Phase composition and thermoelectric properties of the nanocomposite alloys Na x Cu 2 −

Nanocrystalline alloys of the compositions Na 0.05 Cu 1.95 S, Na 0.075 Cu 1.925 S, Na 0.10 Cu 1.90 S, Na 0.125 Cu 1.750 S, Na 0.15 Cu 1.85 S, Na 0.17 Cu 1.80 S, Na 0.20 Cu 1.77 S were synthesized in a melt medium mixtures of hydroxides NaOH and KOH at a temperature of about 165 ◦ C. X-ray phase analysis showed that the alloys are heterophasic and consist of phases of Cu 9 S 5 digenite, CuS 2 copper disulfide, Covellite CuS, Cu 7 S 4 anilite in various combinations. The crystallite sizes range from 16 to 160 nm. The degree of crystallinity of the alloys slightly increases with an increase in the sodium content from 68% in Na 0.05 Cu 1.95 S to 81% in Na 0.20 Cu 1.77 S. A quasi-one-dimensional Na 2 Cu 4 S 3 phase was detected in the composition of the Na 0.20 Cu 1.77 S alloy. The measured values of the conductivity of the alloys are two orders of magnitude lower than in isolated pure Cu 9 S 5 , CuS 2 , CuS, Cu 7 S 4 , of which the alloys consist. An activation temperature dependence of the conductivity is observed in the region from 300 K to 360 K with an activation energy of 0.08 0.15 eV. The reason for the low conductivity of the alloys is assumed to be the presence of weakly conducting interfacial layers and sodium doping of non-stoichiometric phases Cu 9 S 5 (Cu 1.8 S) and Cu 7 S 4 (Cu 1.75 S), leading to the compensation of holes by electrons of impurity sodium atoms. The measured values of the coefficient of thermo-emf alloys at room temperature lie in the range from 0.032 to 0.147 mV/K. Due to the low thermal conductivity of the order of 0.2 W/mK, a rather high dimensionless thermoelectric figure of merit ZT ≈ 0.28 at 570 K was obtained for the composition Na 0.15 Cu 1.85 S.


Introduction
Cu 2−δ S copper sulfide is a superionic semiconductor compound of variable composition, which has recently attracted great attention of researchers with the prospects of using it as a thermoelectric material. The object of this interest is the very low lattice thermal conductivity ( λ ) of copper sulfide in the superionic phase with high electronic conductivity ( σ e ) and Seebeck coefficient ( α e ), which provides high thermoelectric figure of merit ZT = σ e α e 2T/ λ , lying in the range 0.4-1.9 depending on chemical composition and method of sample preparation [1][2][3][4].
Copper sulfide is part of a separate class of superionic thermoelectric materials recently identified among thermoelectrics [5], which are characterized by the effect of the "phonon-liquid electron crystal" [6], which consists in suppressing the propagation of phonons by the "crystal" melt in the superionic state of the material lattice.
This work is a continuation of a series of studies on the study of alloys of copper sulfide with alkali metals and the effect of sodium on the electrophysical, including thermoelectric, properties of alloys.
Recently, Guan M.J. et al. [7] studied Cu 2−x Li x S samples (x = 0, 0.005, 0.010, 0.050, and 0.100) obtained by fusion-quenching-annealing. With lithium contents up to x = 0.05, the samples they obtained were single-phase at room temperature and had a monoclinic structure similar to pure Cu 2 S, which can be considered as the formation of a lithium solid solution in copper sulfide. It was found that the electrical conductivity of Cu 2−x Li x S increases by an order of magnitude or more with increasing lithium content, which Guan M.J. et al. explained by an increase in carrier concentration. However, as expected, the Seebeck coefficient decreases simultaneously, but decreases 2-3 times weaker than the conductivity increases. Interestingly, doping with lithium leads to an increase in not only electronic, but also lattice thermal conductivity. The maximum thermoelectric figure of merit (ZT = 0.84) was observed by Guan M.J. et al. for the composition Cu 1.99 Li 0.01 S at 900 K, which is a third higher than the ZT value for pure copper sulfide obtained by the same method.
It is possible that it would be more promising to choose a non-stoichiometric composition of copper sulfide for alloying in order to have an initially large concentration of holes, since the conductivity of the stoichiometric composition is too low to obtain a high thermoelectric power of the material. This consideration was one of the reasons for the inclusion of non-stoichiometric compositions in the series of samples for our study.
In [7][8][9][10], the effect of doping with lithium and potassium on the thermoelectric properties of copper sulfide is reported. The effect of doping with sodium on transport phenomena in copper sulfide was studied in [11]. Z.H. Ge et al [11] described the thermoelectric properties of bulk samples of Na x Cu 9 S 5 copper sulfide (x = 0, 0.025, 0.05, 0.15, 0.25), consolidated using spark plasma sintering technology from nanopowder with an average nanoparticle size of 3 nm, synthesized by mechanical alloying, and the solubility of sodium in the crystal structure of copper sulfide to a composition of x = 0.05 is shown. The purpose of the doping was to reduce conductivity and increase the Seebeck coefficient. Z.H. Ge et al showed by Hall effect measurements that doping with sodium is expected to reduce the concentration of carriers in Cu 9 S 5 . In addition, the presence of many nanoscale pores and grains was found, which led to a decrease in thermal conductivity by a factor of 2-3. As a result, they achieved a high value of ZT = 1.1 at 500 • C for Na 0.05 Cu 9 S 5 , mainly due to a decrease in thermal conductivity. The solubility of sodium in the interstices of the Cu 9 S 5 lattice is 0.28%; at a higher sodium concentration (for the Na 0.25 Cu 9 S 5 alloy), the formation of inclusions of the Na 2 S and Cu 1.96 S phases is noted.
In this work, we study the phase composition, electrical conductivity, thermal conductivity, Seebeck coefficient of semiconductor nanocrystalline alloys Na 0.05 Cu 1.95 S; Na 0.075 Cu 1.925 S; Na 0.10 Cu 1.90 S; Na 0.125 Cu 1.750 S, Na 0.15 Cu 1.85 S; Na 0.17 Cu 1.80 S; Na 0.20 Cu 1.77 S in order to study the prospects of their practical use as thermoelectric materials.

The experimental procedure
The investigated alloys of the compositions Na 0.05 Cu 1.95 S, Na 0.075 Cu 1.925 S, Na 0.10 Cu 1.90 S, Na 0.125 Cu 1.750 S, Na 0.15 Cu 1.85 S, Na 0.17 Cu 1.80 S, Na 0.20 Cu 1.77 S were synthesized according to the procedure, similar to that described in [10] in a melt medium of a mixture of NaOH and KOH hydroxides at a temperature of about 165 • C. All reagents (CuCl, NaCl, Na 2 S*9H 2 O) were placed in a heated Teflon reactor at the same time. After laying the reagents, the exposure time was 16 hours. The product obtained as a precipitate was washed three times with distilled heated water, then with pure ethanol. The washed powder was dried at 50 • C. The particle sizes of the obtained powder were in the range from 15 to 100 nm.
X-ray phase analysis of the samples was carried out on a D8 ADVANCE ECO diffractometer (Bruker, Germany) using CuK α radiation. To identify the phases and study the crystal structure, Bruker AXSDIFFRAC.EVAv.4.2 software and the ICDD PDF-2 international database were used.
To measure the transport characteristics of the powder, samples in the form of parallelepipeds (2 × 5 × 20) mm in size were pressed under a pressure of (3-5) t/cm 2 . Samples were annealed in argon at 500 • C for 8 hours.
The electrical conductivity and thermo-emf of the Na x Cu 2−x S samples were studied at the ZEM-3 experimental setup (Japan). The setup software corrects for the contribution of metal wires to the measured thermo-emf, since it can introduce a significant error in the study of samples with a low Seebeck coefficient.
The thermal diffusivity and thermal conductivity of solid samples were measured on an LFA 467 HT HyperFlash instrument (NETZSCH, Germany). The thermal diffusivity was determined by the Parker formula: where, a is the thermal diffusivity, l -is the thickness of the sample, t 1/2 -is the time in s, corresponding to a temperature increase of 50%.
Thermal conductivity ( λ ) was defined as where, T -is temperature, a -is thermal diffusivity, ρ -is bulk density, c P -is specific heat.
The density of the sample was determined from measurements of the weight and volume of the sample. The values of c P were determined using a DSCcalorimeter DSC 404 F1 Pegasus company NETZSCH (Germany).

The results of the experiment and their discussion
Phase analysis X-ray diffraction patterns of samples taken at room temperature are shown in Figure 1. Tables 1-7 below show the phase composition of the samples and estimates of their crystallinity, crystallite size, and percentage of phases obtained from the analysis of diffractograms shown in Figure 1.
As can be seen from the results of the analysis, all samples contained a significant fraction of Cu 9 S 5 digenite (from 22 to 52%).
At a sodium content in the samples with x ≤ 0.125, the CuS 2 phase is present, which prevails in Na 0.05 Cu 1.95 S (78%) and almost disappears in the Na 0.125 Cu 1.875 S sample (2%). In samples with x>0.125, the CuS 2 phase does not form.
The crystallite sizes range from 16 to 160 nm. The degree of crystallinity increases slightly with increasing sodium content from 68% for Na 0.05 Cu 1.95 S to 81% for Na 0.20 Cu 1.77 S.
At the highest sodium content in the alloy (the chemical composition of Na 0.20 Cu 1.77 S), the Na 2 Cu 4 S 3 phase appears, which differs from other phases in its quasi-one-dimensional crystalline structure [12]. No other compounds Table 1.
The results of x-ray phase analysis of Na  (Figure 2) obtained on a DSC -DSC 404 F1 calorimeter show sharp exothermic peaks of about (360-370) K, reflecting the phase transition from the rhombohedral modification of digenite to cubic modification.
It is known that copper disulfide at atmospheric pressure is stable only below 200 • C [13]. There is evidence that, at a temperature of 220 • C, the melting of covellite CuS and its decomposition with the formation of copper sulfide Cu 2 S begins [12]. On the other hand, works [14][15] testify to the stability of covellite up to 507 • C when it transforms into cubic digenite.
A sharp decrease in the DTA curve above 200 • C in Figure 2 can be related to the ongoing decomposition of CuS 2 and the formation of Cu 2 S.  Figure 3 shows the temperature dependences of the electronic conductivity of the samples under study in the temperature range (300-600) K.

Electronic conductivity
Since the alloys are heterophase at room temperature, it is difficult to interpret the obtained dependences, however, based on the analysis, certain assumptions can be made in order to have a working hypothesis for further research.
The anomalies in the behavior of the temperature dependence of about (360-400) K for all compositions can be attributed to the manifestation of the superionic phase transition (FP) in digenite, which takes place at 364 K for diagenite of the Cu 9 S 5 composition [16]. Digenite is present as a separate phase in all samples, according to the results of x-ray phase analysis. The scatter in the temperature values of the phase transitions for different compositions can be explained by the effect of dissolved sodium and the influence of non-stoichiometry, which is difficult to control for sulfides.
The lowest conductivity values (below 5 S/cm) are observed for the Na 0.075 Cu 1.925 S alloy, the highest values (from 47 to 68 S/cm) for Na 0.05 Cu 1.95 S.
According to the work of R.A. Munson et al [17], copper disulfide at room temperature has a conductivity of about 500 S/cm, therefore, the presence of this phase in the alloy should increase the conductivity. This assumption is consistent with the fact that the Na 0.05 Cu 1.95 S sample has the highest conductivity of all alloys, in which the copper disulfide content is maximum (78%), and the highly conductive Cu 9 S 5 digenite is also the second phase in it. The conductivity of digenite at room temperature is even higher than that of copper disulfide and is more than 3000 S/cm at room temperature [3]. In our case, when the observed conductivity of the alloys is much lower than 3000 S/cm, it can be assumed that the content of digenite does not exceed the percolation threshold, and the crystallites of digenite are separated by a weakly conducting medium.
Copper disulfide exhibits a metallic character of conductivity in the range of (0-300) K [18] at a temperature of 1.6 K and becomes superconducting. Judging by the fact that the studied alloys exhibit a semiconductor rather than metallic character of conductivity near room temperature, copper disulfide does not determine the conductivity of the alloy, apparently because its content in the samples is small.
Covellite CuS also exhibits excellent metallic properties, its conductivity decreases from 10100 S/cm at 320 K to 6200 S/cm at 580 K, the coefficient of thermo-emf in this case, it increases from 9 to 11.2 µV/K [19]. The covellite phase is present in all samples except Na 0.05 Cu 1.95 S and Na 0.075 Cu 1.925 S, its relative content is from 2 to 25%, however, its presence also does not determine the electrical and thermoelectric properties of the alloy.
Presumably, in the crystallites of digenite and copper disulfide there is sodium dissolved in the lattice, which plays the role of a compensating impurity. It is known that doping with sodium reduces the concentration of digenite holes [11] formed during ionization of vacancies in the copper sublattice; in addition, carrier mobility is reduced due to scattering of impurity (Na) ions. An additional factor in reducing the mobility of carriers is scattering at the boundaries of nanocrystallites, so the specific surface fraction increases significantly with decreasing grain size. Numerous interphase boundaries also lead to a decrease in conductivity.
We also take into account that, according to Roseboom [20], the copper content in digenite increases with temperature, reaching a composition close to stoichiometric (Cu 2 S) at 708 K. The conductivity of stoichiometric copper sulfide is 0.07 S · cm −1 according to the work of Okamoto and Kawai [21].
The fraction of digenite in the phase composition of our samples is 22-52%, therefore, a significant decrease in the conductivity of alloys with increasing temperature can be attributed to a decrease in the hole concentration due to an increase in the copper content in digenite. This may be the reason for a sharp decrease in conductivity above 550 K in the alloys Na 0.15 Cu 1.85 S, Na 0.17 Cu 1.80 S, Na 0.20 Cu 1.77 S, for which n in the ratio σ ≈ T −n is several times greater than 3/2, i.e., the a decrease in mobility due to an increase in scattering due to thermal vibrations of the lattice is not able to explain such a sharp decrease in conductivity with temperature.
For the temperature range up to 360 K, in which the semiconductor nature of the temperature dependence of the conductivity in Figure 3 is observed, the activation energy of conductivity can be determined. The results are shown in Table 8. The presence of activation thermal conductivity can be related to the fact that current carriers overcome energy barriers during transitions between conductive crystallites in an essentially nanocomposite material.
For comparison, we note that in the low-temperature phase of copper sulfide (jarleite Cu 1.92 S) in the work of G.P. Sorokin and A.P. Paradenko [22], the activation energy of electronic conductivity 0.09 eV was obtained.
Thus, the electrical properties of the studied alloys differ from the properties of the metal-like phases Cu 9 S 5 , CuS, CuS 2 included in their composition. The reason may be the presence of weakly conducting interfacial layers and sodium doping of non-stoichiometric Cu 9 S 5 (Cu 1.8 S), which leads to the compensation of holes by electrons of impurity sodium atoms.
Electronic thermo-emf Temperature dependences of the coefficient of electronic thermo-emf samples are presented in Figure 4. The sign of the coefficient is positive for all samples, which corresponds to the hole type conductivity. In general, with increasing temperature, there is a tendency to increase the coefficient of electronic thermo-emf.
The coefficient of thermo-emf increases most strongly above 550 K, the only exception is the alloy Na 0.17 Cu 1.80 S, which has a coefficient of thermo-emf varies slightly between 0.09 and 0.10 mV/K in a wide range of (400-600) K.
In general, the coefficient of thermo-emf in all samples is higher than in pure nanocrystalline Cu 1.8 S (Cu 9 S 5 ), for which the measurement results from [3] are also shown in Figure 4. Figure 5 shows the temperature dependence of the thermal conductivity of the  samples in the temperature range from room temperature to 610 K.

Thermal conductivity
Very low values of thermal conductivity are observed (up to 0.1 Wm −1 K −1 ), which is a favorable factor for the use of this material for thermoelectric purposes. Low thermal conductivity is associated with the "moltenness" of the cationic sublattice of the material, which leads to the suppression of phonon thermal conductivity, as well as nanoscale crystallites and multiphase material, causing additional structural defects on which phonon scattering occurs.
In a recent paper [11], low thermal conductivity was also observed for nanocrystals of copper sulfide doped with sodium; however, for our samples, the thermal conductivity in the range from 300 to 500 K turned out to be several times lower, apparently due to the much lower electronic component of thermal conductivity.

Thermoelectric efficiency
The kinetic parameters were used to determine the dimensionless thermoelectric figure of merit ZT = σ e α 2 e T/k shown in Figure 6. The maximum ZT = 0.28 at 570 K was obtained for the Na 0.15 Cu 1.85 S alloy. This is significantly higher than ZT ≈ 0.2 at the same temperature for sodium doped Cu 9 S 5 , achieved by Z.H. Ge et al [11].

Conclusion
The resulting alloys are Na 0.05 Cu 1.95 S, Na 0.075 Cu 1.925 S, Na 0.10 Cu 1.90 S, Na 0.125 Cu 1.750 S; Na 0.15 Cu 1.85 S, Na 0.17 Cu 1.80 S, Na 0.20 Cu 1.77 S are heterophasic, consisting of a mixture of nanosized crystallites of digenite Cu 9 S 5 , copper disulfide CuS 2 , covellite CuS, anilite Cu 7 S 4 . Some samples showed small sulfur inclusions. Only at the highest sodium content in the alloy (chemical composition of Na 0.20 Cu 1.77 S) Na 2 Cu 4 S 3 phase appears, which differs from other phases in its quasi-one-dimensional crystalline structure. No other compounds containing sodium were detected, although energy dispersive X-ray analysis showed an approximately uniform distribution of sodium in all samples.
All samples contain a significant proportion of Cu 9 S 5 digenite (from 22 to 52%), other phases may be absent.
The crystallite sizes range from 16 to 160 nm. The degree of crystallinity of the alloys slightly increases with an increase in the sodium content from 68% for Na 0.05 Cu 1.95 S to 81% for Na 0.20 Cu 1.77 S.
The electrical properties of the studied alloys are very different from the properties of the metallic phases Cu 9 S 5 , Cu 7 S 4 , CuS, CuS 2 included in their composition. The measured values of the conductivity of the alloys are two orders of magnitude lower than in the pure substances listed above; for the studied alloys, an activation temperature dependence of the conductivity is observed in the region from 300 K to 360 K with an activation energy of (0.08-0.15) eV. The low conductivity of the alloys can be caused by the presence of weakly conducting interfacial layers and sodium doping of non-stoichiometric phases Cu 9 S 5 (Cu 1.8 S) and Cu 7 S 4 (Cu 1.75 S), which leads to the compensation of holes by electrons of impurity sodium atoms.
Sign of the coefficient of thermo-emf corresponds to the hole type of conductivity, the values of the coefficient of thermo-emf at room temperature, they range from 0.032 mV/K for Na 0.125 Cu 1.750 S to 0.147 mV/K for Na 0.15 Cu 1.85 S.
The composition of Na 0.15 Cu 1.85 S exhibits high values of electronic conductivity, coefficient of electronic thermo-emf and low thermal conductivity at the level of 0.2 W/mK, which gives a rather high indicator of dimensionless thermoelectric figure of merit ZT ≈ 0.28 at 570 K and allows us to hope in the future for the possibility of increasing this indicator due to the optimization of the synthesis procedure.