Kan
Chen
*a,
Cono
Di Paola
b,
Savio
Laricchia
b,
Michael J.
Reece
a,
Cedric
Weber
b,
Emma
McCabe
c,
Isaac
Abrahams
*d and
Nicola
Bonini
b
aSchool of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK. E-mail: kan.chen@qmul.ac.uk
bDepartment of Physics, King's College London, London WC2R 2LS, UK
cSchool of Physical Sciences, University of Kent, Canterbury, Kent, CT2 7NH, UK
dSchool of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK. E-mail: i.abrahams@qmul.ac.uk
First published on 15th July 2020
Cu3Sb1−xSnxS4 samples with 0.0 ≤ x ≤ 1.0 were synthesized from pure elements by mechanical alloying combined with spark plasma sintering. The structural and electronic properties of these compounds were characterized by powder X-ray and neutron diffraction, X-ray photoelectron spectroscopy (XPS), magnetic susceptibility and electrical and thermal transport measurements, and the experimental results compared against those calculated from hybrid density functional theory. A full solid solution is found between famatinite (Cu3SbS4) and kuramite (Cu3SnS4), with low x-value compositions in the Cu3Sb1−xSnxS4 system exhibiting the ordered famatinite structure and compositions above x = 0.7 showing progressive disorder on the cation sublattice. The semiconducting behaviour of Cu3SbS4 becomes increasingly more metallic and paramagnetic with increasing Sn content as holes are introduced into the system. Neutron diffraction data confirm that the sulfur stoichiometry is maintained, while XPS results show Cu remains in the monovalent oxidation state throughout, suggesting that hole carriers are delocalized in the metallic band structure. The order–disorder transition is discussed in terms of the defect chemistry and the propensity towards disorder in these compounds.
Here, we explore the structural and electronic properties of the quaternary Cu3Sb1−xSnxS4 system that lies in the compositional space between famatinite, Cu3SbS4, and kuramite, Cu3SnS4. This is an interesting system, as the two end-members share the same underlying zinc blende derived lattice, with structural parameters differing by only about 0.6%,12 suggesting the possibility of forming a solid solution with stable intermediate compositions. On the other hand, the two parent compounds display quite different electronic and structural properties and the possibility of mixing the two phases provides a direct way to explore the coexistence or crossover between the semiconducting (ordered) and metallic (disordered) phases.
Indeed, famatinite (Fig. 1) is a semiconductor with a crystal structure characterized by the ordered arrangement of S-based tetrahedral motifs, where each S atom is surrounded by one antimony and three copper atoms (S–Cu3Sb). The bonding and electronic properties of this compound are intimately related to the fact that the S–Cu3Sb building block provides a way to fully satisfy the octet rule for the sulfur atom; indeed the number of electrons, N, in the valence orbitals of each sulfur is 8, if we assume that Sb and Cu are in the +5 and +1 oxidation states, respectively. In contrast, kuramite is a metallic-like compound that displays partial disorder on the cation sites (Fig. 1). The structure can be viewed as a random arrangement of different S-based motifs, where S atoms are surrounded by four cations, of which at least one is a Cu atom.
While in principle there are four possible building blocks (S–CuSn3, S–Cu2Sn2, S–Cu3Sn and S–Cu4), it is worth noting that in none of these tetrahedra is the sulfur octet rule fully satisfied. Assuming the oxidation state of Sn is +4, N is 9.25, 8.5, 7.75, and 7 for S–CuSn3, S–Cu2Sn2, S–Cu3Sn, and S–Cu4, respectively. One might expect that the more energetically favoured motifs might correspond to smaller deviations from the octet rule, but this has not yet been investigated in detail in this system. In addition, it is important to point out that in the literature it has been suggested that kuramite might also contain Cu in the +2 oxidation state (in particular, two Cu+ and one Cu2+ per formula unit).13 While electron paramagnetic resonance spectroscopy has been used to support this thesis, X-ray photoelectron spectroscopy (XPS) studies have reported contradictory results.14 Indeed, Xiong et al.15 and Hu et al.16 reported the coexistence of Cu+ and Cu2+ in nanorods and tube-like nanoshells, respectively, while more recently Goto et al.17 found no evidence for the presence of Cu2+ in polycrystalline Cu-deficient kuramite samples. To shed light on the local electronic environment around Cu in kuramite (and therefore on the valence state of Cu), what is needed is a better understanding of the mixed ionic-covalent character of the Cu–S bond in kuramite, as well as of the metallic nature of this compound.
In previous work we have shown that famatinite can be doped with group 14 elements such as Ge and Sn, with very positive effects on their thermoelectric properties.6,9 However, while for Ge doping a competitive second phase (Cu2GeS3) was formed even at very low doping concentrations (x ∼ 0.125 on the Sb site), Sn proved to be very soluble at the doping levels investigated (up to x = 0.15), we found evidence that Sn substitutes for Sb atoms in the 2a crystallographic site, with no kuramite-like cation disorder. Thus, it is still unclear what level of Sn content can trigger cation disorder and, more importantly, how the disorder can affect the bonding and electronic properties of the compound. In addition, Sn is a very effective p-type dopant at low concentrations, but the evolution of the electronic structure and the carrier density at high Sn content has not yet been investigated. This is very relevant for thermoelectric applications; even though kuramite exhibits metallic behaviour, it has been shown that the carrier concentration of this compound can be favourably tuned by the addition of excess Sn, as well as in stannite–kuramite solid solutions, Cu2+xFe1−xSnS4−y with x ∼ 0.8.1,3 It is also noteworthy that the metallic character of kuramite has attracted interest in the field of dye-sensitized solar cells, where this compound has been suggested as a platinum-free cathode.18
In the present work, we investigate the stability, and structural and electrical properties of the famatinite–kuramite solid solution system as a function of Sn content. Using XPS, X-ray and neutron diffraction, and magnetic measurements supported by theoretical calculations, a detailed description of the order–disorder transition is presented. This transition is found to leave a fingerprint in the electronic properties at high Sn content.
The phase behaviour of the samples was examined using X-ray powder diffraction (XRD) with a PANalytical X’Pert Pro diffractometer fitted with an X’Celerator detector. Data were collected at room temperature using Ni filtered Cu-Kα (λ1 = 1.54056 Å and λ2 = 1.54439 Å) radiation, in flat plate θ/θ geometry, over the 2θ range 5–120°, in steps of either 0.033° or 0.0167°, with an effective count time of 200 s per step. For detailed structural analysis, neutron powder diffraction data were collected on the Polaris diffractometer at the ISIS Facility, Rutherford Appleton Laboratory, UK. Data collections of ca. 1000 μA h proton beam equivalent were made on samples contained in 11 mm diameter thin walled vanadium cans. Data collected on back-scattering (average angle 146.72°) and 90° (average angle 92.5°) detector banks were used in subsequent refinements. A combined X-ray and neutron Rietveld approach was used for structure refinement using the GSAS suite of programmes.19 The models of Pfitzner et al.12 for Cu3SbS4 and Goto et al.3 for Cu3SnS4, both in space group I2m, were used as starting models for the structure refinement. The fitted diffraction profiles are given in the ESI† (Fig. S1–S4). Crystal and refinement parameters are summarized in Table 1.
a For definition of R-factors see ref. 19. b Main phase Cu3SnS4 (0.9315(7) weight fraction), secondary phase: CuS (0.068(2) weight fraction). | ||||
---|---|---|---|---|
Composition | x = 0.0 | x = 0.4 | x = 0.7 | x = 1.0b |
Formula | Cu3SbS4 | Cu3Sb0.6Sn0.4S4 | Cu3Sb0.3Sn0.7S4 | Cu3SnS4 |
M r | 881.26 g mol−1 | 878.81 g mol−1 | 876.97 g mol−1 | 875.14 g mol−1 |
Crystal system | Tetragonal | Tetragonal | Tetragonal | Tetragonal |
Space group | I2m | I2m | I2m | I2m |
Unit cell dimensions | a = 5.3872(12) Å | a = 5.3809(4) Å | a = 5.3763(5) Å | a = 5.3928(29) Å |
c = 10.748(2) Å | c = 10.7358(8) Å | c = 10.7383(9) Å | c = 10.758 (6) Å | |
Volume | 311.9(2) Å3 | 310.84(7) Å3 | 310.39(8) Å3 | 312.9(5) Å3 |
Z | 2 | 2 | 2 | 2 |
D calc | 4.691 Mg m−3 | 4.695 Mg m−3 | 4.692 Mg m−3 | 4.645 Mg m−3 |
R-factorsa | Neut., b.s. | Neut., b.s. | Neut., b.s. | Neut., b.s. |
R wp = 0.0227 | R wp = 0.0235 | R wp = 0.0230 | R wp = 0.0227 | |
R p = 0.0297 | R p = 0.0331 | R p = 0.0326 | R p = 0.0291 | |
R ex = 0.0035 | R ex = 0.0034 | R ex = 0.0033 | R ex = 0.0034 | |
R F 2 = 0.0653 | R F 2 = 0.0587 | R F 2 = 0.0657 | R F 2 = 0.0481 | |
Neut. 90° | Neut. 90° | Neut. 90° | Neut. 90° | |
R wp = 0.0237 | R wp = 0.0271 | R wp = 0.0264 | R wp = 0.0296 | |
R p = 0.0281 | R p = 0.0383 | R p = 0.0397 | R p = 0.0503 | |
R ex = 0.0023 | R ex = 0.0023 | R ex = 0.0023 | R ex = 0.0023 | |
R F 2 = 0.0874 | R F 2 = 0.1096 | R F 2 = 0.1219 | R F 2 = 0.1237 | |
X-ray | X-ray | X-ray | X-ray | |
R wp = 0.0956 | R wp = 0.0686 | R wp = 0.0704 | R wp = 0.1040 | |
R p = 0.0757 | R p = 0.0525 | R p = 0.0544 | R p = 0.0827 | |
R ex = 0.0873 | R ex = 0.0467 | R ex = 0.0430 | R ex = 0.0898 | |
R F 2 = 0.1710 | R F 2 = 0.1068 | R F 2 = 0.1302 | R F 2 = 0.2186 | |
Totals | Totals | Totals | Totals | |
R wp = 0.0234 | R wp = 0.0259 | R wp = 0.0254 | R wp = 0.0270 | |
R p = 0.0584 | R p = 0.0499 | R p = 0.0519 | R p = 0.0662 | |
χ 2 = 44.37 | χ 2 = 41.37 | χ 2 = 41.36 | χ 2 = 61.34 | |
No. of variables | 109 | 109 | 109 | 119 |
No. of profile points used | 3979 (Neut., b.s.) | 3966 (Neut., b.s.) | 3966 (Neut., b.s.) | 4002 (Neut., b.s.) |
2300 (Neut., 90°) | 2355 (Neut., 90°) | 2355 (Neut., 90°) | 2357 (Neut., 90°) | |
3289 (X-ray) | 6469 (X-ray) | 6580 (X-ray) | 3289 (X-ray) | |
No. of reflections | 1316 (Neut., b.s.) | 1558 (Neut., b.s.) | 1498 (Neut., b.s.) | 2867 (Neut., b.s.) |
1152 (Neut., 90°) | 1424 (Neut., 90°) | 1418 (Neut., 90°) | 2826 (Neut., 90°) | |
181 (X-ray) | 181 (X-ray) | 186 (X-ray) | 363 (X-ray) |
The electrical resistivity and Seebeck coefficient were measured using a commercial instrument (LSR-3/110, Linseis) in a He atmosphere. The uncertainty in resistivity and Seebeck coefficient values is less than 5%. The thermal diffusivity was measured using the flash diffusivity method (LFA 457, Netzsch). The specific heat capacity (Cp) was estimated using the Dulong–Petit law. The uncertainty in thermal diffusivity measurements was less than 5%. The density was measured using the Archimedes method with an uncertainty of less than 1% and all of the samples had a relative density greater than 98%. The thermal conductivity was calculated using the thermal diffusivity, specific heat capacity and density.
Fig. 2 X-ray powder diffraction patterns of compositions in the Cu3Sb1−xSnxS4 system (reference: Cu3SbS4, PDF # 00-035-0581). |
The compositional variation of unit cell volume is shown in Fig. 3. A steady decrease in the unit cell volume is seen up to around x = 0.7. This is inconsistent with the substitution of Sb5+ by the larger Sn4+ cation (r = 0.60 Å and 0.69 Å, respectively, comparison based on 6 coordinate geometry since data for 4-coordinate geometry are unavailable for Sb5+), but would be consistent with the oxidation of some Cu+ to Cu2+ (r = 0.57 Å and 0.46 Å, respectively, for the ions in 4-coordinate geometry).27 Above x = 0.7, the volume increases significantly. Interestingly, the lattice parameter ratio (Fig. S5, ESI†) is seen to reach a maximum at around x = 0.4, indicating that this composition is nearly cubic.
In order to assess changes in local structure, neutron diffraction data were collected for the key compositions x = 0.0, 0.4, 0.7 and 1.0 (Fig. S1–S4, ESI†). In the work of Goto et al.,3 for the x = 1.0 composition, it was assumed that electroneutrality was maintained through S2− vacancies, i.e. that the composition has a stoichiometry approximating to Cu3SnS3.5. In the present case, no evidence was found for S2− vacancies, with refinement of the S site occupancy always resulting in full occupancy. Therefore, in the final refinements the S site occupancy was fixed at 1.0. A number of cation ordering models were refined using the X-ray and neutron data for the x = 1.0 composition. The reliability factors for each of these models is given in the ESI† (Tables S2 and S3). Only the X-ray reliability factors showed significant differences between the models, since the X-ray data show the greatest scattering contrast between Cu and Sn. The results show that for this composition, the ordered model of famatinite gives a poorer fit than most of the disordered models. However, the model of Goto et al.,3 with Sn disordered over 2b and 4d sites, cannot be distinguished from the model with Sn disordered over the 2a and 4d sites, but it does have a marginally smaller χ2 value than the fully random model, with Sn randomly distributed over all cation sites. In fact, the models with Sn distributed over 2b/4d sites and 2a/4d sites are crystallographically almost indistinguishable (both 2b and 2a sites have −42m symmetry and are related by a translation of 0, 0, 0.5) and thus the cation ordering found by Goto et al.3 is confirmed in the present study. It should be noted here that it is possible to model the diffraction data for the x = 1.0 composition with a fully disordered cubic sphalerite structure in space group F3m. The fit yields slightly higher R-factors than any of the tetragonal models (Rwp = 0.0236, 0.0305 and 0.1037, for neutron back scattering, neutron 90° and X-ray data, respectively) and does not differentiate between the 3 cation sites of the I2m structure. The famatinite and kuramite models were refined for compositions x = 0.0, 0.4 and 0.7, and in all cases the famatinite model was found to give a better fit. The results show that with increasing Sn content, the famatinite ordering is maintained up to at least x = 0.7. The increase in unit cell volume at high x-values (Fig. 3) suggests that above x = 0.7 the more disordered kuramite-type structure is adopted.
The final refined structural parameters for x = 0.0, 0.4, 0.7 and 1.0 compositions are given in Table 2, with the corresponding fitted diffraction profiles given in the ESI† as Fig. S1–S4. The degree of distortion of the tetrahedra can be quantified using a simple distortion index DOTO,28 as follows:
(a) | ||||
---|---|---|---|---|
Composition | x = 0.0 | x = 0.4 | x = 0.7 | x = 1.0 |
2a site Occ. | Sb 1.0 | Sb, 0.6 | Sb, 0.3 | Cu 1.0 |
Sn, 0.4 | Sn, 0.7 | |||
2a site Uiso (Å2) | 0.0059(3) | 0.0054(3) | 0.0080(4) | 0.0189(6) |
2b site Occ. | Cu, 1.0 | Cu, 1.0 | Cu, 1.0 | Cu, 0.58(6) |
Sn, 0.42(6) | ||||
2b site Uiso (Å2) | 0.0180(4) | 0.0150(4) | 0.0158(5) | 0.0091(5) |
4d site Occ. | Cu, 1.0 | Cu, 1.0 | Cu, 1.0 | Cu, 0.71(3) |
Sn, 0.29(3) | ||||
4d site Uiso (Å2) | 0.0192(2) | 0.0186(2) | 0.0165(3) | 0.0210(4) |
8i site | S, 1.0 | S, 1.0 | S, 1.0 | S, 1.0 |
8i site x | 0.2519(5) | 0.2541(4) | 0.2556(4) | 0.2497(13) |
8i site z | 0.1298(2) | 0.1290(2) | 0.1304(1) | 0.1261(6) |
8i site Uiso (Å2) | 0.0103(1) | 0.0117(1) | 0.0095(1) | 0.0129(1) |
(b) | ||||
---|---|---|---|---|
2a-S | 2.373(3) | 2.379(3) | 2.396(2) | 2.338(10) |
2b-S | 2.349(3) | 2.328(3) | 2.327(2) | 2.342(9) |
4d-S | 2.302(2) | 2.304(1) | 2.2945(9) | 2.326(4) |
S-2a-S | 110.21(6) × 3 | 109.83(6) × 3 | 109.98(5) × 3 | 109.67(19) × 3 |
S-2a-S′ | 107.99(12) × 3 | 108.76(13) × 3 | 108.46(9) × 3 | 109.1(4) × 3 |
S-2b-S | 110.65(6) × 3 | 110.73(7) × 3 | 111.24(5) × 3 | 109.61(21) × 3 |
S-2b-S′ | 107.15(12) × 3 | 106.98(13) × 3 | 106.00(9) × 3 | 109.2(4) × 3 |
S-4d-S | 111.68(7) × 2 | 111.37(9) × 2 | 111.92(6) × 2 | 110.09(28) × 2 |
S-4d-S′ | 108.38(3) × 4 | 108.53(5) × 4 | 108.26(3) × 4 | 109.16(14) × 4 |
2b-S-4d | 109.79(10) × 2 | 110.26(9) × 2 | 110.60(7) × 2 | 109.34(28) × 2 |
2b-S-2a | 107.57(7) | 107.87(9) | 107.23(6) | 109.13(28) |
2a-S-4d | 108.96(10) × 2 | 108.50(9) × 2 | 108.18(7) × 2 | 109.46(28) × 2 |
4d-S-4d | 111.68(7) | 111.35(9) | 111.88(7) | 110.09(28) |
Fig. 4 Composition variation of tetrahedral distortion index DOTO for tetrahedral sites in the Cu3Sb1−xSnxS4 system. |
Fig. 5 Compositional variation of calculated formation energies for famatinite (red squares) and kuramite-like (blue triangles) structures. |
A close look at the most stable kuramite-like structures obtained in the DFT screening reveals that they are characterized by the coexistence of the S–Cu3Sn (or S–Cu3Sb) motifs (typical of famatinite-like structures), with S–Cu2Sn2 (or S–Cu2SnSb) and S–Cu4 motifs. The minimum energy cost to create these latter types of motif, starting from a famatinite-like arrangement, is the formation energy of CuSn (or CuSb) antisite defects.
The calculations show the that the antisite formation energy in Cu3SbS4 is 3 eV, while in famatinite-like Cu3SnS4 the value is significantly lower, about 0.9 eV (assuming the chemical potentials to be zero). The values clearly indicate a greater propensity to disorder in Cu3SnS4 than in Cu3SbS4. It is interesting to note that when compared to Cu2ZnSnS4, cation disorder, which has a detrimental impact on the electronic transport properties crucial for photovoltaic applications, is less energetically favourable in Cu3SbS4. Indeed, in Cu2ZnSnS4 the CuSn formation energy obtained with hybrid DFT is 2.4 eV, assuming zero chemical potentials, and can decrease down to 1.2 eV, depending on the chemical potentials used.29
Calculated Cu 2p spectra of x = 1.0 based on famatinite-like and kuramite-like ordered DFT models are shown in Fig. 6b and c. DFT reproduces the position of the Cu 2p1/2 peak very well, but underestimates the position of the Cu 2p3/2 peak by about 2 eV. There is no difference in the predicted binding energies for the Cu 2p peaks for the two models. However, the high binding energy tails in the spectrum of the x = 1.0 composition are accurately simulated by Cu+ environments with high numbers of Sn atoms as next-nearest-neighbours. This type of local ordering has a finite statistical probability of occurring in the kuramite model only.
Fig. 7 shows the thermal variation of magnetic susceptibility on heating for the x = 0.0, 0.7 and 1.0 compositions, with the plots for inverse susceptibility inset. Little difference was observed between field-cooled (FC) and zero-field-cooled (ZFC) data. A weak local maximum is observed in the susceptibility data at ∼50 K for the x = 0.0 and x = 1.0 compositions. This may indicate long-range antiferromagnetic order, but could also be associated with the presence of a small amount of antiferromagnetic impurity. Above ∼250 K, Curie–Weiss like behaviour is observed for the x = 0.0 composition and analysis suggests a paramagnetic moment of 0.37 μB per formula unit and a Weiss temperature of ∼ 110 K (Fig. 7 inset). The question therefore arises as to the origins of the weak paramagnetism in Cu3SbS4, since there are nominally no unpaired electrons in this composition. No evidence was seen in the diffraction data at x = 0.0 for a possible paramagnetic impurity, although a small amount of impurity phase could be below the detection limit of the diffraction experiments. Since no evidence was found in the diffraction data or compositional analysis for sulfur vacancies, another possibility is charge compensation through the oxidation of Cu to the 2+ oxidation state or the presence of S2−δ species. This would have the effect of introducing low concentrations of paramagnetic centres into the system, while maintaining overall stoichiometry. Increasing the Sn content increases the magnetic susceptibility which could reflect increasing Pauli paramagnetism as the systems become more metallic with increasing Sn content.
There is little compositional variation in the Sb 3d and Sn 3d XPS peaks (Fig. S6 and Table S4, ESI†), the intensities of the Sb 3d and Sn 3d peaks change accordingly with composition which further confirms that Sb is replaced by Sn. The binding energy of Sb 3d and Sn 3d are consistent with Sb and Sn in predominantly 5+ and 4+ oxidation states, respectively.32,35,36 However, while the Sb 3d XPS data show predominantly Sb in the 5+ oxidation state, the presence of a small amount of Sb3+ would be almost indiscernible, since the binding energies of the 3d electrons on the +5 and +3 oxidation states are separated by only about 3 eV.37,38
Fig. 8 shows the fitted S 2p XPS spectra for selected compositions. At x = 0.0, the S 2p1/2 and S 2p3/2 peaks are located at binding energies of 163.2 eV and 162.0 eV with a separation of 1.2 eV, which are consistent with those reported in other metal sulfides.31,32,39 As the Sn content increases, the S 2p peaks shift to lower binding energies and additional weaker higher energy peaks appear. As discussed above, one possible explanation is to consider the presence of S2−δ species, which in the absence of sulfur vacancies would be required for electroneutrality. This is an attractive hypothesis, and similar conclusions were made in the Ag1−xSn1+xSe2 system, where charge balance was maintained by Se2−δ species, and the Se 3d XPS spectra fitted accordingly. In the present case, fits to two species for the x = 1.0 data, yield fractions of 0.4 and 0.6 for the S2−δ and S2− species, respectively, corresponding to a δ value of 0.625. Calculations for the other compositions reveal similar δ values (Fig. S6, ESI†). Since the system is essentially covalent in nature, this suggests that the bonds to S would weaken with increasing level of Sn substitution and decreasing bond order. Indeed, this is evident in Table 2, where the 2a-S (i.e. Sn/Sb–S) bond length increases from x = 0.0 to 0.7, while the Cu–S bond length shortens over this compositional range. The situation at x = 1.0 is complicated by the randomisation of Sn/Cu site occupation between all three cation sites on transition to the kuramite structure, making direct comparison of bond lengths with lower x-value compositions less clear.
Fig. 8 High resolution S 2p XPS spectra of for Cu3Sb1−xSnxS4 with x = 0.0, 0.5 and 1.0. For x = 0.5 and 1.0 samples, S 2p peaks were fitted into two different S species of S2− and S2−δ. |
It is interesting to note, that for x-values larger than 0.7, there are clear changes in the trends of experimental data for the electrical conductivity (σ) and the thermal conductivity (κ), which deviate from the behaviour predicted by the transport model based on the famatinite structure. This correlates well with the trend in the compositional variation in unit cell volume (Fig. 3) and can be attributed to the disorder on the cation sublattice that accompanies the transition to the kuramite structure. This disorder introduces an extra electronic scattering mechanism that affects electronic transport. The contribution of lattice thermal conductivity, κL, to total thermal conductivity, κ, can be estimated by subtracting the electronic thermal conductivity, κe, from κL, where the electronic contribution was estimated on the basis of the Wiedemann–Franz law and a Lorenz number calculated by using the equation proposed by Kim et al.40 As can be seen in Fig. 9c, the lattice thermal conductivity is fairly independent of Sn content and very close to 1.9 W m−1 K−1 at room temperature found for pristine Cu3SbS4. The results suggest that Umklapp phonon–phonon scattering is the dominant scattering effect. Since this is proportional to the average mass of the sample there is little change is seen in the lattice thermal conductivity as all the samples have similar average mass.41 Hence, as the x-value increases the main contribution to κ arises from κe.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0tc01804j |
‡ The QUESTAAL code is freely available at http://www.questaal.org. |
This journal is © The Royal Society of Chemistry 2020 |