Mild Solvothermal Synthesis and Characterisation of Sulfur Rich Cu2-xS Nanocrystals with Varied Sulfur Precursors for Thermoelectrics

Chong Ka Shing¹, Tam Teck Lip Dexter^2
1Student, River Valley High School
²Institute of Materials Research and Engineering, A*STAR

ABSTRACT

Recent studies have proven that several Cu_2-xS compounds display satisfactory figure of merit (ZT values, which evaluate the conversion efficiency of a thermoelectric material. In this study, sulfur rich Cu_2-xS nanocrystals were synthesised with dithiooxamide or thiourea as sulfur precursors using a mild solvothermal method. Apart from investigating the two synthetic methods of Cu_2-xS, this paper optimises the power factor (PF), where , for Cu_2-xS by uncovering the optimum parameters affecting electrical conductivity and the Seebeck coefficient. X-Ray diffraction (XRD) affirmed the identity of the samples as covellite (CuS), while Energy-dispersive X-Ray spectroscopy (EDX) showed that dithiooxamide samples contained a considerable amount of impurities. Due to high purity, thiourea samples showed a high electrical conductivity of 579^-1m^-1 at room temperature. However, these samples have a moderate Seebeck coefficient and higher thermal conductivity due to their elevated hole concentration. Despite TU2, synthesised from thiourea, having the lowest Seebeck coefficient of 12.3μVK⁻¹, this value is nearly three times greater than that of the single crystalline CuS which has a Seebeck coefficient of 5μVK⁻¹, emphasising the significance of nanostructuring to increase the Seebeck coefficient. Nevertheless, the increment in the figure of merit owing to electrical conductivity is far greater than the deduction in the figure of merit by the Seebeck coefficient and thermal conductivity, especially at lower temperatures. CuS nanocrystals synthesised from the thiourea precursor show great potential as a room temperature thermoelectric device due to their unique temperature dependence of increasing power factor at lower temperatures. TU2 has the highest power factor of 51.4μWm^-1K^-2 at room temperature, and this power factor was found to be substantially higher than that of previously reported CuS by Narjis et al. with a power factor of 4.5μWm^-1K^-2 due to the solvothermal synthesis method adopted. This resulted in a ZT value of 0.00220 at room temperature, or 20% higher than that of CuS synthesized by Tarachand et al., which had a ZT of 0.00183. Chemically stable and non-toxic CuS nanocrystal samples synthesised offer a satisfactory thermoelectric performance with low synthetic cost and fill the research gap of a room temperature thermoelectric material.

Background and Purpose of Research

A temperature gradient induces the flow of charge carriers from the hotter to the cooler end, generating an electric field and creating a voltage difference directly proportional to the temperature difference.^[1] Utilizing low grade heat from industrial processes or waste heat from electrical appliances is vital to reducing the growing carbon emissions of our society.^[2] The Seebeck effect directly recovers electricity from thermal energy, thus receiving much attention as a promising green technology.^[3] One notable thermoelectric material is Cu_2-xS due to its low cost and non-toxicity (refer to Annex E).^[4] Being a p-type semiconductor, Cu vacancies act as charge carriers, making Cu_2-xS an excellent electrical conductor.^[5] Moreover, Cu_2-xS has variable stoichiometric compositions, ranging from sulfur rich CuS to copper rich Cu₂S.^[6] As a result, it has a Cu:S ratio dependent hole concentration and various band gap values ranging from 1.2 to 2.0 eV, suitable for a wide range of applications.^[7] The crystalline structure of Cu_2-xS can be subdivided into groups based on the sulfur packing in the lattice (refer to Annex A). Reported Cu_2-xS can be further classified into covellite (CuS), yarrowite (Cu₁.₁₂S), spionkopite (Cu₁.₄₀S), anilite (Cu₁.₇₅S), digenite (Cu_1.80S), djurleite (Cu₁.₉₇S) and chalcocite (Cu₂S).^[8]

Several Cu_2-xS compounds produced in recent studies displayed satisfactory figure of merit (ZT values^[9], which assess the suitability of a thermoelectric material. , where α is the Seebeck coefficient, is the electrical conductivity, T is the absolute temperature and κ is the thermal conductivity.^[10] Most notably, Cu_1.97S can display a maximum ZT value of 1.5 at 900K, which represents the highest reported value for p-type copper semiconductors.^[11] However, there exists limited reports regarding thermoelectric properties of sulfur rich Cu_2-xS because of the compounds’ inferior ZT merit values, with Tarachand et al. reporting the CuS with a highest ZT of 0.0187.^[12] Nevertheless, recent nanocrystal engineering demonstrated increased Seebeck coefficient and decreased thermal conductivity due to the reduced dimensionality of nanocrystal quantum dot structures.^[13] Hence, this paper studies methods to raise the Seebeck coefficient and electrical conductivity and uncover the potential of CuS through the synthesis of nanocrystals with strong interface phonon-scattering and charge carrier filtering abilities. Despite the current extensive study into Cu_2-xS crystals, prior research has not attempted to compare the trends and relationships between the amount of sulfur source and types of sulfur precursors and their corresponding ZT at different temperatures using solvothermal synthesis. Investigating trends of different sulfur rich Cu_2-xS nanocrystals using different synthetic conditions explores their potential and lays the foundation for future studies.

Different methods for the synthesis of Cu_2-xS with varying oxidation states of Cu have been reported. These include the melting-quenching, solvothermal and microwave assisted synthesis methods.^[14] However, this paper focuses solely on the economically efficient solvothermal synthesis of Cu_2-xS using CuBr₂ with two different sulfur-containing precursors under different conditions: thiourea (TU, SC(NH₂)₂) ^[15] and dithiooxamide (DTO, NH₂(CS)₂NH₂).^[16] Several studies have confirmed that thiourea provides a high reducing power to form a Cu[(NH₂)₂CS]²⁺ complex as an intermediate (Annex B) and likely contains less copper (II) oxide impurities in its final product.^[17] On the other hand, dithiooxamide forms a stable and easily synthesisable Cu-DTO complex intermediate, hence lowering the activation energy of forming CuS. Both synthetic conditions are predicted to form sulfur rich Cu_2-xS nanocrystals.^[18] The two reactions consist of sulfur precursors that form a stable intermediate, eliminating the need for a capping ligand. The synthetic media used is N,N-dimethylformamide (DMF), an inexpensive and common solvent for inorganic synthesis.^[19] One significant synthetic challenge is the controlling of the stoichiometric ratio of copper and sulfur due to the absence of a detailed mechanism to describe their formation.^[20] Apart from investigating the two synthetic methods of Cu_2-xS, this paper optimises the power factor ( ) for Cu_2-xS by uncovering the optimum parameters affecting electrical conductivity and Seebeck effect through evaluating trends related to choosing between different Cu : S stoichiometric ratios and type of sulfur precursor.

Methodology

Different stoichiometric ratios (refer to Annex C) of copper (II) bromide_, thiourea and dithiooxamide were dissolved in DMF and subjected to an oil bath of 160 in an inert atmosphere of nitrogen gas for 24 hours. Stoichiometric ratios were adjusted to produce different phase compositions and morphologies of sulfur rich Cu_2-xS.^[20] This solvothermal process allows for the creation of grain boundaries among Cu_2-xS nanocrystals that had been proven to be effective in phonon scattering and the enriching of defect structures, hence the potential to increase both the Seebeck coefficient and electrical conductivity.^[21] Samples were purified through washing them with DMF twice and methanol once after centrifuging at 4000 rpm for five minutes. They were dried in a vacuum oven of 60 overnight and ground into fine powders before pressing into a pellet. Samples were named with their sulfur precursor as the prefix and the copper to precursor concentration ratio as the suffix (refer to Annex C).

Pellets were tested for electrical conductivity (σ) and the Seebeck coefficient (α) using ZEM-3 while hall measurements were taken using BioRad HL5500. Energy-dispersive X-Ray spectroscopy (EDX) and X-Ray Diffraction (XRD) were carried out using FESEM 7600F and Bruker D8 Advance, respectively.

Results and Discussion

Synthesis of CuS nanocrystals results in the formation of a dark precipitate upon mixing copper (II) bromide and all concentrations of thiourea and dithiooxamide. XRD patterns of the products were recorded using Cu Kα radiation (λ=1.5418Å) in the 2θ range of 10°-85° and plotted in Figure 1. The patterns are in good agreement with CuS of hexagonal structure with cell parameters of a = 3.792Å and c = 16.34Å (JCPDS: 06-0464).

The (006) diffraction peak has a much stronger intensity than the (102) and (103) peaks, suggesting a preferential orientation of the crystals along the (006) plane.^[22] This reveals the possibility to obtain anisotropic conductivity to be advantageous for thermoelectrics.^[23] Average crystallite sizes of each sample were then calculated and recorded in Table 1 using the Scherrer equation, , where D is crystallite size, K is shape factor (0.9), λ is wavelength of Cu Kα emission, θ is Braggs angle corresponding to the maximum of the diffraction peak and β is full width at half maximum (FWHM) of diffraction peaks.^[24] DTO samples have many outliers with massive crystallite sizes due to the presence of impurities

TABLE 1: Average crystallite size calculated from XRD data pattern
Average crystallite Size/nm	DTO1	DTO2	TU1	TU1.5	TU2	TU4
	35.86	29.05	28.09	19.24	29.42	22.82

The chemical compositions of all samples were evaluated by Energy-dispersive X-Ray spectroscopy. Table 2 revealed that all samples give a Cu : S stoichiometric ratio of about 1:1, which reaffirms the identity of covellite. Powders of DTO1 and DTO2 contain elevated amounts of oxygen and nitrogen due to the presence of unreacted dithiooxamide, thus restricting the flow of electrons and decreasing its conductance.

					TABLE 2: EDX analysis of different samples
S.N.		Sample		Atomic %						Total %
				Cu		S	N	O	Br
1		TU1		33.9		34.7	11.7	13.8	5.9	100
2		TU1.5		48.6		38.5	0	12.9	0	100
3		TU2		54.4		45.6	0	0	0	100
4		TU4		53.4		46.6	0	0	0	100
5		DTO1		34.8		34.1	22.9	7.5	0.7	100
6		DTO2		29.8		31.8	31.8	6.6	0	100

Addition of thiourea shifts the equilibrium of the reaction from CuO to CuS, decreasing the atomic percentage of O as a result of its reducing power.

SEM images in Figure 2^[1] illustrate that samples of thiourea precursors contain hexagonal flakes, which exhibit strong thermoelectric properties.^[25] Clusters of nanoparticles are present in TU1 and TU1.5, providing the possibility that there exists another phase of CuS in them.

Measurements of electrical conductivity, Seebeck coefficient, power factor, thermal conductivity and figure of merit at different temperatures are recorded in Table 5 (refer to Annex F) and plotted in Figures 3.1, 3.2, 3.3, 3.4 and 3.5, respectively. The measured electrical conductivities of different samples are plotted in Figure 3.1, with values ranging from 7.94^-1m^-1 to 595.2^-1m^-1. Exceptional purity and hole concentrations in the order of 10¹⁹ cm^-3 are believed to contribute to the remarkable electrical conducting properties of samples synthesised from thiourea (refer to Annex D). This hole concentration is obtained mainly due to the low to minimal band gap value of CuS, which is around 1.2 eV, as well as the presence of grain boundaries, which are shown to create abundant defect states.^[26][27] Since electrical conductivity is given by:

where n, e and μ are the carrier concentration, charge and charge carrier mobility, respectively, the trends among the samples can be evaluated using their grain size and hole concentrations.^[28] Small grain sizes induce a considerable number of grain boundaries which greatly reduce hole mobility by hole scattering.^[29] Hence, electrical conductivity generally rises along with increased grain size, with the anomaly of TU1 due to its exceptionally poor hole concentration. Moreover, the presence of a sizeable amount of impurities reduces the electrical conductivity of TU1 further to a low of 97.1 ^-1m^-1 at room temperature. Among all samples, TU2 has the highest ever reported Cu_2-xS electrical conductivity of 595.2 ^-1m^-1 at room temperature, a factor of 10² higher than that of TU1, labelling it as a suitable thermoelectric material to recover electricity even at room temperature.^[30][31]

Seebeck coefficients are shown in Figure 3.2 in the order of μVK⁻¹. The Seebeck coefficients of CuS nanocrystals are optimistic because of the existence of grain boundaries. Despite increasing interface phonon-scattering^[32] and suppressing the phonon drag effect, preferential scattering of low-energy electrons increases the number of high-energy electrons in CuS, which makes the system more conducive to the movement of charges to lower energy states, increasing Seebeck coefficient. This effect is apparent in TU1.5, which has the most grain boundaries. Seebeck coefficient can be determined using the Mott formula^[33], , where T is absolute temperature, n is the carrier concentration and m* is the effective mass of the carrier. Positive values of Seebeck coefficient indicate the charge carriers as holes.^[34] Generally, p-type materials demonstrate a poor Seebeck coefficient due to the lower m* of holes relative to electrons.^[35] However, because of low hole concentrations, DTO2 reached the highest Seebeck coefficient of 21.3 μVK⁻¹ at 573K, while TU2 had the lowest Seebeck coefficient of 12.3 μVK⁻¹. Regardless, this lowest value is nearly 3 times greater than that of a single crystalline CuS with α = 5 μVK⁻¹, which emphasises the significance of nanostructuring in improving α. Nevertheless, the α² of samples increases less than proportionately than decreases in temperatures higher than 300K, shifting the focus from optimising power factor at room temperature to synthesising samples with higher electrical conductivity in the range where Seebeck coefficient remains similar. The power factor of all samples is determined using . Despite having the lowest Seebeck coefficient, TU2 had the highest power factor of 51.4 μWm^-1K^-2 at room temperature and reached a peak of 55.7 μWm^-1K^-2 at 523K. These values are substantially higher than the previously reported power factors of CuS at 4.5 μWm^-1K^-2 and Cu_1.8S at 1.93 μWm^-1K^-2 at room temperature.^[30][31]

As shown in Figure 3.3, CuS is a potential candidate for a room temperature thermoelectric, as it has a synthetic cost that is relatively inexpensive and a unique power factor dependence on temperature. Owing to its metallic behavior of decreasing electrical conductivity and increasing Seebeck coefficient as temperature rises, there exists a reasonably high power factor of 51.4 μWm^-1K^-2 for CuS at low temperatures, as shown by sample TU2. DTO1 and DTO2 had comparatively lower power factors of 1.33 μWm^-1K^-2 and 2.82 μWm^-1K^-2, respectively, despite their higher Seebeck coefficients. Hence, having pure samples is an indispensable requirement for obtaining the optimum power factor.

Thermal conductivity results from two contributions. , where κ_L is the lattice thermal conductivity, and κ_C is the carrier thermal conductivity. Due to no commercially available device to test for parallel thermal conductivity and the anisotropic properties of all samples as evident by their preferred orientation, κ_C and κ_L were obtained from existing literature and calculations. κ_C was determined using the equation ,^[34] where L is the Lorenz number obtained by the following equation to minimize deviation from experimental thermal conductivity values:^[36] , where L is in 10⁻⁸WΩK⁻² and in µVK^-1. κ_L values were taken from Tarachand et al., who synthesised similar CuS nanocrystals with analogous lattice thermal conductivity^[37] and extrapolated to the desired range. Thermal conductivity was then determined by the sum of κ_C and κ_L. Samples with a high conductivity allow for the transporting of heat with holes and reveal a greater dependence on κ_C than on κ_L, with TU2 having the highest thermal conductivity of 7.10 Wm^-1K^-1 at room temperature. Hence, the key to obtain the optimal power factor is to strive for a good balance among thermal conductivity, electrical conductivity and Seebeck coefficient by varying hole concentration.^[38] This can be engineered by adjusting concentrations of sulfur precursors, which demonstrated a positive relationship with hole concentration in samples.

Thermoelectric figure of merit values were calculated for all samples across a range of temperatures. TU2 had the highest figure of merit of 0.00220 at room temperature, while TU4 had the maximum ZT of 0.00409 at 564K. While DTO samples have a lower thermal conductivity due to limited carrier concentrations, they had an extremely low electrical conductivity resulting in DTO1 having a low ZT of 0.000146 at room temperature. Figure 3.5 supports the hypothesis that power factor is a good comparison of thermoelectric efficiency, as it follows the trend of the figure of merit. Thiourea is evident to be a better sulfur precursor for future exploration of Cu_2-xS thermoelectrics.

Conclusion, Limitations and Suggestions for Further Research

Both synthesis by thiourea or dithiooxamide sulfur precursors result in the formation of sulfur rich Cu_2-xS. Synthesis by dithiooxamide led to the presence of a large amount of impurities, while synthesis with high thiourea concentration produced comparatively pure covellite. Due to the presence of impurities, CuS prepared with dithiooxamide had low electrical conductivity, and hence an unsatisfactory power factor. Alternatively, despite having the lowest Seebeck coefficient, TU2 has a ZT of 0.00220 and power factor of 51.4 μWm^-1K^-2 at room temperature, which exceed those of CuS reported in Tarachand et al with a ZT of 0.00187 and in Najis et al. with a power factor of 4.5 μWm^-1K^-2. Thus, thiourea is a better candidate for the solvothermal synthesis of pure CuS than dithiooxamide, which is also more expensive. A Cu:S stoichiometric ratio of 1:2 should be adopted as evident by the superior power factor of TU2.

Regardless of a relatively low maximum figure of merit, chemically stable CuS nanocrystals overcome the lapse in knowledge of room temperature thermoelectrics by offering satisfactory thermoelectric performance with a low synthetic cost coupled with their non-toxic nature. Despite the lack of thermal conductivity measurements, the lattice and carrier thermal conductivity of samples were determined from existing literature and theoretical equations, respectively. These predicted values allow for a rough comparison of its ZT with other thermoelectric materials despite its limitations. Furthermore, there also exists a possibility in thiourea samples to induce anisotropic conductivity to be beneficial for thermoelectric devices due to the presence of preferred orientation. In addition, there is an absence of mechanisms describing the formation of different grain sizes. Further exploration into these factors will allow for the optimisation of grain boundaries, and thus the optimising of the ZT of CuS. Since α²/κ increases less proportionately than electrical conductivity decreases at room temperature, this study suggests that the basis of synthesising room temperature thermoelectric material in future studies is to enhance electrical conductivity further in the range where there are little fluctuations in the Seebeck coefficient. This can be achieved through tuning grain size to look for the optimal point of power factor at room temperature. Further research conducted on CuS nanocrystals could possibly uncover more of their potential as a room temperature thermoelectric due to their optimised figure of merit at room temperature.

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Annex B
Formation of copper sulfide through the intermediate of a copper-thiourea complex.^[15]
Annex C
TABLE 3: Different stoichiometric ratios of precursors added for samples

Sample	Copper (II) bromide	Dithiooxamide	Thiourea	Dimethylformamide
DTO1	1	1	0	10ml
DTO2	1	2	0	10ml
TU1	1	0	1	10ml
TU1.5	1	0	1.5	10ml
TU2	1	0	2	10ml
TU4	1	0	4	10ml

Annex D
TABLE 4: Carrier concentrations of samples

Carrier Concentration (cm-3)	DTO1	DTO2	TU1	TU1.5	TU2	TU4
	1.6×1017	3.7×1017	1.5×1018	1.6×1018	5.7x 1018	9.3×1018

Annex E


Annex F
TABLE 5: Different samples and their electrical conductivity, Seebeck coefficient, power factor, thermal conductivity and figure of merit at different temperatures

Sample	Temperature/K	Electrical Conductivity/-1m-1	Seebeck Coefficient/ μVK−1	Power Factor/μWm-1K-2	Thermal Conductivity/ Wm-1K-1	Figure of Merit*103
DTO1	305	10.582	11.2	1.33	2.785	0.1459
	322	10.384	11.7	1.41	2.818	0.1613
	369	9.803	12.9	1.63	2.902	0.2074
	418	9.433	14.8	2.08	2.971	0.2927
	467	9.090	16.4	2.44	3.029	0.3762
	515	8.474	17.5	2.59	3.078	0.4334
	564	7.936	20.7	3.42	3.105	0.6213
DTO2	324	16.469	13.1	2.82	2.866	0.3187
	370	15.406	14.2	3.12	2.951	0.3912
	419	14.487	15.8	3.62	3.021	0.5021
	468	13.946	17.6	4.33	3.082	0.6575
	517	13.312	19.3	4.96	3.137	0.8176
	566	12.673	21.3	5.72	3.167	1.0222
TU1	305	97.087	9.79	9.33	3.422	0.8302
	324	95.238	10.6	10.7	3.482	0.9949
	369	102.040	10.5	11.2	3.724	1.1099
	382	103.305	11.2	13	3.827	1.2975
	466	65.359	12.5	10.2	3.658	1.2993
	515	134.770	12.4	20.8	4.640	2.3087
	563	273.224	11.7	37.4	6.698	3.1436
TU1.5	305	8.620	10.1	0.872	2.771	0.0960
	323	8.403	9.98	0.836	2.804	0.0962
	370	23.419	11.3	2.97	3.023	0.3633
	419	31.055	11.6	4.22	3.190	0.5543
	468	19.685	13.6	3.65	3.148	0.5426
	516	28.248	16.8	7.95	3.320	1.2357
	565	158.730	14.6	33.7	5.136	3.7073
TU2	304	595.238	9.28	51.4	7.095	2.2041
	322	571.238	9.31	49.6	7.197	2.2203
	369	515.463	9.87	50.1	7.419	2.4941
	418	460.829	10.1	47.2	7.532	2.6194
	467	413.223	11.4	53.3	7.572	3.2874
	516	378.787	12.1	55.7	7.668	3.7483
	564	348.432	12.3	52.3	7.715	3.8233
TU4	304	375.939	9.05	30.8	5.477	1.7087
	322	359.712	8.91	28.6	5.550	1.6605
	369	327.868	9.36	28.8	5.749	1.8504
	418	299.401	10.1	30.6	5.901	2.1674
	467	272.479	11.5	36.3	5.989	2.8305
	515	248.756	12.8	40.6	6.044	3.4595
	564	233.644	13.8	44.6	6.147	4.0924

1. SEM images of samples synthesized from dithiooxamide are in an amorphous state, hence not shown. ↑

About the Author

 Ka Shing is a Singaporean student from River Valley High School who is interested in Materials Science since 15 years old. He participates in various research attachments to gain insights of how a scientist works.