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Synthesis, crystal structure and physical properties of kiddcreekite Cu6WSnS8 and its congener Cu6WSnSe8
Journal of Solid State Chemistry 278 (2019) 120918
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Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Synthesis, crystal structure and physical properties of kiddcreekite Cu6WSnS8 and its congener Cu6WSnSe8 Menghu Zhou a, b, *, Cheng Dong a, ** a b
Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China University of Chinese Academy of Sciences, Beijing, 100049, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Cu6WSnS8 Cu6WSnSe8 Crystal structure Metal-insulator transition Diamagnetic metals
We for the first time synthesized a rare quaternary sulfide mineral kiddcreekite Cu6WSnS8 and its congener Cu6WSnSe8 in the lab, and studied their crystal structures and physical properties. They have the same cubic crystal structure (space group F-43m) with lattice parameters 10.8299(7) and 11.2785(9) Å, respectively. In the unit cell, Cu, W and Sn occupy the 24f, 4a and 4c Wyckoff positions, respectively, while S or Se atoms occupy two sets of 16e Wyckoff positions. The electrical resistivity measurements reveal that both samples show metallic behaviour at high temperature and undergo metal-insulator transitions around 30 K. Both compounds exhibit diamagnetism at room temperature and Curie-Weiss paramagnetism at low temperature. The magnetic susceptibility analysis indicates that the effective magnetic moments in Cu6WSnS8 and Cu6WSnSe8 are most likely due to the contribution of a small amount of Cu2þ ions. The Cu2þ ions introduce hole carriers into the samples, which makes them show metallicity above 30 K. The Debye temperatures (ΘD) of Cu6WSnS8 and Cu6WSnSe8 are respectively 206.6 and 191.2 K, determined from the low-temperature specific heat measurements. On the basis of the experimental results, we conclude that both compounds belong to diamagnetic metals.
1. Introduction In recent years, quaternary chalcogenides had attracted much attentions in fields such as thermoelectricity, photoelectricity and topological insulators [1–3], whereas it is difficult to prepare them via direct solid-state reactions from the constituent elements due to prone to producing binary and ternary impurity phases. Y. Dong et al. [4] and K. Wei et al. [5] respectively reported the syntheses of bournonite PbCuSbS3 and madocite Pb17(Sb0.75As0.25)16S41 by reactions of binary compounds and studied their crystal structures, electronic structures and thermal conductivities. These works motivated us to explore new quaternary chalcogenides in the minerals and investigate into their physical properties. Kiddcreekite, a quaternary sulfide mineral that rarely exists in the nature [6–8], having the ideal formula Cu6WSnS8 [6,8]. Harris et al. found that kiddcreekite has a face-centered cubic lattice with a ¼ 10.856(2) Å and Z ¼ 4 [6]. Recently, Liu et al. studied the kiddcreekite by micro X-ray diffraction [9] and solved the crystal structure of kiddcreekite by using the direct space method. They revealed that kiddcreekite adopts a cubic structure with space group F-43m and lattice parameter a ¼ 10.8178(3) Å. In the unit cell, Cu, W and Sn atoms occupy the 24f, 4a and 4c Wyckoff
positions respectively and S atoms occupy two sets of 16e Wyckoff positions. However, it is not convenient to investigate the physical properties of Cu6WSnS8 owing to its rarity. The synthesis of large amounts of this mineral in the lab can solve this problem. In this work, we successfully synthesized monophasic samples of Cu6WSnS8 and Cu6WSnSe8 by direct reactions of the component elements. Their electrical, magnetic and thermal properties were studied by electrical resistivity, magnetic susceptibility and specific heat measurements. 2. Experimental The polycrystalline samples of Cu6WSnS8 and Cu6WSnSe8 were synthesized by solid-state reaction. Stoichiometric amounts of Cu (99.9%, Aladdin), W (99.99%, Aladdin), Sn (99.5%, Sinopharm Chemical Reagent, Co., Ltd., China) and S (99.5%, Alfa Aesar)/Se (99.999%, Aladdin) powders were thoroughly mixed, and then pressed into pellets, sealed in evacuated quartz tubes. In the case of Cu6WSnS8, the first heating cycle was performed at 873 K for 3 days. The sample was furnace-cooled to room temperature and then ground, pressed into pellets which were
* Corresponding author. Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China ** Corresponding author. E-mail addresses: [email protected] (M. Zhou), [email protected] (C. Dong). https://doi.org/10.1016/j.jssc.2019.120918 Received 9 July 2019; Received in revised form 15 August 2019; Accepted 20 August 2019 Available online 21 August 2019 0022-4596/© 2019 Elsevier Inc. All rights reserved.
M. Zhou, C. Dong
Journal of Solid State Chemistry 278 (2019) 120918
Fig. 1. EDX spectra of (a) Cu6WSnS8 and (b) Cu6WSnSe8. The corresponding inset panel shows the SEM for a cross-section of the bulk sample.
the crystal structures were examined by the bond-valence theory. The electrical resistivity measurements were performed in a physical property measurement system (Quantum Design, PPMS-9) by using the standard four-probe method. The magnetic susceptibility was measured with a vibrating sample magnetometer (Quantum Design, MPMS-VSM). The specific heat measurements were carried out in the same PPMS by the thermal relaxation method.
Table 1 The average atomic contents and atomic ratios of Cu, W, Sn and S/Se determined from the EDX spectra. Compound
Element
Atomic contents (%)
Atomic ratios
Cu6WSnS8
Cu W Sn S
37.39 6.23 6.31 50.07
5.97 1.00 1.01 8.00
Cu6WSnSe8
Cu W Sn Se
37.24 6.37 6.28 50.11
5.95 1.02 1.00 8.00
3. Results and discussion The synthesized polycrystalline bulk samples of Cu6WSnS8 and Cu6WSnSe8 are brittle and their cross-sections show silver-gray color. We analyzed the chemical compositions of the samples by EDX spectra (shown in Fig. 1 (a) and (b) for the area in the corresponding inset panel). It is evident that the characteristic peaks of Cu, W, Sn and S/Se locate at about 0.9, 1.8, 3.5 and 2.3/1.4 keV, respectively. Taking account of the possible inhomogeneity of the samples, we selected multiple points to acquire the EDX data and took the average. The average atomic contents and the calculated atomic ratios of Cu, W, Sn and S/Se in the samples were listed in Table 1. Apparently, the stoichiometric ratios in both samples are close to the nominal ones. The crystal structure of Cu6WSnS8 has been determined in Ref [9], while that of Cu6WSnSe8 is unknown. In this paper, the crystal structure of Cu6WSnSe8 was solved by using the direct space method (EPCryst package [10]). We find that the two compounds have the same cubic
resealed in evacuated quartz tubes. The sample was annealed at 873 K for one week, and finally furnace-cooled to room temperature. Similar heating process with a lower heating and annealing temperature of 773 K was used to prepare Cu6WSnSe8. The sample compositions were determined from EDX analyses. Scanning electron micrograph (SEM) and energy dispersive X-ray (EDX) spectroscopy were acquired on a Hitachi S-4800 field-emission scanning electron microscope. X-ray diffraction data was collected using a Rigaku Ultima-IV X-ray diffractometer with CuKα radiation. The crystal structure was solved by the direct space method (EPCryst package [10]) and refined by the Rietveld method (FullProf package [11]). The rationality of
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Journal of Solid State Chemistry 278 (2019) 120918
Table 3 Coordination polyhedrons, bond lengths and bond angles in Cu6WSnS8. Coordination polyhedron
Atom
Bonding atoms
Bond length (Å)
Bond angle ( )
Cu(S1)2(S2)2 tetrahedron
Cu Cu Cu W Sn
2S1 2S2 S1–S2 S2 S1
2.301 2.322
105.208 103.919 111.977 109.471 109.471
W(S2)4 tetrahedron Sn(S1)4 tetrahedron
2.240 2.450
Table 4 Crystallographic data and Rietveld refinement results for Cu6WSnSe8 at room temperature. Formula
Cu6WSnSe8
Space group
F-43m (No. 216)
a ¼ b ¼ c ¼ 11.2785(9) Å, V ¼ 1434.65(5) Å3, Z ¼ 4 Rp ¼ 6.61%, Rwp ¼ 7.63%, RB ¼ 2.40%, RF ¼ 1.36%, Rexp ¼ 1.30%
Table 2 Crystallographic data and Rietveld refinement results for Cu6WSnS8 at room temperature. Cu6WSnS8
Space group
F-43m (No. 216)
a ¼ b ¼ c ¼ 10.8299(7) Å, V ¼ 1270.22(4) Å3, Z ¼ 4 Rp ¼ 8.59%, Rwp ¼ 8.55%, RB ¼ 2.39%, RF ¼ 1.31%, Rexp ¼ 1.76% Atom
Wyckoff position
x
y
z
Occ.
B (Å2)
Cu W Sn S1 S2
24f 4a 4c 16e 16e
0.2515(6) 0 1/4 0.3806(2) 0.8805(8)
0 0 1/4 0.3806(2) 0.8805(8)
0 0 1/4 0.3806(2) 0.8805(8)
1 1 1 1 1
0.25 0.34 0.44 0.74 0.67
Wyckoff position
x
y
z
Occ.
B (Å2)
Cu W Sn Se1 Se2
24f 4a 4c 16e 16e
0.2490(6) 0 1/4 0.3825(9) 0.8791(8)
0 0 1/4 0.3825(9) 0.8791(8)
0 0 1/4 0.3825(9) 0.8791(8)
1 1 1 1 1
0.22 0.56 0.27 0.46 0.42
Cu, W and Sn atoms occupy the (S1)2(S2)2/(Se1)2(Se2)2, (S2)4/(Se2)4 and (S1)4/(Se1)4 tetrahedron interstices, respectively. The bond lengths and bond angles are calculated and shown in Table 3 and Table 5. It is obvious that Cu(S1)2(S2)2 and Cu(Se1)2(Se2)2 are irregular tetrahedrons. The molar masses (M) of Cu6WSnS8 and Cu6WSnSe8 are respectively 940.354 and 1315.506 g mol1. Consequently, the theoretical densities (ρt) calculated from the formula ρt ¼ ZM/NAV (where Z is the formula units, M is the molar mass, NA is the Avogadro constant and V is the cell volume) are 4.917 and 6.091 g cm3, respectively. The measured actual density (ρa) values of the polycrystalline pellets are respectively 3.996 and 5.082 g cm3 for Cu6WSnS8 and Cu6WSnSe8. The relative densities (ρr ¼ ρa/ρt) are calculated to be about 0.813 and 0.834, respectively, elucidating that the bulk samples are of high density and thus low porosity levels. This is consistent with the microscopic appearance observed in the SEM images (see Fig. 1). Subsequently, we examined the rationality of the crystal structures on the basis of bond-valence theory. The relation between the bond-valence and the bond length follows an empirical formula vij ¼ exp [(Rij-dij)/b] [12], where vij and dij are respectively the bond-valence and bond length between two atoms i and j, Rij is the bond-valence parameter and b is commonly taken to be a constant value of 0.37 Å. The Rij for Cu–S/Se, Sn–S/Se and W–S/Se bonds can be consulted in Ref [12,13]. For Cu6WSnS8, the calculated vCu-S1, vCu-S2, vSn-S1 and vW-S2 are 0.28, 0.26, 1.0 and 1.5, respectively. In terms of the Pauling’s electrostatic valence rule [14], the valences of Cu, Sn and W in Cu6WSnS8 are around þ1.08, þ4.00 and þ 6.00, respectively. Similarly, the valences of Cu, Sn and W in Cu6WSnSe8 are estimated to be about þ1.02, þ4.00 and þ 6.00, respectively. Thus, the crystallographic data in Tables 2 and 4 is validated by the bond valence calculations. We studied the electrical properties of Cu6WSnS8 and Cu6WSnSe8 by resistivity measurements. The ρ-T curves (temperature range from 2 to 250 K) were plotted in Fig. 4 (a) and (c). It is found that the samples exhibit metallicity at high temperature and insulativity at low temperature, i.e., there exist metal-insulator transitions in Cu6WSnS8 and Cu6WSnSe8. The analyses of atomic valences imply that some atoms may have incomplete electron shells with unpaired electrons in the compounds. This may result in the metallic behaviour at high temperature. Insulator-like tails appear as the temperature decreases, elucidating that the conducting electrons become localized. To determine the transition
Fig. 2. Rietveld refinement profiles for (a) Cu6WSnS8 and (b) Cu6WSnSe8 of the powder X-ray diffraction data. Vertical bars (|) indicate the positions of Bragg peaks. The bottom traces depict the difference between the observed and calculated intensity values.
Formula
Atom
structure (space group: F-43m). Cu, W and Sn occupy the 24f, 4a and 4c Wyckoff positions, respectively, while S or Se atoms occupy two sets of 16e Wyckoff positions in the unit cell. The crystal structures were refined by the Rietveld method (FullProf package [11]) of the powder diffraction data. Fig. 2 shows the observed and calculated X-ray diffraction patterns of Cu6WSnS8 and Cu6WSnSe8. It is noted that no detectable impurity phases were observed in the experimental X-ray diffraction patterns. The refined crystallographic data and the R factors are summarized in Table 2 and Table 4. The Bragg R factors (RB) for both samples converge to about 2.40%, demonstrating that the crystal structures are correct. The crystal structure diagrams are illustrated in Fig. 3. We can see that
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Journal of Solid State Chemistry 278 (2019) 120918
Fig. 3. (a) The crystal structure diagram of Cu6WSnX8 (X ¼ S, Se). (b) Partial structure of Cu6WSnX8 (X ¼ S, Se), displaying the coordination environment of each atom.
both Bloch-Grüneisen (BM)-like and VRH-like. Based on this assumption, the resistivity data (with temperature ranging from 21 to 100 K) can be well fitted by a formula with two components: ρ ¼ ρ1 þ BT þ ρ2 exp [(T0 /T)1/4] (shown in Fig. 6). The fitted ρ1, B, ρ2 and T0 values are respectively 0.25 Ω cm, 7.99 104 Ω cm K1, 0.22 Ω cm and 0.37 K for Cu6WSnS8 and those are respectively 0.093 Ω cm, 1.73 104 Ω cm K1, 0.052 Ω cm and 0.22 K for Cu6WSnSe8. It is evident that the contribution of the VRH-like component to the resistivity increases with temperature decreasing. This is in good agreement with the high temperature BM-like and the low temperature VRH-like electrical resistivity. Fig. 7 shows the temperature dependence of magnetic susceptibilities for Cu6WSnS8 and Cu6WSnSe8 under zero field cooling (ZFC) and field cooling (FC) modes. The χ -T curves under the two modes are perfectly coincident within the whole temperature range. Both samples display diamagnetism at room temperature and Curie-Weiss paramagnetism at low temperature. Their total susceptibilities χ are constituted of two components: the temperature-independent diamagnetic term χ dia and the Curie-Weiss term, respectively stemming from the contribution of saturated electronic structure (Cuþ, W6þ, Sn4þ and S/Se2) and paramagnetic ions (Cu2þ). We performed fitting of the χ -T data with formula χ ¼ χ dia þ C/(T θp). The χ dia, Curie constants C and paramagnetic Curie temperatures θp of Cu6WSnS8 and Cu6WSnSe8 are listed in Table 7. By using the formula μeff ¼ (8C)1/2μB, the effective moments μeff of Cu6WSnS8 and Cu6WSnSe8 are calculated to be 0.11 and 0.14μB, respectively, and hence the average effective moments per atom of Cu in the samples are respectively 0.018 and 0.023μB. The effective magnetic moments are most likely due to the contribution of a small amount of Cu2þ ions. It is known to us that the effective moment of Cu2þ is 1.73μB. Therefore, the concentration of Cu2þ in Cu6WSnS8 and Cu6WSnSe8 are estimated to be 1.04% and 1.33%, respectively. In accordance with the results of valencestate analyses, the valence formula could be expressed as (Cuþ)62þ x(Cu )xWSnX8 (X ¼ S and Se), namely Cu6WSnS8 and Cu6WSnSe8 also can be considered as self-doped compounds. The Cu2þ ions introduce hole carriers into the samples, which makes them show metallicity above 30 K. Fig. 8 (a) and (c) show the temperature dependence of specific heats for Cu6WSnS8 and Cu6WSnSe8. No significant transitions around 30 K were observed on Cp-T curves. The behaviour of specific heat (with temperature ranging from 2 to 9 K and from 2 to 5 K for Cu6WSnS8 and Cu6WSnSe8, respectively) can be formulated by the equation: Cp ¼ γT þ βT3 (i.e., Cp/T ¼ γ þ βT2), where γ and β are respectively the electronic and phononic specific heat coefficient. We plotted the low-temperature Cp/T vs T2 curves of the samples in Fig. 8 (b) and (d). It is revealed that Cp/T vs T2 curves appear strikingly linear behaviour. The obtained γ
Table 5 Coordination polyhedrons, bond lengths and bond angles in Cu6WSnSe8. Coordination polyhedron
Atom
Bonding atoms
Bond length (Å)
Bond angle ( )
Cu(Se1)2(Se2)2 tetrahedron
Cu Cu Cu W Sn
2Se1 2Se2 Se1–Se2 Se2 Se1
2.403 2.410
102.388 106.221 112.097 109.471 109.471
W(Se2)4 tetrahedron Sn(Se1)4 tetrahedron
2.360 2.590
temperatures, the dρ/dT vs T curves were presented in Fig. 4 (b) and (d). The transition temperatures are 30.7 and 29.5 K for Cu6WSnS8 and Cu6WSnSe8, respectively. Meanwhile, we found that the dρ/dT values are constant above 100 K for both samples, indicating linear T dependence of ρ (T) curves. Typically, the contribution of electron-phonon interaction to resistivity ρel-ph in a pure metal obeys the Bloch-Grüneisen law [15]:
ρelph ðTÞ ¼ αelph
T ΘD
5 Z
ΘD T
0
x5 dx ðex 1Þð1 ex Þ
(1)
where αel-ph is a characteristic constant depending on the metal and ΘD is the Debye temperature. When T > 0.5ΘD, equation (1) reduces to ρel-ph (T) ¼ αel-phT/ΘD, namely, ρel-ph ∝ T. The Debye temperatures (ΘD) of Cu6WSnS8 and Cu6WSnSe8 determined from the specific heat measurements (discussed in the following section) are 206.6 and 191.2 K, respectively. Thus, the ρT curves of both samples with temperature above 100 K can be well fitted (the fitted curves are shown in Fig. 4 (a) and (c) by red solid lines) by Matthiessen’s rule: ρ (T) ¼ ρ0 þ AT, where ρ0 is the residual resistivity due to defect scattering and is essentially temperature independent, A is the temperature coefficient. The fitted ρ0 and A are summarized in Table 6. The samples show insulating behaviour (dρ/dT < 0) as temperature below about 30 K. Generally, the conductive mechanism of an insulator could be interpreted by a simple Arrhenius law ρ ¼ ρ∞ exp (Eg/2kBT) [16] or a Mott’s variable range hopping (VRH) model ρ ¼ ρ∞ exp [(T0/T)1/4] [16,17]. The latter is appropriate to fit the experimental data with temperature ranging from 2 to 21 K for both samples (see Fig. 5). The fitted curves by Arrhenius law were also presented in the corresponding panel as comparisons. The facts stated above demonstrate that the insulating behaviour in the compounds is probably due to the random potential fluctuation induced localization of carriers [16]. By fitting, the values of T0 were estimated to be about 11.29 and 0.34 mK for Cu6WSnS8 and Cu6WSnSe8, respectively. As can be seen from Fig. 4 (a) and (c), electrical resistivity at around 30 K is probably composed of two components of
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Journal of Solid State Chemistry 278 (2019) 120918
Fig. 4. Temperature dependence of electrical resistivities for (a) Cu6WSnS8 and (c) Cu6WSnSe8. The red solid lines are fitted curves by the formula ρ ¼ ρ0 þ AT. R2 signifies the goodness-of-fit. dρ/dT vs T curves for (b) Cu6WSnS8 and (d) Cu6WSnSe8. The blue solid lines are guides to the eye. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
values are respectively 0.018 and 0.28 mJ mol1 K2 for Cu6WSnS8 and Cu6WSnSe8 (see the insets of Fig. 8 (b) and (d)), giving rise to finite electron density of states N (EF) (N (EF) ∝ γ), which is consistent with the VRH model (Fermi level lies in a band for VRH conduction as well as for metallic conduction). Evidently, the N (EF) value of Cu6WSnSe8 is larger
Table 6 The fitted ρ0 and A of Cu6WSnS8 and Cu6WSnSe8. Sample
ρ0 (Ω⋅cm)
A ( 104 Ω cm K1)
Cu6WSnS8 Cu6WSnSe8
0.55 0.16
6.37 1.54
Fig. 5. Temperature dependence of electrical resistivities for (a) Cu6WSnS8 and (b) Cu6WSnSe8 with temperature ranging from 2 to 21 K. The red and blue solid lines respectively present the fitted curves by the VRH model and the Arrhenius law. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) 5
M. Zhou, C. Dong
Journal of Solid State Chemistry 278 (2019) 120918
Fig. 6. Temperature dependence of electrical resistivities for (a) Cu6WSnS8 and (b) Cu6WSnSe8 with temperature ranging from 21 to 100 K. The light green and light blue lines are fitted curves by the formula with two components (BM þ VRH): ρ ¼ ρ1 þ BT þ ρ2 exp [(T0 /T)1/4]. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 7. Temperature dependence of magnetic susceptibilities for (a) Cu6WSnS8 and (b) Cu6WSnSe8 under zero field cooling (ZFC) and field cooling (FC) modes in an applied field of 1.0 T. The light green solid lines are fitted curves by using the formula χ ¼ χ dia þ C/(T θp). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
4. Conclusions
Table 7 The diamagnetic susceptibilities χ dia, Curie constants C and paramagnetic Curie temperatures θp of Cu6WSnS8 and Cu6WSnSe8. Compound Cu6WSnS8 Cu6WSnSe8
χ dia
( 104emu⋅mol1⋅Oe1)
C ( 103emu⋅K⋅mol1⋅Oe1)
θp (K)
2.50 3.60
1.57 2.31
2.57 2.02
Cu6WSnS8 and Cu6WSnSe8 were synthesized and characterized via Xray diffraction, electrical resistivity, magnetic susceptibility and specific heat measurements. It is found that both compounds have cubic crystal symmetry with space group F-43m. The lattice parameters of Cu6WSnS8 and Cu6WSnSe8 are 10.8299(7) and 11.2785(9) Å, respectively. Cu, W and Sn occupy the 24f, 4a and 4c Wyckoff positions, respectively, and S or Se atoms occupy two sets of 16e Wyckoff positions. Metal-insulator transitions around 30 K were observed in both samples. They exhibit diamagnetism at room temperature and Curie-Weiss paramagnetism at low temperature. The small amounts of Cu2þ ions introduce hole carriers into the samples, which makes them show metallicity above 30 K. The Debye temperatures of Cu6WSnS8 and Cu6WSnSe8 are respectively 206.6 and 191.2 K. According to the above experimental results, both compounds are considered to be diamagnetic metals.
than that of Cu6WSnS8, verifying the fact that the electrical conductivity of the former is higher than that of the latter (see Fig. 4). The β values are 3.52 and 4.44 mJ mol1 K4 for Cu6WSnS8 and Cu6WSnSe8, respectively. From the β value, we estimated the Debye temperature by the relation ΘD ¼ (12π 4nNAkB/5β)1/3, where n is the number of atoms per formula unit (n ¼ 16 in these compounds). The Debye temperatures of Cu6WSnS8 and Cu6WSnSe8 are calculated to be 206.6 and 191.2 K, respectively.
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Journal of Solid State Chemistry 278 (2019) 120918
Fig. 8. Temperature dependence of specific heats for (a) Cu6WSnS8 and (c) Cu6WSnSe8. Cp/T vs T2 curves of (b) Cu6WSnS8 and (d) Cu6WSnSe8. The light green and light blue lines are fitted curves by the formula C/T ¼ γ þ βT2. R2 denotes the goodness-of-fit. The corresponding inset panel shows an enlarge view of the C/T vs T2 curve near zero temperature. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Acknowledgments
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This work was supported by the National Natural Science Foundation of China (Grant No. 21271183) and the MOST of China (Grand No. 2017YFA0302903). References [1] M.L. Liu, F.Q. Huang, L.D. Chen, I.W. Chen, Appl. Phys. Lett. 94 (2009) 202103. [2] J.J. Scragg, P.J. Dale, L.M. Peter, G. Zoppi, I. Forbes, Phys. Status Solidi 245 (2008) 1772. [3] Y.J. Wang, H. Lin, T. Das, M.Z. Hasan, A. Bansil, New J. Phys. 13 (2011), 085017. [4] Y. Dong, A.R. Khabibullin, K. Wei, J.R. Salvador, G.S. Nolas, L.M. Woods, ChemPhysChem 16 (2015) 3264. [5] K. Wei, J. Martin, S. Maruyama, T. Mori, G.S. Nolas, J. Solid State Chem. 251 (2017) 113.
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Contents lists available at ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Synthesis, crystal structure and physical properties of kiddcreekite Cu6WSnS8 and its congener Cu6WSnSe8 Menghu Zhou a, b, *, Cheng Dong a, ** a b
Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China University of Chinese Academy of Sciences, Beijing, 100049, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Cu6WSnS8 Cu6WSnSe8 Crystal structure Metal-insulator transition Diamagnetic metals
We for the first time synthesized a rare quaternary sulfide mineral kiddcreekite Cu6WSnS8 and its congener Cu6WSnSe8 in the lab, and studied their crystal structures and physical properties. They have the same cubic crystal structure (space group F-43m) with lattice parameters 10.8299(7) and 11.2785(9) Å, respectively. In the unit cell, Cu, W and Sn occupy the 24f, 4a and 4c Wyckoff positions, respectively, while S or Se atoms occupy two sets of 16e Wyckoff positions. The electrical resistivity measurements reveal that both samples show metallic behaviour at high temperature and undergo metal-insulator transitions around 30 K. Both compounds exhibit diamagnetism at room temperature and Curie-Weiss paramagnetism at low temperature. The magnetic susceptibility analysis indicates that the effective magnetic moments in Cu6WSnS8 and Cu6WSnSe8 are most likely due to the contribution of a small amount of Cu2þ ions. The Cu2þ ions introduce hole carriers into the samples, which makes them show metallicity above 30 K. The Debye temperatures (ΘD) of Cu6WSnS8 and Cu6WSnSe8 are respectively 206.6 and 191.2 K, determined from the low-temperature specific heat measurements. On the basis of the experimental results, we conclude that both compounds belong to diamagnetic metals.
1. Introduction In recent years, quaternary chalcogenides had attracted much attentions in fields such as thermoelectricity, photoelectricity and topological insulators [1–3], whereas it is difficult to prepare them via direct solid-state reactions from the constituent elements due to prone to producing binary and ternary impurity phases. Y. Dong et al. [4] and K. Wei et al. [5] respectively reported the syntheses of bournonite PbCuSbS3 and madocite Pb17(Sb0.75As0.25)16S41 by reactions of binary compounds and studied their crystal structures, electronic structures and thermal conductivities. These works motivated us to explore new quaternary chalcogenides in the minerals and investigate into their physical properties. Kiddcreekite, a quaternary sulfide mineral that rarely exists in the nature [6–8], having the ideal formula Cu6WSnS8 [6,8]. Harris et al. found that kiddcreekite has a face-centered cubic lattice with a ¼ 10.856(2) Å and Z ¼ 4 [6]. Recently, Liu et al. studied the kiddcreekite by micro X-ray diffraction [9] and solved the crystal structure of kiddcreekite by using the direct space method. They revealed that kiddcreekite adopts a cubic structure with space group F-43m and lattice parameter a ¼ 10.8178(3) Å. In the unit cell, Cu, W and Sn atoms occupy the 24f, 4a and 4c Wyckoff
positions respectively and S atoms occupy two sets of 16e Wyckoff positions. However, it is not convenient to investigate the physical properties of Cu6WSnS8 owing to its rarity. The synthesis of large amounts of this mineral in the lab can solve this problem. In this work, we successfully synthesized monophasic samples of Cu6WSnS8 and Cu6WSnSe8 by direct reactions of the component elements. Their electrical, magnetic and thermal properties were studied by electrical resistivity, magnetic susceptibility and specific heat measurements. 2. Experimental The polycrystalline samples of Cu6WSnS8 and Cu6WSnSe8 were synthesized by solid-state reaction. Stoichiometric amounts of Cu (99.9%, Aladdin), W (99.99%, Aladdin), Sn (99.5%, Sinopharm Chemical Reagent, Co., Ltd., China) and S (99.5%, Alfa Aesar)/Se (99.999%, Aladdin) powders were thoroughly mixed, and then pressed into pellets, sealed in evacuated quartz tubes. In the case of Cu6WSnS8, the first heating cycle was performed at 873 K for 3 days. The sample was furnace-cooled to room temperature and then ground, pressed into pellets which were
* Corresponding author. Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China ** Corresponding author. E-mail addresses: [email protected] (M. Zhou), [email protected] (C. Dong). https://doi.org/10.1016/j.jssc.2019.120918 Received 9 July 2019; Received in revised form 15 August 2019; Accepted 20 August 2019 Available online 21 August 2019 0022-4596/© 2019 Elsevier Inc. All rights reserved.
M. Zhou, C. Dong
Journal of Solid State Chemistry 278 (2019) 120918
Fig. 1. EDX spectra of (a) Cu6WSnS8 and (b) Cu6WSnSe8. The corresponding inset panel shows the SEM for a cross-section of the bulk sample.
the crystal structures were examined by the bond-valence theory. The electrical resistivity measurements were performed in a physical property measurement system (Quantum Design, PPMS-9) by using the standard four-probe method. The magnetic susceptibility was measured with a vibrating sample magnetometer (Quantum Design, MPMS-VSM). The specific heat measurements were carried out in the same PPMS by the thermal relaxation method.
Table 1 The average atomic contents and atomic ratios of Cu, W, Sn and S/Se determined from the EDX spectra. Compound
Element
Atomic contents (%)
Atomic ratios
Cu6WSnS8
Cu W Sn S
37.39 6.23 6.31 50.07
5.97 1.00 1.01 8.00
Cu6WSnSe8
Cu W Sn Se
37.24 6.37 6.28 50.11
5.95 1.02 1.00 8.00
3. Results and discussion The synthesized polycrystalline bulk samples of Cu6WSnS8 and Cu6WSnSe8 are brittle and their cross-sections show silver-gray color. We analyzed the chemical compositions of the samples by EDX spectra (shown in Fig. 1 (a) and (b) for the area in the corresponding inset panel). It is evident that the characteristic peaks of Cu, W, Sn and S/Se locate at about 0.9, 1.8, 3.5 and 2.3/1.4 keV, respectively. Taking account of the possible inhomogeneity of the samples, we selected multiple points to acquire the EDX data and took the average. The average atomic contents and the calculated atomic ratios of Cu, W, Sn and S/Se in the samples were listed in Table 1. Apparently, the stoichiometric ratios in both samples are close to the nominal ones. The crystal structure of Cu6WSnS8 has been determined in Ref [9], while that of Cu6WSnSe8 is unknown. In this paper, the crystal structure of Cu6WSnSe8 was solved by using the direct space method (EPCryst package [10]). We find that the two compounds have the same cubic
resealed in evacuated quartz tubes. The sample was annealed at 873 K for one week, and finally furnace-cooled to room temperature. Similar heating process with a lower heating and annealing temperature of 773 K was used to prepare Cu6WSnSe8. The sample compositions were determined from EDX analyses. Scanning electron micrograph (SEM) and energy dispersive X-ray (EDX) spectroscopy were acquired on a Hitachi S-4800 field-emission scanning electron microscope. X-ray diffraction data was collected using a Rigaku Ultima-IV X-ray diffractometer with CuKα radiation. The crystal structure was solved by the direct space method (EPCryst package [10]) and refined by the Rietveld method (FullProf package [11]). The rationality of
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Journal of Solid State Chemistry 278 (2019) 120918
Table 3 Coordination polyhedrons, bond lengths and bond angles in Cu6WSnS8. Coordination polyhedron
Atom
Bonding atoms
Bond length (Å)
Bond angle ( )
Cu(S1)2(S2)2 tetrahedron
Cu Cu Cu W Sn
2S1 2S2 S1–S2 S2 S1
2.301 2.322
105.208 103.919 111.977 109.471 109.471
W(S2)4 tetrahedron Sn(S1)4 tetrahedron
2.240 2.450
Table 4 Crystallographic data and Rietveld refinement results for Cu6WSnSe8 at room temperature. Formula
Cu6WSnSe8
Space group
F-43m (No. 216)
a ¼ b ¼ c ¼ 11.2785(9) Å, V ¼ 1434.65(5) Å3, Z ¼ 4 Rp ¼ 6.61%, Rwp ¼ 7.63%, RB ¼ 2.40%, RF ¼ 1.36%, Rexp ¼ 1.30%
Table 2 Crystallographic data and Rietveld refinement results for Cu6WSnS8 at room temperature. Cu6WSnS8
Space group
F-43m (No. 216)
a ¼ b ¼ c ¼ 10.8299(7) Å, V ¼ 1270.22(4) Å3, Z ¼ 4 Rp ¼ 8.59%, Rwp ¼ 8.55%, RB ¼ 2.39%, RF ¼ 1.31%, Rexp ¼ 1.76% Atom
Wyckoff position
x
y
z
Occ.
B (Å2)
Cu W Sn S1 S2
24f 4a 4c 16e 16e
0.2515(6) 0 1/4 0.3806(2) 0.8805(8)
0 0 1/4 0.3806(2) 0.8805(8)
0 0 1/4 0.3806(2) 0.8805(8)
1 1 1 1 1
0.25 0.34 0.44 0.74 0.67
Wyckoff position
x
y
z
Occ.
B (Å2)
Cu W Sn Se1 Se2
24f 4a 4c 16e 16e
0.2490(6) 0 1/4 0.3825(9) 0.8791(8)
0 0 1/4 0.3825(9) 0.8791(8)
0 0 1/4 0.3825(9) 0.8791(8)
1 1 1 1 1
0.22 0.56 0.27 0.46 0.42
Cu, W and Sn atoms occupy the (S1)2(S2)2/(Se1)2(Se2)2, (S2)4/(Se2)4 and (S1)4/(Se1)4 tetrahedron interstices, respectively. The bond lengths and bond angles are calculated and shown in Table 3 and Table 5. It is obvious that Cu(S1)2(S2)2 and Cu(Se1)2(Se2)2 are irregular tetrahedrons. The molar masses (M) of Cu6WSnS8 and Cu6WSnSe8 are respectively 940.354 and 1315.506 g mol1. Consequently, the theoretical densities (ρt) calculated from the formula ρt ¼ ZM/NAV (where Z is the formula units, M is the molar mass, NA is the Avogadro constant and V is the cell volume) are 4.917 and 6.091 g cm3, respectively. The measured actual density (ρa) values of the polycrystalline pellets are respectively 3.996 and 5.082 g cm3 for Cu6WSnS8 and Cu6WSnSe8. The relative densities (ρr ¼ ρa/ρt) are calculated to be about 0.813 and 0.834, respectively, elucidating that the bulk samples are of high density and thus low porosity levels. This is consistent with the microscopic appearance observed in the SEM images (see Fig. 1). Subsequently, we examined the rationality of the crystal structures on the basis of bond-valence theory. The relation between the bond-valence and the bond length follows an empirical formula vij ¼ exp [(Rij-dij)/b] [12], where vij and dij are respectively the bond-valence and bond length between two atoms i and j, Rij is the bond-valence parameter and b is commonly taken to be a constant value of 0.37 Å. The Rij for Cu–S/Se, Sn–S/Se and W–S/Se bonds can be consulted in Ref [12,13]. For Cu6WSnS8, the calculated vCu-S1, vCu-S2, vSn-S1 and vW-S2 are 0.28, 0.26, 1.0 and 1.5, respectively. In terms of the Pauling’s electrostatic valence rule [14], the valences of Cu, Sn and W in Cu6WSnS8 are around þ1.08, þ4.00 and þ 6.00, respectively. Similarly, the valences of Cu, Sn and W in Cu6WSnSe8 are estimated to be about þ1.02, þ4.00 and þ 6.00, respectively. Thus, the crystallographic data in Tables 2 and 4 is validated by the bond valence calculations. We studied the electrical properties of Cu6WSnS8 and Cu6WSnSe8 by resistivity measurements. The ρ-T curves (temperature range from 2 to 250 K) were plotted in Fig. 4 (a) and (c). It is found that the samples exhibit metallicity at high temperature and insulativity at low temperature, i.e., there exist metal-insulator transitions in Cu6WSnS8 and Cu6WSnSe8. The analyses of atomic valences imply that some atoms may have incomplete electron shells with unpaired electrons in the compounds. This may result in the metallic behaviour at high temperature. Insulator-like tails appear as the temperature decreases, elucidating that the conducting electrons become localized. To determine the transition
Fig. 2. Rietveld refinement profiles for (a) Cu6WSnS8 and (b) Cu6WSnSe8 of the powder X-ray diffraction data. Vertical bars (|) indicate the positions of Bragg peaks. The bottom traces depict the difference between the observed and calculated intensity values.
Formula
Atom
structure (space group: F-43m). Cu, W and Sn occupy the 24f, 4a and 4c Wyckoff positions, respectively, while S or Se atoms occupy two sets of 16e Wyckoff positions in the unit cell. The crystal structures were refined by the Rietveld method (FullProf package [11]) of the powder diffraction data. Fig. 2 shows the observed and calculated X-ray diffraction patterns of Cu6WSnS8 and Cu6WSnSe8. It is noted that no detectable impurity phases were observed in the experimental X-ray diffraction patterns. The refined crystallographic data and the R factors are summarized in Table 2 and Table 4. The Bragg R factors (RB) for both samples converge to about 2.40%, demonstrating that the crystal structures are correct. The crystal structure diagrams are illustrated in Fig. 3. We can see that
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Journal of Solid State Chemistry 278 (2019) 120918
Fig. 3. (a) The crystal structure diagram of Cu6WSnX8 (X ¼ S, Se). (b) Partial structure of Cu6WSnX8 (X ¼ S, Se), displaying the coordination environment of each atom.
both Bloch-Grüneisen (BM)-like and VRH-like. Based on this assumption, the resistivity data (with temperature ranging from 21 to 100 K) can be well fitted by a formula with two components: ρ ¼ ρ1 þ BT þ ρ2 exp [(T0 /T)1/4] (shown in Fig. 6). The fitted ρ1, B, ρ2 and T0 values are respectively 0.25 Ω cm, 7.99 104 Ω cm K1, 0.22 Ω cm and 0.37 K for Cu6WSnS8 and those are respectively 0.093 Ω cm, 1.73 104 Ω cm K1, 0.052 Ω cm and 0.22 K for Cu6WSnSe8. It is evident that the contribution of the VRH-like component to the resistivity increases with temperature decreasing. This is in good agreement with the high temperature BM-like and the low temperature VRH-like electrical resistivity. Fig. 7 shows the temperature dependence of magnetic susceptibilities for Cu6WSnS8 and Cu6WSnSe8 under zero field cooling (ZFC) and field cooling (FC) modes. The χ -T curves under the two modes are perfectly coincident within the whole temperature range. Both samples display diamagnetism at room temperature and Curie-Weiss paramagnetism at low temperature. Their total susceptibilities χ are constituted of two components: the temperature-independent diamagnetic term χ dia and the Curie-Weiss term, respectively stemming from the contribution of saturated electronic structure (Cuþ, W6þ, Sn4þ and S/Se2) and paramagnetic ions (Cu2þ). We performed fitting of the χ -T data with formula χ ¼ χ dia þ C/(T θp). The χ dia, Curie constants C and paramagnetic Curie temperatures θp of Cu6WSnS8 and Cu6WSnSe8 are listed in Table 7. By using the formula μeff ¼ (8C)1/2μB, the effective moments μeff of Cu6WSnS8 and Cu6WSnSe8 are calculated to be 0.11 and 0.14μB, respectively, and hence the average effective moments per atom of Cu in the samples are respectively 0.018 and 0.023μB. The effective magnetic moments are most likely due to the contribution of a small amount of Cu2þ ions. It is known to us that the effective moment of Cu2þ is 1.73μB. Therefore, the concentration of Cu2þ in Cu6WSnS8 and Cu6WSnSe8 are estimated to be 1.04% and 1.33%, respectively. In accordance with the results of valencestate analyses, the valence formula could be expressed as (Cuþ)62þ x(Cu )xWSnX8 (X ¼ S and Se), namely Cu6WSnS8 and Cu6WSnSe8 also can be considered as self-doped compounds. The Cu2þ ions introduce hole carriers into the samples, which makes them show metallicity above 30 K. Fig. 8 (a) and (c) show the temperature dependence of specific heats for Cu6WSnS8 and Cu6WSnSe8. No significant transitions around 30 K were observed on Cp-T curves. The behaviour of specific heat (with temperature ranging from 2 to 9 K and from 2 to 5 K for Cu6WSnS8 and Cu6WSnSe8, respectively) can be formulated by the equation: Cp ¼ γT þ βT3 (i.e., Cp/T ¼ γ þ βT2), where γ and β are respectively the electronic and phononic specific heat coefficient. We plotted the low-temperature Cp/T vs T2 curves of the samples in Fig. 8 (b) and (d). It is revealed that Cp/T vs T2 curves appear strikingly linear behaviour. The obtained γ
Table 5 Coordination polyhedrons, bond lengths and bond angles in Cu6WSnSe8. Coordination polyhedron
Atom
Bonding atoms
Bond length (Å)
Bond angle ( )
Cu(Se1)2(Se2)2 tetrahedron
Cu Cu Cu W Sn
2Se1 2Se2 Se1–Se2 Se2 Se1
2.403 2.410
102.388 106.221 112.097 109.471 109.471
W(Se2)4 tetrahedron Sn(Se1)4 tetrahedron
2.360 2.590
temperatures, the dρ/dT vs T curves were presented in Fig. 4 (b) and (d). The transition temperatures are 30.7 and 29.5 K for Cu6WSnS8 and Cu6WSnSe8, respectively. Meanwhile, we found that the dρ/dT values are constant above 100 K for both samples, indicating linear T dependence of ρ (T) curves. Typically, the contribution of electron-phonon interaction to resistivity ρel-ph in a pure metal obeys the Bloch-Grüneisen law [15]:
ρelph ðTÞ ¼ αelph
T ΘD
5 Z
ΘD T
0
x5 dx ðex 1Þð1 ex Þ
(1)
where αel-ph is a characteristic constant depending on the metal and ΘD is the Debye temperature. When T > 0.5ΘD, equation (1) reduces to ρel-ph (T) ¼ αel-phT/ΘD, namely, ρel-ph ∝ T. The Debye temperatures (ΘD) of Cu6WSnS8 and Cu6WSnSe8 determined from the specific heat measurements (discussed in the following section) are 206.6 and 191.2 K, respectively. Thus, the ρT curves of both samples with temperature above 100 K can be well fitted (the fitted curves are shown in Fig. 4 (a) and (c) by red solid lines) by Matthiessen’s rule: ρ (T) ¼ ρ0 þ AT, where ρ0 is the residual resistivity due to defect scattering and is essentially temperature independent, A is the temperature coefficient. The fitted ρ0 and A are summarized in Table 6. The samples show insulating behaviour (dρ/dT < 0) as temperature below about 30 K. Generally, the conductive mechanism of an insulator could be interpreted by a simple Arrhenius law ρ ¼ ρ∞ exp (Eg/2kBT) [16] or a Mott’s variable range hopping (VRH) model ρ ¼ ρ∞ exp [(T0/T)1/4] [16,17]. The latter is appropriate to fit the experimental data with temperature ranging from 2 to 21 K for both samples (see Fig. 5). The fitted curves by Arrhenius law were also presented in the corresponding panel as comparisons. The facts stated above demonstrate that the insulating behaviour in the compounds is probably due to the random potential fluctuation induced localization of carriers [16]. By fitting, the values of T0 were estimated to be about 11.29 and 0.34 mK for Cu6WSnS8 and Cu6WSnSe8, respectively. As can be seen from Fig. 4 (a) and (c), electrical resistivity at around 30 K is probably composed of two components of
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Journal of Solid State Chemistry 278 (2019) 120918
Fig. 4. Temperature dependence of electrical resistivities for (a) Cu6WSnS8 and (c) Cu6WSnSe8. The red solid lines are fitted curves by the formula ρ ¼ ρ0 þ AT. R2 signifies the goodness-of-fit. dρ/dT vs T curves for (b) Cu6WSnS8 and (d) Cu6WSnSe8. The blue solid lines are guides to the eye. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
values are respectively 0.018 and 0.28 mJ mol1 K2 for Cu6WSnS8 and Cu6WSnSe8 (see the insets of Fig. 8 (b) and (d)), giving rise to finite electron density of states N (EF) (N (EF) ∝ γ), which is consistent with the VRH model (Fermi level lies in a band for VRH conduction as well as for metallic conduction). Evidently, the N (EF) value of Cu6WSnSe8 is larger
Table 6 The fitted ρ0 and A of Cu6WSnS8 and Cu6WSnSe8. Sample
ρ0 (Ω⋅cm)
A ( 104 Ω cm K1)
Cu6WSnS8 Cu6WSnSe8
0.55 0.16
6.37 1.54
Fig. 5. Temperature dependence of electrical resistivities for (a) Cu6WSnS8 and (b) Cu6WSnSe8 with temperature ranging from 2 to 21 K. The red and blue solid lines respectively present the fitted curves by the VRH model and the Arrhenius law. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) 5
M. Zhou, C. Dong
Journal of Solid State Chemistry 278 (2019) 120918
Fig. 6. Temperature dependence of electrical resistivities for (a) Cu6WSnS8 and (b) Cu6WSnSe8 with temperature ranging from 21 to 100 K. The light green and light blue lines are fitted curves by the formula with two components (BM þ VRH): ρ ¼ ρ1 þ BT þ ρ2 exp [(T0 /T)1/4]. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Fig. 7. Temperature dependence of magnetic susceptibilities for (a) Cu6WSnS8 and (b) Cu6WSnSe8 under zero field cooling (ZFC) and field cooling (FC) modes in an applied field of 1.0 T. The light green solid lines are fitted curves by using the formula χ ¼ χ dia þ C/(T θp). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
4. Conclusions
Table 7 The diamagnetic susceptibilities χ dia, Curie constants C and paramagnetic Curie temperatures θp of Cu6WSnS8 and Cu6WSnSe8. Compound Cu6WSnS8 Cu6WSnSe8
χ dia
( 104emu⋅mol1⋅Oe1)
C ( 103emu⋅K⋅mol1⋅Oe1)
θp (K)
2.50 3.60
1.57 2.31
2.57 2.02
Cu6WSnS8 and Cu6WSnSe8 were synthesized and characterized via Xray diffraction, electrical resistivity, magnetic susceptibility and specific heat measurements. It is found that both compounds have cubic crystal symmetry with space group F-43m. The lattice parameters of Cu6WSnS8 and Cu6WSnSe8 are 10.8299(7) and 11.2785(9) Å, respectively. Cu, W and Sn occupy the 24f, 4a and 4c Wyckoff positions, respectively, and S or Se atoms occupy two sets of 16e Wyckoff positions. Metal-insulator transitions around 30 K were observed in both samples. They exhibit diamagnetism at room temperature and Curie-Weiss paramagnetism at low temperature. The small amounts of Cu2þ ions introduce hole carriers into the samples, which makes them show metallicity above 30 K. The Debye temperatures of Cu6WSnS8 and Cu6WSnSe8 are respectively 206.6 and 191.2 K. According to the above experimental results, both compounds are considered to be diamagnetic metals.
than that of Cu6WSnS8, verifying the fact that the electrical conductivity of the former is higher than that of the latter (see Fig. 4). The β values are 3.52 and 4.44 mJ mol1 K4 for Cu6WSnS8 and Cu6WSnSe8, respectively. From the β value, we estimated the Debye temperature by the relation ΘD ¼ (12π 4nNAkB/5β)1/3, where n is the number of atoms per formula unit (n ¼ 16 in these compounds). The Debye temperatures of Cu6WSnS8 and Cu6WSnSe8 are calculated to be 206.6 and 191.2 K, respectively.
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Journal of Solid State Chemistry 278 (2019) 120918
Fig. 8. Temperature dependence of specific heats for (a) Cu6WSnS8 and (c) Cu6WSnSe8. Cp/T vs T2 curves of (b) Cu6WSnS8 and (d) Cu6WSnSe8. The light green and light blue lines are fitted curves by the formula C/T ¼ γ þ βT2. R2 denotes the goodness-of-fit. The corresponding inset panel shows an enlarge view of the C/T vs T2 curve near zero temperature. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
Acknowledgments
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