research communications
The
of quaternary (Sn,Pb,Bi)PtaFaculty of Natural Sciences, Institute of Chemistry, Materials for Innovative Energy Concepts, Chemnitz University of Technology, 09107 Chemnitz, Germany, and bMax-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Strasse 40, 01187 Dresden, Germany
*Correspondence e-mail: marc.armbruester@chemie.tu-chemnitz.de
Quaternary (Sn,Pb,Bi)Pt was synthesized by melting of the elements in an evacuated silica glass ampoule. The 0.15Pb0.54Bi0.31)Pt.
was established by single-crystal X-ray diffraction and adopts an atomic arrangement of the NiAs type with additional occupation of the voids. Decisive for the was the composition of the crystals as determined by energy dispersive (EDXS), resulting in a formula of (SnCCDC reference: 2239531
1. Chemical context
Platinum-based intermetallic compounds possess promising properties as electrocatalysts and provide necessary stability for the harsh application conditions in acidic electrolytes (Rössner & Armbrüster, 2019). SnPt, PbPt and BiPt are interesting electrocatalysts for the oxidation of small organic molecules and have the NiAs type of (Oftedal, 1928; Nowotny et al., 1946; Zhuravlev et al., 1962). So far, the existence of a substitutional between PtPb and PtBi was confirmed by powder X-ray diffraction, with the site occupancy deduced from the nominal composition (Zhuravlev et al., 1962), which also holds for all three binary end members. To obtain material for electrocatalytic investigations, the synthesis of single-phase (Sn,Pb,Bi)Pt was attempted. Large hexagonal crystals were found on the top of an otherwise microgranular ingot. Preliminary EDXS analysis indicated the presence of all four elements in the crystal. Further structural investigations besides the original structure reports for PtSn (Harris et al., 1968; Shelton et al., 1981; Durussel et al., 1994), PtPb (Zhuravlev et al. 1962; Sidorov et al., 2021) and PtBi (Zhuravlev & Stepanova, 1962a,b) provide no full structural characterization by means of single-crystal X-ray diffraction. Thus, structural data for binary, ternary or quaternary samples in the (Sn,Pb,Bi)Pt system are incomplete. To provide such data, one of the obtained crystals was studied by means of single-crystal X-ray diffraction.
2. Structural commentary
As a result of the very similar scattering power of three of the four atoms (Bi, Pb and Pt), the direct assignment of the atomic positions to the respective elements was not possible. Atoms were distributed based on crystal-chemical considerations as well as by achieving an agreement between the refined composition and the result of the EDXS analysis (Fig. 1). The 2a site was assigned to Pt in agreement with structural studies of binary endmembers. A mixed occupancy of Sn, Pb and Bi was assumed for the 2c position. The statistical distribution of these elements at the same atomic site is based on the full miscibility of the elements in the molten state and on the missing site preference in the only known binary phase Pb0.7Bi0.3 (Mg type of Kurnakov & Ageeva, 1937). Additional electron density was detected on the 2c (m2) and 4f (3m.) sites, for which two possible scenarios can be considered. Either those positions are occupied by the smaller Sn atoms as a result of the enlarged unit-cell volume of 84.84 Å3, which is 7.2% higher compared to 79.14 Å3 for SnPt (Oftedal, 1928), or the presence of stacking faults. Neither can be proven here.
As a result of the potential partial occupation of 2c (m2) and 4f (3m.) in the hexagonal lattice of the quaternary sample, we assign the to the NiAs type. The refined composition of 7.5%at Sn, 27.0%at Pb, 15.5%at Bi and 50%at Pt is in broad agreement with the results of EDXS measurements (12.35%at Sn, 25.87%at Pb, 9.49%at Bi and 52.29%at Pt) considering the error of this method, which to our experience is up to 5%at for standardless quantifications of non-ideal samples, i.e. mirror-finished surfaces.
3. Synthesis and crystallization
Elements were weighed in an Ar-filled glove-box (O2 and H2O content < 0.1 ppm) according to the nominal composition of 20.83%at Sn (99.999%, granules, ChemPUR), 20.83%at Pb (99.999%, granules, AlutervFKI), 8.33%at Bi (99.997%, granules, AlfaAesar) and 50.00%at Pt (99.95%, foil, Goodfellow), then sealed in an evacuated silica glass ampoule. The ampoule was placed into a furnace at 1473 K for 24 h, then cooled down from 1473 K to 873 K at a rate of 0.2 K min−1. The temperature of 873 K was held for seven days and subsequently the ampoule was quenched in cold water. Single crystals with a hexagonal shape were selected from the top of an otherwise microgranular sample, which was composed of phases with the Cu3Au and NiAs type of based on powder X-ray diffraction data. As a result of the high X-ray absorption of the investigated material, hexagonal-shaped specimens were too large for single crystal X-ray data collection. For this experiment, a relatively small piece was mechanically separated from a hexagonally shaped block. The composition of the investigated single crystal was determined by EDXS (Quantax, Bruker).
4. Refinement
Crystallographic data, data collection and structure .
details are summarized in Table 1To decrease the number of parameters, the Pt site was constrained to full occupation at the 2a (m.) site. Even though the standardless quantification by means of EDXS data is 52.3%at Pt, recent results of bulk samples from the quasi-ternary cut of the quaternary Sn–Pb–Bi–Pt system indicate a strict upper compositional limit of 50%at Pt (Rössner et al., 2023). An initial was done for Pb and Bi, using EDXS values as a starting point, then the additional electron density was considered by adding Sn. After multiple cycles, it was decided that a compromise had to be made between excellent results and compositions close to the ones from EDXS results. The final model is presented here.
Furthermore, it has to be noted that Sn3 was refined with isotropic displacement parameters, as the minor site occupancy (2.7%), does not justify to add additional parameters to enable a
with anisotropic displacement parameters. It has to be stressed that the ratio of 13 parameters for 123 independent reflections is already at the recommended upper limit (ratio parameters:reflections < 1:10).Supporting information
CCDC reference: 2239531
https://doi.org/10.1107/S2056989023000956/wm5665sup1.cif
contains datablocks I, quarternary. DOI:Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989023000956/wm5665Isup2.hkl
Data collection: CrystalClear (Rigaku, 2008); cell
CrystalClear (Rigaku, 2008); data reduction: CrystalClear (Rigaku, 2008); program(s) used to solve structure: SIR-2014 (Burla et al., 2015); program(s) used to refine structure: SHELXL (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg & Putz, 2018); software used to prepare material for publication: SHELXL (Sheldrick, 2015).(Sn·Pb·Bi)Pt | Dx = 15.23 Mg m−3 |
Mr = 389.32 | Mo Kα radiation, λ = 0.710730 Å |
Hexagonal, P63/mmc | Cell parameters from 924 reflections |
a = 4.228 (1) Å | θ = 9.3–43.0° |
c = 5.481 (2) Å | µ = 169.4 mm−1 |
V = 84.84 (5) Å3 | T = 293 K |
Z = 2 | Irregular shaped, grey |
F(000) = 311 | 0.04 × 0.03 × 0.02 mm |
Rigaku AFC7 four-circle diffractometer | 123 independent reflections |
Radiation source: Sealed Tube | 120 reflections with I > 2σ(I) |
Graphite Monochromator monochromator | Rint = 0.043 |
Detector resolution: 28.5714 pixels mm-1 | θmax = 39.8°, θmin = 5.6° |
profile data from φ–scans | h = −7→5 |
Absorption correction: multi-scan (Blessing, 1995) | k = −6→7 |
Tmin = 0.037, Tmax = 0.081 | l = −5→9 |
1549 measured reflections |
Refinement on F2 | 13 parameters |
Least-squares matrix: full | 1 restraint |
R[F2 > 2σ(F2)] = 0.025 | w = 1/[σ2(Fo2) + (0.012P)2 + 0.2655P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.041 | (Δ/σ)max = 0.013 |
S = 1.51 | Δρmax = 2.08 e Å−3 |
123 reflections | Δρmin = −1.43 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Pt1 | 0 | 0 | 0 | 0.0110 (2) | |
Bi1 | 0.3333 | 0.6667 | 0.2500 | 0.0077 (3) | 0.31 (5) |
Pb1 | 0.3333 | 0.6667 | 0.2500 | 0.0077 | 0.54 (5) |
Sn1 | 0.3333 | 0.6667 | 0.2500 | 0.0077 | 0.03 (4) |
Sn2 | 0.3333 | 0.6667 | 0.7500 | 0.0077 | 0.064 (6) |
Sn3 | 0.3333 | 0.6667 | 0.501 (5) | 0.012 (7)* | 0.027 (4) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Pt1 | 0.0133 (3) | 0.0133 | 0.0063 (3) | 0.00667 (13) | 0 | 0 |
Bi1 | 0.0061 (3) | 0.0061 | 0.0108 (4) | 0.00307 (14) | 0 | 0 |
Pb1 | 0.0061 | 0.0061 | 0.0108 | 0.00307 | 0 | 0 |
Sn1 | 0.0061 | 0.0061 | 0.0108 | 0.00307 | 0 | 0 |
Sn2 | 0.0061 | 0.0061 | 0.0108 | 0.00307 | 0 | 0 |
Pt1—Sn3i | 2.4410 (6) | Pb1—Sn3x | 2.797 (13) |
Pt1—Sn3ii | 2.4410 (6) | Pb1—Sn3xiii | 2.797 (13) |
Pt1—Sn3iii | 2.4410 (6) | Sn1—Sn3 | 1.37 (3) |
Pt1—Sn3iv | 2.4410 (6) | Sn1—Sn3i | 1.37 (3) |
Pt1—Sn3v | 2.4411 (6) | Sn1—Sn2ix | 2.4410 (6) |
Pt1—Sn3vi | 2.4411 (6) | Sn1—Sn2x | 2.4410 (6) |
Pt1—Pt1vii | 2.7402 (9) | Sn1—Sn2xi | 2.4410 (6) |
Pt1—Pt1ii | 2.7402 (9) | Sn1—Sn2 | 2.7403 (8) |
Pt1—Bi1viii | 2.7993 (5) | Sn1—Sn2xii | 2.7402 (9) |
Pt1—Sn1viii | 2.7993 (5) | Sn1—Sn3iv | 2.797 (13) |
Pt1—Pb1viii | 2.7993 (5) | Sn1—Sn3ix | 2.797 (13) |
Pt1—Sn2ix | 2.7993 (5) | Sn1—Sn3vi | 2.797 (13) |
Bi1—Sn3 | 1.37 (3) | Sn1—Sn3x | 2.797 (13) |
Bi1—Sn3i | 1.37 (3) | Sn1—Sn3xiii | 2.797 (13) |
Bi1—Sn2ix | 2.4410 (6) | Sn2—Sn3xiv | 1.37 (3) |
Bi1—Sn2x | 2.4410 (6) | Sn2—Sn3 | 1.37 (3) |
Bi1—Sn2xi | 2.4410 (6) | Sn2—Sn1ix | 2.4410 (6) |
Bi1—Sn2 | 2.7403 (8) | Sn2—Pb1ix | 2.4410 (6) |
Bi1—Sn2xii | 2.7402 (9) | Sn2—Bi1ix | 2.4410 (6) |
Bi1—Sn3iv | 2.797 (13) | Sn2—Sn1x | 2.4410 (6) |
Bi1—Sn3ix | 2.797 (13) | Sn2—Sn1xi | 2.4410 (6) |
Bi1—Sn3vi | 2.797 (13) | Sn2—Pb1x | 2.4410 (6) |
Bi1—Sn3x | 2.797 (13) | Sn2—Pb1xi | 2.4410 (6) |
Bi1—Sn3xiii | 2.797 (13) | Sn2—Bi1x | 2.4410 (6) |
Pb1—Sn3 | 1.37 (3) | Sn2—Bi1xi | 2.4410 (6) |
Pb1—Sn3i | 1.37 (3) | Sn3—Sn3ix | 2.4410 (6) |
Pb1—Sn2ix | 2.4410 (6) | Sn3—Pt1xv | 2.4410 (6) |
Pb1—Sn2x | 2.4410 (6) | Sn3—Pt1xvi | 2.4410 (6) |
Pb1—Sn2xi | 2.4410 (6) | Sn3—Pt1vii | 2.4410 (6) |
Pb1—Sn2 | 2.7403 (8) | Sn3—Sn3x | 2.4411 (6) |
Pb1—Sn2xii | 2.7402 (9) | Sn3—Sn3xi | 2.4411 (7) |
Pb1—Sn3iv | 2.797 (13) | Sn3—Sn3xiv | 2.73 (5) |
Pb1—Sn3ix | 2.797 (13) | Sn3—Sn3i | 2.75 (5) |
Pb1—Sn3vi | 2.797 (13) | ||
Sn3i—Pt1—Sn3ii | 180.0 | Sn3i—Sn1—Sn2x | 90.000 (4) |
Sn3iii—Pt1—Sn3iv | 180.0 | Sn2ix—Sn1—Sn2x | 120.0 |
Sn3i—Pt1—Sn3v | 119.999 (5) | Sn3—Sn1—Sn2xi | 90.000 (5) |
Sn3iii—Pt1—Sn3v | 119.999 (4) | Sn3i—Sn1—Sn2xi | 90.000 (4) |
Sn3ii—Pt1—Sn3vi | 119.999 (5) | Sn2ix—Sn1—Sn2xi | 120.0 |
Sn3iv—Pt1—Sn3vi | 119.999 (4) | Sn2x—Sn1—Sn2xi | 120.0 |
Sn3v—Pt1—Sn3vi | 180.0 | Sn3—Sn1—Sn2 | 0.000 (6) |
Sn3i—Pt1—Pt1vii | 90.1 (6) | Sn3i—Sn1—Sn2 | 180.0 |
Sn3ii—Pt1—Pt1vii | 89.9 (6) | Sn2ix—Sn1—Sn2 | 90.0 |
Sn3iii—Pt1—Pt1vii | 90.1 (6) | Sn2x—Sn1—Sn2 | 90.0 |
Sn3iv—Pt1—Pt1vii | 89.9 (6) | Sn2xi—Sn1—Sn2 | 90.0 |
Sn3v—Pt1—Pt1vii | 90.1 (6) | Sn3—Sn1—Sn2xii | 180.0 |
Sn3vi—Pt1—Pt1vii | 89.9 (6) | Sn3i—Sn1—Sn2xii | 0.000 (1) |
Sn3i—Pt1—Pt1ii | 89.9 (6) | Sn2ix—Sn1—Sn2xii | 90.0 |
Sn3ii—Pt1—Pt1ii | 90.1 (6) | Sn2x—Sn1—Sn2xii | 90.0 |
Sn3iii—Pt1—Pt1ii | 89.9 (6) | Sn2xi—Sn1—Sn2xii | 90.0 |
Sn3iv—Pt1—Pt1ii | 90.1 (6) | Sn2—Sn1—Sn2xii | 180.0 |
Sn3v—Pt1—Pt1ii | 89.9 (6) | Sn3—Sn1—Sn3iv | 119.2 (5) |
Sn3vi—Pt1—Pt1ii | 90.1 (6) | Sn3i—Sn1—Sn3iv | 60.8 (5) |
Pt1vii—Pt1—Pt1ii | 180.0 | Sn2ix—Sn1—Sn3iv | 29.2 (5) |
Sn3i—Pt1—Bi1viii | 150.6 (6) | Sn2x—Sn1—Sn3iv | 115.87 (13) |
Sn3ii—Pt1—Bi1viii | 29.4 (6) | Sn2xi—Sn1—Sn3iv | 115.87 (13) |
Sn3iii—Pt1—Bi1viii | 64.1 (3) | Sn2—Sn1—Sn3iv | 119.2 (5) |
Sn3iv—Pt1—Bi1viii | 115.9 (3) | Sn2xii—Sn1—Sn3iv | 60.8 (5) |
Sn3v—Pt1—Bi1viii | 64.1 (3) | Sn3—Sn1—Sn3ix | 60.8 (5) |
Sn3vi—Pt1—Bi1viii | 115.9 (3) | Sn3i—Sn1—Sn3ix | 119.2 (5) |
Pt1vii—Pt1—Bi1viii | 119.305 (9) | Sn2ix—Sn1—Sn3ix | 29.2 (5) |
Pt1ii—Pt1—Bi1viii | 60.695 (9) | Sn2x—Sn1—Sn3ix | 115.87 (13) |
Sn3i—Pt1—Sn1viii | 150.6 (6) | Sn2xi—Sn1—Sn3ix | 115.87 (13) |
Sn3ii—Pt1—Sn1viii | 29.4 (6) | Sn2—Sn1—Sn3ix | 60.8 (5) |
Sn3iii—Pt1—Sn1viii | 64.1 (3) | Sn2xii—Sn1—Sn3ix | 119.2 (5) |
Sn3iv—Pt1—Sn1viii | 115.9 (3) | Sn3iv—Sn1—Sn3ix | 58.5 (10) |
Sn3v—Pt1—Sn1viii | 64.1 (3) | Sn3—Sn1—Sn3vi | 119.2 (5) |
Sn3vi—Pt1—Sn1viii | 115.9 (3) | Sn3i—Sn1—Sn3vi | 60.8 (5) |
Pt1vii—Pt1—Sn1viii | 119.305 (9) | Sn2ix—Sn1—Sn3vi | 115.87 (13) |
Pt1ii—Pt1—Sn1viii | 60.695 (9) | Sn2x—Sn1—Sn3vi | 115.87 (13) |
Bi1viii—Pt1—Sn1viii | 0.0 | Sn2xi—Sn1—Sn3vi | 29.2 (5) |
Sn3i—Pt1—Pb1viii | 150.6 (6) | Sn2—Sn1—Sn3vi | 119.2 (5) |
Sn3ii—Pt1—Pb1viii | 29.4 (6) | Sn2xii—Sn1—Sn3vi | 60.8 (5) |
Sn3iii—Pt1—Pb1viii | 64.1 (3) | Sn3iv—Sn1—Sn3vi | 98.2 (6) |
Sn3iv—Pt1—Pb1viii | 115.9 (3) | Sn3ix—Sn1—Sn3vi | 128.3 (3) |
Sn3v—Pt1—Pb1viii | 64.1 (3) | Sn3—Sn1—Sn3x | 60.8 (5) |
Sn3vi—Pt1—Pb1viii | 115.9 (3) | Sn3i—Sn1—Sn3x | 119.2 (5) |
Pt1vii—Pt1—Pb1viii | 119.305 (9) | Sn2ix—Sn1—Sn3x | 115.87 (13) |
Pt1ii—Pt1—Pb1viii | 60.695 (9) | Sn2x—Sn1—Sn3x | 29.2 (5) |
Bi1viii—Pt1—Pb1viii | 0.0 | Sn2xi—Sn1—Sn3x | 115.87 (13) |
Sn1viii—Pt1—Pb1viii | 0.0 | Sn2—Sn1—Sn3x | 60.8 (5) |
Sn3i—Pt1—Sn2ix | 64.2 (3) | Sn2xii—Sn1—Sn3x | 119.2 (5) |
Sn3ii—Pt1—Sn2ix | 115.8 (3) | Sn3iv—Sn1—Sn3x | 128.3 (3) |
Sn3iii—Pt1—Sn2ix | 150.8 (6) | Sn3ix—Sn1—Sn3x | 98.2 (6) |
Sn3iv—Pt1—Sn2ix | 29.2 (6) | Sn3vi—Sn1—Sn3x | 128.3 (3) |
Sn3v—Pt1—Sn2ix | 64.2 (3) | Sn3—Sn1—Sn3xiii | 119.2 (5) |
Sn3vi—Pt1—Sn2ix | 115.8 (3) | Sn3i—Sn1—Sn3xiii | 60.8 (5) |
Pt1vii—Pt1—Sn2ix | 60.695 (9) | Sn2ix—Sn1—Sn3xiii | 115.87 (13) |
Pt1ii—Pt1—Sn2ix | 119.305 (10) | Sn2x—Sn1—Sn3xiii | 29.2 (5) |
Sn3—Bi1—Sn3i | 180.0 | Sn2xi—Sn1—Sn3xiii | 115.87 (13) |
Sn3—Bi1—Sn2ix | 90.000 (1) | Sn2—Sn1—Sn3xiii | 119.2 (5) |
Sn3i—Bi1—Sn2ix | 89.999 (1) | Sn2xii—Sn1—Sn3xiii | 60.8 (5) |
Sn3—Bi1—Sn2x | 90.000 (4) | Sn3iv—Sn1—Sn3xiii | 98.2 (6) |
Sn3i—Bi1—Sn2x | 90.000 (4) | Sn3ix—Sn1—Sn3xiii | 128.3 (3) |
Sn2ix—Bi1—Sn2x | 120.0 | Sn3vi—Sn1—Sn3xiii | 98.2 (6) |
Sn3—Bi1—Sn2xi | 90.000 (5) | Sn3x—Sn1—Sn3xiii | 58.5 (10) |
Sn3i—Bi1—Sn2xi | 90.000 (4) | Sn3xiv—Sn2—Sn3 | 180.0 |
Sn2ix—Bi1—Sn2xi | 120.0 | Sn3xiv—Sn2—Sn1ix | 89.999 (1) |
Sn2x—Bi1—Sn2xi | 120.0 | Sn3—Sn2—Sn1ix | 90.000 (1) |
Sn3—Bi1—Sn2 | 0.000 (6) | Sn3xiv—Sn2—Pb1ix | 89.999 (1) |
Sn3i—Bi1—Sn2 | 180.0 | Sn3—Sn2—Pb1ix | 90.000 (1) |
Sn2ix—Bi1—Sn2 | 90.0 | Sn1ix—Sn2—Pb1ix | 0.0 |
Sn2x—Bi1—Sn2 | 90.0 | Sn3xiv—Sn2—Bi1ix | 89.999 (1) |
Sn2xi—Bi1—Sn2 | 90.0 | Sn3—Sn2—Bi1ix | 90.000 (1) |
Sn3—Bi1—Sn2xii | 180.0 | Sn1ix—Sn2—Bi1ix | 0.0 |
Sn3i—Bi1—Sn2xii | 0.000 (1) | Pb1ix—Sn2—Bi1ix | 0.0 |
Sn2ix—Bi1—Sn2xii | 90.0 | Sn3xiv—Sn2—Sn1x | 90.000 (6) |
Sn2x—Bi1—Sn2xii | 90.0 | Sn3—Sn2—Sn1x | 90.000 (6) |
Sn2xi—Bi1—Sn2xii | 90.0 | Sn1ix—Sn2—Sn1x | 120.0 |
Sn2—Bi1—Sn2xii | 180.0 | Pb1ix—Sn2—Sn1x | 120.0 |
Sn3—Bi1—Sn3iv | 119.2 (5) | Bi1ix—Sn2—Sn1x | 120.0 |
Sn3i—Bi1—Sn3iv | 60.8 (5) | Sn3xiv—Sn2—Sn1xi | 90.000 (7) |
Sn2ix—Bi1—Sn3iv | 29.2 (5) | Sn3—Sn2—Sn1xi | 90.000 (7) |
Sn2x—Bi1—Sn3iv | 115.87 (13) | Sn1ix—Sn2—Sn1xi | 120.0 |
Sn2xi—Bi1—Sn3iv | 115.87 (13) | Pb1ix—Sn2—Sn1xi | 120.0 |
Sn2—Bi1—Sn3iv | 119.2 (5) | Bi1ix—Sn2—Sn1xi | 120.0 |
Sn2xii—Bi1—Sn3iv | 60.8 (5) | Sn1x—Sn2—Sn1xi | 120.0 |
Sn3—Bi1—Sn3ix | 60.8 (5) | Sn3xiv—Sn2—Pb1x | 90.000 (6) |
Sn3i—Bi1—Sn3ix | 119.2 (5) | Sn3—Sn2—Pb1x | 90.000 (6) |
Sn2ix—Bi1—Sn3ix | 29.2 (5) | Sn1ix—Sn2—Pb1x | 120.0 |
Sn2x—Bi1—Sn3ix | 115.87 (13) | Pb1ix—Sn2—Pb1x | 120.0 |
Sn2xi—Bi1—Sn3ix | 115.87 (13) | Bi1ix—Sn2—Pb1x | 120.0 |
Sn2—Bi1—Sn3ix | 60.8 (5) | Sn1x—Sn2—Pb1x | 0.0 |
Sn2xii—Bi1—Sn3ix | 119.2 (5) | Sn1xi—Sn2—Pb1x | 120.0 |
Sn3iv—Bi1—Sn3ix | 58.5 (10) | Sn3xiv—Sn2—Pb1xi | 90.000 (7) |
Sn3—Bi1—Sn3vi | 119.2 (5) | Sn3—Sn2—Pb1xi | 90.000 (7) |
Sn3i—Bi1—Sn3vi | 60.8 (5) | Sn1ix—Sn2—Pb1xi | 120.0 |
Sn2ix—Bi1—Sn3vi | 115.87 (13) | Pb1ix—Sn2—Pb1xi | 120.0 |
Sn2x—Bi1—Sn3vi | 115.87 (13) | Bi1ix—Sn2—Pb1xi | 120.0 |
Sn2xi—Bi1—Sn3vi | 29.2 (5) | Sn1x—Sn2—Pb1xi | 120.0 |
Sn2—Bi1—Sn3vi | 119.2 (5) | Sn1xi—Sn2—Pb1xi | 0.0 |
Sn2xii—Bi1—Sn3vi | 60.8 (5) | Pb1x—Sn2—Pb1xi | 120.0 |
Sn3iv—Bi1—Sn3vi | 98.2 (6) | Sn3xiv—Sn2—Bi1x | 90.000 (6) |
Sn3ix—Bi1—Sn3vi | 128.3 (3) | Sn3—Sn2—Bi1x | 90.000 (6) |
Sn3—Bi1—Sn3x | 60.8 (5) | Sn1ix—Sn2—Bi1x | 120.0 |
Sn3i—Bi1—Sn3x | 119.2 (5) | Pb1ix—Sn2—Bi1x | 120.0 |
Sn2ix—Bi1—Sn3x | 115.87 (13) | Bi1ix—Sn2—Bi1x | 120.0 |
Sn2x—Bi1—Sn3x | 29.2 (5) | Sn1x—Sn2—Bi1x | 0.0 |
Sn2xi—Bi1—Sn3x | 115.87 (13) | Sn1xi—Sn2—Bi1x | 120.0 |
Sn2—Bi1—Sn3x | 60.8 (5) | Pb1x—Sn2—Bi1x | 0.0 |
Sn2xii—Bi1—Sn3x | 119.2 (5) | Pb1xi—Sn2—Bi1x | 120.0 |
Sn3iv—Bi1—Sn3x | 128.3 (3) | Sn3xiv—Sn2—Bi1xi | 90.000 (7) |
Sn3ix—Bi1—Sn3x | 98.2 (6) | Sn3—Sn2—Bi1xi | 90.000 (7) |
Sn3vi—Bi1—Sn3x | 128.3 (3) | Sn1ix—Sn2—Bi1xi | 120.0 |
Sn3—Bi1—Sn3xiii | 119.2 (5) | Pb1ix—Sn2—Bi1xi | 120.0 |
Sn3i—Bi1—Sn3xiii | 60.8 (5) | Bi1ix—Sn2—Bi1xi | 120.0 |
Sn2ix—Bi1—Sn3xiii | 115.87 (13) | Sn1x—Sn2—Bi1xi | 120.0 |
Sn2x—Bi1—Sn3xiii | 29.2 (5) | Sn1xi—Sn2—Bi1xi | 0.0 |
Sn2xi—Bi1—Sn3xiii | 115.87 (13) | Pb1x—Sn2—Bi1xi | 120.0 |
Sn2—Bi1—Sn3xiii | 119.2 (5) | Pb1xi—Sn2—Bi1xi | 0.0 |
Sn2xii—Bi1—Sn3xiii | 60.8 (5) | Bi1x—Sn2—Bi1xi | 120.0 |
Sn3iv—Bi1—Sn3xiii | 98.2 (6) | Sn3xiv—Sn2—Bi1 | 180.0 |
Sn3ix—Bi1—Sn3xiii | 128.3 (3) | Sn3—Sn2—Bi1 | 0.000 (6) |
Sn3vi—Bi1—Sn3xiii | 98.2 (6) | Sn1ix—Sn2—Bi1 | 90.0 |
Sn3x—Bi1—Sn3xiii | 58.5 (10) | Pb1ix—Sn2—Bi1 | 90.0 |
Sn3—Pb1—Sn3i | 180.0 | Bi1ix—Sn2—Bi1 | 90.0 |
Sn3—Pb1—Sn2ix | 90.000 (1) | Sn1x—Sn2—Bi1 | 90.0 |
Sn3i—Pb1—Sn2ix | 89.999 (1) | Sn1xi—Sn2—Bi1 | 90.0 |
Sn3—Pb1—Sn2x | 90.000 (4) | Pb1x—Sn2—Bi1 | 90.0 |
Sn3i—Pb1—Sn2x | 90.000 (4) | Pb1xi—Sn2—Bi1 | 90.0 |
Sn2ix—Pb1—Sn2x | 120.0 | Bi1x—Sn2—Bi1 | 90.0 |
Sn3—Pb1—Sn2xi | 90.000 (5) | Bi1xi—Sn2—Bi1 | 90.0 |
Sn3i—Pb1—Sn2xi | 90.000 (4) | Sn2—Sn3—Bi1 | 180.0 |
Sn2ix—Pb1—Sn2xi | 120.0 | Sn2—Sn3—Pb1 | 180.0 |
Sn2x—Pb1—Sn2xi | 120.0 | Bi1—Sn3—Pb1 | 0.0 |
Sn3—Pb1—Sn2 | 0.000 (6) | Sn2—Sn3—Sn1 | 180.0 |
Sn3i—Pb1—Sn2 | 180.0 | Bi1—Sn3—Sn1 | 0.0 |
Sn2ix—Pb1—Sn2 | 90.0 | Pb1—Sn3—Sn1 | 0.0 |
Sn2x—Pb1—Sn2 | 90.0 | Sn2—Sn3—Sn3ix | 90.2 (13) |
Sn2xi—Pb1—Sn2 | 90.0 | Bi1—Sn3—Sn3ix | 89.8 (13) |
Sn3—Pb1—Sn2xii | 180.0 | Pb1—Sn3—Sn3ix | 89.8 (13) |
Sn3i—Pb1—Sn2xii | 0.000 (1) | Sn1—Sn3—Sn3ix | 89.8 (13) |
Sn2ix—Pb1—Sn2xii | 90.0 | Sn2—Sn3—Pt1xv | 90.1 (6) |
Sn2x—Pb1—Sn2xii | 90.0 | Bi1—Sn3—Pt1xv | 89.9 (6) |
Sn2xi—Pb1—Sn2xii | 90.0 | Pb1—Sn3—Pt1xv | 89.9 (6) |
Sn2—Pb1—Sn2xii | 180.0 | Sn1—Sn3—Pt1xv | 89.9 (6) |
Sn3—Pb1—Sn3iv | 119.2 (5) | Sn3ix—Sn3—Pt1xv | 179.7 (19) |
Sn3i—Pb1—Sn3iv | 60.8 (5) | Sn2—Sn3—Pt1xvi | 90.1 (6) |
Sn2ix—Pb1—Sn3iv | 29.2 (5) | Bi1—Sn3—Pt1xvi | 89.9 (6) |
Sn2x—Pb1—Sn3iv | 115.87 (13) | Pb1—Sn3—Pt1xvi | 89.9 (6) |
Sn2xi—Pb1—Sn3iv | 115.87 (13) | Sn1—Sn3—Pt1xvi | 89.9 (6) |
Sn2—Pb1—Sn3iv | 119.2 (5) | Sn3ix—Sn3—Pt1xvi | 60.000 (1) |
Sn2xii—Pb1—Sn3iv | 60.8 (5) | Pt1xv—Sn3—Pt1xvi | 120.000 (4) |
Sn3—Pb1—Sn3ix | 60.8 (5) | Sn2—Sn3—Pt1vii | 90.1 (6) |
Sn3i—Pb1—Sn3ix | 119.2 (5) | Bi1—Sn3—Pt1vii | 89.9 (6) |
Sn2ix—Pb1—Sn3ix | 29.2 (5) | Pb1—Sn3—Pt1vii | 89.9 (6) |
Sn2x—Pb1—Sn3ix | 115.87 (13) | Sn1—Sn3—Pt1vii | 89.9 (6) |
Sn2xi—Pb1—Sn3ix | 115.87 (13) | Sn3ix—Sn3—Pt1vii | 60.000 (5) |
Sn2—Pb1—Sn3ix | 60.8 (5) | Pt1xv—Sn3—Pt1vii | 120.000 (4) |
Sn2xii—Pb1—Sn3ix | 119.2 (5) | Pt1xvi—Sn3—Pt1vii | 120.000 (4) |
Sn3iv—Pb1—Sn3ix | 58.5 (10) | Sn2—Sn3—Sn3x | 90.2 (13) |
Sn3—Pb1—Sn3vi | 119.2 (5) | Bi1—Sn3—Sn3x | 89.8 (13) |
Sn3i—Pb1—Sn3vi | 60.8 (5) | Pb1—Sn3—Sn3x | 89.8 (13) |
Sn2ix—Pb1—Sn3vi | 115.87 (13) | Sn1—Sn3—Sn3x | 89.8 (13) |
Sn2x—Pb1—Sn3vi | 115.87 (13) | Pt1xv—Sn3—Sn3x | 60.0 |
Sn2xi—Pb1—Sn3vi | 29.2 (5) | Pt1xvi—Sn3—Sn3x | 60.000 (1) |
Sn2—Pb1—Sn3vi | 119.2 (5) | Pt1vii—Sn3—Sn3x | 179.7 (19) |
Sn2xii—Pb1—Sn3vi | 60.8 (5) | Sn2—Sn3—Sn3xi | 90.2 (13) |
Sn3iv—Pb1—Sn3vi | 98.2 (6) | Bi1—Sn3—Sn3xi | 89.8 (13) |
Sn3ix—Pb1—Sn3vi | 128.3 (3) | Pb1—Sn3—Sn3xi | 89.8 (13) |
Sn3—Pb1—Sn3x | 60.8 (5) | Sn1—Sn3—Sn3xi | 89.8 (13) |
Sn3i—Pb1—Sn3x | 119.2 (5) | Pt1xv—Sn3—Sn3xi | 59.999 (4) |
Sn2ix—Pb1—Sn3x | 115.87 (13) | Pt1xvi—Sn3—Sn3xi | 179.7 (19) |
Sn2x—Pb1—Sn3x | 29.2 (5) | Pt1vii—Sn3—Sn3xi | 60.000 (6) |
Sn2xi—Pb1—Sn3x | 115.87 (13) | Sn2—Sn3—Sn3xiv | 0.0 |
Sn2—Pb1—Sn3x | 60.8 (5) | Bi1—Sn3—Sn3xiv | 180.0 |
Sn2xii—Pb1—Sn3x | 119.2 (5) | Pb1—Sn3—Sn3xiv | 180.0 |
Sn3iv—Pb1—Sn3x | 128.3 (3) | Sn1—Sn3—Sn3xiv | 180.0 |
Sn3ix—Pb1—Sn3x | 98.2 (6) | Sn3ix—Sn3—Sn3xiv | 90.2 (13) |
Sn3vi—Pb1—Sn3x | 128.3 (3) | Pt1xv—Sn3—Sn3xiv | 90.1 (6) |
Sn3—Pb1—Sn3xiii | 119.2 (5) | Pt1xvi—Sn3—Sn3xiv | 90.1 (6) |
Sn3i—Pb1—Sn3xiii | 60.8 (5) | Pt1vii—Sn3—Sn3xiv | 90.1 (6) |
Sn2ix—Pb1—Sn3xiii | 115.87 (13) | Sn3x—Sn3—Sn3xiv | 90.2 (13) |
Sn2x—Pb1—Sn3xiii | 29.2 (5) | Sn3xi—Sn3—Sn3xiv | 90.2 (13) |
Sn2xi—Pb1—Sn3xiii | 115.87 (13) | Sn2—Sn3—Sn3i | 180.0 |
Sn2—Pb1—Sn3xiii | 119.2 (5) | Bi1—Sn3—Sn3i | 0.0 |
Sn2xii—Pb1—Sn3xiii | 60.8 (5) | Pb1—Sn3—Sn3i | 0.0 |
Sn3iv—Pb1—Sn3xiii | 98.2 (6) | Sn1—Sn3—Sn3i | 0.0 |
Sn3ix—Pb1—Sn3xiii | 128.3 (3) | Sn3ix—Sn3—Sn3i | 89.8 (13) |
Sn3vi—Pb1—Sn3xiii | 98.2 (6) | Pt1xv—Sn3—Sn3i | 89.9 (6) |
Sn3x—Pb1—Sn3xiii | 58.5 (10) | Pt1xvi—Sn3—Sn3i | 89.9 (6) |
Sn3—Sn1—Sn3i | 180.0 | Pt1vii—Sn3—Sn3i | 89.9 (6) |
Sn3—Sn1—Sn2ix | 90.000 (1) | Sn3x—Sn3—Sn3i | 89.8 (13) |
Sn3i—Sn1—Sn2ix | 89.999 (1) | Sn3xi—Sn3—Sn3i | 89.8 (13) |
Sn3—Sn1—Sn2x | 90.000 (4) | Sn3xiv—Sn3—Sn3i | 180.0 |
Symmetry codes: (i) x, y, −z+1/2; (ii) −x, −y, z−1/2; (iii) x−1, y−1, −z+1/2; (iv) −x+1, −y+1, z−1/2; (v) x, y−1, −z+1/2; (vi) −x, −y+1, z−1/2; (vii) −x, −y, z+1/2; (viii) −x, −y, −z; (ix) −x+1, −y+1, −z+1; (x) −x+1, −y+2, −z+1; (xi) −x, −y+1, −z+1; (xii) x, y, z−1; (xiii) −x+1, −y+2, z−1/2; (xiv) x, y, −z+3/2; (xv) −x, −y+1, z+1/2; (xvi) −x+1, −y+1, z+1/2. |
Funding information
LR and MA gratefully acknowledge the financial support of the European Social Fund and the State of Saxony provided for the NeMaCell project (project No. 100382169). YG acknowledges the support of the Deutsche Forschungsgemeinschaft (grant: GR1793/19–1).
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