3 (a) High resolution transmission electron microscope (HRTEM) image of the Bi2Te3 / In2Te3 interface; (b,c,d) diffraction patterns of Bi2Te3 and In2Te3 showing the crystallographic orientation relationship (001)Bi2Te3//(031)In2Te3, [010]Bi2Te3//[100]In2Te3, and (e) a schematic illustration showing the crystal structures and orientation relationship of Bi2Te3 and In2Te3.
ACCEPTED MANUSCRIPT 3.2 Effect of Bi2Te3/In2Te3 interface on thermoelectric properties of (Bi, In)2Te3 alloys For analyzing the effects of the Bi2Te3/In2Te3 interfaces on the thermoelectric properties of Bi2Te3-In2Te3, an anisotropic solid solution of composition Bi-8.5In-60Te was prepared by seeding zone melting as described in our previous work [26]. The In concentration of 8.5% in the Bi2Te3
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phase is the maximum solubility that is found at the eutectic temperature. Preparation of the solid solution is not straightforward, because according to steady-state growth theory, for continuous single phase growth at maximum solubility, the composition of the melt in front of the growing interface must be precisely the eutectic composition. Thus, upon cooling also the eutectic structure
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of alternating Bi2Te3 and In2Te3 layers can solidify directly from the melt. In the present work, zone melting with a seed crystal of Bi-16.5In-60Te was used to prepare single phase Bi-8.5In-60Te with
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enhanced chemical homogeneity and defined orientation and crystal anisotropy (see earlier work [26, 27]). A constant In concentration of 8.5 at% over a length of 30 mm was obtained, as shown in Fig. 4. An initial transient region of ~10 mm in length with a small concentration gradient was found. The abrupt jump of the composition on the left side in Fig. 4 indicates the transition from eutectic to single phase microstructure. The sample for property characterization was taken from the
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homogeneous single phase region of 8.5 at% In.
Fig. 4 Concentration profiles (Bi in blue, In in black and Te in red) along the growth direction of Bi-8.5In-60Te prepared by zone melting with a seed crystal of composition Bi-16.5In-60Te, solidified at a growth rate of 0.5 ߤm/s and a temperature gradient of 20K/mm.
The comparison of the temperature dependent thermoelectric properties between single phase Bi-8.5In-60Te, off-eutectic Bi-13.5In-60Te and eutectic Bi-16.5In-60Te is shown in Fig. 5. All
ACCEPTED MANUSCRIPT samples exhibit n-type transport behavior, as can be seen from negative Seebeck coefficients (Fig. 5(c)). Eutectic Bi-16.5In-60Te exhibits the lowest thermal conductivity (ktot and (ktot-ke)) and electrical conductivity, and the highest absolute Seebeck coefficient. ktot values of 0.66 W m-1 K-1 and (ktot- ke) values of 0.5 W m-1 K-1 are found for eutectic Bi-16.5In-60Te at 60°C. This can be
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attributed to phonon scattering at the densely distributed Bi2Te3/In2Te3 interfaces in the fully eutectic Bi-16.5In-60Te sample. Off-eutectic Bi-13.5In-60Te exhibit higher thermal conductivities (ktot and (ktot-ke)) mainly due to less Bi2Te3/In2Te3 interfaces. An interesting observation is that the two eutectic composites exhibit different temperature dependences of the thermal conductivity (ktot and
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(ktot-ke)) and Seebeck coefficient as compared to single phase Bi-8.5In-60Te. Although a lower thermal conductivity was observed in the fully eutectic Bi-16.5In-60Te sample, the eutectic
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composites exhibit a higher increase rate of thermal conductivities with temperature. Bi-8.5In-60Te is an n-type semiconductor. According to EDX analysis in the TEM, In2Te3 layers exhibit stoichemetric composition and negligible Bi content. According to Ref. 23, pure In2Te3 was reported as a p-type insulator. Thus, besides the small band gap of the Bi2Te3 phase, a resulting bipolar conductivity effect may contribute to the steeper increase rate of (ktot-ke) with temperature for the
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eutectic samples. This also holds for the higher (ktot-ke) of Bi-13.5In-60Te as compared to Bi-8.5In-60Te. Besides the reduced thermal conductivity, the eutectic samples exhibit an enhanced Seebeck coefficient, i.e. from |S|max=63 ߤV K-1 at 200 ℃ for Bi-8.5In-60Te to |S|max=110 ߤV K-1 at 100 ℃ for Bi-16.5In-60Te. A reversion of the temperature dependence trend of the Seebeck
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coefficient, where a transition from a decreasing to an increasing trend occurs at a relatively high temperature, was observed for all the three samples. Such a transition can be often seen in Bi2Te3
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based materials, which is mainly due to the small band gaps Eg (Bi-16.5In-60Te: 0.085 eV; Bi-13.5In-60Te: 0.076 eV; Bi-8.5In-60Te: 0.06 eV; obtained by Eg=2e|S|maxTmax [28]), and due to the fact that minority carriers can acquire enough energy with higher temperature to get from the valence band to the conductive band. It is interesting that the temperature dependence trend of the electrical conductivity of all three samples is nearly the same, which is quite different from Seebeck coefficients and thermal conductivities. At a first glance, the deteriorated electrical conductivities in the eutectic samples could be connected to the enhanced Seebeck coefficients. However, there is more to it than this, which will be discussed in the following section.
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Fig. 5 Temperature dependent (a) total thermal conductivity ktot, (b) (ktot- ke), (c) Seebeck coefficient and (d) electrical conductivity of the solid solution Bi-8.5In-60Te the partly eutectic Bi-13.5In-60Te and the eutectic Bi-16.5In-60Te along the crystal growth direction. The dotted lines in (d) depict calculated electrical conductivity values based on ߪ = ߪ் ்ܸ + ߪூ் ܸூ் [14], where BT stands for the Bi2Te3 phase and IT stands for the In2Te3 phase. The dark dotted
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line is for Bi-13.5In-60Te, the red one for Bi-16.5In-60Te.
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3.3 Enhancement of power factor and zT In the present work, the properties along the direction of the eutectic plates were characterized. According to research on multiphase materials [14], a “parallel model”, which is mainly used for predicting the upper limit of physical properties, may be suitable for predicting the effective physical properties of the Bi2Te3-In2Te3 composites. Nevertheless, it is worth noting that in the parallel model, the effect of Bi2Te3/In2Te3 interfaces on the transport of carriers is neglected. Hence, the comparison between real experimentally measured properties and the predicted values indicate the influence of the Bi2Te3/In2Te3 interfaces on the thermoelectric properties. According to the parallel model [14], the Seebeck coefficient of the eutectic structure along the
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ܵ=
ௌಳ ఙಳ ಳ ାௌ ఙ
(1)
ఙಳ ಳ ାఙ
where BT refers to the Bi2Te3 phase with 8.5 at%In in solution, and IT refers to the In2Te3 phase.
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In2Te3 was reported to be an insulator of ultra low electrical conductivity of the order of 10-3 S m-1 [23, 24], which is nearly 6 orders smaller than that of the Bi2Te3 phase containing 8.5 at%In. Due to the much smaller electrical conductivity of In2Te3 and according to equation (1), the Seebeck coefficient of the eutectic composites should be dominated by Bi2Te3, i.e. S≈SBT. In other words, the
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same Seebeck coefficient as that of Bi-8.5In-60Te is expected for the eutectic samples when the interface effect is neglected. It is worth noting that the parallel model provides the upper limit for the
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property prediction based on different models, for example, the effective medium theory (EMT) or the general effective medium theory (GEMT) [29-33]. However, higher |S| values than the upper limit were experimentally determined in the two-phase structures.
According to the “parallel model”, the electrical conductivity of Bi2Te3-In2Te3 composites can be
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calculated as:
ߪ = ߪ் ்ܸ + ߪூ் ܸூ்
(2)
When composing the properties from the properties of the constituent phases, the electrical
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conductivity of the eutectic structure should be smaller than that of Bi-8.5In-60Te, i.e. proportional to the volume fraction of Bi2Te3. The values calculated based on eq. (2) are illustrated by the dashed
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lines in Fig. 5(d). Clearly, the measured values are smaller than the calculated ones. The “parallel model” was also used related to the resistivity of a two-phase material, as illustrated in Eq. (3) for Bi2Te3-In2Te3:
ߩ = ߩ் ்ܸ + ߩூ் ܸூ்
(3)
As mentioned before, In2Te3 exhibits a resistivity that is 6 orders of magnitude higher than that of Bi2Te3. Although the volume fraction of In2Te3 only ranges from 16% to 22%, the electrical resistivity of the eutectic microstructures should be dominated by In2Te3, implying that the electrical
ACCEPTED MANUSCRIPT conductivity of Bi2Te3-In2Te3 should be of the order of 10-3 S m-1, which is far lower than the measured values. Based on above discussion, it can be seen that the physical properties of Bi2Te3-In2Te3 are more complex than predicted by different rules of mixtures. This indicates the influence of the Bi2Te3/In2Te3 interfaces on the transport of charged carriers and phonons, and thus
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on the resulting thermoelectric properties of the material. Nevertheless, a high power factor (PF=ܵ ଶ ߪ) as shown in Fig. 6(a) is obtained for the two-phase structures. Combined with the lower thermal conductivity, the fully eutectic Bi-16.5In-60Te exhibits a zT value that is 3 times higher than that of Bi-8.5In-60Te at 100 ℃, as shown in Fig. 6(b). The enhancement of the power factor is in line with
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previous work on two-phase materials [34], in which higher thermoelectric power factors than the power factors of the pure components are predicted, especially for composites of parallel slabs
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microstructures. This demonstrates the potential of engineering the thermoelectric properties via the design of eutectic lamellar structures. Higher zT values than those in the constituent phases were first experimentally found in nanostructured SiGe-Si [35, 36] in recent years, which was attributed to band engineering across the hetero-phase interface. Further work on analysis and further optimization of the band structure across Bi2Te3/In2Te3 interfaces will be performed, aiming for
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better understanding and improved performance. Optimization of electrical conductivity and Seebeck coefficient via modification of charge carriers is needed. Additionally, n-type dopants for In2Te3 may also help to prevent the bipolar effect induced by the p-type transportation behavior of
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the undoped In2Te3.
Fig. 6 Temperature dependent (a) power factor and (b) figure of merit zT values of of Bi-8.5In-60Te, Bi-13.5In-60Te and Bi-16.5In-60Te along the crystal growth direction.
ACCEPTED MANUSCRIPT 4 Conclusions Directionally solidified eutectic structures with designed interfacial effects exhibit potential for a practical application as thermoelectric materials. Aligned eutectic Bi2Te3-In2Te3 structures with coherent Bi2Te3/In2Te3 interfaces and well defined crystallographic orientation were generated by
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directional solidification. Such interfaces not only contribute to phonon scattering and the resulting reduction in thermal conductivity, but also lead to an enhanced Seebeck coefficient and power factor, overall resulting in a 3 times higher figure of merit zT than each constituent. Further engineering of carrier concentration and band gap via proper doping is expected to further improve the
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thermoelectric performance.
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Acknowledgements
Financial support by the German Research Foundation [Deutsche Forschungsgemeinschaft: DFG; granted number Re1261/15-1] is gratefully acknowledged. References
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ACCEPTED MANUSCRIPT 1.
Anisotropic aligned Bi2Te3-In2Te3 eutectic lamellar structure was generated.
2.
Coherent Bi2Te3-In2Te3 interface sharing Te layer was determined by HRTEM.
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3. Bi2Te3-In2Te3 interfaces contribute to enhanced thermoelectric properties.
S0925-8388(18)31071-5
DOI:
10.1016/j.jallcom.2018.03.201
Reference:
JALCOM 45431
To appear in:
Journal of Alloys and Compounds
Received Date: 23 January 2018 Revised Date:
14 March 2018
Accepted Date: 15 March 2018
Please cite this article as: D. Liu, C. Dreβler, M. Seyring, S. Teichert, M. Rettenmayr, Reduced thermal conductivity of Bi-In-Te thermoelectric alloys in a eutectic lamellar structure, Journal of Alloys and Compounds (2018), doi: 10.1016/j.jallcom.2018.03.201. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Reduced thermal conductivity of Bi-In-Te thermoelectric alloys in a eutectic lamellar structure Dongmei Liu1,*, Christian Dreβler2, Martin Seyring1, Steffen Teichert2, Markus Rettenmayr1,3† Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Löbdergraben 32, D-07743 Jena, Germany 2
University of Applied Sciences Jena, Carl Zeiss Promenade 2, 07745 Jena, Germany
Center for Energy and Environmental Chemistry, Philosophenweg 7, D-07743 Jena, Germany
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Abstract: Directional solidification of Bi2Te3-In2Te3 eutectic alloys allows for exploiting both crystal anisotropy and internal interface density for the enhancement of thermoelectric properties. A lamellar structure with a spacing of 2 µm was produced for the eutectic alloy Bi-16.5In-60Te (at%). Coherent Bi2Te3-In2Te3 interfaces sharing the same Te atomic layer were found. The Bi2Te3-In2Te3
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composites are n-type thermoelectric materials with lower thermal conductivity than each of the constituent phases. The eutectic alloy with a higher interface density exhibits a lower phonon thermal conductivity than off-eutectic alloys. The disparity between experimentally determined
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values and calculations using composite models concerning the thermoelectric properties demonstrates the enhanced potential of internal interfaces for improving thermoelectric properties.
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Key words: Bi2Te3-In2Te3; thermoelectric material; lamellar eutectic; thermal conductivity.
* †
Corresponding author: Dongmei Liu, E-mail: [email protected] Corresponding author: Markus Rettenmayr, E-mail: [email protected]
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Introduction
Thermoelectric materials have received long standing attention due to their ability of direct conversion of thermal to electrical energy. Thermoelectric composites consisting of two or more different phases exhibit an enhanced figure of merit zT due to the low lattice thermal conductivity.
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The low thermal conductivity of composite materials is generally assumed to be connected with the enhanced phonon scattering by nano/meso-scale interfaces, either grain boundaries or hetero-phase interfaces. This assumption inspired extensive research on understanding the function of nanostructures and the synthesis of nanostructured thermoelectric materials. Among others,
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superlattice/quantum well thin film thermoelectric materials exhibit a particularly high figure of merit zT. However, the production of such materials often involves thin film technologies with a
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limited yield in the order of milligrams, which limits their practical applicability. It is highly desirable to produce materials with similar structures, but via bulk processing that warrants availability in practically applicable large quantities. Lamellar eutectic structures resemble superlattice structures, but of enlarged layer thicknesses/distances and thus are promising candidates. Eutectic thermoelectric materials such as PbTe-Sb2Te3 [1, 2], PbTe-Bi2Te3 [3, 4], PbTe-Si/Ge [5],
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Ag2Te-PbTe-Sb2Te3 [6], PbTe-Te-Ag5Te3 [7], PbTe-MnTe [8], Mn-Si [9], Bi2Te3-Te [10,11], GeTe-Ag8GeTe6 [12], InSb-Sb [13], among others, have been studied especially in the recent five
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Up to present, research on eutectic thermoelectric materials was mainly conducted on randomly
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oriented eutectic structures. Considering that the constituent phases of a composite necessarily have different physical properties, the transport behavior along the hetero-phase interface will be different than that across the interfaces, as e.g. theoretically predicted by models for physical properties of composite materials [14, 15] and shown by experimental observations [16]. This suggests that the thermoelectric properties of isotropic eutectics with randomly distributed interface orientations do not satisfactorily distinguish the influence of the interfaces from other factors. It is highly desirable to study the influence of microstructural features such as length scales, volume fractions and crystallographic orientation distribution separately. Directional solidification with defined orientation of eutectic lamellae is suitable to separate crystal anisotropy from microstructural features. This can further help to optimize the thermoelectric performance of eutectic thermoelectric
ACCEPTED MANUSCRIPT composites. In the present study, we directionally solidified quasi-binary Bi2Te3-In2Te3 near-eutectic alloys, particularly Bi-13.5In-60Te and Bi-16.5In-60Te (at%), for generating an aligned eutectic structure. The quasi-binary Bi2Te3-In2Te3 phase diagram is shown in Fig. 1 based on previously published
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work [17] and our own work [18, 19]. The two constituent phases are a Bi2Te3 solid solution containing In and a stoichiometric In2Te3. The (Bi,In)2Te3 solid solution was reported to be a promising candidate for thermoelectric applications [20, 21], as it exhibits relatively low thermal conductivity at In concentrations around 8 at% [22]. In2Te3 was suggested to be an insulator of wide
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band gap (1.1 eV) [23, 24], which is supposed to act as Bi2Te3/In2Te3 interface raiser. In the present work, thorough characterization of the eutectic structure with respect to the influence of the internal
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interfaces on the thermoelectric conductivity is carried out. Additionally, a comparison between the properties of eutectic Bi2Te3-In2Te3 including the (Bi,In)2Te3 phase with the pure (Bi,In)2Te3 phase of
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the same composition as in the eutectic is presented.
Fig. 1 Quasi-binary Bi2Te3-In2Te3 phase diagram [17-19]. The compositions of the alloys used in the present work are illustrated by dashed lines.
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Experimental
Ingots of compositions Bi-13.5In-60Te and Bi-16.5In-60Te were produced from Bi, In and Te of 99.99% purity supplied by Haines & Maassen Metallhandelsgesellschaft mbH. The loss of Te by evaporation during melting was experimentally determined, and an additional amount of Te (+10%)
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was added to reach the nominal composition. The metallic elements were loaded into quartz tubes of 6 mm in diameter. The quartz tubes were first evacuated to 5×10-6 bar, and then charged with Ar to 0.5 bar. This gas pressure reduces Te evaporation and prevents bursting of the tube because of the pressure increase during heating. The evacuation process was repeated for 3 times, and the tube was
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sealed. The metallic elements were then induction melted. After complete melting of all metallic elements, the melt was held for 10 minutes under strong convection to ensure homogeneity of the
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ingot. By the subsequent directional solidification in a Bridgman type furnace, rod-shaped samples of 6 mm diameter were produced. The samples were prepared metallographically by grinding with a series of SiC papers up to a grit size of 4000, polishing with 3 µm and 1 µm Al2O3 powder and finally polishing with 50 nm colloidal silica. A scanning electron microscope (SEM) equipped with a back-scattered electron (BSE) detector and energy dispersive X-ray (EDX) spectrometry was used
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for microstructural observations. The image analysis software Image J was used to determine the volume fraction of each phase and the lamellar spacing. Transmission electron microscopy (TEM) was used to analyze the crystallographic orientation relationship between Bi2Te3 and In2Te3. TEM
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[25].
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samples were prepared by focused ion beam (FIB). More details can be found in our previous work
Thermoelectric property measurements were performed for all samples. Rectangular parallelepipeds of 3×3×12 mm2 were cut parallel to the orientation of the eutectic lamellae for Seebeck coefficient (S) and electrical conductivity (ߪ) characterization that were performed using a LSR-3 device (Linseis Seebeck and Resistivity) from 50 oC to 300 oC. Disks of ∅6 × 1 mm2 were cut in the direction perpendicular to the growth direction for measuring the thermal diffusivity (α) using a laser flash method (LFA-457). All the properties were characterized in the direction parallel to the growth direction during directional solidification. The thermal conductivity was calculated by ݇ = ߙܥ ߩ, where CP is the heat capacity measured by differential scanning calorimetry (DSC-STA PT1600) and ρ is the density measured by the Archimedes method. CP was determined using a differential
ACCEPTED MANUSCRIPT scanning calorimeter (Netzsch STA-449FA). The electronic contribution to the thermal conductivity (ke) was determined from the electrical conductivity utilizing the Wiedemann-Franz law, ke=LσT, where L is the Lorenz number and L=2.44×10-8 W Ω K-2. Results and discussion
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3.1 Generating an aligned lamellar eutectic of Bi2Te3-In2Te3 by directional solidification
According to the Bi2Te3-In2Te3 pseudo-binary phase diagram (Fig. 1), the eutectic reaction: liquid → Bi2Te3 + In2Te3 occurs at 571 ℃ [17]. The exact In concentration at the eutectic point is not
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precisely known due to disparities in literature [17, 25]. The microstructures of the longitudinal section of directionally solidified Bi-13.5In-60Te and Bi-16.5In-60Te alloys produced at a growth
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rate of 10 ߤm/s and a temperature gradient of 20K/mm are shown in Fig. 2. Based on a series of spot EDX analyses, the bright phase was identified as Bi2Te3 of composition of 32 ±0.5 at%Bi, 8.5±0.15 at%In and 59.5±1 at%Te, and the dark phase as stoichiometric In2Te3 (40±0.5 at%In and 60±0.5 at%Te) with negligible Bi content. Coexistence of primary Bi2Te3 and eutectic colonies consisting of aligned Bi2Te3/In2Te3 layers with an orientation parallel to the growth direction was
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observed for Bi-13.5In-60Te, as shown in Fig. 2(a) and (b). As opposed to that, the composition Bi-16.5In-60Te led to a fully eutectic structure, as shown in Fig. 2(c) and (d). The same microstructure of alternating Bi2Te3 and In2Te3 layers was also observed in the cross sections,
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confirming the lamellar growth of eutectic Bi2Te3-In2Te3 during directional solidification. The statistics of volume fraction of each phase and lamellar spacing was assessed using the
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microstructure of cross sections. The volume fraction of In2Te3 is 16% and ∼22% for the compositions 13.5In and 16.5In, respectively. The eutectic lamellar structure of the two samples exhibits a similar distribution of the lamellar spacing, generally ranging from 0.4 to 3 ߤm, with the majority of spacings between 1 and 2 ߤm. The thickness of In2Te3 ranges from 300 to 600 nm.
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Fig. 2 BSE microstructures in longitudinal sections of directionally solidified Bi-13.5In-60Te (a,b) and Bi-16.5In-60Te (c, d) grown with a temperature gradient of 20K/mm and a growth rate of 10 µm/s. The bright phase represents Bi2Te3 of ~ 8.5±0.15 at%In in solution, and the dark phase represents
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stoichiometric In2Te3 with negligible Bi content.
The interface between the Bi2Te3 and In2Te3 phases was further examined by high resolution
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transmission electron microscopy (HRTEM). Coherency of the Bi2Te3/In2Te3 interface was found, as shown in Fig. 3 (a). This can be attributed to the small lattice mismatch between the two phases in
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the given orientation, only approximately 0.8% using the respective nearest neighbor distance between Te atoms in Bi2Te3 (4.395 Å) and In2Te3 (4.359 Å). The In2Te3 phase exhibits a superstructure accompanied by the diffraction pattern of an orthorhombic crystal structure, as illustrated by arrows in Fig. 3(d). Such a superstructure does not exist for In2Te3 precipitated from a (Bi,In)2Te3 matrix during solid state transformation [19], indicating different crystallographic orientations between the two phases and different influence mechanism of In2Te3 layers on physical properties. The crystallographic relationship between the two phases was determined as (003)Bi2Te3//(031)In2Te3, [010]Bi2Te3//[100]In2Te3. A schematic illustration of the coherent Bi2Te3/In2Te3 interface sharing the same Te layer is shown in Fig. 3 (e).
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Fig. 3 (a) High resolution transmission electron microscope (HRTEM) image of the Bi2Te3 / In2Te3 interface; (b,c,d) diffraction patterns of Bi2Te3 and In2Te3 showing the crystallographic orientation relationship (001)Bi2Te3//(031)In2Te3, [010]Bi2Te3//[100]In2Te3, and (e) a schematic illustration showing the crystal structures and orientation relationship of Bi2Te3 and In2Te3.
ACCEPTED MANUSCRIPT 3.2 Effect of Bi2Te3/In2Te3 interface on thermoelectric properties of (Bi, In)2Te3 alloys For analyzing the effects of the Bi2Te3/In2Te3 interfaces on the thermoelectric properties of Bi2Te3-In2Te3, an anisotropic solid solution of composition Bi-8.5In-60Te was prepared by seeding zone melting as described in our previous work [26]. The In concentration of 8.5% in the Bi2Te3
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phase is the maximum solubility that is found at the eutectic temperature. Preparation of the solid solution is not straightforward, because according to steady-state growth theory, for continuous single phase growth at maximum solubility, the composition of the melt in front of the growing interface must be precisely the eutectic composition. Thus, upon cooling also the eutectic structure
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of alternating Bi2Te3 and In2Te3 layers can solidify directly from the melt. In the present work, zone melting with a seed crystal of Bi-16.5In-60Te was used to prepare single phase Bi-8.5In-60Te with
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enhanced chemical homogeneity and defined orientation and crystal anisotropy (see earlier work [26, 27]). A constant In concentration of 8.5 at% over a length of 30 mm was obtained, as shown in Fig. 4. An initial transient region of ~10 mm in length with a small concentration gradient was found. The abrupt jump of the composition on the left side in Fig. 4 indicates the transition from eutectic to single phase microstructure. The sample for property characterization was taken from the
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homogeneous single phase region of 8.5 at% In.
Fig. 4 Concentration profiles (Bi in blue, In in black and Te in red) along the growth direction of Bi-8.5In-60Te prepared by zone melting with a seed crystal of composition Bi-16.5In-60Te, solidified at a growth rate of 0.5 ߤm/s and a temperature gradient of 20K/mm.
The comparison of the temperature dependent thermoelectric properties between single phase Bi-8.5In-60Te, off-eutectic Bi-13.5In-60Te and eutectic Bi-16.5In-60Te is shown in Fig. 5. All
ACCEPTED MANUSCRIPT samples exhibit n-type transport behavior, as can be seen from negative Seebeck coefficients (Fig. 5(c)). Eutectic Bi-16.5In-60Te exhibits the lowest thermal conductivity (ktot and (ktot-ke)) and electrical conductivity, and the highest absolute Seebeck coefficient. ktot values of 0.66 W m-1 K-1 and (ktot- ke) values of 0.5 W m-1 K-1 are found for eutectic Bi-16.5In-60Te at 60°C. This can be
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attributed to phonon scattering at the densely distributed Bi2Te3/In2Te3 interfaces in the fully eutectic Bi-16.5In-60Te sample. Off-eutectic Bi-13.5In-60Te exhibit higher thermal conductivities (ktot and (ktot-ke)) mainly due to less Bi2Te3/In2Te3 interfaces. An interesting observation is that the two eutectic composites exhibit different temperature dependences of the thermal conductivity (ktot and
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(ktot-ke)) and Seebeck coefficient as compared to single phase Bi-8.5In-60Te. Although a lower thermal conductivity was observed in the fully eutectic Bi-16.5In-60Te sample, the eutectic
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composites exhibit a higher increase rate of thermal conductivities with temperature. Bi-8.5In-60Te is an n-type semiconductor. According to EDX analysis in the TEM, In2Te3 layers exhibit stoichemetric composition and negligible Bi content. According to Ref. 23, pure In2Te3 was reported as a p-type insulator. Thus, besides the small band gap of the Bi2Te3 phase, a resulting bipolar conductivity effect may contribute to the steeper increase rate of (ktot-ke) with temperature for the
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eutectic samples. This also holds for the higher (ktot-ke) of Bi-13.5In-60Te as compared to Bi-8.5In-60Te. Besides the reduced thermal conductivity, the eutectic samples exhibit an enhanced Seebeck coefficient, i.e. from |S|max=63 ߤV K-1 at 200 ℃ for Bi-8.5In-60Te to |S|max=110 ߤV K-1 at 100 ℃ for Bi-16.5In-60Te. A reversion of the temperature dependence trend of the Seebeck
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coefficient, where a transition from a decreasing to an increasing trend occurs at a relatively high temperature, was observed for all the three samples. Such a transition can be often seen in Bi2Te3
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based materials, which is mainly due to the small band gaps Eg (Bi-16.5In-60Te: 0.085 eV; Bi-13.5In-60Te: 0.076 eV; Bi-8.5In-60Te: 0.06 eV; obtained by Eg=2e|S|maxTmax [28]), and due to the fact that minority carriers can acquire enough energy with higher temperature to get from the valence band to the conductive band. It is interesting that the temperature dependence trend of the electrical conductivity of all three samples is nearly the same, which is quite different from Seebeck coefficients and thermal conductivities. At a first glance, the deteriorated electrical conductivities in the eutectic samples could be connected to the enhanced Seebeck coefficients. However, there is more to it than this, which will be discussed in the following section.
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Fig. 5 Temperature dependent (a) total thermal conductivity ktot, (b) (ktot- ke), (c) Seebeck coefficient and (d) electrical conductivity of the solid solution Bi-8.5In-60Te the partly eutectic Bi-13.5In-60Te and the eutectic Bi-16.5In-60Te along the crystal growth direction. The dotted lines in (d) depict calculated electrical conductivity values based on ߪ = ߪ் ்ܸ + ߪூ் ܸூ் [14], where BT stands for the Bi2Te3 phase and IT stands for the In2Te3 phase. The dark dotted
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line is for Bi-13.5In-60Te, the red one for Bi-16.5In-60Te.
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3.3 Enhancement of power factor and zT In the present work, the properties along the direction of the eutectic plates were characterized. According to research on multiphase materials [14], a “parallel model”, which is mainly used for predicting the upper limit of physical properties, may be suitable for predicting the effective physical properties of the Bi2Te3-In2Te3 composites. Nevertheless, it is worth noting that in the parallel model, the effect of Bi2Te3/In2Te3 interfaces on the transport of carriers is neglected. Hence, the comparison between real experimentally measured properties and the predicted values indicate the influence of the Bi2Te3/In2Te3 interfaces on the thermoelectric properties. According to the parallel model [14], the Seebeck coefficient of the eutectic structure along the
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ܵ=
ௌಳ ఙಳ ಳ ାௌ ఙ
(1)
ఙಳ ಳ ାఙ
where BT refers to the Bi2Te3 phase with 8.5 at%In in solution, and IT refers to the In2Te3 phase.
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In2Te3 was reported to be an insulator of ultra low electrical conductivity of the order of 10-3 S m-1 [23, 24], which is nearly 6 orders smaller than that of the Bi2Te3 phase containing 8.5 at%In. Due to the much smaller electrical conductivity of In2Te3 and according to equation (1), the Seebeck coefficient of the eutectic composites should be dominated by Bi2Te3, i.e. S≈SBT. In other words, the
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same Seebeck coefficient as that of Bi-8.5In-60Te is expected for the eutectic samples when the interface effect is neglected. It is worth noting that the parallel model provides the upper limit for the
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property prediction based on different models, for example, the effective medium theory (EMT) or the general effective medium theory (GEMT) [29-33]. However, higher |S| values than the upper limit were experimentally determined in the two-phase structures.
According to the “parallel model”, the electrical conductivity of Bi2Te3-In2Te3 composites can be
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calculated as:
ߪ = ߪ் ்ܸ + ߪூ் ܸூ்
(2)
When composing the properties from the properties of the constituent phases, the electrical
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conductivity of the eutectic structure should be smaller than that of Bi-8.5In-60Te, i.e. proportional to the volume fraction of Bi2Te3. The values calculated based on eq. (2) are illustrated by the dashed
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lines in Fig. 5(d). Clearly, the measured values are smaller than the calculated ones. The “parallel model” was also used related to the resistivity of a two-phase material, as illustrated in Eq. (3) for Bi2Te3-In2Te3:
ߩ = ߩ் ்ܸ + ߩூ் ܸூ்
(3)
As mentioned before, In2Te3 exhibits a resistivity that is 6 orders of magnitude higher than that of Bi2Te3. Although the volume fraction of In2Te3 only ranges from 16% to 22%, the electrical resistivity of the eutectic microstructures should be dominated by In2Te3, implying that the electrical
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on the resulting thermoelectric properties of the material. Nevertheless, a high power factor (PF=ܵ ଶ ߪ) as shown in Fig. 6(a) is obtained for the two-phase structures. Combined with the lower thermal conductivity, the fully eutectic Bi-16.5In-60Te exhibits a zT value that is 3 times higher than that of Bi-8.5In-60Te at 100 ℃, as shown in Fig. 6(b). The enhancement of the power factor is in line with
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previous work on two-phase materials [34], in which higher thermoelectric power factors than the power factors of the pure components are predicted, especially for composites of parallel slabs
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microstructures. This demonstrates the potential of engineering the thermoelectric properties via the design of eutectic lamellar structures. Higher zT values than those in the constituent phases were first experimentally found in nanostructured SiGe-Si [35, 36] in recent years, which was attributed to band engineering across the hetero-phase interface. Further work on analysis and further optimization of the band structure across Bi2Te3/In2Te3 interfaces will be performed, aiming for
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better understanding and improved performance. Optimization of electrical conductivity and Seebeck coefficient via modification of charge carriers is needed. Additionally, n-type dopants for In2Te3 may also help to prevent the bipolar effect induced by the p-type transportation behavior of
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Fig. 6 Temperature dependent (a) power factor and (b) figure of merit zT values of of Bi-8.5In-60Te, Bi-13.5In-60Te and Bi-16.5In-60Te along the crystal growth direction.
ACCEPTED MANUSCRIPT 4 Conclusions Directionally solidified eutectic structures with designed interfacial effects exhibit potential for a practical application as thermoelectric materials. Aligned eutectic Bi2Te3-In2Te3 structures with coherent Bi2Te3/In2Te3 interfaces and well defined crystallographic orientation were generated by
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directional solidification. Such interfaces not only contribute to phonon scattering and the resulting reduction in thermal conductivity, but also lead to an enhanced Seebeck coefficient and power factor, overall resulting in a 3 times higher figure of merit zT than each constituent. Further engineering of carrier concentration and band gap via proper doping is expected to further improve the
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Acknowledgements
Financial support by the German Research Foundation [Deutsche Forschungsgemeinschaft: DFG; granted number Re1261/15-1] is gratefully acknowledged. References
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ACCEPTED MANUSCRIPT 1.
Anisotropic aligned Bi2Te3-In2Te3 eutectic lamellar structure was generated.
2.
Coherent Bi2Te3-In2Te3 interface sharing Te layer was determined by HRTEM.
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3. Bi2Te3-In2Te3 interfaces contribute to enhanced thermoelectric properties.