During the past years, metal sulfide Ag₂S has attracted much attention due to its excellent physical and chemical properties that enable it with various applications in fields of catalysis, sensing, optoelectronics and so on^{[1,2,3,4,5,6]}. For example, Dong, et al^[7] reports Ag₂S-nanowire is an ideal candidate for making nano temperature and photoelectric sensors as its photoconductivity is always positive under 532 or 1064 nm laser radiation. Du, et al^[8] declares Ag₂S Quantum Dots may act as nontoxic carrier for potential in vivo bioimaging. Zhang, et al^[9] confirms that the Ag₂S Quantum Dots indeed open up the possibility of in vivo anatomical imaging and early stage tumor diagnosis owing to their high emission efficiency in NIR-II imaging window. Besides, Ag₂S is also found suitable for solar cell and infrared sensitivity device fabrication attribute to its semiconductor character which has a ~1.0 eV band gap^[10]. Recently, it is announced that Ag₂S exhibits a fantastic room-temperature ductile behavior. Its compression deformation can reach 50%, the bending variable surpassing 20%, and the stretching variable up to 4.2%. These shape variables are far more than known ceramic and semiconductor materials, and are equivalent to the mechanical properties of some metals. Consequently, Ag₂S provides a possibility is quest of producible inorganic semiconductors/ceramics for flexible electronic devices^[11].

In order to develop more interesting functions of Ag₂S, the authors focus on its potential thermoelectric (TE) behavior according to the concept of Seebeck-Peltier effect^[12]. The TE device can supply green and reliable energy by direct conversion of heat into electricity. Thus, it is expected to have wide applications in power generation. The efficiency of a thermoelectric material is usually evaluated by the dimensionless figure of merit ZT, ZT= (S²Tσ)/κ. Where S is Seebeck coefficient, T is absolute temperature, σ is electrical conductivity and κ is thermal conductivity^[13]. From the view of this formula, it is obvious that the TE material with ultra-low thermal conductivity is one of a significant factor for high ZT. Based on this recognition, the TE behavior of Ag₂S is worthy of study as it has very small thermal conductivity. Wang, et al^[14] have fabricated Ag₂S ceramic using a solution method and the thermal transport analysis indicates that its total thermal conductivity is 0.4- 0.6 W·m^-1·K^-1 in range of 300-600 K, which is lower than most solid TE materials. Ultimately, a maximum ZT=0.55 (580 K) is obtained which implies that Ag₂S is a promising middle-temperature TE material. In present work, a zone melting method which has the advantage of purifying materials is introduced for Ag₂S compound fabrication. Its electrical/thermal transport properties are systematically investigated and the final figure of merit ZT is demonstrated.

99.999% high purity Ag and S elements were used as start materials for Ag₂S synthesis, they were weighed in accordance with the standard stoichiometric ratio and the total weight was about 60.5 g. The start materials were loaded into a ϕ18 mm quartz ampoule and then sealed with a vacuum less than 10^-2 Pa, after that, the quartz ampoule was placed into a 1000 ℃ rocking furnace. After Ag and S totally melted, the rocking system worked at a rate of 20 r/min for 30 min to enhance Ag₂S synthesis homogeneity. Ultimately, Ag₂S compound was obtained as the furnace was cooled to room temperature naturally. Subsequently, the synthesized Ag₂S raw material with the same ampoule was put into a homemade zone melting furnace. The ampoule was supported by a Al₂O₃ pedestal and a pair of thermal-couples was installed near the bottom for temperature indication. Fig. 1(a) shows the schematic diagram of the zone melting furnace which was heated by a couple of Si-Mo heaters to form a narrow high temperature zone. Fig. 1(b) is the temperature profile along vertical direction, the temperature gradient for Ag₂S solidification was about 30-35 ℃/cm. The furnace temperature was controlled at 920 ℃. After Ag₂S raw material was melted, the quartz ampoule was lowered down at the speed of 3.0 mm/h until all solution was exhausted. The parameters for Ag₂S solidification are summarized in Table 1.

The density ρ was measured by Archimedes principle. Phase structure of the material was analyzed by X-ray diffraction (XRD, Bruker D8, Germany) using Cu Kα radiation (λ=0.15406 nm) at room temperature. The morphological and chemical composition were investigated using Scanning Electron Microscope (SEM, JSM-6610, JEOL Ltd.) and Energy Dispersive Spectroscopy (EDS, JED-2300T) equipment. The Seebeck coefficient and electrical conductivity were measured simultaneously (ULVAC-RIKO ZEM-3) from 300 to 650 K. The thermal diffusivity D was tested by laser flash method (Netzsch, LFA-457, Germany). The total thermal conductivity κ was obtained using κ=D·ρ·C_p, where C_p is specific heat capacity.

The as-grown Ag₂S ingot (ϕ18 mm× 50 mm) is easily separated from quartz ampoule and displays bright metallic luster, as Fig. 2 shows. Such phenomenon indicates that Ag₂S has none reaction with quartz ampoule during the whole process. Its density is measured to be 7.20 g/cm³ that is nearly 100% close to the theoretical value 7.23 g/cm³. Fig. 3(a) is the XRD pattern of Ag₂S powder, it is observed that all diffraction peaks are matched well to those of standard α-Ag₂S monoclinic P2₁/c space group (PDF#14-0072) at room temperature. The lattice parameters a, b and c are calculated via a general structure analysis system, and the values are 0.4251, 0.6962 and 0.7873 nm, respectively. EDS measurement implies the atom percent of Ag is 67.2% and S is 32.8% in matrix that agrees well with the standard stoichiometric composition of Ag₂S, as Fig. 3(b) shows.

During SEM testing, it is interesting that some micro size particles oozed from the material. Fig. 4(a) shows the original Ag₂S surface under 25 kV voltage. However, in a very short time, numerous white particles came up and then gradually grew up for about 30 s, as Fig. 4(b,c) demonstrating. Thereafter, the particle sizes are kept stable. EDS analysis reveals the particle composition is 100% Ag. This result is mainly attributed to the special liquid-like character of Ag₂S. As previous literature^[15] reported, Ag ions are weakly bonded to the neighbour atoms in silver chalcogenides Ag₂M (M=S, Se, Te) semiconductors, and apt to migrate from one site to another if there is sufficient energy force on them. For example, the external heat or voltage are both able to drive Ag ions movement. Therefore, it is easy to understand the high energy electron beam in SEM system plays a significant role causing the deposition of Ag. In fact, similar metal element deposition is also noticed in other type of liquid-like materials, such as Cu₂Se, Cu₂S, Ag₈SnSe₆ and so on^[16,17,18].

As for thermoelectric property evaluation, sample 1# for electrical transport measurement is cut parallel to Ag₂S solidification direction, and sample 2# for thermal transport testing is processed along perpendicular orientation, as the insert in Fig. 5(a) shows. Here, we should note that such sample processing modes are widely adopted in other zone melting thermoelectric materials, such as Bi₂Te₃, SnSe, etc^[19,20]. In Fig. 5(a), the relationship of temperature with Seebeck coefficient S is displayed. It is found that negative S that means Ag₂S is a n-type semiconductor. This conductive behavior might be due to the Ag interstitial ions in crystal structure that act as donor impurities providing additional electrons^[14]. Near room temperature, S is about -1200 µV·K^-1. As the temperature increased to 440 K, S linearly deceased to -680 µV·K^-1. However, when temperature continuously increased to 450 K, S undergoes a sharp decline and the value is around -100 µV·K^-1. This dramatic change is mainly attributed to the phase transition of Ag₂S. Below 450 K, the material has an α-Ag₂S monoclinic structure. Nevertheless, it would transfer to β-Ag₂S body centered cubic structure as temperature surpasses 450 K. After that, S maintains a relative stable state regardless the increasing of temperature to 650 K. Fig. 5(b) shows the dependence of conductivity σ on temperature. It is amazing that the σ of α-Ag₂S is almost zero before 450 K. However, the σ value sharply jumps to ~40000.5 S·m^-1 as the material just finishes phase transition. Then, σ gradually deceases to 33256.2 S·m^-1 near 650 K. Fig. 5(c) exhibits power factor PF vs temperature that calculated from PF= S²σ. It is observed that the PF of α-Ag₂S is much poor because of its weak conductive property. As for β-Ag₂S, PF is practically a constant ~6 µW·cm^-1·K^-2 in temperature range of 450-650 K.

In order to better understand the electrical transport behavior of Ag₂S, the Hall properties are also characterized. Fig. 6(a) shows the temperature dependence of carrier concentration n_H. Near room temperature, the n_H value is on level of ~10¹⁷ cm^-3. Then, as temperature is increased to the threshold of phase transition, n_H is climbed to ~10¹⁸ cm^-3. This phenomenon is mainly due to the increase of carrier concentration from valence band to conduction band when temperature is added. As expected, when Ag₂S is transformed from monoclinic to body centered cubic structure, n_H is increased suddenly to ~10¹⁹ cm^-3 near 450 K. Later, a growing number of carriers are generated in β-Ag₂S, and n_H rises to a highest ~10²⁰ cm^-3 level at 650 K. Fig. 6(b) is the carrier mobility µ_H diagram varied with temperature. Similar to carrier concentration, µ_H has a dramatic jump during phase transition. Besides, it is noticed µ_H is always declined when it is in α-Ag₂S and β-Ag₂S states, respectively. The maximum µ_H= 161.6 cm²·V^-1·s^-1 happens at the moment as Ag₂S finishes phase transition.

As for thermal transport property, the relationship of total thermal conductivity κ with temperature is given in Fig. 7. When Ag₂S is in monoclinic structure, κ is 0.20 W·m^-1·K^-1 at room temperature and is 0.21 W·m^-1·K^-1 near 400 K. Here it is necessary to mention that the thermal conductivity is deduced from the measured thermal diffusion coefficient and then approximately calculated through Dulong-Petit law. Thus, there may be certain errors to the accurate κ of the material. However, the result indicates that the thermal conductivity of α-Ag₂S is indeed ultralow and very stable. In α-Ag₂S, 2 S atoms and 6 Ag atoms form weak chemical bonds along (100) plane. Thus, α-Ag₂S would show low phonon vibration frequency because of the weak binding force of S to Ag^[11]. As a result, the low-frequency optical branch dominated by Ag atoms can strongly scatter lattice phonons which have similar frequency. This is the key reason why α-Ag₂S has ultra-low thermal conductivity. When α-Ag₂S turns to β-Ag₂S, κ is quickly increased and keeps steady between 450-600 K and the value is ~0.45 W·m^-1·K^-1. It should be noted that the sulfur element might have slight volatilization during experiment. However, the effect of possible sulfur loss on thermoelectric properties is negligible, as the Ag₂S hardly allows stoichiometric deviation of 2∶1 according to the Ag-S phase diagram. Even though any sulfur loss takes place, the excessive Ag would precipitate on the sample surface to maintain Ag₂S composition stability.

Ultimately, the temperature dependence of ZT is displayed in Fig. 8. Due to the extremely weak electrical transport property, α-Ag₂S has very small ZT although its thermal transport is quite low. Nevertheless, the ZT of β-Ag₂S is about 0.35 at 450 K and reaches 0.57 near 600 K. The present maximum ZT is comparable to that of Ag₂S fabricated by melting method (ZT=0.55, 580 K)^[14], and is on the same level compared with other Ag-based materials, such as Ag₂Se, Ag₂Te, CuAgSe and so on^[21,22,23]. This result verifies that such metal sulfide Ag₂S is a potential low-temperature thermoeletric material. In the future, Ag₂S with element doping is suggested to do help for thermoelectric property improvement.

A ϕ18 mm×50 mm Ag₂S ingot was fabricated using zone melting method. It undergoes a phase transition from α-Ag₂S monoclinic P2₁/c space group to β-Ag₂S body centered cubic structure near 450 K, which has remark influence on its electrical and thermal properties. Ag₂S is a n-type semiconductor as the Seebeck constant S is always negative. The PF of α-Ag₂S is much poor because of the weak conductive behavior, but the value would suddenly jump to ~6 µW·cm^-1·K^-2 when phase transition happens. The κ of α-Ag₂S and β-Ag₂S are ~0.20 W·m^-1·K^-1 and ~0.45 W·m^-1·K^-1, respectively. Finally, Ag₂S displays a largest ZT= 0.57 near 580 K that means it might be a potential middle-temperature TE material.