Rare-Earth Nd Inducing Record-High Thermoelectric Performance of (GeTe)85(AgSbTe2)15

As a promising midtemperature thermoelectric material with both higher thermoelectric performance and mechanical property, Tellurium Antimony Germanium Silver (TAGS-x), written as (GeTe)x(AgSbTe2)1-x, especially (GeTe)0.85(AgSbTe2)0.15 (TAGS85), has attracted wide attention. Herein, we innovatively use Nd doping to synergistically decrease the carrier concentration to the optimal level leading to enhanced dimensionless figure of merit, zT. Our density-functional theory calculation results indicate that Nd-doping reduced carrier concentration should be attributed to the enlargement of band gap. The optimized carrier concentration results in an ultrahigh power factor of ~32 μWcm K at 727K in Ge0.74Ag0.13Sb0.11Nd0.02Te. Simultaneously, the lattice thermal conductivity of Ge0.74Ag0.13Sb0.11Nd0.02Te retained as low as ~0.5 at 727K. Ultimately, a record-high zT of 1.65 at 727K is observed in the Ge0.74Ag0.13Sb0.11Nd0.02Te. This study indicates rare-earth Nd doping is effective in boosting the thermoelectric performance of TAGS-85 and approached a record-high level via synergistic effect.


Introduction
Fossil fuel overexploitation and the corresponding environment pollution have called for growing development of sustainable energy-utilization technologies [1]. Thermoelectrics, which can achieve the reciprocal energy conversion between heat and electricity, are one promising candidate [2,3]. However, the wide commercialization of thermoelectrics is limited by the low thermoelectric energy conversion efficiency, evaluated by the dimensionless figure of merit, zT = S 2 σT/κ total . Here, S is the Seebeck coefficient, σ is the electrical conductivity, and κ total represents the total thermal conductivity (accumulation of electron (κ e ) and lattice (κ l ) parts) [4]. S 2 σ is defined as the power factor to evaluate the overall electrical performance. To enhance zT, both high S 2 σ and low κ total are required. Multiple strategies have been developed to enhance S 2 σ of thermoelectric materials, such as carrier concentration (n, n p for holes) optimization [5,6], resonance level engineering [7], band convergence [8][9][10], energy filtering [11], quantum confinement [12], and Rashba effect [13]. Alternatively, hierarchical phonon scattering centers, including point defects, dislocations, stacking faults, dense grain boundaries [14,15], and phase interfaces, can effectively decrease κ l and κ total to achieve high zT values [16,17].
IV-VI tellurides (Ge/Sn/Pb-Te) are promising midtemperature thermoelectric materials due to their relatively high zT values [5,[18][19][20][21]. For example, PbTe-based thermoelectric material has approached the high zT value of 2.2 at 915 K in PbTe-4 mol.% SrTe with 2 mol.% Na [18,22]. However, the high toxicity of Pb limits its practical application. Alternatively, κ l of SnTe is relatively higher which leads to lower zT value of only 1.51 at 800 K [23] comparing with PbTe [18] and GeTe [24]. Therefore, nontoxic and highperformance GeTe-based thermoelectric materials, with the peak zT values higher than 2 [24,25], have attracted extensive attention. To boost the thermoelectric performance of GeTe with good mechanical property and make it suitable for application, rhombohedral GeTe is alloyed with cubic AgSbTe 2 and forms a continuous solid solution, called as Tellurium Antimony Germanium Silver (TAGS-x, written as (GeTe) x (AgSbTe 2 ) 1-x , where x ranges from 0.7 to 0.9) [26,27]. TAGS-85, which can also be written as Ge 0.74 Ag 0.13 Sb 0.13 Te, has approached the highest peak zT (zT max ) of 1.36 at 700 K with good mechanical properties (elastic modulus of 50 GPa and Poisson's ratio of 0.24) [27]. However, the thermoelectric performance of TAGS-85 is still lower than other state-of-the-art thermoelectric materials, such as PbTe [28]. Thus, recent studies of TAGS-85 focus on further improving the thermoelectric performance. Selfdoping achieved by tuning the ratio of Ag/Sb ratio can effectively enhance the zT max value of TAGS-85 up to 1.6 at 750 K [29]. Levin et al. [30,31] reported that the large atomic size and localized magnetic moment of rare-earth elements Dy, Yb, and Ce can increase zT values of TAGS-85. For example, 1% Ce and 1% Yb substitution in Te site can boost up S by 16% to 205 μV K -1 [30], attributed to the localized paramagnetic moment, leading to an enhanced zT max of 1.5 at 700 K.
To better understand the influence of rare-earth element doping on thermoelectric performance of TAGS-85, we selected Nd as the dopant to optimize thermoelectric performance of TAGS-85. As a rare-earth element, Nd as dopant can affect transport properties of thermoelectric materials in many ways: (a) Nd doping in TAGS-85 can result in local lattice distortion due to larger atomic size; (b) multielectron Nd 3+ can affect carrier concentration due to different valence electron counts or influence of the chemical bond [32]; (c) different with large localized magnetic moments of Ce (4f 1 5d 1 6s 2 ) and Yb (4f 13 6s 2 ), Nd (4f 4 6s 2 ) has small localized magnetic effect, which can induce interesting change to S [30,31]. Considering the complex crystal structure of TAGS-85, three cation sites (Ge, Ag, and Sb) can be substitute by Nd (Figure 1(a)). Figure 1(b) compares the formation energy of Nd substitution at different cation sites of TAGS-85. As can be seen, Nd can preferentially substitute Sb due to the lowest formation energy. Here, we design the sample with nominal composition as Ge 0.74 Ag 0.13 Sb 0.13-x Nd x Te (x = 0, 0.02, and 0.04). Figure 1

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Aldrich, Australia), Te (99.999%, Sigma-Aldrich, Australia), Ag (99.99%, Sigma-Aldrich, United States), Sb (99.999%, Alfa Aesar, United States), and Nd (99.999%, Alfa Aesar, United States), were weighed following the nominal compositions. The weighted precursors were sealed in quartz ampules and heated in 1223 K for 12 hours followed by water quenching. The obtained samples were further annealed at 873 K for 2 days and quenched again. This two-step quenching method is designed to reduce Ge vacancies and inhibit the formation of the second phase, Ag 8 GeTe 6 [33]. The resultant products were further ground into powders and sintered into pellets (SPS, 65 MPa and 673 K) for performance measurement. 2.3. Thermoelectric Property Measurement. S and σ of the sintered pellets were simultaneously measured by ZEM-3 (ULVAC Technologies, Inc., Japan). κ total is calculated by κ total = D × C p × ρ, where C p is the specific heat estimated from the Dulong-Petit approximation [34], ρ is the pellet densities measured by Archimedes method, the densities are shown in supporting information Table S1, and D is the thermal diffusivity coefficient measured by the laser flash diffusivity apparatus (LFA 457, Netzsch, Germany). The Hall coefficient (R H ) was measured based on the Van der Pauw technique [35]. n p and hole mobility (μ) were through the equation n p = 1/ðeR H Þ and μ = σR H , where e is the electron charge.

Density Functional Theory
Calculations. Band structures were calculated by using the plane-wave self-consistent field code [36]. A uniform mesh of 2 × 2 × 2k-points was used in sampling integrations over the Brillouin zone.  GeTe (space group R3m) whose structure is a slightly distorted rock-salt structure along the [111] direction [20]. Ge precipitates (purple triangle) were detected as normal due to the nature of easily formed Ge vacancies in GeTe-based thermoelectric materials [37][38][39]. When the Nd doping level reaches as high as x = 0:04, NdTe 2 (yellow diamond) and NdTe 3 (blue square) impurities can be found. Figure 2  The observed reduced σ should be attributed to reduced n p as shown in Figure 3 Figure 5(a), κ total of TAGS-85 slightly decreases after Nd doping. However, with increasing the content of Nd to 0.04, the room temperature κ total increases to 1.76 W m -1 K -1 . To better understand the effect of Nd doping on the thermal transport properties of TAGS-85, κ e and κ l were further calculated as shown in Figures 5(b) and 5(c). κ l was estimated by subtracting κ e from κ total . κ e and the Lorenz number (L) were calculated based on the classic single parabolic band model. As can be seen, κ e decreases from 0.85 to 0.65 W m -1 K -1 at room temperature with increasing the Nd content due to reduced σ. With 2% Nd doping, κ l shows no obvious change. When the Nd doping level further increases to 4% to surpass the solubility limit, the room temperature κ l increases from 0.70 to 1.11 W m -1 K -1 due to additional impurity phases NdTe 2 and NdTe 3 [40].     Figure 5(e) compares the zT max values of this study with previously reported Ce-, Yb-, and Dy-doped TAGS-85 [30,31]. In our study, Nd tends to substitute the Sb site, which is different from Ce, Yb (Te site), and Dy (Ge site). Different occupation sites can result in various effects on electrical and thermal properties. Thus, Nd doping in the Sb site can decrease both the carrier concentration and thermal conductivity. This results in the highest zT value of 1.65 at 727 K. Figure 5(f) presents the reproductivity of Ge 0.74 Ag 0.13 Sb 0.11 Nd 0.02 Te in three cycling tests, suggesting high stability of the Nd-doped TAGS-85.

Conclusion
In this study, we achieve a record-high zT of 1.65 at 727 K in Ge 0.74 Ag 0.13 Sb 0.11 Nd 0.02 Te mainly due to κ total reduction while maintaining high S 2 σ. Reduced κ total should be attributed to reduced σ due to decreased n p . Although reduced n p deteriorates σ, reduced n p also slightly increases S, leading to nearly unchanged S 2 σ. Our DFT calculation suggests that reduced n p is caused by the Nd doping-induced band gap enlargement.
Comparing with other rare-earth elements, Nd is more effective in enhancing the thermoelectric performance of TAGS-85. The Nd-doped TAGS-85 also shows high stability.

Data Availability
All data required to support this study are presented in the paper and the supporting document. Additional data are available upon request from the authors.

Conflicts of Interest
The authors declare that they have no conflicts of interest.