Electron Density Optimization and the Anisotropic Thermoelectric

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Functional Inorganic Materials and Devices

Electron density optimization and the anisotropic thermoelectric properties of Ti self-intercalated Ti1+xS2 compounds Min Zhang, Cheng Zhang, Yonghui You, Hongyao Xie, Hang Chi, Yan Sun, Wei Liu, Xianli Su, Yonggao Yan, Xinfeng Tang, and Ctirad Uher ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b10449 • Publication Date (Web): 30 Aug 2018 Downloaded from http://pubs.acs.org on September 1, 2018

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ACS Applied Materials & Interfaces

Electron density optimization and the anisotropic thermoelectric properties of Ti self-intercalated Ti1+xS2 compounds

Min Zhang,1 Cheng Zhang,1 Yonghui You,1 Hongyao Xie,1 Hang Chi,2 Yan Sun,3 Wei Liu,1,＊ Xianli Su,1 Yonggao Yan,1 Xinfeng Tang,1,＊Ctirad Uher2 1

State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China

2

Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

3

Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany

＊

Corresponding Emails: [email protected], [email protected]

1

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Abstract Polycrystalline Ti1+xS2 (0.111 ≤ x ≤ 0.161) with high density and controllable composition were successfully prepared using solid state reaction combined with plasma activated sintering. Ti1+xS2 showed strong (00l) preferred orientation with Lotgering factor of 0.32 - 0.60 perpendicular to the pressing direction (⊥), while preferred orientation was not obvious along the pressing direction (||). This structural anisotropy resulted in distinct anisotropic thermoelectric transport properties in Ti1+xS2. At 300 K, while the Seebeck coefficient was weak anisotropic, the power factor and lattice thermal conductivity of Ti1+xS2 was much larger in the perpendicular direction as compared to that of the parallel direction, with an anisotropic ratio of 1.8 - 2.7 and 1.3 - 1.7, respectively. Theoretical calculations of formation energy of defects suggested that the excess Ti was most probably intercalated into the van der Waals gaps in metal-rich Ti1+xS2, consistent with X-ray diffraction, HRTEM characterization and transport measurements. With increasing x, the carrier concentration and power factor of Ti1+xS2 dramatically increased due to the donor behavior of Ti interstitials, which was accompanied by a significant decrease in the lattice thermal conductivity owing to the strengthened phonon scattering from structural disorder. Due to its strongest (00l) preferred orientation and largest carrier mobility among all samples, Ti1.112S2 had the highest power factor of 22 µW cm-1 K-2 at 350 K perpendicular to the pressing direction, close to the value (37.1 µW cm-1 K-2) achieved in single crystal TiS2. We found out that, the maximum power factor and dimensionless figure of merit ZT could be achieved at an optimum carrier 2


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concentration of about 5.0×1020 cm-3. Finally, Ti1.142S2 acquired the highest ZT value of 0.40 at 725 K perpendicular to the pressing direction, because of the beneficial preferred orientation, the improved power factor and the reduced lattice thermal conductivity. Key words: TiS2, Ti excess, Self-intercalation, Anisotropy, Thermoelectric properties

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1.

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Introduction The growing demand for energy from fossil fuels throughout the world has been

causing the greenhouse effect and serious environmental pollution. As a kind of clean energy materials, thermoelectric (TE) materials can achieve the direct and reversible conversion between heat and electricity, and thus have attracted widespread interests from the international community in the past several decades. It is well known that the energy conversion efficiency of TE materials mainly depends on their dimensionless figure of merit ZT, defined as ZT = α2σT/(κe + κph), where α, σ, κe, κph, and T are the Seebeck coefficient, the electrical conductivity, the electronic thermal conductivity, the lattice thermal conductivity, and the absolute temperature, respectively.1-3 A good TE material should possess an outstanding ZT, which requires a high power factor (PF = α2σ) together with a low thermal conductivity (κ = κe + κph). To date, high ZTs have been obtained in the state-of-the-art BiSbTe alloys,4-5 filled skutterudites,6-8 PbTe-based materials,9,

10

half-Heusler alloys,11 Mg2Si-Mg2Sn solid solutions,12,

13

SnSe,14, 15 copper chalcogenides,16, 17 diamond-like compounds18 and so on. However, most of them contain toxic, easily oxidizable and expensive elements, preventing their large-scale commercial applications. As a new type TE material, TiS2 exhibits a layered-structure with a trigonal space group of P 3 m1 , which has advantages of low cost, abundant constituent elements and environmental friendliness. It contains edge sharing TiS6 octahedra that are tightly held by strong covalent bonds within every layer (ab-plane). The layer stacks are jointed via the weak van der Waals (vdW) force along the c-axis.19, 20 TiS2 was well 4


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known for its metallic conductivity and an outstanding PF of 37.1 µW cm-1 K-2 at 300 K, obtained in the ab-plane of a single crystal. However, its high κ of about 6.78 W m-1 K-1 at 300 K, impeded the acquisition of high ZTs.19 Hence, in the past several years, tremendous efforts were focused on polycrystalline TiS2 with suppressed κ. The main strategy for developing TiS2 was to intercalate or dope this material with various metal cations such as Cu,21, 22 Co,23, 24 Nb,25, 26 Nd,27 Cd,28 Mg,29 Ag,30 and Ta31. Intercalation (including self-intercalation32-34) and foreign elements doping can tune the electron density and electrical properties into an optimized level whilst reducing the κph through the strengthened alloy phonon scattering. An optimized ZTmax of 0.3 0.5 could be achieved in TiS2 when the electron density was adjusted in the range of 1020 - 1021 cm-3.21, 22, 25, 26, 30-33 In addition, a recent report by Wan et al. demonstrated that intercalating TiS2 with organic molecules in the vdW gaps is a prospective route of fabricating flexible TE materials for emerging applications in wearable electronic devices.35, 36 The compacted bulk TiS2 tends to grow in a metal-rich form due to sulfur volatilization during the high-temperature synthesis process, leading to Ti over-stoichiometric Ti1+xS2. The excess Ti has been assumed to intercalate into the vdW gap of TiS2, and transfers valence electrons to the Ti 3d band of the host, giving rise to a remarkable increase in the electron density and electrical conductivity. As reported by Beaumale et al.,32 the electrical conductivity of Ti1+xS2 (0 ≤ x ≤ 0.05) could significantly enhance from 0.4×104 S m-1 to 14.3×104 S m-1 at 700 K, due to increasing the electron density from 1.10×1020 cm-3 to 1.22×1022 cm-3 at 300 K, when 5



the Ti excess amount x was increased up to 0.05. Ohta et al. also discovered the very high electron density of 4.5×1021 cm-3 and 7.9×1021 cm-3 at 300 K in the Ti over-stoichiometric Ti1.008S2 and Ti1.031S2, respectively.33 The increase of the Ti/S ratio and electron density could be achieved either by supplying a reduced amount of S in the raw material or by enhancing the sintering temperature and/or sintering pressure. Due to its layered structure, the consolidated bulk TiS2 always shows an anisotropic structure with strong (00l) preferred orientation perpendicular to the pressing direction, which could be explained by the alignment of TiS2 grains along their cleavage planes under high pressure. Guélou et al. illustrated the preferred orientation in the sintered bulk TiS2,24 where the ratio of the intensity of (00l) against the strongest (011) reflection could exceed 30, while in the powder form it was only about 0.57. Similarly, Sever et al. found out that, the sintered bulk TiS2 indicated the strong (00l) orientation and a high Lotgering factor (LF) of 0.64 perpendicular to the pressing direction.34 It was reported in the single crystal TiS2 that, the anisotropy ratio (defined as the value in the ab-plane divided by that along the c-axis) was much greater in the electrical conductivity (e.g., 750 at 300 K and 1500 at 5 K) than in the thermal conductivity (1.61 at 300 K),19 indicating a much better TE performance in the direction with preferred (00l) orientation. Recent works revealed that Ti self-intercalation was likely sufficient to achieve the optimum doping effect,32-34 along with similar effects on TE properties as introduced by foreign elements substitution in TiS2 based compounds.21-31 In addition, recent researches on the transport properties of TiS2 primarily focused on the direction 6


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with (00l) preferred orientation, i.e., perpendicular to the pressing direction.19, 21, 23, 25-31

Transport properties perpendicular and parallel to the pressing direction of TiS2

were first reported by Wan et al.,35 and were also compared by several other research groups.22, 24, 33, 34 However, the relationship between the transport properties and the degree of (00l) preferred orientation has not been explored in TiS2-based polycrystalline compounds. In order to further understand the transport behavior of TiS2, it is of significant importance to simultaneously investigate the degree of (00l) preferred orientation and transport properties of TiS2-based compounds. In this work, we used solid state reaction combined with plasma-activated sintering (PAS) to prepare compacted bulk Ti1+xS2. Through optimization of the sintering temperature, samples with relative density of 99% and controllable composition were obtained. The influence of the excess Ti on the degree of (00l) preferred orientation, electrical and thermal transport properties were systematically investigated in both directions of perpendicular and parallel to the pressing direction. The ionization rate of the excess Ti and its existing form were also discussed. The crystalline orientation and the excess of Ti dominated the thermoelectric transport properties of Ti1+xS2. Finally, an optimum ZT value of 0.40 at 725 K was achieved in Ti1.142S2 along the perpendicular direction with the strong (00l) preferred orientation and an optimal doping level.

2. Experimental Dense bulk polycrystalline TiS2 samples were synthesized via solid state reaction and subsequent PAS process. High purity powder Ti (99.99%) and S (99.99%) were 7



weighted and mixed according to stoichiometric Ti1+xS2 (0 ≤ x ≤ 0.04), cold pressed, sealed in quartz tubes under vacuum and then heated at 923 K for 24 h. Subsequently, the resulting polycrystalline Ti1+xS2 samples were manually ground into fine powders, sieved down to 200 mesh and densified by PAS (Elenix, Ed-PAS III, Japan) with uniaxial pressure of 45 MPa, at 873 - 973 K for 10 min. The relative density of samples was measured by the Archimedes method. As shown in Table 1, the sintering temperature significantly affected the relative density of the bulk TiS2, which was improved from 90% to 99% with the temperature increasing from 873 K to 973 K. The bulk samples were cut by a wire cutting machine into appropriate sizes of 3 mm × 3 mm × 10 mm and 8 mm × 8 mm × 1.5 mm for electrical and thermal transport measurements, respectively. The sintered pellets were 16 mm in diameter and 15 mm in thickness, which allowed two sets of samples to be cut from both perpendicular to the pressing direction (labeled as ⊥) and parallel to the pressing direction (marked as ||). The phase of the reacted products was determined by X-ray diffraction (XRD, PANalytical Empyrean, Netherlands) with Cu Kα radiation. The XRD measurement was carried out in the range of 10o – 80o with a step size of 0.02o. The fractured surface of samples was characterized by a field emission scanning electron microscopy (FESEM SU8020, Hitachi). The morphology of bulk samples was investigated utilizing high resolution transmission electron microscopy (HRTEM, JEM-2100F, JEOL). The chemical composition of samples was determined using electron probe microanalysis (EPMA JXA-8230, JEOL) equipped with a wavelength 8


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dispersive spectrometer (WDS). The detecting accuracy of WDS is better than 0.1%. In order to discuss the influence of the actual composition on the thermoelectric transport properties, the prepared Ti1+xS2 samples were labeled by their actual composition in the following discussion. Density functional theory (DFT) calculations were performed using the Vienna ab-initio simulation package (VASP) with projected augmented wave (PAW) potential.37 The exchange and correlation energy were considered in the generalized gradient approximation (GGA).38 A 2×2×2 supercell was invoked to estimate the formation energy of various defects, whose lattice constants were relaxed via a 10×10×8 k-grid. The electrical conductivity and the Seebeck coefficient in the range of 300 - 725 K were acquired using a commercial ZEM-3 system (Ulvac Sinku Riko) under helium atmosphere. The Hall coefficient RH and the electrical conductivity σ in the range of 10 - 300 K were measured in a Physical Property Measurement System (PPMS-9, Quantum Design) using standard five-probe method, respectively. The carrier concentration and the carrier mobility were then calculated from n = 1/eRH (with e being the electron charge) and µH = RHσ, respectively. The thermal conductivity was calculated by κ = λCpρ, where λ is the thermal diffusivity acquired by a laser flash method (LFA-457, Netzsch), Cp is the specific heat calculated by the Dulong-Petit law, and ρ is the sample density determined by the Archimedes method. The electrical and thermal transport properties were measured both perpendicular (⊥) and parallel (||) to the pressing direction. Uncertainties in measurements of the electrical conductivity, Seebeck coefficient, thermal conductivity and Hall coefficient were estimated to be 9



±3%, ±5%, ±7%, and ±5%, respectively.

3. Results and Discussion 3.1 Phase Composition and Microstructure Figure 1(a) shows the powder XRD patterns of the Ti1+xS2 samples. All samples prepared by the solid state reaction and the PAS process were single phase TiS2 compounds (PDF #03-065-0296). No detectable secondary phase could be found. Figure 1(b) indicates the lattice parameters (along the a-axis and c-axis) of the prepared Ti1+xS2 as determined by the Rietveld refinement method using Fullprof software. The lattice parameter c increased with the increase of the Ti excess amount x, while the lattice parameter a remained almost constant, similar to reported results.32, 34 This suggested the c axis of Ti1+xS2 was expanding with increasing x, and the excess Ti tended to intercalate into the vdW gap, consistent with other related reports.21, 32, 34 Figures 1(c) and 1(d) show the XRD patterns of sintered bulk Ti1+xS2 measured on surfaces perpendicular to the pressing direction (⊥) and parallel to the pressing direction (||), respectively. It is obvious that, the intensity of the (00l) diffractions is much stronger in the perpendicular direction (⊥), as compared to that in the parallel direction (||). This signified the sintered bulk Ti1+xS2 had the (00l) preferred orientation in the perpendicular direction. In order to evaluate the degree of grain orientation, we calculated the Lotgering factor (LF) of the bulk Ti1+xS2 in both directions utilizing the XRD data. The LF of (00l) diffractions is calculated by the following formulae:39

10


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P-P0 , 1-P0

(1)

I ( 00l ) , ∑ I ( hkl )

(2)

I 0 ( 00l ) , ∑ I 0 ( hkl )

(3)

LF=

where,

P=

P0=

I(hkl) and I0(hkl) are the peak integral intensities in the measured sample and randomly oriented sample, respectively. A higher value of LF means stronger preferred orientation. The LF value of the prepared bulk Ti1+xS2 samples is summarized in Table 2. All the sintered Ti1+xS2 samples showed a strong (00l) preferred orientation and a high LF value greater than 0.3 in the perpendicular direction (⊥). On the contrary, the LF value was less than 0.07 in the parallel direction (||), indicating the preferred orientation was not obvious in this direction. Figure 2 shows the surface morphology of sintered bulk Ti1.112S2 fractured perpendicular to the pressing direction (a) and parallel to the pressing direction (b-c). As indicated in Figure 2(a), the sample showed a random structure perpendicular to the pressing direction, similar to other polycrystalline samples without preferred orientation. In the direction parallel to the applied pressure, as shown in Figure 2(b), a well-organized texture was observed and was corresponding to the layered structure of TiS2, which was further confirmed by the enlarged image of Figure 2(c). This feature verified the XRD results that, TiS2 grains would align along the slip plane (the weak vdW gap) under high uniaxial pressure during the PAS process, resulting in (00l) preferred orientation in the sintered Ti1+xS2 perpendicular to the pressing direction. 11



The Ti1.142S2 sample was selected as the typical example for HRTEM analysis in order to assess the microstructure of Ti1+xS2 compounds, see Figure 3. Figure 3(b), 3(c) and 3(e) display the enlarged view in regions of 1, 2 and 3 in Figure 3(a) and 3(d), respectively. We resolved the inter-planar crystal spacing of ∼ 0.57 nm, corresponding to the (001) plane of trigonal TiS2 (d(001) = 0.569 nm, PDF #03-065-0296) and in fair agreement with literatures.30, 36 Moreover, we observed slightly larger d(001) of 0.583 nm and 0.597 nm in regions of 1 and 2, implying the intercalation of Ti into the vdW gap and the uneven distribution of interstitial Ti atoms. We also detected nano-sized structural disorders in Ti1.142S2, which was marked by dashed circle in Figure 3(e). Figure 3(f) showed the selective area electron diffraction (SAED) image in area 4 of Figure 3(d). The diffraction spots were very bright and sharp, confirming the excellent crystallinity of TiS2. Table 2 lists the composition, the Lotgering factor and room temperature physical parameters for Ti1+xS2 bulk samples. As indicated in Table 1 and Table 2, the preferred orientation along the perpendicular direction (⊥) was improved and the LF increased from 0.39 to 0.60 when the sintering temperature of PAS increased from 873 K to 973 K. Meanwhile, the increase of the Ti excess amount x would weaken the preferred orientation along the perpendicular direction (⊥), and resulted in a reduced LF from 0.60 to 0.32 when x increased from 0.112 to 0.161. The anisotropic microstructure would lead to strongly anisotropic electrical and thermal transport properties. For example, in single crystal Bi2Te3 based alloys,40 the anisotropic factor in between the basal plane and along the c-axis was about 3 - 4 and 2 for the electrical 12


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conductivity and thermal conductivity, respectively. Therefore, Ti1+xS2 bulk samples would possess rather distinct transport properties in different directions (⊥ and ||). In principle, the electron density n has no anisotropy, and the anisotropy in the electrical conductivity (σ = neµ) should come from the carrier mobility µ. As shown in Table 2, the electron density was similar in both directions, with a small difference within the experimental uncertainty. An exception was found in Ti1.161S2, where the difference in electron density was about 18% from two directions (⊥ and ||), which should be related to its largest amount of excess Ti and likely its uneven distribution in the bulk sample. The Seebeck coefficient of Ti1+xS2 showed a weak anisotropy in two directions, stemming from its anisotropic crystal structure and band structure.14, 15 Furthermore, Ti1+xS2, except for x = 0.142, possessed relatively larger Seebeck coefficient in the perpendicular direction as compared to that of the parallel direction, consistent with literatures.22, 24, 34-35 The significant anisotropy of power factor (PF =

α2σ = neµα2) was the combined effect of the strong anisotropy in carrier mobility and the weak anisotropy in Seebeck coefficient. At 300 K, the anisotropic ratio of µ⊥/µ||,

σ⊥/σ||, PF⊥/PF||, and κph⊥/κph||, was 1.0 - 1.6, 1.3 - 2.5, 1.8 - 2.7 and 1.3 - 1.7, respectively, indicating that the preferred orientation remarkably affected the electrical and thermal transport of Ti1+xS2 samples. The anisotropic ratio of σ⊥/σ|| and κ⊥/κ|| could be well compared to reported results, e.g., σ⊥/σ|| ≈ 1.6 and κ⊥/κ|| ≈ 1.4 were reported by E. Guilmeau et al.22 and by Wan et al..35 As compared to the perpendicular direction (⊥), the much lower µ and κph in the parallel direction (||) was due to the enhanced boundary scattering of electrons and phonons along the stacking 13



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direction of TiS2 layers. The ratio of PF⊥/PF|| was larger than κph⊥/κph||, and therefore, Ti1+xS2 bulk should display a higher ZT value in the perpendicular direction (⊥).

3.2 Intrinsic defects in Ti1+xS2 The excess of Ti introduces three types of defects: the interstitial Ti in the vdW gap (Tii), the antisite defects with the excess Ti occupying the S sites (TiS), and the S vacancies (VS). According to the electron counting, defects of TiS should be electron acceptors and defects of Tii and VS should be electron donors. Based on the volatilization of sulfur and the resulting excess of Ti during the synthesis process, the defects reaction equations can be described as follows: TiS2 → (1-y)TiTi+(2-2y)SS+2yS(g)↑+(yVTi4++2yVS2-)+yTii4++4ye-,

(1)

TiS2 → (1-y)TiTi+(2-3y)SS+3yS(g)↑ +(yVTi4++2yVS2-)+yTiS2-+2yh+,

(2)

TiS2 → TiTi+(2-2y)SS+2yS(g)↑+2yVS2++4ye-,

(3)

As shown in Table 2, the electron density increased with the excess amount of Ti in Ti1+xS2, manifesting that the excess Ti would introduce interstitial Tii and/or vacancies VS. Several previous studies have suggested that the excess Ti would introduce interstitial Tii and thus donate free electrons to Ti1+xS2.32-34 In order to understand which type of defects would dominate the electrical transport of Ti1+xS2, we carried out first-principles calculations on the formation energy of different defects. Figure 4 shows the structure of the TiS2 2×2×2 supercell: the original supercell (a), the interstitial Tii in the vdW gap (b), the antisite defect of TiS (c) and the vacancies VS (d). The results are summarized in Table 3. The formation energy of Tii, TiS and VS was -3.00 eV, 2.16 eV and 1.05 eV, respectively. From our calculations, only Tii 14


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possessed the negative formation energy (Ef = -3.0 eV/supercell) and was therefore energetically favored in Ti1+xS2 with the excess of Ti. This well explained the increased electron density of Ti1+xS2 with increasing Ti amount and supported previous studies. Ideally, one Tii would donate 4 valence electrons to the host structure of Ti1+xS2 in the case of full ionization. However, previous studies rarely discussed the relationship between the actual Ti excess amount and the electron density in TiS2.32-34 Figure 5 depicts the relationship between the electron density and the actual excess amount of Ti in Ti1+xS2. The result showed that the doping efficiency of Tii was very low and not linear with the excess amount of Ti. The ionization efficiency of Tii increased from 5% to a little more than 10%, when the actual Ti excess amount varied from 0.111 to 0.161. This rather low ionization rate of Tii implied that the intercalated Ti bonded very weakly with the adjacent S atoms.

3.3 Electrical transport properties In the previous section, we have studied the (00l) preferred orientation and the intrinsic defects in Ti1+xS2. In this section, we discuss their influence in detail on the electrical and thermal transport properties of Ti1+xS2. TiS2 is an intrinsically n-type semiconductor with electrons dominating the charge transport. As shown in Table 2, the electron density of Ti1+xS2 dramatically increased from 3.8×1020 cm-3 to 1.6×1021 cm-3 at 300 K, when the actual Ti excess amount x increased from 0.111 to 0.161. Meanwhile, in samples of Ti1.111S2 and Ti1.112S2 with very similar Ti excess amount of x = 0.111 and 0.112, the electron density was enhanced from 3.8×1020 cm-3 to 15



5.4×1020 cm-3 when the sintering temperature was elevated by 100 K, indicating that sintering parameters also had significant effect on the electronic transport.34 The carrier mobility remained relatively constant with increasing x, except for the sample x = 0.112 with the highest degree of (00l) preferred orientation. Therefore, the electrical conductivity of Ti1+xS2 was significantly improved with the increase of x, verifying that interstitial Tii defects could effectively adjust the Fermi energy and the electrical transport properties. The temperature dependence of the electron density (a) and the carrier mobility (b) of Ti1+xS2 (0.111 ≤ x ≤ 0.161) in the range of 10 - 300 K is depicted in Figure 6. The electron density of Ti1+xS2 increased remarkably with the x value, while it remained nearly constant as a function of temperature. This indicates that the band structure of Ti1+xS2 did not markedly change with temperature and could be well described using a rigid band model. The almost temperature independent electron density suggested that the doping level of interstitial Tii was very shallow in Ti1+xS2, and the interstitial Tii donated available free electrons to the matrix even at very low temperature, e.g., 10 K. This result further confirmed that the electron density had no anisotropy, within the experimental uncertainty, in the two directions measured (⊥ and ||). We found out that, the carrier mobility did not monotonically decrease with increasing x, regardless of the structural disorder and the enhanced carrier-carrier scattering after introducing more interstitial Tii in the vdW gap. Instead, the degree of (00l) preferred orientation seemed to have an obvious effect on the carrier mobility of Ti1+xS2. Ti1.112S2 had the largest LF parameter along the perpendicular direction (⊥), 16


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which possessed the largest mobility (µ⊥) of 8.9 cm2 V-1 s-1 at 300 K, significantly larger than that of other samples (µ⊥ = 5.2 - 5.8 cm2 V-1 s-1). Regarding the temperature dependence, the carrier mobility of Ti1+xS2 decreased with increasing temperature in both directions, due to the strengthened carrier scattering from lattice vibrations at elevated temperatures. Above 100 K, the carrier mobility of Ti1+xS2 followed the T-3/2 dependence (µ⊥, µ|| ∝ T-3/2), which suggested that the acoustic phonon scattering became the dominant carrier scattering mechanism.41 Figure 7 shows the temperature dependent electrical conductivity (a-b), the Seebeck coefficient (c-d) and the power factor (e-f) of Ti1+xS2 (0.111 ≤ x ≤ 0.161) in both directions (⊥ and ||). All Ti1+xS2 samples exhibited a metallic like conduction behavior, in which the electrical conductivity decreased with the increase of temperature. The electrical conductivity of Ti1+xS2 increased with increasing x. When x increased from 0.111 to 0.161, the perpendicular electrical conductivity (σ⊥) of Ti1+xS2 increased from 4.0 ×104 S m-1 to 15.1×104 S m-1 at 300 K, primarily due to the largely enhanced electron density. The perpendicular electrical conductivity (σ⊥) of Ti1+xS2 was much higher than that in the parallel direction (σ||), reflecting the anisotropy in the carrier mobility (µ⊥

>

µ||). Similar to other heavily doped TE

materials,4-13, 15 the Seebeck coefficient of Ti1+xS2 exhibited an opposite trend with composition and temperature as compared to the electrical conductivity: the absolute value of the Seebeck coefficient (|α|) decreased with the x value and increased with temperature. The Seebeck coefficient of Ti1+xS2 showed no turnover with temperature up to 725 K, which was a result of the rather large band gap (estimated optical band 17



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gap of about 1.2 eV).42 Moreover, the Seebeck coefficient of Ti1+xS2 was essentially isotropic in the two directions (⊥ and ||) and across the entire measured range of temperatures. Recent studies have reported the TE transport properties of TiS2 with different dopants, in which the electrical conductivity and the power factor were significantly enhanced. The intercalations of Cu,21,

22

Co23 and Ag30, and the

substitution of Nb25, 26 and Ta31 for Ti, proved to be very effective for improving electrical conductivity of TiS2-based compounds, e.g., σ⊥ as high as about 15.0×104 S m-1 at 300 K was observed.21, 30 In our study, the σ⊥ and α⊥ of Ti1.161S2 reached 15.1×104 S m-1 and -79 µV K-1 at 300 K, respectively. This indicated that, the self-intercalation of Ti was, indeed, equally effective in tuning the electrical properties of TiS2 as in case of foreign elements. Compared to our Ti1.161S2 sample, the Ag intercalated sample of Ag0.1TiS2 possessed a relatively lower σ⊥ = 14.3×104 S m-1 and still relatively smaller |α⊥| = 64 µV K-1, at 300 K,30 which was likely due to the difference in the degree of (00l) preferred orientation and the actual electron density of samples. In our research and from previous studies,34 we have realized that different synthesis processes or synthesis parameters (e.g., sintering temperature and sintering pressure) would probably induce different amount of S loss or Ti excess in TiS2, leading to a wide range of σ and PF. It is worth mentioning again that, Ti1.111S2 and Ti1.112S2 possessed nearly the same composition but quite different electron density, due to the different sintering temperature during the PAS process. This implied that the synthesis process affects the doping efficiency of the intercalated Ti in TiS2-based compounds. In addition, in the case of foreign elements doping, it was 18


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hard to distinguish the individual contribution from Ti intercalation and foreign elements doping in TiS2-based compounds, since the intrinsic Ti intercalation itself was already effective in adjusting the electronic transport properties. The power factor of Ti1+xS2 (0.111 ≤ x ≤ 0.161) was then calculated and is shown in Figure 7 (e-f). The results indicate that, the introduction of excess Ti significantly improved the PF of Ti1+xS2, especially at high temperatures. The different PF in two directions (PF⊥ and PF||) mainly reflect the difference in the carrier mobility (µ⊥ and

µ ||). Ti1.112S2 possessed the highest PF⊥ among the batch of Ti1+xS2 compounds, which resulted from its moderately high electron density of 5.4×1020 cm-3 and prominent mobility µ ⊥ of 8.9 cm2 V-1 s-1 (at 300 K) due to the highest degree of (00l) preferred orientation (LF = 0.60). The PF⊥ of Ti1.112S2 reached 22 µW cm-1 K-2 at 350 K, which was the best PF ever achieved in the polycrystalline TiS2 based compounds and close to the value of 37.1 µW cm-1 K-2 in the single crystal TiS2 slab.19 The anisotropy ratio of PF in the two directions, i.e., PF⊥/PF||, was in the range of 1.8 - 2.7 at 300 K, due to the larger σ⊥/σ（ || 1.3 – 2.5 at 300 K), which was two orders of magnitude lower than the value reported for a single crystal TiS2 (σa-b/σc = 750 at 300 K).19 If this reported giant anisotropy in single crystals could be maintained, polycrystalline TiS2 would become an important example of quasi-two-dimensional electronic materials with huge anisotropy in the electronic transport properties. The Seebeck coefficient depends on the electron density and the effective mass of carries of TE materials. Based on the single parabolic band model and assumed that carrier scattering is dominated by acoustic phonons, the Seebeck coefficient of 19



Page 20 of 43

degenerate semiconductors can be expressed by the following equation:2, 43

α=

8π 2 k B2 3eh 2

π     3n 

2/3

m ∗T ,

(4)

where kB is the Boltzmann constant, h is the Planck constant, and m* is the effective mass. Hence, the effective mass can be calculated from the experimental values of the Seebeck coefficient and the electron density. Figure 8(a) shows the Seebeck coefficient as a function of the electron density in Ti1+xS2 compounds at 300 K. We did not observe a significant change in the effective mass of Ti1+xS2 with different x values and electron density. All experimental data of Ti1+xS2 fell on the theoretical Pisarenko curve with m* = 4.84 m0, independent of the x value and the electron density. We also included the data of foreign elements doped samples from the literature, and we found out that the n-S relation roughly fell on the Pisarenko curve.44 Thus, it was concluded that, doping was effective in adjusting the electron density and the Fermi level of TiS2 based compounds, but it had no remarkable influence on the band structure. Figure 8(b) summarizes the relationship of the maximum power factor (PFmax) and the room temperature electron density of TiS2-based compounds. Most samples showed PFmax of ∼ 15 µW cm-1 K-2, while our Ti1.112S2 and Ti1.35S2 samples owned higher PFmax when the electron density was ∼ 5.0×1020 cm-3. The PFmax of TiS2-based compounds was quite scattered as a function of the electron density, different from widely researched thermoelectric materials possessing a clear optimal carrier density range.2, 4-13, 15 From the summarized data, it was likely that the optimal electron density in TiS2-based compounds should be about 5.0×1020 cm-3 in order to achieve maximum PFs.

20


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3.4 Thermal Conductivity Temperature dependent thermal conductivity (a-b) and lattice thermal conductivity (c-d) of Ti1+xS2 (0.111 ≤ x ≤ 0.161) in both directions (⊥ and ||) is depicted in Figure 9. The thermal conductivity (κ) of Ti1+xS2 decreased with the increase of temperature, showing that the Umklapp phonon process dominated the thermal transport.2, 41, 45 The κ in the perpendicular direction (κ⊥) increased with x from 0.111 - 0.161, while the κ in the parallel direction, κ|| remained nearly unchanged for all Ti1+xS2 samples. In order to understand the influence of Ti intercalation on thermal transport, we calculated the lattice thermal conductivity (κph) of Ti1+xS2 by subtracting the electronic thermal conductivity (κe) from the measured total thermal conductivity via κph = κ – κe, where κe = LσT with L being the Lorenz number in the Wiedemann-Franz law. By assuming the single parabolic band model, the Lorenz number L can be calculated by Eq. (5).46, 47 2 2   k B   ( r + 7 / 2 ) F1+5/ 2 (η )  ( r + 5 / 2 ) F1+3/ 2 (η )   L=   −  ,  e   ( r + 3 / 2 ) F1+1/ 2 (η )  ( r + 3 / 2 ) F1+1/2 (η )    

(5)

Here, the reduced Fermi energy ƞ and the Fermi integral Fn(η) can be calculated from the Seebeck coefficient by Eqs. (6) and (7).44 The scattering factor r = -0.5 when acoustic phonon scattering dominates the transport.48, 49

α=

 k B  ( r + 5 / 2 ) F1+3/2 (η ) −η ,  e  ( r + 3 / 2 ) F1+1/2 (η ) 

Fn (η ) = ∫

χn

∞

0

1 + e χ −η

d χ,

(6)

(7)

The thermal transport of Ti1+xS2 was dominated by κph, where at 300 K, κe only

21



accounted for less than 30% of the total κ. The κph of Ti1+xS2 obviously decreased with increasing of the x value from 0.112 - 0.161 in both directions (⊥ and ||), due to the strengthened phonon scattering from the structural disorder introduced by the intercalation of Ti. In the perpendicular direction, the room temperature κph of Ti1+xS2 decreased from 4.40 W m-1 K-1 to 2.71 W m-1 K-1 with the x value from 0.112 - 0.161, while, in the parallel direction, at 300 K, κph decreased from 2.54 W m-1 K-1 to 1.78 W m-1 K-1. Moreover, the κph of Ti1+xS2 in the perpendicular direction was much lower than the values in the single crystal TiS2 slab (6.35 W m-1 K-1),19 which was chiefly due to the enhanced grain boundary phonon scattering in polycrystalline samples. The Ti1+xS2 possessed a higher κph in the perpendicular direction as compared to that of the parallel direction, owing to the weaker grain boundary phonon scattering associated with the higher LF values in the perpendicular direction. The κph of Ti1+xS2 in the perpendicular direction was about 50% larger as compared to the value obtained in the parallel direction, close to the reported results, e.g. the κph⊥ and κph|| values of TiS2 being 2.4 and 1.2 W m-1 K-1 at 575 K, respectively, as reported by Guélou et al..24 At 725 K, Ti1.161S2 reached the minimum κph of 1.76 W m-1 K-1 and 1.19 W m-1 K-1 in the perpendicular direction and in the parallel direction, respectively, the smallest values among all samples.

3.5 ZT values The temperature dependent ZT values of Ti1+xS2 (0.111 ≤ x ≤ 0.161) in both directions (⊥ and ||) are shown in Figure 9 (e-f). Due to the much reduced κph and the improved PF at high temperatures, Ti1.142S2 possessed the highest ZT⊥ of 0.40 at 725 22


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K among all samples, while Ti1.161S2 with x = 0.161 possessed the highest ZT// of 0.33 at 725 K among all samples, representing about 33% and 14% enhancement over the pristine sample of Ti1.111S2, respectively. Due to the highest κph⊥ among all samples, the ZTmax of Ti1.112S2 was limited to 0.31, although it had the largest PF. This result verified that, the Ti intercalation was effective to optimize both the electrical and thermal transport properties of Ti1+xS2, and, hence, the ZT values. Figure 10 summarizes the relationship between the ZTmax and the electron density of TiS2-based compounds reported in the literature. Our Ti1+xS2 possessed comparable ZTmax with Cu-doped samples,21, 22 and slightly better than that of samples doped by elements of Co23,24, Nb25-26 and others. The difference in the ZT values of TiS2-based compounds was caused by a small difference in the doping effect on the electrical and thermal transport properties and in the degree of (00l) preferred orientation. Since the κph of TiS2 was still a rather high value and was the dominant component of κ, further enhancement of ZT values in TiS2-based compounds will mainly rely on reducing their κph by methods such as nanostructuring.4, 5, 8, 10

4. Conclusion In this work, dense bulk Ti1+xS2 (0.111 ≤ x ≤ 0.161) compounds with different Ti excess amount were prepared by solid state reaction combined with plasma activated sintering. The influence of the Ti excess amount and the preferred orientation on the electrical and thermal transport properties of Ti1+xS2 was systematically investigated. All prepared bulk Ti1+xS2 samples were single phases and possessed (00l) preferred orientation perpendicular to the pressing direction (⊥), while there was no preferred 23



orientation in the parallel direction (||). The excess Ti would intercalate into the vdW gaps of Ti1+xS2 and donate free electrons to the host, which was consistent with calculations of the formation energy of defects, HRTEM characterization and transport measurements. With the increase of the Ti excess amount, the n and the σ of Ti1+xS2 were remarkably improved, leading to much enhanced PF. In addition, Ti1+xS2 possessed much higher σ⊥ and PF⊥ in the perpendicular direction as compared to the parallel direction, mainly due to the significant (00l) preferred orientation in the perpendicular direction and therefore much higher µ. Ti1.112S2 showed the highest PF⊥ of 22 µW cm-1 K-2 at 350 K in the perpendicular direction among all samples, which was the best result ever reported in the polycrystalline samples. This excellent PF was due to the electron density n of Ti1.112S2 being within the optimum doping range, and also resulted from the highest degree of (00l) preferred orientation and the largest µ⊥ among all samples. We found out that, the intercalation of the excess Ti into the vdW gaps markedly reduced κph of Ti1+xS2 in both the perpendicular and the parallel directions due to the enhanced phonon scattering from disordered structure. The κph in the perpendicular direction was about 50% greater as compared to that of the parallel direction, the consequence of the strengthened phonon scattering from grain boundaries in the parallel direction. Owing to the optimized PF and much reduced κph, Ti1.142S2 possessed the highest ZT value of 0.40 at 725 K in the perpendicular direction among all samples. Since the κph was still relatively high, further investigations could focus on how to reduce the κph of TiS2-based compounds via introducing nanostructures and high density grain boundaries in the matrix. 24


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Corresponding Author *E-mail: [email protected] (W.L.) *E-mail: [email protected] (X.T)

Notes The authors declare no competing financial interest.

Acknowledgements We acknowledge the supports from the Natural Science Foundation of China (Grant No. 51521001 and 51632006), the 111 Project of China (Grant No. B07040) and the Fundamental Research Funds for the Central Universities (WUT: 2017IVA097 and 2018Ⅲ043GX).

25



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Figure 1: (a) Powder XRD patterns of Ti1+xS2; (b) The lattice parameter vs. the x value of Ti1+xS2; (c) XRD patterns of bulk Ti1+xS2 measured on surfaces perpendicular to the pressing direction (⊥); (d) XRD patterns of bulk Ti1+xS2 collected on surfaces parallel to the pressing direction (||).

33



Figure 2: FESEM images of the fresh surface of Ti1.112S2: (a) fractured perpendicular to the pressing direction; (b) fractured along the pressing direction; (c) enlarged view of the square area in (b).

Figure 3: (a) and (d) The low-magnification TEM images of Ti1.142S2 sample showing different structures; (b), (c) and (d) HRTEM images of small square areas 1, 2 and 3, respectively, in Figure (a) and Figure (b); (f) The selected area electron diffraction image of the square area 4.

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Figure 4: The 2×2×2 supercell of TiS2: (a) original supercell; (b) interstitial Ti, Tii; (c) Ti substituting for the S, TiS; (d) S vacancy, VS. The smaller earth-yellow colored atoms represent S atoms, and the larger dark-blue colored atoms are Ti atoms. The defects of Tii, TiS and VS are indicated by the red arrows.

35



Figure 5: The relationship between the actual excess Ti amount and the electron density in Ti1+xS2. One interstitial Ti atom was assumed to donate 4 free electrons to the matrix. The dotted line represented the calculated electron density by assuming the ionization efficiency of interstitial Ti being 5%, 10% and 20%, respectively. The solid symbols indicated our experimental results at room temperature.

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Figure 6: The temperature (10 - 300 K) dependence of the electron density (a) and the carrier mobility (b) of Ti1+xS2 (0.111 ≤ x ≤ 0.161) in the perpendicular (⊥) and parallel (||) to the pressing direction.

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Figure 7: The temperature dependence of the electrical conductivity (a-b), the Seebeck coefficients (c-d) and the power factor (e-f) of Ti1+xS2 (0.111 ≤ x ≤ 0.161) in the perpendicular (⊥) and parallel (||) to the pressing direction. 38


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Figure 8: (a) the |α| and (b) the PFmax as a function of electron density at 300 K for our Ti1+xS2 samples in both directions (⊥ and ||). The data from literature was taken from the perpendicular to the pressing direction (⊥). The dotted line represented the calculated Pisarenko curve with m* = 4.84 m0.

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Figure 9: The temperature dependence of the total thermal conductivity (a-b), the lattice thermal conductivity (c-d) and ZT values (e-f) of Ti1+xS2 (0.111 ≤ x ≤ 0.161) in the perpendicular (⊥) and parallel (||) to the pressing direction. 40


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Figure 10: ZTmax values as a function of the carrier concentration for our samples of Ti1+xS2 in both directions (⊥ and ||). The data from literatures in the perpendicular to the pressing direction (⊥) was also plotted for comparison.

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Table 1: The nominal and actual composition, sintering parameters and relative density for bulk Ti1+xS2. Nominal

Actual

composition

composition

T (K)

P (MPa)

t (min)

density

TiS2

Ti1.111S2

873

45

10

90%

TiS2

Ti1.112S2

973

45

10

99%

Ti1.015S2

Ti1.135S2

973

45

10

98%

Ti1.025S2

Ti1.142S2

973

45

10

99%

Ti1.04S2

Ti1.161S2

973

45

10

100%

Sintering parameters

Relative

Table 2: The Lotgering factor and room temperature physical parameters for bulk Ti1+xS2. µ

n

LF

Sample

20

-3

2

-1

4

(cm V S )

(10 cm )

α

σ -1

-1

(10 S m )

PF -1

-1

(µV K )

κph -2

(µW cm K )

(W m-1 K-1)

⊥

||

⊥

||

⊥

||

⊥

||

⊥

||

⊥

||

⊥

||

Ti

S

0.39

0.07

3.8

3.6

5.8

3.6

4.0

2.4

-180

-170

13

7

3.22

2.48

Ti

S

0.60

0.06

5.4

4.9

8.9

5.7

7.3

5.2

-168

-148

21

11

4.40

2.54

Ti

S

0.35

0.04

7.9

7.8

5.2

3.5

8.7

4.4

-130

-118

15

6

3.62

2.41

Ti

S

0.34

0.03

9.5

8.6

5.3

3.3

10.7

4.3

-99

-113

11

6

3.02

2.24

Ti

S

0.32

0.03

16.1

13.8

5.8

5.5

15.1

11.0

-79

-69

9

5

2.71

1.78

1.111 2

1.112 2

1.135 2

1.142 2

1.161 2

Table 3: The formation energy of three types of defects (Ef) in Ti1+xS2: the excess Ti in the vdW gap (Tii), the excess Ti substituting the S sites (TiS), and the excess Ti introducing S vacancies (VS). System

Tii

TiS

VS

Ef（eV）

-3.00

2.16

1.05

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Table of Contents graphic

43


Electron Density Optimization and the Anisotropic Thermoelectric

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