1 TRANSPORT PHENOMENA IN SUPERIONIC ...

TRANSPORT PHENOMENA IN SUPERIONIC NaхCu2-хS (х = 0,05; 0,1; 0,15; 0,2) COMPOUNDS By M. Kh. Balapanov1, R.Kh. Ishembetov1, K.A. Kuterbekov2, M.M. Kubenova2, R.F. Almukhametov1, and R.A. Yakshibaev1 1

2

Bashkir State University, Ufa, Russia L.N. Gumilyov Eurasian National University , Astana, Kazakhstan e-mail: [email protected], phone +7 3472725904

For citation: Ionics , 2018. V.24. No 5. P. 1349–1356. DOI: 10.1007/s11581-017-2299-z Original Paper, First Online: 19 October 2017 The electronic and ionic conductivity, the electronic and ionic Zeebeck coefficients, and the thermal conductivity of NaxCu2-xS (x = 0.05, 0.1, 0.15, 0.2) compounds were measured in the temperature range of 20 - 450 оС. The total cationic conductivity of Na0.2Cu1.8S is about 2 S/cm at 400 оС (the activation energy ≈ 0.21 eV). Over the studied compounds, the composition Na0.2Cu1.8S has the highest electronic conductivity (500-800 S/cm) in the temperature range from 20 to 300 оС, and the highest electronic Zeebeck coefficient (about 0.2 mV/K) in the same temperature range is observed for Na0.15Cu1.85S composition; the electronic Zeebeck coefficient increases abruptly above 300 оС for all compounds. The thermal conductivity of superionic Na0.2Cu1.8S is low, which causes high values of the dimensionless thermoelectric figure of merit ZT from 0.4 to 1 at temperatures from 150 to 340 оС. INTRODUCTION. Copper and sulfur form a wide variety of compounds, ranging from chalcocite (Cu2S) to villamaninite (CuS2) with other intermediates: covellite (CuS), jurleite (Cu1.96S), roxbyite (Cu58S32), digenite (Cu1.8S ) and anilite (Cu1.75S) [1,2]. Copper sulfides have potential for practical applications in solar cells, optical filters, superionic materials, thin films and composite materials, including high-capacity cathode materials for lithium storage batteries, nanosized switches, catalysts and nonlinear optical materials [3-9]. Excellent copper thermoelectric properties were also observed for copper sulfide [10-15]. Information in the literature on the crystal structure of various phases of copper sulfide is entangled and contradictory. In our opinion, both the strong disordering of the crystal structure and its dependence on the synthesis conditions and on prehistory of the samples are main reasons of the observed situation. D. J. Chakrabarti and D. E. Laughlin [1] also mark a strong tendency for forming several metastable phases in this system and extreme sensitivity to applied pressure. Below 104 oC a low-chalcocite γ-Cu2S is described by monoclinic space group P21/c, with a unit cell containing 48 sulfur atoms and 96 copper atoms [16]. The structure is based on hexagonal-close-packed frame-work of sulfur atoms, with copper atoms occupying mainly triangular interstices. The similar set of X-ray diffraction lines for γ-Cu2S often described by orthorhombic or pseudo-orthorhombic cell too [17]. Between 104 oC and 435 oC a chalcocite β-Cu2S is hexagonal with ah =3.95, ch = 6.75 Ǻ and with space group P63/mmc. The polymorphic transformation temperature of γ-Cu2S low-chalcocite depends on chemical composition and occurs over the temperature range from 90 to 103.5 oC. For Cu-saturated chalcocite the transformation occurs via a peritectoid reaction at 103.5 ± 0.5 oC [1], for Cu1.993S composition the eutectoid type transformation take place at 90 ± 2 oC [1, 18]. Above 435 oC chalcocite α-Cu2S has the cubic close-packed digenite Fm3m structure. The fourth chalcocite phase is considered metastable [17]. Djurleite is orthorhombic, diffraction aspect corresponds to P*n* space group with cell dimensions a=26.90, b= 15.72, c= 13.57 Ǻ. The diffraction aspect is also compatible with the monoclinic space group P21/n. Djurleite, originally thought to be Cu1.97S [18], later was considered to be a solid solution with a composition range from about Cu1.93S to Cu1.97S [16, 19]. In reports of Roseboom and Potter [18, 19] it was resumed that djurleite Cu1.96S decomposes to hexagonal chalcocite and high-temperature digenite above 93oC, whereas Cook [20] found that djurleite transformes to a tetragonal form above 93oC. This tetragonal form, first described by Djurle [21], has sulfur atoms in approximately cubic close-packing. Chakrabarti and Laughlin in their review of Cu-S phase diagram [1] notes that orthorhombic djurleite of nominal composition Cu1.96S stable up to 72±3 oC at Cu1.934S and up to 93±2 oC at Cu1.971S composition. According to Sands et al [22] both low-chalcocite and low-djurleite are composed of an ordered superlattice of copper within a distorted hexagonal-close-packed sulfur sublattice and intertransitions between the two phases are usual phenomena. According to G. Will et al. [23] two modifications of digenite (Cu1.8S) exists, a low-temperature form (below 91 oC) and high-temperature form (above 91 oC). The crystal structures of high-digenite have been determined at 200 °C, 300 °C, 400 °C, and 500 °C. The four sulfur atoms (per unit cell) forms FCC lattice in Fm3m, while the 7.2 Cu atoms occupy statistically three types of sites. With temperature increasing, copper atoms leave the 1

8c sites and migrate to the 4b sites. All Cu positions are only partially filled. Above 436 °C high-digenite crystallizing in Fm3m space group. Potter [24] found that high-digenite covers a broad phase field and that above 436 °C only a sulfide with composition Cu2S can be obtained, in equilibrium with copper. At 500 °C cubic high-digenite has the composition Cu2S and is identical with cubic chalcocite, i.e. “digenite” with composition Cu1.8S does not exist above 436 °C. At 500 °C 8c sites are occupied with 25% probability and 4b sites to about 6%. Below 436 °C high - chalcocite crystallizes in hexagonal lattice with space group P63/mmc [23]. The orthorhombic compound anilite of Cu1.75S composition is stable up to 75±3 oC [1]. The hexagonal compound covellite of CuS composition is stable up to 507±2 oC [1]. For nanosized copper sulfides the essential changing of phase transformation points is observed [25]. For example, temperature-induced solid-solid phase transition in copper sulfide nanorods from low- to high-chalcocite shifts from 104 oC to 52 oC when particle sizes decrease from bulk state to 5 nm. We have previously studied the effect of lithium doping on the electrical and diffusion properties of Cu2-xS and Cu2-xSe [26-32]. The substitution resulted in a decrease in both the ionic and electronic conductivity of the compound. The wide range of homogeneity of copper sulfide (from Cu 2S to Cu1.75S) enables doping with other metals while maintaining the type of crystal structure, allowing to obtain homogeneous samples with the desired useful properties. In this paper the studies of the effect of partial substitution of copper by sodium on the transport phenomena in Cu2-xS mixed superionic conductor are presented. We know only one research work on copper sulphide doped with sodium. Last year Z.H. Ge et al [33] reported about thermoelectric properties of NaxCu9S5 (x = 0, 0.025, 0.05, 0.15, 0.25) nanopowders with an average size of 3 nm prepared by ball milling and compacted by spark plasma method. The main characteristic of an thermoelectric material, dimensionless thermoelectric figure-of-merit (zT) is defined as zT = α2σT/χ , where α, T, σ, χ are the Seebeck coefficient, absolute temperature, electronic conductivity, total thermal conductivity, respectively. The highest thermoelectric ZT = 1.1 was obtained for Na0.05Cu9S5 sample at 500 оС that is nearly twice of that for pure Cu1.8S and is comparable to the modified PbS materials (ZT ≈ 1.2 at 650 оС). The properties of binary sodium sulphide are well studied. Sodium sulfide Na 2S has the crystal structure of antifluorite type and exhibits superionic properties at temperatures close to the melting point (T m = 1276 K). In the low-temperature range from room temperature to 180 оС the ionic conductivity of Na2S not exceeds 10-6 S cm-1 , the activation energy of cation migration equals 0.59 eV. The lattice parameter is 6.5373 Ǻ, the degree of the cation sublattice filling is 0.988 [34]. In its electronic properties, sodium sulfide is a direct-gap semiconductor with a band width of 2.23 - 3.05 eV, with a high degree of ionicity of the bond [35, 36]. The electron density is minimal in the cation’s vicinities, and is mainly concentrated around the anion positions. In paper [37] M. Kizilyalli et al reported that two new crystal modifications of Na2S obtained at high temperatures were identified in addition to the previously reported antifluorite structure. They were designated as cubic Form II and orthorhombic Form III. The approximate unit cell dimensions were found to be a = 11.29 Å for the cubic form and a = 15.94, b = 16.00, and c = 16.18 Å for the orthorhombic form. 1. Materials and Methods. NaxCu2-xS (x = 0.05, 0.1, 0.15, 0.2) samples were synthesized in a mixed melt medium of NaOH and KOH hydroxides. All reagents (CuCl, NaCl, Na2S * 9H2O) were placed in a heated Teflon vessel with melted hydroxides simultaneously. The NaxCu2-xS nanopowder formed inside the vessel at a temperature near 180 ° C for several hours. The obtained product was washed three times with distilled hot water, and then it washed with ethanol. The particle sizes of the powder obtained were in the range of 50 to 500 nm. We did not obtain samples of narrow fractions in particle sizes, so we do not discuss here the effect of the grain size on the kinetic properties. For the transport phenomena studies, the samples were pressed at a pressure of 200-300 MPa and then annealed during 24 hours at 400 ° C. X-ray diffraction phase analysis was carried out using the Bruker D8 ADVANCE ECO diffractometer with a Cu-α radiation and a graphite filter. Diffraction patterns were recorded with step 0.02 o (2θ). To identify the phases the BrukerAXSDIFFRAC.EVAv.4.2 software and the international ICDD PDF-2 and COD databases were used. Mixed type of conductivity of the studied materials does not allow the use of conventional methods of conductivity measuring, so the electronic and the ionic conductivities were measured by well-known method of suppressing of undesirable current component, described, for example, in [38, 39]. To separate the electronic and ionic conductivity, one of the current components was suppressed by selecting the appropriate current electrodes and potential probes. For measurements of the ionic conductivity in the range of 330-440 оС, the Cu/CuBr current filters and potential probes were used. The electronic component of the conductivity was measured using graphite inert current electrodes and Pt potential probes. The measurements were carried out in a dry argon atmosphere. For measurements of electronic and ionic Zeebeck coefficients Wagner’s method [40 ] was used. The measurement error for conductivity did not exceed 45%, for Zeebeck coefficient it was in range of 5-8%. For thermal conductivity measurements, a comparison method 2

was used, in which a tablet of fused quartz served as a reference sample. The error in measuring of the thermal conductivity was 7-10%. Differential scanning calorimetry of the samples was carried out on a DSC-1 device from "Metler" company at heating rate of 10 degrees per minute. Human and animal rights were not affected during the experiments. 2. Results 2.1. X-ray diffraction and differential scanning calorimetry Figure 1 presents X-ray diffraction pattern at room temperature for the Na 0.2Cu1.8S sample slowly cooled after heating to 530 oC. Reflections of two phases are seen on the diffraction pattern - orthorhombic djurleite Cu1.97S and orthorhombic low chalcocite Cu2S. We consider that the sodium atoms occupy positions of copper in the voids of the crystal lattices of jurleite and chalcocite phases, forming a substitution alloy, without changing the type of original structures.

Fig.1 X-ray diffraction pattern at room temperature for the Na0.2Cu1.8S sample slowly cooled after heating to 530 oC Differential scanning calorimetry of the Na0.1Cu1.9S sample revealed weak endothermic effects near 75 ° C and 100 ° C (Fig. 2). The similar peaks are observed also at 75 ° C and 104 ° C for the Na0.2Cu1.8S specimen. These two effects occupy a continuous range from about 67 to 105 ° C for Na0.1Cu1.9S (Fig. 3). This range can include phase transitions in digenite (91 оС [23]), in jurleite Cu1.96S (93 оС [1, 18-20], and in chalcocite Cu2S (104 оС [1, 16, 17]. For Na0.2Cu1.8S, these two thermal effects are seen separately on the DSC curve.

Fig.2 DSC curve for Na0.1Cu1.9S sample

Fig.3 DSC curve for Na0.2Cu1.8S sample 2.2. Ionic conductivity and ionic Zeebeck coefficient Figures 4 and 5 show the experimental temperature dependences of the ionic conductivity and ionic 3

Zeebeck coefficient for Na0.2Cu1.8S compound in the range of 350-440 ° C. The obtained values, in our opinion, should be attributed to the total ionic conductivity and to the total ionic Zeebeck coefficient of the compound, which can be composed of the copper ionic and sodium ionic partial contributions correspondingly.

Fig.4 Ionic conductivity of Na0.2Cu1.8S versus temperature

Fig.5 Ionic Zeebeck coefficient of Na0.2Cu1.8S sample versus temperature The ionic conductivity σi values increase exponentially from 1.5 to 2.3 S cm-1 in the temperature range from 630 to 690 K. Observed σi values are comparable with the level of the ionic conductivity of the binary copper sulfide [41]. The activation energy of the ionic conductivity, calculated from the data presented on Fig.4, is equal 0.21 eV. Observed values of the ionic Zeebeck coefficient αi (Fig. 5) lie in the range from 0.32 to 0.44 mV / K. In our opinion, high αi values are caused by strong temperature dependence of the crystal structure disordering degree. The coefficient of ionic thermopower in superionic conductors can be described by the equation [42]

- So

i = S

Me 

where S

Me 

Me 

o Me 

and S

- Qi /eT -  Pt (1)

are entropies of Me+ ions in the superionic compound and one in the pure metal

correspondingly, Qi is a heat of the ion transport of the compound and α Pt is a contribution of metal contacts to the measured Zeebeck effect, which is negligible quantity in this case. The entropy of mobile ions in superionic conductors is even higher than in liquids [43], so the difference S

Me

- So

Me

may reach the significant values.

2.3. ELECTRONIC CONDUCTIVITY AND ZEEBECK EFFECT. Figure 6 shows the temperature dependences of the electronic conductivity of Na 0.05Cu1.95S, Na0.1Cu1.9S, Na0.15Cu1.85S, Na0.2Cu1.8S samples. Because of the large difference in the conductivity values, natural logarithms of the conductivity are plotted along the ordinate axis.

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Fig.6 Temperature dependences of the electronic conductivity of Na xCu2-xS samples (x = 0.05, 0.1, 0.15, 0.2) The conductivity of the Na0.2Cu1.8S compound at room temperature turned out to be the largest among the studied compositions and amounted to about 800 S∙cm-1. Na0.05Cu1.95S and Na0.15Cu1.85S samples demonstrate a low conductivity of about 60 S∙cm-1 at ambient temperature. The temperature dependences of the electronic conductivity of the investigated Na0.05Cu1.95S, Na0.1Cu1.9S, Na0.15Cu1.85S, Na0.2Cu1.8S compounds in the range from 20 to 450 oC demonstrate several extrema. The anomalies near 90 and 100 oC obviously are caused by the phase transitions in chalcocite and djurleite phases. The deep minima of the conductivity near 350-400 oC perhaps reflects the phase transition to the superionic cubic phase. In stoichiometric Cu2S the phase transition occurs at 435 oC, but in the NaхCu2-хS compounds the copper deficit shifts the phase transition point to lower temperatures obviously. The temperature dependences of the coefficient of the electronic thermo-e.m.f. were measured in the temperature range from 20 ° C to 500 ° C also (Fig. 7). The signs of αе Zeebeck coefficients for all Na0.05Cu1.95S, Na0.1Cu1.9S, Na0.15Cu1.85S, Na0.2Cu1.8S compounds are positive. In the range of 360 -440 oC of the temperature dependences the maxima are observed, which origin, apparently, is related with the phase transition into the cubic phase of the compounds. The highest value 1.2 mV/K of Zeebeck coefficient is achieved for Na0.05Cu1.95S composition. With the measured values of the electronic conductivity σ and the electronic Zeebeck coefficient αe the values of the power factor W = σα2 of the samples NaxCu2-xS (x = 0.05, 0.1, 0.15, 0.2) have been determined and presented in Fig. 8. The maximal thermoelectric power is observed for Na 0.2Cu1.8S composition, and it remains rather high (250 ÷ 400 μW∙K-2m-1) over a wide temperature range from 160 to 340 oC. Figure 8 shows an increase in the thermoelectric power factor during a phase transition from the low-temperature phase to the hexagonal phase (weak maxima in the 90-100 ° C range) and at the phase transition from the hexagonal phase to the cubic phase (sharp peaks in the 360-440 ° C range).

Fig.7 Temperature dependences of the electronic Zeebeck coefficient for Na xCu2-xS samples (x = 0.05, 0.1, 0.15, 0.2)

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Fig.8 Temperature dependences of the power factor W = σeα2 for NaxCu2-xS (х = 0.05; 0.1; 0.15; 0.2) samples 2.4. Heat conductivity and thermoelectric figure merit. The temperature dependence of the total thermal conductivity of Na 0.2Cu1.8S compound is presented in Fig. 9. There are low values of thermal conductivity lying in the range 0.3-0.4 W m-1 K-1 at temperature change from 70 to 430 оС.

Fig.9 The temperature dependence of the total thermal conductivity of Na0.2Cu1.8S sample

Fig.10 The dimensionless thermoelectric figure merit ZT = σeαe2T/χ of Na0.2Cu1.8S sample as a function of temperature Figure 10 shows the dimensionless thermoelectric efficiency ZT = σeαe2T/χ of Na0.2Cu1.8S sample as a function of temperature. As can be seen in Fig. 10, the thermoelectric figure merit ZT first increases rapidly after 100 оС, levels off at the value ZT≈0.4 in the region of the existence of the hexagonal phase, and then again grows in the region of transformation to the cubic phase, reaching the maximum ZT ≈ 1 at the temperature of 340 оС. Since the material properties strongly depend on non-stoichiometry, the observed high ZT value suggests that it is possible to improve this index with a variation in the copper or sodium content within the homogeneity range of the material. 6

The reality of this suggestion shows the recent success of Chinese researchers [44], who received highest ZT = 1.23 for the non-stoichiometric composition of Cu1.94S.

3. Discussion Mixed superionic conductors in recent years have become the object of extraordinary attention due to their excellent thermoelectric properties. The presence of a "liquid-like phase" inside the "solid" lattice hampers the normal propagation of phonons ("Phonon-liquid Electron-crystal" concept (PLEC) or "Phonon-glass Electroncrystal" (PGEC) [45, 46]); therefore, superionic copper chalcogenides, and copper sulfide in particular, exhibit very low lattice thermal conductivity. Additional factors of the decrease of the total thermal conductivity in the investigated compositions are impurity ions of sodium, causing an increase in the scattering of phonons and electrons, as well as nanodispersity of grains that increases the number of structural defects at the phase boundaries. In addition, the fact of Seebeck coefficient increasing in the process of rearrangement of the crystal lattice during transition to the superionic state is known [47-49]. In copper chalcogenides, the superionic phase transitions are diffuse in a certain temperature range. The mentioned factors allowed us to obtain high values of ZT = 0.4 ÷ 1 for Na0.2Cu1.8S composition at sufficiently low temperatures of 150-340 oC. The decrease in the working temperature of the material is of special importance because of the high ionic conductivity of copper sulfide and its alloys, which leads to degradation due to the release of copper during the operation of the thermocouple [50]. In our opinion, the possibility of improving the thermoelectric characteristics by controlling the phase nonstoichiometry makes these compositions even more attractive for thermoelectric applications. Conflict of Interest: The authors declare that they have no conflict of interest. References 1. Chakrabarti DJ, Laughlin DE (1983) The Cu-S (Copper-Sulfur) system. J Phase Equilibria 4(3):254-271. doi: 10.1007/BF02868665 2. Madelung O, Rössler U, Schulz M (1998) Copper sulfides (Cu2S, Cu2-xS) crystal structure, lattice parameters In: Landolt-Börnstein (ed) Group III Condensed Matter, Springer, pp 1-2 3. Kalanur SS, Chae SY and Joo OS (2013) Transparent Cu1.8S and CuS thin films on FTO as efficient counter electrode for quantum dot solar cells. Electrochim Acta 103:91-95 4. Shuai X, Shen W, Hou Zh, Ke S, Xu Ch, Jiang Ch. (2014) A versatile chemical conversion synthesis of Cu2S nanotubes and the photovoltaic activities for dye-sensitized solar cell. Nanoscale Res Lett 9:513. doi:10.1186/1556-276X-9-513 5. Tamura T, Hasegawa T, Terabe K, Nakayama T, Sakamoto T, Sunamura H, Kawaura H, Hosaka S and Aono M. (2007) Material dependence of switching speed of atomic switches made from silver sulfide and from copper sulfide. J of Physics: Conf Series 61:1157–1161 6. Wu Y, Wadia C, Ma W, Sadtler B, Alivisatos AP (2008) Synthesis and photovoltaic application of copper (I) sulfide nanocrystals. Lawrence Berkeley National Laboratory publ. http://www.escholarship.org/uc/item/2rv992xd 7. Capezzuto F., Ciampa F, Carotenuto G, Meo M, Milella E, Nicolais F. (2010) A smart multifunctional polymer nanocomposites layer for the estimation of low-velocity impact damage in composite structures. Comp Struct 92:1913-1919. doi: 10.1016/j.compstruct.2010.01.003 8. Jache B, Mogwitz B, Klein F, Adelhelm P (2014) Copper sulfides for rechargeable lithium batteries: Linking cycling stability to electrolyte composition. J Power Sources 247:703-711. doi: 10.1016/j.jpowsour.2013.08.136 9. Muradov MB, Nuriev MA, Eivazova GM (2007) Sensitivity of composites based on gelatin and nanoparticles Cu2S and CdS to vapors of some organic compounds. Surf Eng and Appl Electrochem 43:512–515. 10. Akkad FE, Mansour B and Hendeya T (1981) Electrical and thermoelectric properties of Cu2Se and Cu2S. Mat Res Bull 16:535-539. doi: 10.1016/0025-5408(81)90119-7 11. Konev VN, Bikkin KM, Fomenkov SA (1983) Thermo-e.m.f. of Cu2-δX (X-S,Se). Inorganic materials (Izvestiya academii nauk USSR. Neorganicheskie materialy) 19:1066-1069 12. Ge ZH, Zhang BP, Chen YX, Yu ZX, Liu Y, Li JF (2011) Synthesis and transport property of Cu1.8S as a promising thermoelectric compound. Chem Comm 47:12697-12699. doi: 10.1039/C1CC16368J 13. Qin P, Qian X, Ge ZH, Zheng L, Feng J and Zhao LD (2017) Improvements of thermoelectric properties for p-type Cu1.8S bulk materials via optimizing the mechanical alloying process. Inorg Chem Front 4:1192-1199. doi: 10.1039/C7QI00208D 14. Zhao L, Fei FY, Wang J, Wang F, Wang C, Li J, Wang J, Cheng Z, Dou S, Wang X (2017) 7

Improvement of thermoelectric properties and their correlations with electron effective mass in Cu1.98SxSe1−x. Sci Rep 7:40436-40446. doi: 10.1038/srep40436 15. Tang YQ, Ge ZH and Feng J (2017) Synthesis and Thermoelectric Properties of Copper Sulfides via Solution Phase Methods and Spark Plasma Sintering. Cryst 7:141. doi:10.3390/cryst7050141 16. Evans HT (1979) The crystal structures of low chalcocite and djurleite. Zeitschrift für Krist 150:299320. doi: 10.1524/zkri.1979.150.1-4.299 17. Putnis A (1977) Electron diffraction study of phase transformations in copper sulfides. Amer Min 62:107-114. 18. Roseboom EH (1966) An investigation of the system Cu-S and some natural copper sulfides between 25o and 700oC. Econ Geol 61:641-672. 19. Potter RW (1974) Metastable phase relations in the system Cu-S. Geol Soc Am Abstracts with Progr 6: 915-916. 20. Cook WR (1972) Phase changes in Cu2S as a function of temperature. Nat Bur Stand Spec Pub 364:703-711. 21. Djurle S (1958) An X-ray study on the system Cu-S. Acta Chem Scand 12:1415-1426. 22. Sands TD, Washburn J, Gronsky R (1982) High Resolution Observations of Copper Vacancy Ordering in Chalcocite (Cu2S) and the Transformation to Djurleite (Cu1.97 to 1.94S). phys stat sol (a) 72:551-559. doi: 10.1002/pssa.2210720216 23. Will G, Hinze E and Abdelrahman AR (2002) Crystal structure analysis and refinement of digenite, Cu1.8S, in the temperature range 20 to 500 °C under controlled sulfur partial pressure. Eur J Miner 14:591-598. doi 10.1127/0935-1221/2002/0014-0591 24. Potter RW (1977) An electrochemical investigation of the system copper- sulfur. Econ Geol 72:15241542. doi: 10.2113/gsecongeo.72.8.1524 25. Rivest JB, Fong LK, Jain PK, Toney MF, Alivisatos AP (2011) Size Dependence of A Temperature Induced Solid - Solid Phase Transition in Copper (I) Sulfide. J Phys Chem Lett 2:2402–2406. doi: 10.1021/jz2010144 26. Balapanov MK, Yakshibaev RA, Gafurov IG, Ishembetov RK, Kagarmanov SM (2005) Superionic conductivity and crystal structure of LixCu2-xS alloys. Bull Rus Acad Sci: Phys 69:623-626. 27. Balapanov MK, Zinnurov IB, Mukhamedyanov UK (2007) Ionic conduction and chemical diffusion in solid solutions of superionic conductors Cu2X-Me2X (Me = Ag, Li; X = S, Se). Rus J Electrochem 43:585-589. 28. Balapanov MK (2007) Grain size effect on diffusion processes in superionic phases Cu1.75Se, Li0.25Cu1.75Se, and Li0.25Cu1.75S. Rus J Electrochem 43:590-594. 29. Balapanov MK, Gafurov IG, Mukhamed’yanov UK, Yakshibaev RA, and Ishembetov RK (2004) Ionic conductivity and chemical diffusion in superionic LixCu2-xS (0 ≤ x ≤ 0.25). phys stat sol (b) 241:114– 119. 30. Ishembetov RK, Balapanov MK, Yulaeva YK (2011) Electronic Peltier effect in LixCu(2-x)-δS. Rus J Electrochem 47:416-419. 31. Balapanov MK, Ishembetov RK, Kuterbekov KA, Nurakhmetov TN, Urazaeva EK, Yakshibaev RA (2014) Influence of the cation sublattice defectness on the electronic thermoelectric power of LixCu(2-x)-δS(x ≤ 0.25). Inorg mater 50:930-933. 32. Balapanov MK, Nadejzdina AF, Yakshibayev RA, Lukmanov DR, Gabitova RY (1999) Ionic conductivity and chemical diffusion in LixCu2-xSe superionic alloys. Ionics 5:20-22. 33. Ge ZH, Liu X; Feng D, Lin J, He J (2016) High-Performance Thermoelectricity in Nanostructured Earth-Abundant Copper Sulfides Bulk Materials. Adv En Mat 6:1600607. doi: 10.1002/aenm.201600607 34. Bertheville B, Low D, Bill H, Kubel F (1997) Ionic conductivity of Na2S single crystals between 295 and 1350 K experimental setup and first results. J Phys and Chem Sol 58:1569-1577 35. Eithiraj RD, Jaiganesh G, Kalpana G, and Rajagopalan M (2007) First-principles study of electronic structure and ground-state properties of alkali-metal sulfides – Li2S, Na2S, K2S and Rb2S. phys stat sol (b) 244:1337–1346. doi: 10.1002/pssb.200642506 36. Zhuravlev YN, Kosobutskii AB, and Poplavnoi AS (2005) Energy Band Genesis from Sublattice States in Sulfides of Alkali Metals with an Antifluorite Lattice. Russ Phys J. 48:138- 142. doi:10.1007/s11182-005-0096-z 37. Kizilyalli M, Bilgin M, Kizilyalli HM (1990) Solid-state synthesis and X-ray diffraction studies of Na2S. J Sol Stat Chem 85:283-292. doi: 10.1016/S0022-4596(05)80085-4 38. Weppner W, Huggins RA (1978) Electrochemical Methods for Determining Kinetic Properties of Solids. Ann Rev Mater Sci 8: 269-311. doi:10.1146/annurev.ms.08.080178.001413 39. Yokota I (1961) On the Theory of Mixed Conduction with Special Reference to Conduction in Silver Sulfide Group Semiconductors. J Phys Soc Jpn 16:2213-2223. doi:10.1143/JPSJ.16.2213 40. Wagner C (1972) The Thermoelectric Power of Cells with Ionic Compounds Involving Ionic and Electronic Conduction. Progr Sol Chem Phys 7:1-37. 41. Yakshibaev RA, Balapanov MK, Konev VN (1986) Ionic conductivity and diffusion in superionic conductor Cu2S. Fizika Tverdogo Tela (USSR) 28:1566-1568. 8

42. Girvin S (1978) Thermoelectric Power of Superionic Conductors. J Sol St Chem 25:65. doi: 10.1016/0022-4596(78)90044-0 43. Korzhuev MA (1998) Entropy of crystallization of materials from a “molten” sublattice of superionic conductors. Phys Solid State 40:204-205. 44. Zheng LJ, Zhang BP, Li HZ, Pei J, Yu JИ (2017) CuxS superionic compounds: Electronic structure and thermoelectric performance enhancement. J All and Comp 722:17-24. doi: 10.1016/j.jallcom.2017.06.078 45. Liu H, Shi X, Xu F, Zhang L, Zhang W, Chen L, Li Q, Uher C, Day T, Snyder GJ (2012) Copper ion liquid-like thermoelectric. Nat Mater 11:422-5. doi: 10.1038/nmat3273 46. Qiu P, Shi X, Chen L (2016) Cu-based thermoelectric materials. En Stor Mat 3:85–97. doi: 10.1016/j.ensm.2016.01.009 47. Xiao XX, Xie WJ, Tang XF and Zhang QJ (2011) Phase transition and high temperature thermoelectric properties of copper selenide Cu2−xSe (0 ≤ x ≤ 0.25). Chin Phys B 20:087201. doi: 10.1088/1674-1056/20/8/087201 48. Brown DR, Day T, Borup KA, Christensen S, Iversen BB, and Snyder GJ (2013) Phase transition enhanced thermoelectric figure-of-merit in copper chalcogenides. APL Mat 1:052107. doi: 10.1063/1.4827595 49. Liu HL, Shi X, Kirkham M, Wang H, Li Q, Uher C, Zhang WQ, Chen LD (2013) Structuretransformation-induced abnormal thermoelectric properties in semiconductor copper selenide. Mater Lett 93:121– 124 50. Dennler G, Chmielowski R, Jacob S, Capet F, Roussel P, Zastrow S, Nielsch K, Opahle I, Madsen GKH (2014) Are binary copper sulfides/selenides really new and promising thermoelectric materials? Adv Energy Mater 4:1301581. doi: 10.1002/aenm.201301581

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