Crystal structure of mechanochemically synthesized Ag₂CdSnS₄

2.1 Structural relationship between hexagonal diamond and the wurtzstannite-/wurtzkesterite-type structure

As it can be seen in the Bärnighausen tree [22], [23], elucidating the relationship between the hexagonal diamond (lonsdaleite) and the wurtzstannite-/wurtzkesterite-type structures (Fig. 3), space group Cmc2₁, as a subgroup to that of the wurtzite-type structure, is proposed either for binary compounds as well as for compounds with a statistical distribution of their cations/anions on one position. For Ag₂CdSnS₄, space group Cmc2₁ is mentioned in the literature with Ag, Cd, and Sn distributed statistically on the position 4a with (0, 0.167, 0.370) and S on another 4a position with (0, 0.176, 0.997) [20].

Fig. 3:

Group-subgroup scheme (Bärnighausen formalism) for the group-theoretical relation between hexagonal diamond (lonsdaleite) and the wurtzstannite-/wurtzkesterite-type structure with data taken from [26] for lonsdaleite, [27] for wurtzite, [20] for space group Cmc2₁, [4] for wurtzstannite-type Cu₂CdGeS₄, and [28] for wurtzkesterite-type Cu₂ZnSiS₄.

Similar compounds containing silver either crystallize in cubic diamond/sphalerite-related structures such as the stannite- or kesterite-type structure (such as Ag₂ZnSnS₄ [14], Ag₂FeSnS₄ [13], Ag₂ZnGeS₄ [24]) or in crystal structures derived from the hexagonal diamond/wurtzite type providing non-equivalent positions for the cations/anions (the wurtzstannite-type structure (space group Pmn2₁) and its derivatives with space group Pn (wurtzkesterite-type structure) or Pna2₁). Compounds crystallizing in the wurtzstannite-type structure are Ag₂CdGeS₄ [4] and Ag₂HgSnS₄ [15], whereas Ag₂MnSnS₄ [18] and Si-bearing compounds such as Ag₂FeSiS₄ [16] and Ag₂ZnSiS₄ [17] crystallize in the wurtzkesterite-type structure. Due to the close structural relationships between these three structures, it can be quite difficult to distinguish between them when using conventional methods. For Ag₂CdGeS₄, two polymorphs have been reported exhibiting the space groups Pmn2₁ [4] and Pna2₁ [25], respectively.

2.2 The high-temperature phase of Ag₂CdSnS₄

Starting with the high-temperature phase, it should be noted that an orthorhombic unit cell could be found by the Werner algorithm using the program WinXPOW 1.2 (STOE & Cie GmbH, Darmstadt, Germany) [29] for the sample at T=300°C. The lattice parameters were refined to a=8.2263 Å, b=7.0655 Å, and c=6.7051 Å leaving no reflection behind. The volume of the unit cell was calculated to 389.7 ų. It should be mentioned that the lattice parameter a given by the Werner algorithm is two times larger than that of the proposed crystal structure with space group Cmc2₁ for Ag₂CdSnS₄ [4], [20]. Examples of A₂^IB^IIC^IVX₄ compounds with a lattice parameter a of around 8.23 Å (and similar values for the lattice parameters b and c) within the orthorhombic crystal system have also been described by other authors [15].

For the Rietveld refinement of the high-temperature phase space group Pmn2₁ (wurtzstannite-type structure) is used. As depicted in Fig. 4, the experimental pattern is in good agreement with the theoretical one. Crystallographic details as well as atomic and structural parameters are listed in Tables 2 and 3. The Debye Waller factors of sulfur were set to a value of 1 and not refined, also the site occupation factors of all atoms. As Pmn2₁ is a polar space group and therefore possesses one origin-free direction (the z direction), the z parameter of the Ag atom position was fixed. As Ag, Cd, and Sn are not distinguishable using conventional X-ray diffraction methods, the distribution of these cations in the wurtzstannite- (and also wurtzkesterite-) type structure was set to that of the related compounds described in the literature.

Fig. 4:

X-ray diffraction pattern of the high-temperature phase (measured at T=300°C) of Ag₂CdSnS₄ with the results of the Rietveld refinement in space group Pmn2₁ (red: measured; black: calculated; blue: measured–calculated).

The wurtzstannite-type structure (space group Pmn2₁) of the high-temperature phase of Ag₂CdSnS₄ can be described as a hexagonal diamond/wurtzite-derived structure with a hexagonal closest packing of sulfur anions. Ag is located at a fourfold position whereas Cd and Sn occupy two non-equivalent twofold positions. Three crystallographically independent sulfur positions are present, where S1 is located on a fourfold position and S2 as well as S3 atoms occupy two twofold positions. Considering the honeycomb set-up, the wurtzstannite-type structure is built up of consecutive Ag and Cd/Sn layers (in general: A^I and B^II/C^IV layers). This is manifested in alternating layers of Ag-centered and Cd/Sn-centered polyhedra along the b axis (Fig. 5). These alternating stacking sequence appears to be in line with that of the stannite type [5], [30], the analogous structure type derived from the cubic diamond/sphalerite-type structure. All atoms in the wurtzstannite-type structure are surrounded tetrahedrally. Each cation is coordinated by two S1 atoms, one S2 atom, and one S3 atom. The sulfur atoms are coordinated by two Ag and one Cd atom as well as one Sn atom.

Fig. 5:

Crystal structure of the high-temperature phase of Ag₂CdSnS₄ (Pmn2₁) with cation-centered polyhedra viewed along the [010] direction (left) and the honeycomb set-up with stacking sequence of alternating Ag and Cd/Sn layers viewed along the [001] direction (right).

2.3 The low-temperature phase of Ag₂CdSnS₄

For the crystal structure determination of the low-temperature phase, all four direct subgroups of Pmn2₁ (P2₁, Pm, Pn, and Pna2₁) (Fig. 6) were considered and tested as refinement models. For example, the symmetry reduction from space group Pmn2₁ to Pn is expressed by the splitting of the fourfold Ag atom position 4b into two non-equivalent twofold positions 2a. The atomic and lattice parameters for the refinements in the four subgroups were generated by the program Transtru found on the Bilbao Crystallographic Server [31], [32], [33]. For the space groups Pna2₁ and Pn, we also used reported structural parameter of related compounds [25], [28] as starting values in the Rietveld refinements.

Fig. 6:

Group-theoretical relation (Bärnighausen formalism) between space group Pmn2₁ (wurtzstannite-type structure) and its direct subgroups P2₁, Pm, Pn, and Pna2₁.

In the subgroups P2₁, Pm, and Pna2₁ convergence problems occurred during the refinements (profile, atomic positions, Debye-Waller factors). However, a successful refinement was achieved in space group Pn, the wurtzkesterite-type structure. The experimental diffraction pattern is in good agreement with the theoretical one (Fig. 7). Crystallographic details are summarized in Table 2; atomic and structural parameters are presented in Table 4. The Debye-Waller factors of the sulfur atoms were kept fixed at a value of 1, and the site occupation factors were not refined. Space group Pn also belongs to the group of polar/origin-free space groups. This particular space group exhibits two origin-free directions (x and z). For the refinement in Pn, the x and z parameters of the Ag1 atom position were kept fixed to define the origin.

Fig. 7:

X-ray diffraction pattern of the low-temperature phase (measured at T=25°C) of Ag₂CdSnS₄ with the results of the Rietveld refinement in space group Pn (red: measured; black: calculated; blue: measured–calculated).

The low-temperature phase of Ag₂CdSnS₄ crystallizes in the space group Pn (wurtzkesterite-type structure) with a=6.704, b=7.038, c=8.217 Å, and β=90.16°. The wurtzkesterite-type structure can be derived from the hexagonal diamond structure and is composed of a hexagonal closest packed arrangement of the sulfur anions (Fig. 8). The crystal structure contains two independent Ag positions Ag1 and Ag2, one Cd, and one Sn position where all cations are located on twofold positions. This setup occurs also for the anions with in total four independent sulfur positions on twofold positions. Keeping in mind the honeycomb set-up, alternating Ag/Cd and Ag/Sn layers (in general A^I/B^II and A^I/C^IV layers) are distinguishable which is analogous to the kesterite-type structure [5] derived from the cubic diamond structure. Interatomic Ag–S distances range from 2.46(3) to 2.52(4) Å with an average of 2.50 Å for Ag1–S and from 2.52(3) to 2.58(2) Å with an average of 2.55 Å for Ag2–S. The Ag–S bond lengths correlate quite well with those known from Ag₂CdGeS₄ (Ag–S: 2.52–2.57 Å) [34] and are slightly smaller than those reported for Ag₂FeSiS₄ (Ag1–S: 2.52–2.58 Å; Ag2–S: 2.54–2.61 Å) [16]. Cd–S bond lengths range from 2.51(3) to 2.58(3) Å with an average of 2.55 Å and are in good agreement with those found in Cu₂CdGeS₄ (Cd–S: 2.51–2.60 Å) [4] and Ag₂CdGeS₄ (Cd–S: 2.49–2.57 Å) [34]. Interatomic Sn–S distances vary from 2.39(3) to 2.51(3) Å and are in average 2.43 Å which is somewhat longer than those in Li₂CdSnS₄ (Sn–S: 2.38–2.39 Å) [35] and Li₂ZnSnS₄ (Sn–S: 2.35–2.42 Å) [36].

Fig. 8:

Crystal structure of the low-temperature phase of Ag₂CdSnS₄ crystallizing in space group Pn with cation-centered polyhedra (view along the [01̅0] direction, left) and the honeycomb set-up with a stacking sequence of alternating Ag/Cd and Ag/Sn layers viewed along the [100] direction.

2.4 Stabilization of the high-temperature phase at room temperature

The observed phase transition seems to be of first order. Consequently, it is no surprise that the stabilization of the high-temperature phase of Ag₂CdSnS₄ at room temperature was feasible by annealing the sample at T=300°C for 3 h in an evacuated and closed silica tube in a vertically positioned tube furnace (Nabertherm RT 50-250/13; C450 controller) and subsequently quenching it in dry ice. Rietveld refinements were done in space group Pmn2₁ as well as in Pn and confirmed that the quenched sample crystallizes in the orthorhombic space group Pmn2₁. As expected, the difference of the residual values R_wp between the space groups Pmn2₁ and Pn is not significant (R_wp=10.9 for Pmn2₁ and R_wp=10.7 for Pn, respectively). Additionally, convergence problems occurred for the refinement in space group Pn. The powder diffraction pattern of the stabilized high-temperature phase of Ag₂CdSnS₄ quenched to room temperature is shown in Fig. 9. Crystallographic details as well as atomic and structural parameters are presented in Tables 2 and 5. The refinement strategy was similar to that of the sample measured in-situ.

Fig. 9:

X-ray diffraction pattern of the high-temperature phase of Ag₂CdSnS₄ stabilized at room temperature with the results of the Rietveld refinement in space group Pmn2₁ (red: measured; black: calculated; blue: measured–calculated).

The interatomic Ag–S distances in the quenched high-temperature phase vary from 2.505(12) to 2.521(15) Å with an average of 2.52 Å and correlate well with the Ag1–S distances (2.46(3)–2.52(4) Å) found in the low-temperature phase of Ag₂CdSnS₄. However, they are somewhat smaller than the Ag2–S distances (2.52(3)–2.58(2) Å) reported for Ag₂CdGeS₄ (Ag–S: 2.52–2.57 Å) [34] and Ag₂FeSiS₄ (Ag1–S: 2.52–2.58 Å; Ag2–S: 2.54–2.61 Å) [16]. Cd–S bond lengths range from 2.531(17) to 2.59(3) Å with an average value of 2.56 Å. This correlates pretty well with reported Cd–S distances for Cu₂CdGeS₄ (Cd–S: 2.51–2.60 Å) [4] and Ag₂CdGeS₄ (Cd–S: 2.49–2.57 Å) [34] as well with the ones in our low-temperature phase of Ag₂CdSnS₄ (2.51(3)–2.58(3) Å). For the Sn–S distances, the values vary from 2.39(3) to 2.491(17) Å with an average of 2.45 Å. They are in agreement with those found in the low-temperature phase (2.39(3)–2.51(3) Å) and also with those reported for Li₂CdSnS₄ (Sn–S: 2.38–2.39 Å) [35] and Li₂ZnSnS₄ (Sn–S: 2.35–2.42 Å) [36].

For the high- and the low-temperature phase of our Ag₂CdSnS₄ sample, additional refinements were undertaken in different space groups. These include the centrosymmetric space group Pnma as well as the non-centrosymmetric space group Pmc2₁. In addition, refinements in the triclinic crystal system have been performed. All refinements in these aforementioned space groups resulted in severe convergence problems. Consequently, we exclude all these space groups as possible candidates for Ag₂CdSnS₄.

Rietveld refinements in Pmn2₁ and Pn were done for all temperatures (25–300°C, 25 K steps). The monoclinic angle β was plotted against the temperature for the whole temperature range (black dots in Fig. 10). The plotted results point to the fact that β abruptly becomes 90°, the value of the orthorhombic high-temperature phase, at about 200°C. This again indicates a first order transition from the wurtzkesterite-type structure to the wurtzstannite-type structure. The area around 200–225°C may be considered as two-phase region. The error bars at temperatures ≤200°C are smaller than those >200°C. For the refined cell volume, no significant jump in the region around 200°C can be observed (red squares in Fig. 10).

Fig. 10:

Monoclinic angle β and cell volume plotted against temperature (from Rietveld refinements in space group Pn for β and from refinements in Pn (T≤200°C) and Pmn2₁ (T>200°C) for the cell volume).

2.5 UV/Vis spectroscopy

The optical properties of Ag₂CdSnS₄ were measured in reflectance mode, and the optical band gaps were determined using the Tauc plot method [37], [38]. For the direct optical band gap a value of E_g=1.93 eV was calculated whereas a narrower indirect optical band gap of E_g=1.82 eV was obtained (Fig. 11). The color of our sample (black with violet accents) points to a direct optical band gap of E_g=1.93 eV which is in good agreement with the experimentally determined band gap mentioned in literature [39].

Fig. 11:

UV/Vis spectra of Ag₂CdSnS₄ with Tauc plot determinations of the direct (left) and indirect (right) optical band gap.

4.1 Synthesis

Ag₂CdSnS₄ was synthesized by ball milling in a high-energy planetary Mono Mill (Pulverisette 6, Fritsch, Idar-Oberstein, Germany), followed by an annealing step under an atmosphere of H₂S. As starting materials Ag₂S (Schuchardt), CdS, SnS, and sulfur (Fluka, 99.99%) were used which were filled in a 45 mL zirconia-made grinding beaker with 6 zirconia balls with a diameter of 15 mm. A rotational speed of 350 rpm and a milling time of 5 h were set. In order to obtain a highly crystalline product, the grounded powder was annealed at T=550°C for 2 h under H₂S atmosphere. A 0.1 m Cd(CH₃CO₂)₂ solution and H₂S (Air Liquide, 99.5%) were used for precipitation of CdS. SnS was synthesized using the high-temperature solid-state reaction of the elements tin (Merck, 99.9%) and sulfur (Fluka, 99.99%) in an evacuated and sealed SiO₂ ampoule.

4.2 Structural and chemical characterization

X-ray powder diffraction investigations as well as in-situ high-temperature X-ray diffraction experiments (25–300°C, N₂ atmosphere) were carried out with a RIGAKU SmartLab 3 kW system equipped with a Kα1 unit (Johansson-type Ge crystal, CuKα₁ radiation, λ=1.54060 Å). The diffraction data were obtained in Bragg-Brentano geometry over an angular range of 2θ=10–120° for room temperature and 2θ=10–80° for high-temperature measurements. Rietveld refinements [40] were performed using the program FullProf [41] by applying a pseudo-Voigt function. Backgrounds were fitted using a set of various background points with refinable heights. It should be mentioned that anisotropic strain broadening terms were used due to anisotropic reflection broadening.

Further details of the crystal structure investigation may be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: +49-7247-808-666; e-mail: crysdata@fiz-karlsruhe.de, http://www.fiz-informationsdienste.de/en/DB/icsd/depot_anforderung.html) on quoting the deposition numbers CSD-1979198 and CSD-1979199.

For the chemical characterization of Ag₂CdSnS₄, energy dispersive X-ray spectroscopy (EDX) using a DSM 982 GEMINI spectrometer (Carl Zeiss AG, Oberkochen, Germany) equipped with a XFlash 6|60 detector (Bruker, Billerica, USA) were performed. For the determination of the sulfur content, an instrumental error of 5% is given. The EDX measurements were carried out at the Zentrum für Elektronenmikroskopie (ZELMI) of the TU Berlin. For the confirmation of the sulfur content, additional analyses were carried out using a FlashEA 1112 elemental analyzer (Thermo Scientific™, Waltham, USA). Hereby, a device error of 2% is assumed.

Thermoanalytical analysis (DTA) were carried out using a STA 7300 thermogravimeter (Hitachi, Chiyoda, Japan). These measurements were performed under nitrogen atmosphere up to 300°C with a heating and cooling rate of 3 K min⁻¹; alumina crucibles were used as reference and sample container.

4.3 UV/Vis spectroscopy

The optical band gaps were determined by UV/Vis measurements using a V670 UV/Vis-NIR spectrometer (Jasco Deutschland GmbH, Pfungstadt, Germany). The spectra obtained in diffuse reflectance mode were converted into absorption spectra by the Kubelka-Munk function; the optical band gaps were received from the absorption spectra using the Tauc plot method [37], [38]. The standard deviation for E_g was estimated close to 0.05 eV. For sample preparation, Ag₂CdSnS₄ was mixed with a white standard (MgO) in a mass ratio of 1:1.