1. Introduction
In previous years, the interest of several leading research groups has focused on materials in the tetrahedrite group. They occur naturally as a mineral with the formula Cu
12Sb
4S
13. They crystallize in the cubic crystal system, space group I-43m, and have a complex crystal structure with a unit cell of 58 atoms, presented in
Figure 1. The source of the very low thermal conductivity of tetrahedrites (~0.5 W·m
−1·K
−1 T > 300 K) is anharmonic vibrations of Cu atoms with trigonal coordination due to interactions with the lone pair of electrons located at the antimony atom. The low thermal conductivity is a very desirable feature in high performance thermoelectric materials for energy conversion. It is, among other things, the low thermal conductivity that has led to great interest in tetrahedrites and intensive research on these compounds. The undoped tetrahedrite Cu
12Sb
4S
13 is a
p-type semiconductor showing metallic character with high electrical conductivity of 10
5 S·m
−1 at 300 K and a moderately high Seebeck coefficient, which together with very low thermal conductivity values allows for achieving a
ZT parameter of 0.56 (at T = 673 K) [
1]. Appropriate doping allows an increase in
ZTmax of tetrahedrites, which has been shown in many works [
2,
3,
4,
5,
6]. Due to the high carrier i.e., electron holes, concentration of pure tetrahedrite, mainly dopants and structural modifications reducing the hole concentration, i.e., donor-type dopants, are used to increase the
ZT value. The second group of modifications includes isovalent dopants, with the main purpose of decreasing thermal conductivity. Among the modifications of the Cu
12Sb
4S
13 structure described in the literature, we can find: doping of s-, d-,
p- block elements in the Cu sublattice (Cu
12−xT
xSb
4S
13, where T = Mg, Fe, Cd, Co, Mn, Zn, Ni, Ge, Sn) [
1,
2,
3,
4,
5,
7,
8,
9,
10,
11];
p block elements doping in Sb sublattice (Cu
12Sb
4−xM
xS
13, M = Bi, Te [
12,
13,
14]); selenium doping in sulfur sublattice (Cu
12Sb
4S
13−xSe
x [
15]); sulfur deficiency (Cu
12Sb
4S
13−x [
15]); and excess Cu (Cu
12+xSb
4S
13 [
16]) in structural voids at Wyckoff position 24g. An additional result of the aliovalent doping may be a reduction in the thermal conductivity of pure tetrahedrite from about 1 W·m
−1·K
−1 to about 0.4 W·m
−1·K
−1 [
10,
17]. As a result, the highest reported
ZT values for doped
p-type tetrahedrites exceed 1 (
ZTmax = 1.13 at T = 575 K for Cu
11MnSb
4S
13 [
11]) and indicate that they can be a viable alternative to lead-containing acceptor type materials based on PbTe in the temperature range of 570–670 K [
18]. Although many dopants with a donor character have been studied, so far it has not been possible to find one that allows a change in electrical conductivity to the
n-type. Obtaining
n-type tetrahedrites with good thermoelectric properties would be beneficial for constructing thermoelectric modules based on the tetrahedrites. The use of
p- and
n-type tetrahedrites in such modules would eliminate many design problems resulting from differences in thermal expansion coefficients and the selection of different materials for diffusion barriers and metallic contacts.
The substitution of native atoms by dopant atoms leads, in addition to transport changes, to noticeable variations in the crystal structure, the most obvious of which is a change in the lattice parameter. The change in this parameter resulting from changes in interatomic distances is also one of the pieces of evidence of dopant incorporation into the structure. For d-block metal dopants, it was experimentally proved that they substitute Cu
2+ cations at the 12d position. This is in agreement with theoretical findings, which predicts preference of the 12d Wyckoff position for multivalent dopants, while for the monovalent dopants e.g., Ag, the 12e site of trigonally coordinated Cu would be preferred. For most d-block dopants introduced in the copper position, the lattice parameter increases. This is especially so for the Cd dopant, which for a compound with the formula Cu
12−xTr
xSb
4S
13 for x = 1.5, results in an increase in the lattice parameter
a to 10.47 Å (1.047 nm) [
3]. A similar increase in the lattice parameter can be observed for the Mn [
19] dopant, where for x = 1.8, the lattice parameter is higher than 10.43 Å. An increase in the lattice parameter to about
a = 1.038 nm for x = 2 can be observed for Zn doping. For Co doping, the lattice parameter increases slightly to about
a = 10.34 Å [
4], while for Ni doping the lattice parameter hardly changes, 10.319–10.323 Å [
2]. These changes are consistent with the ionic radii of the listed divalent atoms decreasing in the series Cd, Mn, Zn, Co, Ni, and if we assume a 2+ charge of the ion, they are all larger than the Cu
2+ ionic radius. Similar results were observed for elements other than d-block metals in the copper site, such as
p-block elements Sn (
a = 10.375 Å) and Ge (
a = 10.339 Å) [
19]. The open structure of tetrahedrite also allows atoms to be inserted into structural voids [
16,
20]. Vaqueiro et al. investigated the effect of excess copper introduced into structural voids for Cu
12+xSb
4S
13 (0 ≤
x ≤ 2) and showed that it is possible [
16]. The introduced excess copper occupies void 24g site (0.28, 0.28, 0.041) and above 393 K becomes mobile, with the whole material showing superionic conductivity. Similar atomic coordinates for excess copper (0.29, 0.29, 0.03) were determined in single crystal studies by Makovicky and Skinner [
20]. As expected, the introduced excess copper decreased electrical conductivity and increased the Seebeck coefficient of all samples compared to the undoped material, with simultaneous decrease of thermal conductivity, which lead to the maximum value of
ZTmax~0.6 (
T = 573 K) for Cu
14Sb
4S
13 [
16]. The authors suggest that the exceptionally low thermal conductivity for excessive copper tetrahedrites is consistent with the assumptions of the PLEC theory (phonon liquid electron crystal) valid for the superionic materials. Changes in the lattice constant, as can be seen, are an important parameter in doping studies, and the results presented here provide an important reference point in our research.
All of these results clearly indicate that the introduction of dopants can be an effective way to optimize the transport properties of tetrahedrites and thus
ZT parameter increase. These results also show that it is possible to introduce into the structural voids an excess of atoms/cations with small ionic radii, such as Cu. This possibility inspired us to search for a dopant that could be introduced as a small cation into structural voids. As potential dopants we considered elements of groups I and II of the periodic table, due to their high susceptibility to ionization and small ionic radii. Both simple considerations based on electron count and first rough DFT calculations performed by us showed that such introduction of atoms into the voids will lead to the formation of donor states, which, at appropriate concentration, may lead to the formation of
n-type material. In the case of divalent metals such as Mg or Ca, this should occur at two times lower dopant concentration compared to monovalent metals such as Li or Na. Moreover, in the meantime, a paper devoted to Mg-doped tetrahedrite Mg
xCu
12−xSb
4S
13 was published by Levinski et al. [
7] and a surprisingly large increase in the lattice parameter upon doping was observed (
a = 10.40 Å for x = 1.5). In our opinion, this increase is difficult to explain by Mg substitution for Cu, due to the fact that the ionic radius of Mg is equal or slightly smaller than that of copper, and suggests that this lattice parameter increase may be the result of the filling of structural voids in the tetrahedrite structure. Although, in the aforementioned work, it was assumed that Mg substitutes Cu, and the change in lattice parameter was attributed to the incorporation of Mg into the tetrahedrite structure, the exact localization of Mg in the structure was not experimentally determined. Therefore, we decided to check if the novel concept of introducing a dopant into the structural voids of tetrahedrites is possible and if in this way it will be possible to obtain an
n-type conductivity tetrahedrite, which has not previously been obtained. We have selected Mg as the dopant for the reasons outlined above and due to the tendency of magnesium to form non-directional bonds with spherical symmetry, which may additionally result in a decrease in thermal conductivity, thereby increasing
ZT. A series of Mg
xCu
12Sb
4S
13 tetrahedrite samples were synthesized and compacted and selected thermoelectric parameters were investigated. These studies were combined with ab initio theoretical calculations of the electronic structure and electron density topology.
2. Materials and Methods
2.1. Ab Initio Calculations
Ab initio calculations of electronic structure and electron density topology were performed with the WIEN2k computational package for a series of model structures. WIEN2k employs Full Potential Linearized Augmented Plane Wave (FP-LAPW) approximation within Density Functional Theory formalism, which is well suited to solids. For all WIEN2k calculations, the following parameters were used: GGA PBEsol as exchange-correlation potential, cutoff parameters RMTKMAX = 8 and GMAX = 20, 256 k-points in irreducible Brillouin zone for unmodified structure (and closely matching number of k-points for other structures) and convergence criteria of ΔE = 10−5 Ry for energy, Δq = 10−5 e for charge and ΔF = 10−1 mRy a0−1 for forces. These data were further processed using Brown’s Bond Valence Model (BVM) for a more global view of the structure’s properties, including strain factor and global instability index.
2.2. Synthesis
Stoichiometric amounts of the substrates were weighed and inserted into quartz ampoules in a glove box under anaerobic conditions. In the course of the research, it was found that the best results are obtained by conducting a multi-step synthesis by direct solid-phase reaction with a preliminary melting step. The ampoule was placed in a rocking furnace for 24 h at 940 K. Due to the decomposition of the tetrahedrite phase to Cu3SbS4 and Cu3SbS3 at temperatures above 720 K, the furnace was cooled to 720 K and the ampoules were annealed at this temperature for one week. The resulting ingots were crushed, resealed in quartz ampoules and annealed for two weeks at 720 K.
2.3. Structural, Microstructural and Chemical Characterization
The phase composition was determined based on X-Ray Diffraction (XRD) measurements using Phillips X’Pert Pro diffractometer (CuKα1 = 15,406 Å, 2θ = 10–120°). The Rietveld refinement implemented in HighScore software was used to determine lattice parameters, atomic positions and phase weight fractions. Because of the average goodness of fit (GoF) (GoF ≈ 1.9 for as synthesized and GoF ≈ 8.3 for sintered samples) other parameters were not considered. The microstructure of produced materials was analyzed using two scanning electron microscopes (SEM) coupled with an energy-dispersive spectrometer (EDS), which allowed analysis of the chemical composition of selected points/areas of the sample. Qualitatively, the EDS analysis results obtained from both instruments were in agreement with each other, but in this paper we present the results obtained only from the Thermo Fisher Scientific Phenom XL scanning electron microscope due to smaller errors in the quantitative analysis of the chemical composition. During the analysis, it was found that accurate quantification of the chemical composition, in both point and surface analysis, is only possible for areas having precipitates of impurity phases, such as Cu2S and MgS. In other cases, systematic errors did not allow for obtaining reproducible and quantitatively consistent results of composition analysis. For this reason, the specimen names we use in this paper correspond to their nominal compositions.
The established procedure made it possible to obtain practically pure Cu12Sb4S13 and Mg-doped MgxCu12Sb4S13 with small amounts of impurities, which was confirmed by XRD studies and SEM observation with EDS composition analysis.
2.4. Sintering
Subsequently, the selection of densification conditions of the obtained powders by Field Assisted Sintering/Spark Plasma Sintering (FAST/SPS) was investigated. They showed that there are no single universal densification parameters for pure and doped tetrahedrite. When using higher temperatures >430 °C and pressures of the order of 50 MPa, the densification time was about 2 min, but severe cracking of the samples was observed after the process. When the temperature was lowered to below 380 °C, densification of the material below 80% of the theoretical density combined with low mechanical strength was observed. For pure tetrahedrite, the optimal sintering conditions were found to be 430 °C and 50 MPa for 15 min, yielding densities above 95% of the theoretical density. In Mg-doped tetrahedrites, the conditions were set at: T = 400–420 °C, depending on the dopant concentration; p = 30 MPa, t = 15–20 min, depending on the observed sintering curve.
2.5. Electrical Characterisation
The Seebeck coefficient was measured using steady state conditions and variable temperature gradient across the specimen up to 5 K. Electrical resistivity was measured using a four-probe method using variable DC polarization. Both of these measurements were carried out in the same apparatus during heating and cooling cycle on cylindrical specimens 10 mm in diameter and 12 mm long. Measurements were carried out in the temperature range from the room temperature to 680 K. Results shown are for both heating and cooling cycle. Experimental error was below 5% for the Seebeck coefficient measurements and 1.5% for the electrical resistivity measurements.
4. Conclusions
We obtained a series of tetrahedrites MgxCu12Sb4S13 with excess Mg, which, as shown by structural analysis, at room temperature, consist mostly of one or two phases with a tetrahedrite structure. The first of these phases, HLC, has a lattice constant of about 10.45 Å and the second, LLC, whose weight content increases with the amount of Mg, has a lower lattice constant of about 10.37 Å. These tetrahedrite phases are accompanied by impurities of Sb, MgS, Cu2S and MgO.
DFT ab initio calculations for tetrahedrite structures containing excess copper in the 6b and 24g voids, Cu12+xSb4S13, showed that by far the energetically preferred location of Cu is the structural void at the 24g position. Similarly performed calculations for the tetrahedrite structures MgxCu12Sb4S13 with excess Mg, supported by the experimental results, show that the most probable location of Mg is the void in the Wyckoff’s position 6b (0, 0, ½).
The experimental results do not unambiguously exclude other locations of the dopant, so it is possible that a partial substitution of Cu by Mg and occupation of some Cu in voids at the 24g position occur simultaneously. Presumably, the two phases of tetrahedrite, which are observed in some of the samples, have different types of defects, as can be seen from the slightly different directions of the atomic shifts. The insertion of Mg atoms into the structural void 6b is, as suggested by the experimental results, most likely for the HLC phase with a higher lattice constant.
The theoretical calculations of the formation energy of Mgx6bCu12Sb4S13 showed that there should be a limit of solubility of Mg in the tetrahedrite structure at x = 0.5~1. These predictions are mainly confirmed by the results of EDS analysis, which showed that the observed Mg content in the samples is more or less constant.
The electrical results show that Mg behaves as a donor dopant. The high value of the Seebeck coefficient indicates that by introducing Mg into the tetrahedrite structure (presumably into the voids), it was possible to significantly reduce the concentration of holes. Unfortunately, due to the existence of a solubility limit of Mg of below x = 1, tetrahedrites of n-type conductivity could not be obtained. However, finding another filler atom with a higher filling fraction limit or combining magnesium with another donor dopant can lead to n-type tetrahedrites.