English

• 1. INTRODUCTION

  Thermoelectric (TE) materials can convert thermal energy from a temperature gradient into electrical energy and vice versa. The TE devices composed of n- and p-type TE materials have been the alternative source of global sustainable energies because of its many excellent advantages, such as no moving parts, long operating lifetimes, reliability and simplicity^[1-3]. The high TE efficiency of TE devices should require both a large working temperature gradient and a high TE figure-of-merit ZT = S²σ T /κ , where S, σ, κ, and T are Seebeck coefficient, electrical conductivity, total thermal conductivity and absolute temperature, respectively. Therefore, the TE materials having high ZT values paly a key role in the TE application. Among the huge family of TE materials, several TE materials containing heavy metals such as Pb, Bi, Sb and Te have been developed so far and they are mostly toxic or rare in the earth. Therefore, the researches on the environment friendly and earth-abundant TE materials are of great important such as the lead-free In₄Se₃-based TE materials.

  As shown in Fig. 1a, the quasi two-dimensional layered crystal structure of In₄Se₃ consists of In⁺ ions and [In₃Se₃]^- corrugated layers, that is, In₄Se₃ = [In]⁺[In₃]⁵⁺[Se^2-]₃. The anionic layers of [In₃Se₃]^- are interconnected by In⁺ ions (In4 atoms) via ionic bonding interactions and in each layer, the (In3)₅+ multivalent clusters which comprise In1, In2 and In3 atoms are connected by Se ions (Se 1～3) with covalent bond^{[4, 5]}. As a new kind of n-type chalcogenide TE material, In₄Se₃-based TE materials have become the promising medium temperature (500～900 K) n-type TE material candidates since the remarkable ZT = 1.48 at 705 K (In₄Se_2.35 single crystal) along the bc plane^[6] was reported. The intrinsically low lattice thermal conductivity (κ_lat) and high Seebeck coefficient of In₄Se_3-δ crystals (with Se-deficiency, δ) originate from the quantum confinement effect and the charge density wave induced by Periels distortion along the quasi-1D indium chain^[6]. Nevertheless, the In₄Se₃-δ single crystals suffer strong anisotropy^{[6, 7]} and the cleavage habit, which are not perfect for application, so it is very necessary to research on the In₄Se₃-δ polycrystalline compounds.

  It is a feasible approach to improve TE properties of In₄Se₃-based TE materials by Se-deficiency^[8-10] and dual even multi-doping^[11-13]. It aims at increasing the power factor (PF = S²σ) through optimizing conductivity performance because of the unsatisfied carrier concentration (n_e ～ 1017 cm^-3) in In₄Se₃ polycrystalline compound^[14-16]. In the past years, the doping effect of many cationic dopants on the In₄Se₃-based TE materials have been reported and the results indicate that doping in different lattice sites have distinct influence on the conductivity performance. For example, cationic mono-doping at In2 (e. g. Sn)^{[17, 18]} or In3 (e. g. Zn and Ga)^[18] is reported to be non-effective for optimizing conductivity performance, while substitution at In4 (e. g. Na, Ca and Pb)^{[12, 18]} or intercalation sites (e. g. Cu)^[12] is verified to be more effective to optimizing conductivity performance because of the obviously increased n_e. Herein, given that the atomic radius of Ag is smaller than that of In, and most importantly, Ag should be easier to ionize than Cu as a donor when doping at intercalation sites due to its lower first ionization energy, we investigated experimentally and theoretically the effect of Ag mono-doping on the TE properties of In₄Se_2.95 polycrystalline compounds. The maximum ZT of 0.92 at 723 K is obtained byIn_3.98Se₉₈₃ Ag_0.02 compound which is 15% enhancement over that of the un-doped one.

  2. EXPERIMENTAL

  2.1. Synthesis and characterization

  In_4-xSe_2.95Ag_x (x = 0.0, 0.01, 0.02, 0.03 and 0.05) polycrystalline compounds were synthesized by the solid state methods and hot-press technique. Stoichiometric amounts of In (granular, 99.995%), Se (granular, 99.999%) and Ag (granular, 99.999%) were weighed and mixed in quartz tubes in an Ar-filled glove box. The tubes were flame sealed under 0.1 Pa and then slowly heated to 1173 K in tube furnace and kept for 1 day followed by water quenching. The melted ingots were annealed at 743 K for 5 days and then ground into fine powders and subsequently sintered by hot-press technique under uniaxial pressure of 57 MPa at 793 K for 50 minutes under vacuum. The experimental relative densities of all hot-press samples were above 98%.

  The powder X-ray diffraction (PXRD) data were obtained on a MiniFlex II powder diffractometer with a CuKα radiation in a 2θ range from 10° to 60° with a step size of 0.02°. The electrical resistivity (ρ) and Seebeck coefficient (S) were measured simultaneously from room temperature to 723 K under an argon atmosphere by using a standard four-probe method with the aid of a ULVAC-RIKO ZEM-3 instrument system. The total thermal conductivity (κ_tot) was calculated byκ _tot =αC_pd , where α, C_p and d were thermal diffusivity, specific heat and density, respectively. The thermal diffusivity was measured on a sample disk with about 10.0 mm in diameter and about 2.0 mm in thickness by a laser flash method (LFA-457, NETZSCH, Germany) under an argon atmosphere in the temperature range of 300～723 K. The specific heat was directly derived from Dulong-Petit value (0.2508 J·K^-1·g^-1)^{[6, 19]}. The measured density was determined using the dimensions and mass of the sample and then reconfirmed by measurements using Archimedes' principle on a home-built device.

  2.2. Details of the first-principle calculations

  The calculations were based on density functional theory (DFT)^[20], with the aid of Vienna ab-initio simulation package (VASP). The generalized gradient approximation (GGA)^[21] was implemented by Perdew, Burke, and Ernzerhof (PBE) for the exchange correlation energy functional and a plane-wave basis with the projector augmented wave (PAW)^[22] potentials was used. We took into account In₄Se₃ ^structure with unit cell composed of 28 atoms including 16 indium and 12 selenium atoms to investigate the effect of metal substitution in an indium site. There are seven different sites in the unit cell of In₄Se₃ (e.g. four sites for indium and three sites for selenium) and each site occupies four equivalent atomic positions. Each site of indium atoms at four different indium sites was chosen for the metal substitution, coupled with the interstitial position. In the geometrical optimization, an energy cutoff of 400 eV and a k-point spacing with 0.03 Å^-1 in the Brillouin zone was used. Atomic positions were fully relaxed until the Hellman- Feynman force on each atom was less than 0.02 eV·Å^-1. In the static self-consistent-field calculation, a plane-wave cutoff energy of 500 eV and threshold of 10^-5 eV were set. A k-point spacing with 0.02 Å^-1 in the Brillouin zone was used by the tetrahedron method^[23].

  3. RESULTS AND DISCUSSION

  Fig. 1b shows PXRD patterns of the In_4-xSe_2.95Ag_x (x = 0～0.5) samples which are well indexed as Pnnm In₄Se₃ (PDF-83-0039) with no noticeable impurity peaks except for the x = 0.03 and 0.05 samples. The arrival of detectable impurity phase InSe (PDF-34-1431) indicates that the maximum solubility of Ag (x_m) is reached (x_m < 0.03). It is worth to mention that the reason why the element Ag can not be found in PXRD patterns is that the amount of Ag dopant is below the detective limit of XRD technique (usually 5 wt%). Besides, it is known that the atom radius of Ag (1.75 Å) is smaller than that of In (2.0 Å). Thus, to evaluate the stability of Ag atom occupying the In1, In2, In3, In4 and intercalating (Ag_int) sites, the formation energy calculation was carried out and shown as follows:

  In₁₆Se₁₂-In + Ag → In₁₅AgSe₁₂

  (substituting the In site)

  In₁₆Se₁₂ + Ag → In₁₆AgSe₁₂

  (entering the intercalating site)

  E_f = E_t (In₁₅Ag₁Se₁₂) - Et (In₁₆Se₁₂) +

  E_t (In) - E_t (Ag)

  E_f = E_t (In₁₆Ag₁Se₁₂) - Et (In₁₆Se₁₂) - E_t (Ag)

  Figure 1

  

  Figure 1.  a) Crystal structure of In₄Se₃ viewed along the c axis with selected atom numbers and unit cell marked. b) PXRD of the In_4-xSe_2.95Ag_x (x = 0～0.05) polycrystalline compounds. Column chart in the bottom and asterisks (^*) refer to In₄Se₃ and InSe phases, respectively

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  where E_f is the formation energy, and Et the total energy of each material. The formation energies for Ag occupying each site are shown in Table 1. Obviously, the formation energies in the intercalating and In4 sites are lower than the values in that of other In 1～3 sites. The result shows that Ag occupying the intercalating or In4 sites is more energetically stable than in other In sites.

  Table 1

  

  Table 1.  Formation Energies in eV at Each Site for Ag-doped In₄Se₃

  DownLoad: CSV

  In1In2In3In4Ag_intAg1.5041.3511.580.5870.556

  The temperature dependence electrical resistivity ρ(T) of In_4-xSe_2.95Ag_x samples is shown in Fig. 2a. The ρ of all samples decreases and tends to convergence with the elevated temperature, while it is unsatisfied because the electrical conductivity behavior is not drastically optimized by cationic Ag-doping. Based on the density of states (DOS) calculation shown in Fig. 2d, after Ag doping, the Fermi level moves into the conduction band for Ag inserting the intercalating site while it is nearly unchanged for Ag substituting in the In4 site. Therefore, it predicts an n-type transport behavior for Ag in intercalation site as the Cu-doping^[12] in the intercalation site. However, the maximum solubility of Ag (x_m < 0.03) is so low that the Ag-doping effect on the electrical conductivity behavior is not significant. Besides, the negative values of S (Fig. 2b) confirm that all samples are n-type TE materials. It is noted that there exists a peak in the S (T) curve as similar with many previous studies^[10-13], which is related to the electron-hole bipolar transport. In the bipolar region, the contribution to the final S value should include positive and negative charge carriers and the S can be expressed by the conductivity weighted average^{[24, 25]}:

  1 $S=\frac{{{\sigma }_{p}}{{S}_{p}}-{{\sigma }_{n}}\left. {{S}_{n}} \right.}{{{\sigma }_{p}}+{{\sigma }_{n}}}$ $

  Figure 2

  

  Figure 2.  Temperature dependence of thermoelectric properties in In_4-xSe_2.95Ag_x (x = 0～0.05) samples: a) Electrical resistivity (ρ); b) Seebeck coefficient (S); c) Power factor (PF = S2σ); d) DOS for un-doped In₄Se₃ and Ag doped In₄Se_2.95, where the Fermi level has been specified as zero

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  At low temperature, the population of minority carriers (holes for n-type TE materials) is so small that the contribution to the overall S value mainly stems from the electron conductivity (σ_n); while at higher temperature, the minority carrier conductivity (σ_p) will increase rapidly, thus resulting in the reduction in S. Therefore, the peak appears. The electron-hole bipolar effect mainly happens at the narrow band gap semiconductor, and the band gap can be estimated via the relation developed by Goldsmid and Sharp^[25]:

  2 ${{E}_{g}}=2e{{\left. S \right.}_{\max }}{{T}_{\max }}$ $

  The estimated band gaps of all samples are located at the range of 0.425～0.435 eV which indicates that the amount of Ag doping is too small to change the band gap of In₄Se_2.95 compound. According to the above analysis, it can be clearly seen that owing to the slight effect of Ag doping on optimizing electrical conductivity behavior, the power factors (PF = S²σ) of all samples increase with increasing temperature but not enhanced significantly as displayed in Fig. 2c. In detail, the maximum value of PF = 5.38 μ·W·K^-2·cm^-1 at 723 K is obtained by In_3.98Se₉₈₃ Ag_0.02 compound.

  Fig. 3a shows the temperature-dependent total thermal conductivity κ_tot (T) of all samples. This conventional 1/T behavior is mainly caused by an acoustic phonon contribution to thermal transport. In the temperature range of 300 to 723 K, when x < 0.03, the κ_tot values of all samples are lower that of un-doped one, and then increase with the increased Ag doping concentration. Interestingly, the κ_tot (T) curves of In_4-xSe_2.95Ag_x (x = 0.01, 0.02) samples are nearly coincident and the same phenomenon happens in the In_4-xSe_2.95Ag_x (x = 0.03, 0.05) samples. At 723 K, the κ_tot of In_4-xSe_2.95Ag_x (x = 0.01, 0.02) and In_4-xSe_2.95Ag_x (x = 0.03, 0.05) samples are 0.42 and 0.47 W·m^-1·K^-1, respectively. In general, the κ_tot is the sum of electrical thermal conductivity (κe) and lattice thermal conductivity (κ_lat). The κ_e can be calculated by the Wiedemann- Franz relationκ _e = LT / ρ , where L is the Lorenz number. In metallic system, the L0 = π²/3(kB/e)₂ = 2.45×10^-8 W·Ω·K^-2. However, the Lorenz number is incorrect for a degenerate semiconductor. Herein, to obtain a more reliable Lorenz number, the L is calculated based on the single parabolic band (SPB) model dominated by acoustic phonon scattering (r = -1/2) (Fig. 3b) as the following expressions^[26-28]:

  3 $S=\frac{{{k}_{B}}}{e}=\left[ \frac{2{{F}_{1}}\left( \eta \right)}{{{F}_{0}}\left( \eta \right)}-\eta \right]$ $

  4 ${{F}_{n}}\left( \eta \right)=\int_{0}^{\infty }{\frac{{{x}^{n}}}{1+{{e}^{x-\eta }}}}dx$ $

  5 $L={{\left( \frac{{{k}_{B}}}{e} \right)}^{2}}\frac{3{{F}_{0}}\left( \eta \right){{F}_{2}}\left( \eta \right)-4F_{1}^{2}\left( \eta \right)}{F_{0}^{2}\left( \eta \right)}$ $

  Figure 3

  

  Figure 3.  Temperature dependence of thermoelectric properties in In_4-xSe_2.95Ag_x (x = 0~0.05) samples: a) Total thermal conductivity (κ_tot); b) Lorenz number (L); c) lattice thermal conductivity (κ_lat) and electrical thermal conductivity (κe); and d) Dimensionless figure-of-merit ZT

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  where η, F_n (η), k_B and h are the reduced Fermi energy (η = E_F / k_B T ), n^th order Fermi integral, Boltzmann constant and Planck constant, respectively. Therefore, using the calculated L and ρ, we can obtain κ_e (T) and then κ_lat (T) by subtracting κ_e from κ_tot, as shown in Fig. 3c. All doped samples exhibit similar κe but differ in κ_lat which results in various κ_tot. Therefore, the lower κ_tot mainly comes from the reduced κ_lat, especially for x = 0.01 and 0.02 samples. Basically, the low κ_lat of In₄Se₃-based TE materials is closely related to the positive effect of Peierls distortion^[6].

  As manifested in Fig. 3d, the ZT values increase with increasing the temperature for all samples. Obviously, a maximum ZT value reaching 0.92 at 723 K inIn_3.98Se₉₈₃ Ag_0.02 sample is about 15% enhancement over the pristine In₄Se_2.95 sample (ZT = 0.8, 723 K). The enhanced ZT for x = 0.01 and 0.02 samples mainly originates from the reduced κ_tot because of the reduced κ_lat. A download trend of ZT value when x > 0.03 may be also connected with the existence of InSe impurity phase because the negative influence of InSe phase was also found in the In₄Pb_0.01Sn_0.03Se_2.9Cl_0.06 compound^[27]. The results indicate that Ag mono-doping is not obviously effective to improve the TE property of In₄Se_2.95 polycrystalline compounds.

  4. CONCLUSION

  In summary, In_4-xSe_2.95Ag_x (x = 0～0.05) polycrystalline compounds are synthesized successfully and the effect of Ag mono-doping on the electrical and thermal properties are investigated theoretically and experimentally. The maximum solubility of Ag-dopant (x_m) in In₄Se_2.95 is very low (x_m < 0.03). According to the formation energy calculation, Ag-occupation at intercalating or In4 sites is more energetically stable than at other In sites. However, the electrical transport behavior is nearly unchanged by the cationic Ag mono-doping. Consequently, the maximum ZT of 0.92 (723 K) obtained by In_3.98Se₉₈₃ Ag_0.02 polycrystalline compound is 15% enhancement over the pristine one. The enhancement on ZT mainly benefits from the slightly enhanced PF and the reduced κ_tot. Considering the dual even multi-doping effect and self-doping effect of Se-deficient, further researches on the In₄Se₃- based TE materials can focus on the synergistic effect of Se deficiency and Ag-doping or the co-doping of Ag and another element.

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• 

  Figure 1  a) Crystal structure of In₄Se₃ viewed along the c axis with selected atom numbers and unit cell marked. b) PXRD of the In_4-xSe_2.95Ag_x (x = 0～0.05) polycrystalline compounds. Column chart in the bottom and asterisks (^*) refer to In₄Se₃ and InSe phases, respectively

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  Figure 2  Temperature dependence of thermoelectric properties in In_4-xSe_2.95Ag_x (x = 0～0.05) samples: a) Electrical resistivity (ρ); b) Seebeck coefficient (S); c) Power factor (PF = S2σ); d) DOS for un-doped In₄Se₃ and Ag doped In₄Se_2.95, where the Fermi level has been specified as zero

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  Figure 3  Temperature dependence of thermoelectric properties in In_4-xSe_2.95Ag_x (x = 0~0.05) samples: a) Total thermal conductivity (κ_tot); b) Lorenz number (L); c) lattice thermal conductivity (κ_lat) and electrical thermal conductivity (κe); and d) Dimensionless figure-of-merit ZT

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  Table 1.  Formation Energies in eV at Each Site for Ag-doped In₄Se₃

  In1In2In3In4Ag_intAg1.5041.3511.580.5870.556

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•