n-Type thermoelectric metal chalcogenide (Ag,Pb,Bi)(S,Se,Te) designed by multi-site-type high-entropy alloying

A metal chalcogenide (Ag,Pb,Bi)(S,Se,Te) with an NaCl-type structure was designed by multi-site-type high-entropy alloying (MST-HEA), and the thermoelectric properties were investigated. In this material, both cation and anion sites were alloyed and thus its total entropy of mixing ΔS mix (total) achieved 2.00R (R: gas constant). It was found that present sample is an n-type semiconductor with ultra-low lattice thermal conductivity (κ L) of 0.62 Wm−1K−1 at room temperature and 0.46 Wm−1K−1 at T = 723 K. Very low κ L and good power factor resulted in figure of merit of 0.54 at T = 723 K. IMPACT STATEMENT We report on the material design synthesis and thermoelectric properties on new high-entropy alloy-type compound with an NaCl-type structure (Ag,Pb,Bi)(S,Se,Te)


Introduction
Thermoelectric generators have attracted much attention due to their direct conversion of heat into electricity vice versa. The conversion efficiency of a thermoelectric material depends primarily on the dimensionless figure of merit, ZT = (S 2 Tρ −1 κ total −1 ), where S, T, ρ and κ total are the Seebeck coefficient, absolute temperature, electrical resistivity and thermal conductivity, respectively [1]. κ total has two main components, namely κ e and κ L , which are carrier and lattice thermal conductivity, respectively. To realize the high ZT value, it is obvious that low ρ and high S are essential, although they depend on the carrier concentration and contradict each other. Another main strategy is realization of low κ L because κ L is independent of the electronic properties.
Metal chalcogenides (MCh) such as lead chalcogenides (PbTe, PbSe, PbS) have extensively studied as a thermoelectric system available at medium temperature (500-900 K) range [2][3][4]. The attempts to enhance the thermoelectric properties of MCh have been made by nano-structuring [5] and phase solution of pseudobinary PbTe-PbSe [6][7][8] and ternary PbTe-PbSe-PbS [9,10] alloys, which achieve low κ L and lead to improvements in power factor by band convergence [1,6,7]. In Supplemental data for this article can be accessed here. https://doi.org /10.1080/21663831.2021.1929533 addition to the above-mentioned strategy, the introduction of bonding heterogeneity and the enhancement of lattice anharmonicity have been reported in AgPbBiSe 3 [11] with quite low κ L of 0.50 Wm −1 K −1 at room temperature and 0.41 Wm −1 K −1 at 818 K. The fundamental origin of this ultra-low κ L is originated from the synergistic presence of bonding heterogeneity and lattice anharmonicity arising from 6s 2 lone pairs of Bi and Pb [11].
As a brand-new method of alloying, high-entropy alloys (HEAs) have attracted much attention in the fields of materials science and engineering because of their tunable properties as structural materials, such as excellent mechanical performance under extreme conditions [12,13]. HEAs are typically defined as alloys containing at least five elements with concentrations between 5 and 35 at%, resulting in high configurational mixing entropy ( S mix ), defined as S mix = -R i c i lnc i , where c i and R are the compositional ratio and the gas constant, respectively [13]. Most of HEA materials are structurally simple alloys with bcc, α-Mn, CsCl, and hcp crystal structures have mainly been studied so far [12][13][14]. Thus far, we have extended the concept of HEA to compounds, for instance layered structure and non-layered compounds of NaCl-type metal chalcogenide, as superconductors with high S mix [15][16][17][18][19][20][21][22]. Furthermore, as an efficient way to increase total entropy of mixing, we proposed multi-site alloying of compounds and its evaluation way by summing the entropy of mixing at each alloying site [20]. A higher S mix , which exceeds the typical S mix for equimolar 6 elements for single site, is achieved by this method. It is well known that alloying is the effective way to reduce κ L due to the enhancement of scattering of phonons by lattice disorder [8,23]. Based on this fact, the high-entropy alloying by the multi-site alloying method also could be the effective way to reduce the κ L , for instance, by introducing the severe lattice distortion [24].
As HEA thermoelectric materials, AlCoCrFeNi [25] was first reported by Shafeie et al. in 2015. However, the ZT values are low due to the high σ , low S and high κ. After the report, some papers incorporating the HEA concept into thermoelectric materials have been reported: such as half-Huesler; NdFeSb-based [26], Ti 2 NiCoSnSb [27] and MCh; AgSnSbSe 3−x Te x [28]. Among them, AgSnSbSe 3−x Te x exhibited high ZT values of 1.14 at 723 K as p-type thermoelectric materials. Very recently, n-type MCh of Pb 0.99−y Sb 0.012 Sn y Se 1−2x Te x S x was reported with significantly high ZT values of 1.8 at 900 K [29]. On this basis, we aimed to synthesize new NaCl-type MCh with higher S mix value.
In this letter, we synthesized a high-entropy alloy-type (Ag,Pb,Bi)(S,Se,Te) by inducing alloying an anion site of n-type AgPbBiSe 3 with low κ L . Hereafter, we denote the concept that alloying multiple crystallographic site as 'multi-site-type high-entropy alloying (MST-HEA)'. We successfully synthesized MST-HEA (Ag,Pb,Bi)(S,Se,Te) with highest S mix (total) value of 2.00R as a thermoelectric material to the best of our knowledge. It was found that the present sample was an n-type semiconductor with ultra-low κ L of 0.62 Wm −1 K −1 at room temperature, and it reached 0.46 Wm −1 K −1 at 723 K. Compared to AgPbBiSe 3 , the present sample exhibited lower ρ without large decrease of S, resulted in the enhancement of power factor and ZT. Our results indicate that the MST-HEA MCh could be a promising n-type thermoelectric material.
To obtain high-density samples, hot pressing was performed at 400°C for 30 min under a uniaxial pressure of 70 MPa, and subsequently, the furnace was cool down. The density of hot-pressed sample was estimated from its weight and size. The relative density of sample was 97.4%. The actual composition was analyzed by energydispersive X-ray spectroscopy (EDX) on a TM-3030 (Hitachi Hightech) equipped with an EDX-SwiftED analyzer (Oxford). The phase purity and the crystal structure of the Ag 0.25 Pb 0.50 Bi 0.25 S 0.40 Se 0.50 Te 0.10 sample were examined by powder synchrotron XRD with an energy of 25 keV (λ = 0.495395 Å) at the beamline BL02B2 of SPring-8. The synchrotron XRD experiments were performed at room temperature with a sample rotator system, and the diffraction data were collected using a high-resolution one-dimensional semiconductor detector MYTHEN [Multiple mythen system] [30] with a step of 2θ = 0.006 o . The crystal structure parameters were determined by Rietveld analysis using the RIETAN-FP [31]. The crystal structure was depicted using VESTA [32].
To investigate the thermoelectric properties of sample, the electrical resistivity (ρ) and the Seebeck coefficient (S) were measured using the four-probe method under a helium atmosphere with a ZEM-3 (Advance Riko) instrument. The κ total was calculated using the equation κ total = DC p d s , where D, C p and d s are the thermal diffusivity, specific heat and sample density, respectively. D was measured by the laser-flash method with a TC1200-RH (Advance Riko) instrument. The C p value of 0.20 Jg −1 K −1 was obtained from the Dulong-Petit model, C p = 3nR, where n is the number of atoms per formula unit and R is the gas constant. Noted that the actual C p values of PbTe and PbSe increase few percent at high temperature [33,34], implying that the present C p value could also be increased few percent at 723 K. Hall coefficient was measured using a physical property measurement system (PPMS, Quantum Design) at room temperature.

Results and discussion
Powder XRD patterns for Ag 0.25 Pb 0.50 Bi 0.25 S 0.40 Se 0.50 Te 0.10 are shown in Figure 1. Although the peaks showed slightly asymmetry, the single-phase and no peak split were observed, indicating the homogeneity of the sample. Note that different compositional ratio of samples resulted in phase separation or inhomogeneity of the composition (Supplemental Fig. S1), thus we report the thermoelectric properties of above compositional sample which showed the best homogeneity. It has been reported that Pb(S/Te) with NaCl type has very low atomic solubility [35]. In this study as well, homogeneity sample was obtained with a composition in smaller ratio of Te than S, in which S and Te were 40% and 10%, respectively. XRD peaks of the phase can be indexed by the NaCl-type structural model (space group: Fm3m, #225). Lattice constant is estimated as 5.94858(5) Å. No compositional segregation was detected by EDX mapping (Fig. S2). The average chemical composition of the obtained sample is estimated as Ag 0.257(10) Pb 0.508 (24) Bi 0.235(9) S 0.360(17) Se 0.520 (7) Te 0.120 (14) . The obtained composition is almost same as the nominal composition, within the error of the equipment, thus to simplify, we call the sample Ag 0.25 Pb 0.50 Bi 0.25 S 0.40 Se 0.50 Te 0.10 in this study. To estimate total S mix for our sample, S mix for both anionic and cationic sites were separately calculated using actual compositions. Subsequently, we took the sum of those values to obtain total S mix according to the following formula, which is based on our new concept of evaluating S mix (total) in compositionally and crystallographically complicated compounds [20].
where n is the number of crystallographically independent sites in the unit cell. Here, S i mix is calculated by where N and x i are number of the component at the mixed site and the atomic fraction of the component, respectively. According to the above formula, present sample possesses S i mix (cation Site) = 1.03R and S i mix (anion site) = 0.96R, respectively (see inset of Figure 1). Finally, S mix (total) = 2.00R can be obtained. Let us mention that a similar situation has already been seen for CsCl-type superconductors (Sc,Zr,Nb,Ta) 0.65 (Rh,Pd) 0.35 reported by Stolze et al [36] and NaCl-type MCh [22,28,29]. The obtained S mix exhibited the highest S mix (total) value among all HEA thermoelectric materials. A schematic image of crystal structure for MST-HEA MCh is shown in inset of Figure 1 together with its mother compound of PbSe. Figure 2(a) shows the temperature dependences of ρ and S above room temperature with the data of AgPbBiSe 3 (Ag 1/3 Pb 1/3 Bi 1/3 Se) [11] as a reference. Compared to the upturn behavior of ρ for Ag 1/3 Pb 1/3 Bi 1/3 Se, that for Ag 0.25 Pb 0.50 Bi 0.25 S 0.40 Se 0.50 Te 0.10 linearly increased with increasing temperature, and the magnitude value was less than four times at around room temperature. The ρ values for present sample and Ag 1/3 Pb 1/3 Bi 1/3 Se were 8.0 m cm and 17.3 m cm at around 723 K, respectively. To discuss the suppression of ρ with the actual carrier concentration, Hall effect measurement was performed at room temperature. The Hall coefficient (R H ) exhibited negative value, indicating the electron carrier is dominant. The estimated carrier concentration was 8.04 × 10 19 cm −3 , which is larger than that of 1.44 × 10 18 cm −3 for Ag 1/3 Pb 1/3 Bi 1/3 Se, indicating that the suppression of ρ is caused by increase of carrier concentration possibly due to the deficiency. Considering the increase of electron carrier, the deficiency of chalcogen elements and/or Ag 1+ is possible. On the other hand, carrier mobility of present sample (μ = 18.52 cm 2 V −1 s −1 ) became lower than that of Ag 1/3 Pb 1/3 Bi 1/3 Se (μ = 273.07 cm 2 V −1 s −1 ). Lowering of mobility can be attributed to the increase of randomness by alloying and/or increase of carrier concentration. A negative value of the S also indicates the n-type polarity of the sample (Figure 2b). The magnitude of the S increased with increasing temperature. Unlike the ρ behavior, the S exhibited almost same trend as the reference and both values are close.  shows the temperature dependence of κ total . Very low κ total of less than 0.75 Wm −1 K −1 is obtained at room temperature, which decreased with heating to 0.61 Wm −1 K −1 at 723 K. The κ L was determined by subtracting the electronic thermal conductivity (κ e ) from κ total (Figure 4b). κ e was estimated using the following Wiedemann-Franz law, κ e = LTρ −1 , where L is the Lorenz number and estimated using an equation L = 1.5 + exp(-|S|/116) [37]. The value of κ L at room temperature is around 0.62 Wm −1 K −1 and decreased to 0.46 Wm −1 K −1 at T = 723 K. Noted that the actual C p values of PbTe and PbSe increase few percent at high temperature [33,34], implying that the present C p value could also be increased few percent at 723 K. Contrast to the small temperature dependence of κ L in Ag 1/3 Pb 1/3 Bi 1/3 Se, the decrease of κ L with increasing temperature indicates that the phonon scattering process is dominated by the Umklapp scattering process. Although the κ L at room temperature showed some difference, they became almost same value at 723 K. In Ag 1/3 Pb 1/3 Bi 1/3 Se [11], the fundamental origin of this ultra-low κ L was explained by the synergistic presence of bonding heterogeneity and lattice anharmonicity arising from 6s 2 lone pairs of Bi and Pb. They revealed the existence of bonding heterogeneity, which is due to the presence of weak and strong bonding between the Se anion and cation with different electropositivity, using the firstprinciples density functional theory and electron localization function. In addition, the presence of 6s 2 lone pair electrons around Pb and Bi fosters the lattice anharmonicity, which also contributes the reduction of low lattice thermal conductivity. Considering the similarity between the Ag 1/3 Pb 1/3 Bi 1/3 Se and present sample, we presumed the ultra-low κ L for present sample is realized by the same situation. Compared to Ag 1/3 Pb 1/3 Bi 1/3 Se, the present sample exhibited slightly higher lattice thermal conductivity, which is possibly due to the inclusion of lighter element of S with 40% in anion site. Note that, considering the inclusion of both lighter and heavier elements of S with 40% and Te with 10% in anion site, the suppression and enhancement of lowering for thermal conductivity also coexists. This might result in the similar values of κ L between Ag 1/3 Pb 1/3 Bi 1/3 Se and the present sample. In any case, various synergistic effects, different atomic weight, chemical disorder, solid-solution effect and bonding heterogeneity due to the introduction of MST-HEA would contribute to the suppression of κ L . Further investigation for the quantification of the above components and the HEA effect in thermoelectric properties would be required for the development of HEA-type thermoelectric materials, for instance the systematic tuning of atomic weight with same S value. Figure 4(a) shows the temperature dependences of the power factor (S 2 ρ −1 ). The power factor increases with increasing temperature and reaches the maximum value of 4.4 μWcm −1 K −2 at 723 K. The power factor of the sample exhibited over two times higher value within the measured temperature range. Contrast to the close value of S for both results, the around one-third of decrease of ρ for the obtained sample results in the enhancement of power factor. Figure 4(b) shows the temperature dependences of ZT. Relatively high ZT value of 0.54 was obtained at 723 K. The ZT value of the present sample exhibited higher than that of the reference at the measured temperature range.

Conclusion
We have synthesized polycrystalline sample of new multisite-type high-entropy alloyed (MST-HEA) metal chalcogenide Ag 0.25 Pb 0.50 Bi 0.25 S 0.40 Se 0.50 Te 0.10 with an NaCltype structure using conventional solid-state reaction. For present sample, S mix reached 2.00R, which exceed ideal value of S mix = 1.79R for the single-site alloying with six different elements. The concept of MST-HEA in complicated compounds would be useful to develop new HEA-type thermoelectric materials with very high entropy of mixing. The Seebeck coefficient (S) and Hall coefficient demonstrated the nature of n-type polarity for the present sample. Compared to the upturn behavior of electrical resistivity (ρ) for Ag 1/3 Pb 1/3 Bi 1/3 Se, the ρ linearly increased with increase in temperature for MST-HEA sample and the ρ was suppressed approximately one quarter than that of Ag 1/3 Pb 1/3 Bi 1/3 Se without large decrease of S, resulted in the enhancement of power factor. The ultra-low κ L around 0.62 Wm −1 K −1 at room temperature and 0.46 Wm −1 K −1 at T = 723 K were achieved possibly due to the synergistic presence of bonding heterogeneity and lattice anharmonicity arising from 6s 2 lone pairs of Bi and Pb. The ultra-low κ L and relatively high ZT value suggest that this new MST-HEA MCh could be the promising candidate as an n-type thermoelectric material by further investigation of carrier tuning.

Disclosure statement
Experimental data are available via reasonable requests to the corresponding author. No potential conflict of interest was reported by the author(s).

Funding
This work was supported by JST-CREST (JPMJCR20Q4) and the Tokyo Metropolitan Government Advanced Research (H31-1).