2.2.3.1 Diffraction data analysis
In order to obtain strong resonant scattering effects, the data were collected very close to the absorption edges. Tentative refinements using just one dataset clearly show that the distribution of the element near the corresponding absorption edge strongly influences R values and that the refinement of the corresponding site occupancy is highly significant. The aim of the final refinement was to refine the site occupancy of each element on all crystallographic positions, regardless of its value (e.g. if it is significantly larger than zero or not), in order to prove the element distribution ab initio and to employ as few presumptions as possible. In order to suppress the correlation with the overall scale factor, it proved sufficient to fix the overall composition (element ratios) according to the formula SnSb2Te4 (but not the total number of
atoms in the unit cell). Vacancies were allowed on the cation positions. It is possible to also allow anion vacancies, however, such refinements yield slightly negative site occupancies for some atoms on some sites (but all of them are zero within their standard deviation). For the sake of positive site occupancies, which are required in refinement input files, the anion sites were constrained according to full occupancy, which is chemically reasonable as cation vacancies are much more likely than anion vacancies in comparable compounds. The dispersion correction factors Δf’ and Δf’’ were calculated with the program CROSSEC implemented in the CCP4 program suite [32] and compared to values interpolated from various databases.[33,34] Manually varying the values for Δf’ in joint refinements shows that the refined element distribution is very robust and does not change more than a few standard deviations when Δf’ is changed by about ±0.5. Therefore, the overall result does not depend significantly on the exact values used. The best option was the refinement of Δf’ for those values that are strongly affected by resonant scattering (Sn at the Sn-K edge etc.) using JANA2006 [30] and to keep all others as an average
from different calculations. The refinement did not change the calculated values in an unreasonable way (max. 1.5 electrons). It is remarkable that increased absorption and fluorescence do not pose a serious problem even when data were collected at the Te-K edge which also means significant resonant scattering for Sn and Sb. The absorption coefficient for this unfavorable situation is still in the same range as for a normal laboratory measurement with Mo-Kα radiation.
The final refinement (SHELX) converged at R1 = 0.028 for all five datasets. All site occupancies could be refined independently (Table 2). The precision of site occupancies is about 1%. The correlation between site occupancies is about 60-65%. In the same final refinement, all atoms have been refined anisotropically; the correlation between site occupancies and displacement parameters does not exceed 65%. Although the amount of Sn and Sb on the anion positions as well as the concentration of cation vacancies turns out not to be significant, the corresponding parameters have not been fixed to zero in order to demonstrate the stability of the refinement and to evaluate the standard deviations.
2.2.3.1 Structure description
In accordance with literature,[14-17] the structure of 21R-SnSb2Te4 exhibits three rocksalt-type
blocks with 7 alternating cation and anion layers each as shown in Fig. 1. The distance between Te anion layers (distance Te-Te: 3.6973(7) Å) at the van der Waals gap points to a partially covalent character as it is significantly shorter than the sum of van der Waals radii (4.0 Å). The Te atoms in these Te layers show a unifacial cation coordination which leads to a stronger interaction with the cations in the [Sn/SbTe6] octahedra next to the gap. The cations form shorter
bonds toward the gap and longer bonds toward the block center, leading to the 3 + 3 coordination with bond lengths of 2.9818(6) Å and 3.2266(7) Å. The [Sn/SbTe6] octahedra in the center of the
blocks are more regular with bond lengths of 3.0905(5) Å. These bond lengths are in accordance with the results reported in the literature.
The refinement shows that cations and anions are almost perfectly separated in the structure (cf. Fig. 2). There is no anti-site disorder except for a small amount of Te on one cation position. Although it is statistically significant, this should not be over-interpreted (small systematic errors might occur in any refinement and are not represented by standard deviations based on counting statistics only). Sn and Sb are disordered on the cation positions, however. The disorder is not random. Sn concentrates on the 3a position in the center of the blocks while Sb is enriched on the 6c position near the van der Waals gaps. Probably, the higher formal charge of SbIII compared to SnII is better suited to saturate the coordination of Te positions unifacially
surrounded by cations. This result is in accordance with the mixed site occupancies reported for the isotypic phases GeSb2Te4 and PbSb2Te4, which also show a preferred occupation of the 6c
position with Sb and a preferred occupation of the 3a position with Ge or Pb, respectively.[10-13] The interatomic distances in these compounds vary in the same way with respect to their position in the blocks (cf. Fig. 2). This means that the Ge, Sn and Sb compounds are strictly isotypic also with respect to the cation distribution.
Figure 2. Atom distribution (occupancy factors for the elements in each compound, top right, arrows indicate the corresponding atom position) and selected interatomic distances (bottom right, the corresponding “bonds” are indicated) in the refined model of SnSb2Te4 (left,
displacement ellipsoids are drawn at 90 % probability level). For comparison, the corresponding values are given for GeSb2Te4[10] and PbSb2Te4.[12,13]