High thermoelectric performance of superionic argyrodite compound Ag

Cite this:J. Mater. Chem. C,2016, 4, 5806

High thermoelectric performance of superionic argyrodite compound Ag

₈

SnSe

₆

†

Lin Li,^aYuan Liu,^bJiyan Dai,^cAijun Hong,^aMin Zeng,^dZhibo Yan,^aJun Xu,^a Dong Zhang,^eDan Shan,^aShilei Liu,^eZhifeng Ren*^band Jun-Ming Liu*^a

A good thermoelectric material usually has a high power factor and low thermal conductivity for high figure of merit (ZT), and is also environmentally friendly and economical. Superionic compounds are heavily studied because of their ultra-low thermal conductivity even though the thermal stability remains an issue.

In this work, we report a superionic argyrodite compound Ag8SnSe6 as a promising mid-temperature thermoelectric material because of its highZTand good thermal stability up to 5501C. It is revealed that Ag8SnSe6exhibits a decent Seebeck coefficient (n-type) and electrical conductivity. At the same time, its thermal conductivity is lower than the glass limit with the thermal capacity CV below 3NkBat high temperature, whereNis the Avogadro’s number andkBthe Boltzmann constant. Detailed microstructural and thermodynamic characterization of this compound is performed to understand the electronic and phononic origins of the thermoelectric properties. The highly random ionic occupations in the cubic phase, leading to the molten silver sublattice and phononic mode softening, are responsible for the very low thermal conductivity andZTB1.1 at 4501C.

I. Introduction

With serious environmental pollution due to high energy demand for fossil fuels, people are eager for increasing energy conversion efficiency and also new and clean energy sources.

Thermoelectric (TE)-based energy-conversion represents one class of the possibilities since it can convert heat into electrical energy andvice versawith no mechanical moving parts and no pollution. TE materials that can work up to 5001C with good performance are ideal for waste heat recovery.¹

It is known that the power output and conversion efficiency of a TE material are governed by the power factor (PF) and figure of meritZT, respectively, where PF =S²sandZT= (PF/ktot)T,Sis the Seebeck coefficient,sthe electrical conductivity,Tthe absolute temperature, and k_tot the total thermal conductivity. k_tot is actually the sum of electronic thermal conductivity (ke), lattice

(phononic) thermal conductivity (kL), and the bipolar effect.^2–4 As a good approximation, thek_ecan be estimated from the Wiedemann–Franz relation k_e = LsT, where Lis the Lorenz number.^2,3Therefore,ZTcan be rewritten asZT=S²/[(1 +k_L/k_e)L]

by ignoring the bipolar effect since it is usually small. It is clear that reducing thek_L/k_eratio can increaseZT,^2,4which can be achieved by lowering the lattice thermal conductivity (k_L) ifk_e remains unaffected.

For suppressing the k_L, phonon-scattering is commonly utilized by nanostructuring the materialsviaintroducing var- ious features such as embedded nanoparticles, superlattices, nanoscale precipitates, atomic defects, grain boundaries, and so on.^2,3,5–8In addition, it is known that some TE compounds may have lattice thermal conductivity close to the glass limit, called the phonon-glasses, due to the structural complexities.

Typical materials include Ba8Ga16Ge30,^9,10Na8Si136,^11,12PbTe–

PbSe(S),^13,14AgSbTe2,¹⁵AgBiSe2,¹⁶CoSb3,¹⁷etc.They have well- connected electron transport networks but very complicated struc- tures, leading to strong phonon scattering. Besides, the interstitials and substitutions in these structures can also seriously scatter phonons.

Superionic compounds are more or less amorphous or liquid- like in structure with superionic mobility.^18–24Typical materials are Cu₂(Se,Te,S),^18–22Ag₂Se,²³etc.First, the ionic occupation is highly disordered with the joint probability density function (JPDF) far below one.²⁴ Second, defects or vacancies in these structures are of atomic size, resulting in a low thermal diffusion coefficient. Third, these randomly occupied ions may move easily

aLaboratory of Solid State Microstructures & Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.

E-mail: liujm@nju.edu.cn; Tel:+86-25-83596595

bDepartment of Physics and TcSUH, University of Houston, Houston, TX 77204, USA. E-mail: zren@uh.edu; Tel:+1-617-552-2832

cDepartment of Applied Physics, Hong Kong Polytechnic University, China

dInstitute for Advanced Materials, South China Normal University, Guangzhou 510006, China

eKey Laboratory of Modern Acoustics (MOE), Department of Physics,

Collaborative Innovation Center of Advanced Microstructure, Nanjing University, Nanjing 210093, China

†Electronic supplementary information (ESI) available. See DOI: 10.1039/c6tc00810k Received 25th February 2016,

Accepted 16th May 2016 DOI: 10.1039/c6tc00810k

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viaatom-vacancy exchange. Therefore, these superionic com- pounds are expected to offer a thermal conductivity lower than the phonon glass limit, and one may name them as phonon liquids while the electron transport networks are maintained for fairly good electrical conductivity. Indeed, for the high-T cubic phase of Cu₂Se, Cu atoms have many equivalent positions in the unit cell, leaving sufficient empty sites and thus relatively low thermal diffusion coefficient belowB0.4 mm²s¹.¹⁸The isometric specific heat C_V is even lower than 3Nk_B where N is the Avogadro’s number and kB the Boltzmann constant.¹⁸ Furthermore, if the anionic sites are properly doped, the lattice thermal conductivity can be further lowered, such as the case of Cu2Se with doping by iodine I into Se.²⁰ However, the struc- ture’s thermal stability is a major concern.^25,26We realized that superionic compounds do not necessarily have high ionic motion/diffusion at the service temperature especially for appli- cations where a small electric field is good enough. Therefore, they could still be considered as good TE candidates.

Superionic compounds have a big family. Argyrodites with a general formula A12y/xx+B^y+Q₆²(A = Cu, Ag; B = Si, Ge, Sn, P, As; Q = S, Se) in the high-T cubic phase are some of the well-known superionic semiconductors.^24,27–33First, they usually possess high ionic conductivity as a result of the cooperative interaction of mobile cation Ag⁺ions between vacancies at high temperature. This feature is quite similar to Cu⁺in Cu2Se, but difference from Cu2Se is the presence of tetragonal BQ4units in argyrodite A12y/xx+B^y+Q62, which form periodic networks. This network-like structure may benefit from additional phonon scattering on one hand and partially prevent the motion of Ag⁺ ions in the lattice on the other hand. Therefore, it is possible that the lattice thermal conductivity of argyrodite A12y/xx+B^y+Q62

can be even lower than that of Cu2Se-based materials but the structural thermal stability may be better.

It is noted that Ag₈SnSe₆changes the structure from thebto gphase atB801C.²⁷The lattice structures of theb-phase and the gphase are presented in Fig. 1.^24,34Theb-phase is orthorhombic with space group Pmn2₁ and is not superionic (Fig. 1(a)).

However, theg-phase has the face-centered-cubic structure with

space groupF%43m(Fig. 1(b)). Thisg-phase can be viewed as the Se²cubic framework in which four tetrahedral [SnSe4]⁴units plus four Se²ions occupy the tetrahedral voids, and the Ag⁺ cations partially occupy the other voids of the framework. For a clearer illustration, we plot separately the Se²framework and the tetrahedral [SnSe₄]⁴units in Fig. 1(c) and (d). In Fig. 1(d), the Ag⁺occupation probability at each site is measured by the colors with the wine color for occupation and the white color for un-occupation. It is clearly seen that all these sites are occupied with quite low probability, allowing Ag⁺cations to move among these sites. This highly random occupation configuration does cause substantial scattering to the phonon transport although the long-range movement of Ag⁺cations may not be kinetically true unless temperature is sufficiently high. It will be shown that for theg-phase Ag8SnSe6, such a movement does not occur until 5501C.

Furthermore, it is noted that Ag8SnSe6among the argyrodites has a relatively high melting point (B6801C).²⁹These species are also environmentally friendly, toxicity free, and economical. Our preliminary calculations and experiments suggested that this compound has a reasonable bandgap and good thermal stability.

In this work, we report our results on the synthesis and character- ization of Ag₈SnSe₆. It will be shown that Ag₈SnSe₆does exhibit extremely low lattice thermal conductivity.

II. Experimental details

2.1. Sample synthesis & structural characterization

Polycrystalline Ag8SnSe6samples were synthesized from high- purity Sn, Se, and Ag in appropriate ratios loaded into quartz tubes at a N2-filled glove box. The tubes were sealed under high vacuum (less than 10² Pa).⁸ Subsequently, the quartz tubes were slowly heated up to 10001C for 24 hours and maintained at this temperature for 12 hours, then cooled down to 5001C for 100 hours and annealed at 5001C for 48 hours. Finally, the as-grown chunks were crushed into fine powder and loaded into graphite dies with an inner diameter of 12.7 mm both inside the N2-filled glove-box. The powder filled graphite dies were taken out of the glove-box and immediately sintered using a home-made dc hot-press machine at 5201C under a hydrostatic pressure of 60 MPa. The eventually obtained Ag8SnSe6samples were cut into thin disks with a diameter of 12.7 mm and a thickness of 1.1 mm for subsequent thermal transport measurements and square- crossed long bars with a dimension of 3 3 12 mm³ for electrical conductivity and thermodynamic measurements.

For structural characterization, the samples were ground into fine powder for X-ray diffraction (XRD) using the Bruker Advanced D8 powder X-ray diffractometer with Cu Karadiation in a reflection geometry operating at 40 kV and 40 mA with temperature between room temperature and 200 1C, so that the structural evolution with the b-g phase transition can be investigated. The structural refinement of the XRD spectrum was performed using the GSAS program.³⁵The microstructural feature was obtained by scanning electron microscopy (SEM, Ultra 55, Zeiss). The possible ultrafine precipitates and high-resolution Fig. 1 (a) Orthorhombic structure of Ag8SnSe6with space groupPmn21.

(b) Cubic structure of Ag8SnSe6with space group F%43m. (c) The cubic structure can be seen as Se²anions forming a cubic framework with four Se²and four tetrahedral [SnSe₄]⁴units inside the tetrahedral voids. (d) The Ag⁺ions are delocalized throughout the cubic structure. The green spheres are selenium, the medium purple spheres are tin, and the fully filled and partially filled wine spheres are Ag⁺.

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lattice details were observed using transmission electron micro- scopy (TEM) with the JEOL 2100F microscope operating at 200 kV.

The TEM specimens were prepared by standard cutting, grinding, dimpling, polishing, and Ar-ion milling procedures on the liquid N₂cooled stage. The sample mass densityDwas measured using an Archimedes method, and shown in Table 1.

2.2. Optical absorption and TE property measurements For detecting the band gap of Ag8SnSe6, the optical reflectance spectra were collected in a near-infrared range (800–2400 nm) using a UV3600 spectrometer equipped with an integrating sphere, and the data for BaSO₄as the 100% reflectance standard.

The gap was estimated by converting the reflectance into absorp- tion ratio according to the Kubelka–Munk (K–M) relationship:

F(R) =a/K= (1R)²/2R, whereRis the reflectance,aandKare the absorption and scattering coefficients.¹³The measuredF(R) data as a function of photon energyEshow a linearly decaying region;

the band gapEgcan be obtained by linear extrapolationF(R) to theE-axis.

For electrical properties, the electrical resistivityr(conductivity s = 1/r) and the Seebeck coefficient S were measured using a commercial TE measuring unit (ZEM-3, ULVAC) in the standard procedure. The Hall coefficient RH measurements were carried out on a quantum design physical property measurement system (PPMS-9, quantum design) with the standard cross geometry, given an electrical current of 5 mA and varying the magnetic field up to 2 T. The carrier densitynand mobilitym_Hwere then evaluated from theR_Hand electrical resistivity data, and shown in Table 1.

For thermal properties, the linear thermal expansion coeffi- cientawas measured on a commercial instrument (DIL 402, Netzsch) at a rate of 51C min¹. A differential scanning calori- meter (DSC) was used to detect the heat absorption and release behaviors, and thermo gravimetric analysis (TG) was employed to probe the mass loss, both as a function of temperatureT. The TG–DSC curves were measured on a commercial system (DSC 404C, Netzsch) with a rate of 101C min¹. At the same time, the sample’s isobaric specific heat CP as a function of T was evaluated by the differential scanning calorimetry (DSC 404 C, Netzsch) following the standard procedure. The thermal diffusiv- ityDas a function of Twas measured on a commercial laser flash system (LFA 457, Netzsch). Consequently, the total thermal conductivity k_totwas calculated byk_tot= DC_Pd, whered is the volume density determined using the Archimedes method.

For evaluating the lattice thermal conductivity (k_L), we measured the longitudinal and transverse sound velocities using the ultrasound technique at room temperature.²⁴The bulk modulus B and shear modulus G were calculated using equationsn_l= ((B+ 4G/3)/d)^1/2andn_t= (G/d)^1/2, wherevlandvtare

the longitudinal and transverse sound velocities. The values of the two velocities and two moduli are shown in Table 1.

It is noted that all parametersC_P,D,a,k_tot,d, andSare the averages from at least four separate cycles under identical con- ditions, and good reproducibility in these measurement is observed.

III. Results and discussion

3.1. Structural and thermal characterization

TheT-dependent XRD spectra of the as-prepared sample are presented in Fig. 2. The standardg-phase Ag8SnSe6diffraction peaks, referred from Joint Committee On Powder Diffraction Standards (JCPDS) card number of #19-1133 for the single FCC structure with space group ofF%43m,²⁷are inserted in Fig. 2(a), while the standardb-phase spectrum from the Inorganic Crys- tal Structure Database number of #95093 for the orthorhombic structure with space group ofPmn2₁²⁷is inserted in Fig. 2(b).

No impurity phase is observed and all the reflections can be indexed precisely by either the g-phase or the b-phase. The structure transition occurs between 80 1C and 90 1C (Tbg) without the two-phase coexistence within theT-uncertainty of B21C. The XRD data are further analyzed using the structure Table 1 Measured Sample mass density D, carrier concentration n, Hall mobility mH, sound velocity nland nt, mean sound velocity nm, Debye temperatureYD, and bulk moduliBandGat room temperature

Material D(g cm³) n10¹⁸(cm³) m_H(cm²v¹s¹) n_l(m s¹) n_t(m s¹) n_m(m s¹) Y_D(K) B(GPa) G(GPa)

Ag8SnSe6 6.87 1.69 905 2977 1711 1900 199 35.6 20.99

Fig. 2 TheT-dependent powder XRD spectra for theg-phase (a) and the b-phase (b). (c) The lattice constants of Ag₈SnSe₆as a function ofT.

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refinement method, and the lattice constants at differentTare plotted in Fig. 2(c). The structural transition atT=TbgB821C is clearly identified. In spite of some uncertainties, for the low-T b-phase, the lattice expands along theb-axis and thec-axis but contracts slightly along thea-axis with Tincreasing untilTbg

at which theb)gstructural transition occurs. A slight lattice expansion in theg-phase with increasingTwas observed too, a reasonable outcome.

We also studied the microstructure and chemical homogene- ity of the room-temperatureb-phase. As shown in Fig. 3(a), the SEM image shows a highly dense and uniform microstructure without micrometer-scale precipitates. On this scale, even no clear grain boundaries can be identified. In order to check the structures at the nanometer scale, we studied the microstructure using high-resolution TEM, shown in Fig. 3(b). We used the Fast Fourier Transform (FFT) of a selected area to analyze the diffrac- tion spots in the reciprocal space, as shown in the inset of Fig. 3(b). The normal direction of the image area is along the [1 2% 3] direction. We look at the three bright spots as circled in% Fig. 3(b): one is from the central spot (0 0 0) and the other two are from the (1 1 1) and (2 1 0) planes. The reciprocal distances% between the central spot and the two sets of planes are 0.201 Ź and 0.283 Ź, respectively, with an angle of 74.21. These identi- fications are consistent with the orthorhombic structure of the low-Tb-phase.

The structural transition atTbgB831C was also identified by the selected area electron diffraction (SAED), shown in Fig. 3(c) and (d). At room temperature, the zone axis is [33 1], and the% reciprocal distance ratio of the two labeled spots from (0 0 0) is B1.68 at an angle of 72.31, implying that the two spots corre- spond to the (0 1 3) and (1 1 0) planes. AtTB1801C, as shown in Fig. 3(d), the zone axis changes to [03 1], and then the ratio of the%

reciprocal distances of the two labeled spots from (0 0 0) becomes B1.67 and the angle is 72.11, which are close to thed-spacing ratio of the (1 1 3) and (2 0 0) planes (the calculated ratio and angle are B1.66 and 72.451, respectively). It is noted that the difference in thed-spacing ratio and the angle between the two phases are very small. The reason is that the room temperature lattice constants O2a,O2b, and c for theb-phase are approxi- mately equal to one and another (less than 2%, as shown in Fig. 2(c)). They are almost identical to the cubic lattice constant for theg-phase atTB1801C.

Besides the structural characterization, the thermal stability of theg-phase is a critical issue. Several as-prepared samples were submitted to TG–DSC measurements and the data are repro- ducible. One set of DSC and TG curves is presented in Fig. 4.

In consistence with the structural change as detected in the XRD data and as reported in earlier works,^27,28a sharp DSC peak at B901C was identified and its left shoulder begins at B831C, indicating the first-order structural transition from theb-phase to theg-phase. No more anomaly above this transition point until 7001C was observed. A sharp DSC peak and rapid TG loss appear above 7001C suggesting that the sample is no longer stable above this temperature.

3.2. Thermal transport properties

Due to theb–gtransition, we only studied the TE properties of theg-phase. The evaluatedCP(T) data are plotted in Fig. 5(a), where two reference lines 3NkBand 2NkBare plotted. The sharp peak marks the b–g transition, noting that the left-shoulder of the peak begins atTbgB 831C and the peak is located at B98 1C. For a solid crystal, the theoretical top-limit (the Dulong–Petit limit) of C_P in the high-T range should be B3NkB. However, the values of C_P(ZC_V) for the g-phase are lower than 3NkBatT44001C, similar to the case of Cu2Se.¹⁸ The difference betweenCPand 3NkBatT44001C is signifi- cant, shown in Fig. 5(b) for clearer illustration, indicating the high disordered lattice vibrations. This may disable some phonon modes, leading to reduced thermal conductivity. An evaluation of CV(T) from CP(T) data was reported,^18,36 and a brief description is given here. We consult the well-known relationship:

CP=Cph+Ce+ 9a²BVT, (1) whereCphis the excitation of the phonon modes,i.e. CV, and Ce,a,B, andVare the carrier contribution to the specific heat, Fig. 3 The SEM image (a) and the high resolution TEM image (b) of

Ag8SnSe6observed at room temperature. The inset in (b) is the Fast Fourier Transformation data from the selected area. The selected area electron diffraction (SAED) patterns at room temperature and 1801C are shown in (c and d) respectively.

Fig. 4 Measured TG–DSC curves indicating theb–gphase transition at B831C and melting/decomposition atB7001C.

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thermal expansion coefficient, bulk elastic modulus, and aver- age volume per atom, respectively. TermCeis small and can be ignored safely.^36,37 The measured a is 2.0 10⁵ K¹ from room temperature to 5851C and 4.4610⁵K¹from 5851C to 6501C. The bulk modulusBfor theb-phase is calculated from the sound velocity data measured at room temperature and it is B35.6 GPa (also shown in Table 1). The value of B for the g-phase would be smaller than this value.³⁸ Therefore, term 9a²BVTin the concernedT-range can be safely ignored too. The evaluated C_V data are plotted in Fig. 5(a) and (b), which are almost identical toCP(T), below 3NkBatT44001C. Such low CV(B0.257 J g¹K¹at 4001C) suggests the superionic nature of theg-phase.^18,22

For a high symmetry crystal or an ionic disorder lattice, all the lattice vibrations can be expressed by one longitudinal and two transverse modes,³⁹ and the CV(T) relation follows the Dulong–Petit law. However, for a liquid, atoms or molecules are not fixed but jump irregularly, preventing the propagation of two transverse waves, and C_V is below the Dulong–Petit limit.³⁹Quite a few so-called PLEC (phononic liquid + elec- tronic crystal) materials, such as Cu₇PSe₆, Cu₂S and Cu₂Se, show their C_V values in-between 3Nk_B and 2Nk_B.^18,22,24 The present Ag₈SnSe₆, with the superionic Ag⁺ behaving like a liquid in the cubic lattice, also has itsC_Vbelow 3Nk_Bin the high-Trange.

The measured D(T) for the g-phase is plotted in Fig. 5(c), showing values as low asB0.2 mm²s¹and weakT-dependence over the wholeT-range. The evaluatedk_tot(T) curve is plotted in Fig. 5(d), which is quite small and only 0.2–0.45 W m¹ K¹ over the whole T-range except the anomalies around the b–g transition. Sincek_tot =k_e +k_L, one needs to discuss the two components separately. The measureds(to be shown below) is not very large, and thus k_e is not crucial as seen from the Wiedemann–Franz lawk_e=LsT. The major contribution tok_tot

is fromk_L. The Debye temperatureY_Dfor theb-phase (not the g-phase) obeys the following equation:²⁴

Y_D ¼ n_mh 2pk_B

6p² V 1=3

n_m¼ 1 3

1 n_l³þ 2

n_t³

1=3

;

(2)

whereVandhare the average volume per atom and the Planck constant, respectively, andn_mis the mean sound velocity which is 1900 m s¹. The as-evaluatedY_Dis 199 K. Theg-phase should have a lowerY_Dthan the low-Tb-phase if the bulk modulusB and shear modulus G in the g-phase are smaller, as argued above. Such a lowY_Dis unusual unless the material is a much less rigid crystal.²⁴It is known that the thermal conductivity at the amorphous limit, as proposed by Cahill, is:^10,40

kmin ¼ p 6

1=3

kBV²⁼³X

i

ni

T Y_i

2ðYi=T 0

x³e^x e^x1dx Y_i¼ðn_ih=2pk_BÞ 6p²

V1=3

;

(3)

here n_iis the sound velocity of the three sound modes (one longitudinal mode and two transverse modes), and Y_i is the corresponding cutoff frequency for these modes. The calculated glassy limit k_min(T) curve from eqn (3) is plotted in Fig. 5(d) (dashed red line). Interestingly,k_min(T) is even higher than the measured k_tot in the high-T range, similar to the cases of Cu7PSe624and Cu2X (X = S, Se, Te)^18,22 etc. Any case with a thermal conductivity lower thank_minimplies that portions of the phonon modes are lost or softened,^18,24,39 making no contributions to the thermal conduction.^18,22,24

Consequently, the ultralowk_Lis attributed to two reasons.

One is the low thermal diffusion coefficient and the other is the ultralow specific heat. The Ag⁺ ions occupy the fixed atomic positions with the random occupancy and may jump from one position to another.²⁴ The minimum distance between the neighboring positions is just of sub-angstrom magnitude, allow- ing strong phonon scattering. The consequent thermal transport is much weaker than that of well-known TE materials such as Bi2Te38,41half-Heusler alloys^6,7and PbTe.⁴²

3.3. Electronic transport properties

The optical absorption data plotted as a function of photon energy are shown in Fig. 6(a), from which we got a band gap of B0.8 eV for the low-Tb-phase Ag8SnSe6, consistent with the reported value of 0.83 eV.²⁸The electronegativities of Ag, Sn, Se are 1.93, 1.96, 2.55, respectively, and the biggest electronegativity difference is 0.62 between Ag and Se elements. According to the empirical criteria,^2,3a favored TE material should have a band gap ofB10kBT(B0.62 eV atTB4501C) and the electronegativity differences should be as low as 0.5. It is expected that the high-T g-phase would have a favourable band gap, just like other super- ionic conducting materials with good TE properties.¹⁸

The measured s(T) data are shown in Fig. 6(b). The rapid change aroundTbgis reasonable, while a monotonous decrease of s(T) with T slowly from 205 S cm¹ to 175 S cm¹ was Fig. 5 (a) Measured C_P(T) and C_V(T) curves. The high-T data are

re-plotted in (b) for clearness. The dashed dark-yellow line and the dashed green line are the Dulong–Petit limit forCVand the lowest theoretical value of CV in a liquid, respectively. The measured thermal diffusive coefficientD(T) data are plotted in (c), and the measured total thermal conductivity (ktot) and the glass limit lattice thermal conductivity (kmin) are plotted in (d).

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observed. The Seebeck coefficientS(T), presented in Fig. 6(c), gradually increases from136mV K¹to180mV K¹withT.

The negative S and its dependence on T indicate an extrinsic semiconducting behavior with electrons as charge carriers, without a sign of contribution from the dipolar effect. Fig. 6(d) is the plot of PF as a function ofT, which first falls fromB550mW m¹K²in theb-phase and then increases up toB575mW m¹K²in the g-phase. Such PF values are relatively high in comparison with other superionic TE materials such as Cu₂X (X = S, Se, Te),^18,22 considering its large electronegativity difference (B0.62) and bandgap (B0.8 eV).

3.4. ZTand discussion

Eventually, we calculate theZTas a function of Tand the results are plotted in Fig. 7. Apart from a big change around theb–g transition, the ZT value increases withTat T 4 1001C, and reachesB1.1 atTB4501C. This ZTcan be probably further enhanced by further optimization,e.g.by band structure opti- mizationviacarrier substitution and microstructural processing, allowing even better TE performance.

Finally, we have also performed thermal stability testing of the as-prepared samples. The testing was carried outviatwo ways.

First, the fresh samples were submitted to thermal cycling and the TE properties were measured between two consecutive cycles.

The TE properties for four consecutive cycles remain identical within the measuring uncertainties. Second, the samples were submitted to thermal annealing at 4501C in the He atmosphere of 0.01 MPa for 7 days (168 hours) and then the microstructures and TE properties of the samples were characterized. The XRD data, SEM images, and chemical composition data of the annealed sample are shown in the ESI†(Fig. S1–S3). It is seen that the crystallinity, microstructures, and compositions of the annealed samples are quite similar to those of the fresh samples.

The data of TE properties of the fresh samples after the four consecutive cycles and the annealed samples are plotted in Fig. 8(a)–(d). Clearly, parameterss,S, andk_totdata before and

Fig. 6 Measured optical absorption spectrum (a), electrical conductivity s(b), Seebeck coefficientS(c), and power factor PF (d). The optical band-gap is evaluated by the best fitting using the Kubelka–Munk (K–M) function.

Fig. 7 The temperature dependentZTcurve.

Fig. 8 Measured TE parameters as a function of Tfor the fresh sample after four consecutive measuring cycles (before annealing) and the ther- mally annealed sample at 4501C for 168 hours in the He atmosphere (after annealing): (a) electrical conductivity s(T), (b) Seebeck coefficient S(T), (c) power factor PF(T), and total thermal conductivityk_tot(T).

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after the thermal annealing show no significant difference within the measuring uncertainties, suggesting that the thermal stability of the TE properties of this compound is quite good. This also allows us to suggest that the superionic transport may not occur if temperature is not very high in spite of the nature of the superionic structure with the Ag⁺liquid-like behaviour. The kinetically active superionic transport may appear above 500 1C, allowing this compound to be a good mid-TTE material up to this temperature.

IV. Conclusions

We have successfully synthesized an n-type superionic TE compound Ag₈SnSe₆ using the hot-press sintering technique, and carefully characterized the microstructure, optical bandgap, and the TE properties. It is revealed that the thermal conductivity of theg-phase above 2001C is below the glass limit due to the isometric specific heat (C_V) below 3Nk_Band the ultralow thermal diffusion coefficient. The g-phase Ag8SnSe6 appears to be a superionic semiconductor with a molten Ag⁺¹sublattice leading to a softening of the phonon modes and thus low thermal conductivity. At the same time, theg-phase Ag8SnSe6also has good TE performance including a PF ofB570mW m¹K²and aZTof B1.1 at 4501C. It is concluded that Ag8SnSe6could be a promising TE material in the intermediate temperature range.

Author contributions

L. Li and J. M. Liu designed the research; L. Li and Y. Liu performed the XRD, optical reflectance spectra, thermoelectric parameters and specific heat experiments; J. Y. Dai performed the TEM experiment; S. L. Liu and D. Zhang performed the sound velocity experiments; D. Shan and J. Xu performed the Hall experiment; L. Li, A. J. Hong and J. M. Liu analysed the experiment data; L. Li, Z. F. Ren and J. M. Liu wrote the paper.

Acknowledgements

We thank Shanghai Application Lab of NETZSCH Company for the linear expansion coefficient measurement. This work was supported by the National 973 Projects of China (Grant No.

2015CB654602), the Natural Science Foundation of China (Grant No. 51301084, 51431006, and 11374155), the Natural Science Foundation of Jiangsu, China (Grant No. BK20130576), the Program B for Outstanding PhD Candidate of Nanjing University, and ‘‘Solid State Solar Thermal Energy Conversion Center (S³TEC)’’, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Science under award number DE-SC0001299.

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