| Literature DB >> 31392021 |
Lotfi Rghioui1, Lahcen El Ammari2, Abderrazzak Assani2, Mohamed Saadi2.
Abstract
The crystal structures of dirubidium potassium dysprosium bis-(vanadate), Rb2KDy(VO4)2, and caesium potassium gadolinium bis-(vanadate), Cs1.52K1.48Gd(VO4)2, were solved from single-crystal X-ray diffraction data. Both compounds, synthesized by the reactive flux method, crystallize in the space group P m1 with the glaserite structure type. VO4 tetra-hedra are linked to DyO6 or GdO6 octa-hedra by common vertices to form sheets stacking along the c axis. The large twelve-coordinate Cs+ or Rb+ cations are sandwiched between these layers in tunnels along the a and b axes, while the K+ cations, surrounded by ten oxygen atoms, are localized in cavities.Entities:
Keywords: Cs1.52K1.48Gd(VO4)2; IR and Raman spectroscopy; Rb2KDy(VO4)2; X-ray diffraction; crystal growth; crystal structure; orthovanadates
Year: 2019 PMID: 31392021 PMCID: PMC6659331 DOI: 10.1107/S2056989019008685
Source DB: PubMed Journal: Acta Crystallogr E Crystallogr Commun
Figure 1Layer of VO4 tetrahedra linked to DyO6 octahedra by vertex sharing in the structure of Rb2KDy(VO4)2.
Figure 2Three-dimensional view along the a axis of the crystal structure showing Rb+ (or Cs+) in the channels.
Figure 3View along the c axis of a layer in the structure of the title compounds, showing the cavities in which the K/Rb+ (or K/Cs+) cations are located.
Figure 4Three-dimensional view of the crystal structure showing Rb+ (or Cs+) cations between the layers stacked along the c axis.
Figure 5Three-dimensional perspective view along c axis of the crystal structure of Rb2KDy(VO4)2.
Figure 6Raman spectrum of Rb2KDy(VO4)2.
Figure 7Infrared spectrum of Rb2KDy(VO4)2.
Raman and Infrared band assignments (cm−1) for Rb2KDy(VO4)2
| Raman | Infrared | Attribution |
|---|---|---|
| 935 | 925 | Stretching vibrations of VO4 groups |
| 875 | 830 | |
| 740 | 755 | |
| 385 | 377 | Deformation modes of VO4 groups |
| 370 | 365 | |
| 340 | 311 | |
| 200 | 230 | External modes |
| 160 | 177 | |
| 125 | 130 | |
| 95 | 120 |
Experimental details
| Rb2KDy(VO4)2 | Cs1.52K1.48Gd(VO4)2 | |
|---|---|---|
| Crystal data | ||
|
| 602.42 | 646.74 |
| Crystal system, space group | Trigonal, | Trigonal, |
| Temperature (K) | 296 | 296 |
|
| 5.9728 (1), 7.7780 (1) | 6.0321 (1), 7.9821 (2) |
|
| 240.30 (1) | 251.53 (1) |
|
| 1 | 1 |
| Radiation type | Mo | Mo |
| μ (mm−1) | 20.10 | 14.37 |
| Crystal size (mm) | 0.35 × 0.28 × 0.25 | 0.34 × 0.26 × 0.22 |
| Data collection | ||
| Diffractometer | Bruker X8 | Bruker X8 |
| Absorption correction | Multi-scan ( | Multi-scan ( |
|
| 0.357, 0.749 | 0.639, 0.747 |
| No. of measured, independent and observed [ | 10549, 647, 631 | 14472, 678, 666 |
|
| 0.049 | 0.038 |
| (sin θ/λ)max (Å−1) | 0.926 | 0.925 |
| Refinement | ||
|
| 0.016, 0.042, 1.11 | 0.010, 0.028, 1.09 |
| No. of reflections | 647 | 678 |
| No. of parameters | 24 | 25 |
| Δρmax, Δρmin (e Å−3) | 1.35, −1.35 | 0.63, −0.94 |
Computer programs: APEX2 and SAINT-Plus (Bruker, 2009 ▸), SHELXT2014 (Sheldrick, 2015a ▸), SHELXL2018 (Sheldrick, 2015b ▸), ORTEP-3 for Windows (Farrugia, 2012 ▸), DIAMOND (Brandenburg, 2006 ▸), Mercury (Macrae et al., 2008 ▸) and publCIF (Westrip, 2010 ▸).
| Rb2KDy(VO4)2 | |
| Mo | |
| Trigonal, | Cell parameters from 647 reflections |
| θ = 2.6–41.1° | |
| µ = 20.10 mm−1 | |
| Block, colourless | |
| 0.35 × 0.28 × 0.25 mm |
| Bruker X8 APEX diffractometer | 647 independent reflections |
| Radiation source: fine-focus sealed tube | 631 reflections with |
| Graphite monochromator | |
| φ and ω scans | θmax = 41.1°, θmin = 2.6° |
| Absorption correction: multi-scan (SADABS; Krause | |
| 10549 measured reflections |
| Refinement on | 0 restraints |
| Least-squares matrix: full | |
| (Δ/σ)max < 0.001 | |
| Δρmax = 1.35 e Å−3 | |
| Δρmin = −1.35 e Å−3 | |
| 647 reflections | Extinction correction: SHELXL2018 (Sheldrick, 2015 |
| 24 parameters | Extinction coefficient: 0.0124 (15) |
| 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. |
| Occ. (<1) | |||||
| Rb1 | 0.000000 | 0.000000 | 0.500000 | 0.03556 (16) | |
| Dy1 | 0.000000 | 0.000000 | 0.000000 | 0.00791 (6) | |
| K1 | 0.333333 | 0.666667 | 0.8013 (9) | 0.0098 (8) | 0.5 |
| Rb2 | 0.333333 | 0.666667 | 0.7969 (5) | 0.0191 (6) | 0.5 |
| V1 | 0.333333 | 0.666667 | 0.24618 (6) | 0.00765 (8) | |
| O1 | 0.17571 (17) | 0.82429 (17) | 0.1720 (3) | 0.0273 (4) | |
| O2 | 0.333333 | 0.666667 | 0.4567 (4) | 0.0389 (10) |
| Rb1 | 0.0463 (3) | 0.0463 (3) | 0.0141 (2) | 0.02314 (13) | 0.000 | 0.000 |
| Dy1 | 0.00565 (6) | 0.00565 (6) | 0.01243 (8) | 0.00282 (3) | 0.000 | 0.000 |
| K1 | 0.0082 (10) | 0.0082 (10) | 0.0128 (18) | 0.0041 (5) | 0.000 | 0.000 |
| Rb2 | 0.0194 (7) | 0.0194 (7) | 0.0185 (12) | 0.0097 (4) | 0.000 | 0.000 |
| V1 | 0.00766 (10) | 0.00766 (10) | 0.00763 (16) | 0.00383 (5) | 0.000 | 0.000 |
| O1 | 0.0219 (5) | 0.0219 (5) | 0.0424 (10) | 0.0141 (6) | −0.0081 (3) | 0.0081 (3) |
| O2 | 0.0542 (15) | 0.0542 (15) | 0.0084 (10) | 0.0271 (8) | 0.000 | 0.000 |
| Rb1—O1i | 3.133 (2) | K1—O1xvii | 2.9951 (5) |
| Rb1—O1ii | 3.133 (2) | K1—O1xviii | 2.9951 (6) |
| Rb1—O1iii | 3.133 (2) | K1—O1iii | 2.9951 (6) |
| Rb1—O1iv | 3.133 (2) | K1—O1xix | 2.9951 (5) |
| Rb1—O1v | 3.133 (2) | K1—O1i | 2.9951 (5) |
| Rb1—O1vi | 3.133 (2) | K1—O1xx | 3.312 (7) |
| Rb1—O2vii | 3.4648 (3) | K1—O1xxi | 3.312 (7) |
| Rb1—O2viii | 3.4648 (3) | K1—O1xxii | 3.312 (7) |
| Rb1—O2ix | 3.4648 (3) | K1—V1xx | 3.460 (7) |
| Rb1—O2 | 3.4648 (3) | K1—V1vii | 3.4681 (8) |
| Rb1—O2iii | 3.4649 (3) | Rb2—O2 | 2.647 (5) |
| Rb1—O2iv | 3.4649 (3) | Rb2—O1xvi | 2.9976 (4) |
| Dy1—O1x | 2.2569 (17) | Rb2—O1xvii | 2.9976 (4) |
| Dy1—O1vi | 2.2569 (17) | Rb2—O1xviii | 2.9976 (4) |
| Dy1—O1xi | 2.2569 (17) | Rb2—O1iii | 2.9976 (4) |
| Dy1—O1iv | 2.2569 (17) | Rb2—O1xix | 2.9976 (4) |
| Dy1—O1xii | 2.2569 (17) | Rb2—O1i | 2.9976 (4) |
| Dy1—O1ii | 2.2569 (17) | Rb2—O1xx | 3.342 (4) |
| Dy1—K1xiii | 3.779 (3) | Rb2—O1xxi | 3.342 (4) |
| Dy1—K1vii | 3.779 (3) | Rb2—O1xxii | 3.342 (4) |
| Dy1—K1xiv | 3.779 (3) | Rb2—V1vii | 3.4646 (4) |
| Dy1—K1ix | 3.779 (3) | Rb2—V1iii | 3.4647 (4) |
| Dy1—K1xv | 3.779 (3) | V1—O2 | 1.637 (3) |
| Dy1—K1iii | 3.779 (3) | V1—O1 | 1.7297 (16) |
| K1—O2 | 2.681 (8) | V1—O1vi | 1.7297 (16) |
| K1—O1xvi | 2.9951 (5) | V1—O1xxiii | 1.7297 (16) |
| O1i—Rb1—O1ii | 180.0 | O1xviii—K1—V1xx | 86.02 (15) |
| O1i—Rb1—O1iii | 60.33 (5) | O1iii—K1—V1xx | 86.02 (15) |
| O1ii—Rb1—O1iii | 119.67 (5) | O1xix—K1—V1xx | 86.02 (15) |
| O1i—Rb1—O1iv | 119.67 (5) | O1i—K1—V1xx | 86.02 (15) |
| O1ii—Rb1—O1iv | 60.33 (5) | O1xx—K1—V1xx | 29.49 (7) |
| O1iii—Rb1—O1iv | 180.0 | O1xxi—K1—V1xx | 29.49 (7) |
| O1i—Rb1—O1v | 60.33 (5) | O1xxii—K1—V1xx | 29.49 (7) |
| O1ii—Rb1—O1v | 119.67 (5) | O2—K1—V1vii | 83.89 (12) |
| O1iii—Rb1—O1v | 60.33 (5) | O1xvi—K1—V1vii | 148.26 (4) |
| O1iv—Rb1—O1v | 119.67 (5) | O1xvii—K1—V1vii | 148.26 (4) |
| O1i—Rb1—O1vi | 119.67 (5) | O1xviii—K1—V1vii | 92.20 (4) |
| O1ii—Rb1—O1vi | 60.33 (5) | O1iii—K1—V1vii | 92.20 (4) |
| O1iii—Rb1—O1vi | 119.67 (5) | O1xix—K1—V1vii | 29.92 (3) |
| O1iv—Rb1—O1vi | 60.33 (5) | O1i—K1—V1vii | 29.92 (3) |
| O1v—Rb1—O1vi | 180.0 | O1xx—K1—V1vii | 125.60 (19) |
| O1i—Rb1—O2vii | 48.95 (6) | O1xxi—K1—V1vii | 81.25 (8) |
| O1ii—Rb1—O2vii | 131.05 (6) | O1xxii—K1—V1vii | 81.25 (8) |
| O1iii—Rb1—O2vii | 102.09 (5) | V1xx—K1—V1vii | 96.11 (12) |
| O1iv—Rb1—O2vii | 77.91 (5) | O2—Rb2—O1xvi | 94.63 (9) |
| O1v—Rb1—O2vii | 102.09 (5) | O2—Rb2—O1xvii | 94.63 (9) |
| O1vi—Rb1—O2vii | 77.91 (5) | O1xvi—Rb2—O1xvii | 63.36 (7) |
| O1i—Rb1—O2viii | 131.05 (6) | O2—Rb2—O1xviii | 94.63 (9) |
| O1ii—Rb1—O2viii | 48.95 (6) | O1xvi—Rb2—O1xviii | 56.21 (7) |
| O1iii—Rb1—O2viii | 77.91 (5) | O1xvii—Rb2—O1xviii | 119.36 (3) |
| O1iv—Rb1—O2viii | 102.09 (5) | O2—Rb2—O1iii | 94.63 (9) |
| O1v—Rb1—O2viii | 77.91 (5) | O1xvi—Rb2—O1iii | 119.36 (3) |
| O1vi—Rb1—O2viii | 102.09 (5) | O1xvii—Rb2—O1iii | 56.21 (7) |
| O2vii—Rb1—O2viii | 180.00 (11) | O1xviii—Rb2—O1iii | 170.08 (18) |
| O1i—Rb1—O2ix | 102.09 (5) | O2—Rb2—O1xix | 94.63 (9) |
| O1ii—Rb1—O2ix | 77.91 (5) | O1xvi—Rb2—O1xix | 119.36 (3) |
| O1iii—Rb1—O2ix | 102.09 (5) | O1xvii—Rb2—O1xix | 170.08 (18) |
| O1iv—Rb1—O2ix | 77.91 (5) | O1xviii—Rb2—O1xix | 63.36 (7) |
| O1v—Rb1—O2ix | 48.95 (6) | O1iii—Rb2—O1xix | 119.36 (3) |
| O1vi—Rb1—O2ix | 131.05 (6) | O2—Rb2—O1i | 94.63 (9) |
| O2vii—Rb1—O2ix | 119.065 (18) | O1xvi—Rb2—O1i | 170.08 (18) |
| O2viii—Rb1—O2ix | 60.935 (18) | O1xvii—Rb2—O1i | 119.36 (3) |
| O1i—Rb1—O2 | 77.91 (5) | O1xviii—Rb2—O1i | 119.36 (3) |
| O1ii—Rb1—O2 | 102.09 (5) | O1iii—Rb2—O1i | 63.36 (7) |
| O1iii—Rb1—O2 | 77.91 (5) | O1xix—Rb2—O1i | 56.21 (7) |
| O1iv—Rb1—O2 | 102.09 (5) | O2—Rb2—O1xx | 150.80 (5) |
| O1v—Rb1—O2 | 131.05 (6) | O1xvi—Rb2—O1xx | 61.07 (8) |
| O1vi—Rb1—O2 | 48.95 (6) | O1xvii—Rb2—O1xx | 61.07 (8) |
| O2vii—Rb1—O2 | 60.935 (18) | O1xviii—Rb2—O1xx | 85.09 (8) |
| O2viii—Rb1—O2 | 119.065 (18) | O1iii—Rb2—O1xx | 85.09 (8) |
| O2ix—Rb1—O2 | 180.0 | O1xix—Rb2—O1xx | 110.99 (11) |
| O1i—Rb1—O2iii | 102.09 (5) | O1i—Rb2—O1xx | 110.99 (11) |
| O1ii—Rb1—O2iii | 77.91 (5) | O2—Rb2—O1xxi | 150.80 (5) |
| O1iii—Rb1—O2iii | 48.95 (6) | O1xvi—Rb2—O1xxi | 85.09 (8) |
| O1iv—Rb1—O2iii | 131.05 (6) | O1xvii—Rb2—O1xxi | 110.99 (11) |
| O1v—Rb1—O2iii | 102.09 (5) | O1xviii—Rb2—O1xxi | 61.07 (8) |
| O1vi—Rb1—O2iii | 77.91 (5) | O1iii—Rb2—O1xxi | 110.99 (11) |
| O2vii—Rb1—O2iii | 119.064 (18) | O1xix—Rb2—O1xxi | 61.07 (8) |
| O2viii—Rb1—O2iii | 60.936 (18) | O1i—Rb2—O1xxi | 85.09 (8) |
| O2ix—Rb1—O2iii | 119.064 (18) | O1xx—Rb2—O1xxi | 49.99 (8) |
| O2—Rb1—O2iii | 60.935 (18) | O2—Rb2—O1xxii | 150.80 (5) |
| O1i—Rb1—O2iv | 77.91 (5) | O1xvi—Rb2—O1xxii | 110.99 (11) |
| O1ii—Rb1—O2iv | 102.09 (5) | O1xvii—Rb2—O1xxii | 85.09 (8) |
| O1iii—Rb1—O2iv | 131.05 (6) | O1xviii—Rb2—O1xxii | 110.99 (11) |
| O1iv—Rb1—O2iv | 48.95 (6) | O1iii—Rb2—O1xxii | 61.07 (8) |
| O1v—Rb1—O2iv | 77.91 (5) | O1xix—Rb2—O1xxii | 85.09 (8) |
| O1vi—Rb1—O2iv | 102.09 (5) | O1i—Rb2—O1xxii | 61.07 (8) |
| O2vii—Rb1—O2iv | 60.936 (18) | O1xx—Rb2—O1xxii | 49.99 (8) |
| O2viii—Rb1—O2iv | 119.064 (18) | O1xxi—Rb2—O1xxii | 49.99 (8) |
| O2ix—Rb1—O2iv | 60.936 (18) | O2—Rb2—V1vii | 84.45 (7) |
| O2—Rb1—O2iv | 119.065 (18) | O1xvi—Rb2—V1vii | 148.32 (3) |
| O2iii—Rb1—O2iv | 180.0 | O1xvii—Rb2—V1vii | 148.32 (3) |
| O1x—Dy1—O1vi | 180.00 (12) | O1xviii—Rb2—V1vii | 92.23 (3) |
| O1x—Dy1—O1xi | 88.46 (9) | O1iii—Rb2—V1vii | 92.23 (3) |
| O1vi—Dy1—O1xi | 91.54 (9) | O1xix—Rb2—V1vii | 29.95 (3) |
| O1x—Dy1—O1iv | 91.54 (9) | O1i—Rb2—V1vii | 29.95 (3) |
| O1vi—Dy1—O1iv | 88.46 (9) | O1xx—Rb2—V1vii | 124.76 (11) |
| O1xi—Dy1—O1iv | 180.00 (9) | O1xxi—Rb2—V1vii | 80.89 (5) |
| O1x—Dy1—O1xii | 88.46 (9) | O1xxii—Rb2—V1vii | 80.89 (5) |
| O1vi—Dy1—O1xii | 91.54 (9) | O2—Rb2—V1iii | 84.45 (7) |
| O1xi—Dy1—O1xii | 88.46 (9) | O1xvi—Rb2—V1iii | 92.23 (3) |
| O1iv—Dy1—O1xii | 91.54 (9) | O1xvii—Rb2—V1iii | 29.95 (3) |
| O1x—Dy1—O1ii | 91.54 (9) | O1xviii—Rb2—V1iii | 148.32 (3) |
| O1vi—Dy1—O1ii | 88.46 (9) | O1iii—Rb2—V1iii | 29.95 (3) |
| O1xi—Dy1—O1ii | 91.54 (9) | O1xix—Rb2—V1iii | 148.32 (3) |
| O1iv—Dy1—O1ii | 88.46 (9) | O1i—Rb2—V1iii | 92.23 (3) |
| O1xii—Dy1—O1ii | 180.00 (10) | O1xx—Rb2—V1iii | 80.89 (5) |
| O1x—Dy1—K1xiii | 52.42 (5) | O1xxi—Rb2—V1iii | 124.76 (11) |
| O1vi—Dy1—K1xiii | 127.58 (5) | O1xxii—Rb2—V1iii | 80.89 (5) |
| O1xi—Dy1—K1xiii | 52.42 (5) | V1vii—Rb2—V1iii | 119.07 (2) |
| O1iv—Dy1—K1xiii | 127.58 (5) | O2—V1—O1 | 109.49 (8) |
| O1xii—Dy1—K1xiii | 119.51 (12) | O2—V1—O1vi | 109.49 (8) |
| O1ii—Dy1—K1xiii | 60.49 (12) | O1—V1—O1vi | 109.45 (8) |
| O1x—Dy1—K1vii | 127.58 (5) | O2—V1—O1xxiii | 109.49 (8) |
| O1vi—Dy1—K1vii | 52.42 (5) | O1—V1—O1xxiii | 109.45 (8) |
| O1xi—Dy1—K1vii | 127.58 (5) | O1vi—V1—O1xxiii | 109.45 (8) |
| O1iv—Dy1—K1vii | 52.42 (5) | O2—V1—K1xiv | 180.0 |
| O1xii—Dy1—K1vii | 60.49 (12) | O1—V1—K1xiv | 70.51 (8) |
| O1ii—Dy1—K1vii | 119.51 (12) | O1vi—V1—K1xiv | 70.51 (8) |
| K1xiii—Dy1—K1vii | 180.0 | O1xxiii—V1—K1xiv | 70.51 (8) |
| O1x—Dy1—K1xiv | 119.51 (12) | O2—V1—K1vii | 96.11 (12) |
| O1vi—Dy1—K1xiv | 60.49 (12) | O1—V1—K1vii | 154.40 (15) |
| O1xi—Dy1—K1xiv | 52.42 (5) | O1vi—V1—K1vii | 59.72 (4) |
| O1iv—Dy1—K1xiv | 127.58 (5) | O1xxiii—V1—K1vii | 59.72 (4) |
| O1xii—Dy1—K1xiv | 52.42 (5) | K1xiv—V1—K1vii | 83.89 (12) |
| O1ii—Dy1—K1xiv | 127.58 (5) | O2—V1—K1iii | 96.11 (12) |
| K1xiii—Dy1—K1xiv | 104.42 (12) | O1—V1—K1iii | 59.72 (4) |
| K1vii—Dy1—K1xiv | 75.58 (12) | O1vi—V1—K1iii | 59.72 (4) |
| O1x—Dy1—K1ix | 60.49 (12) | O1xxiii—V1—K1iii | 154.40 (15) |
| O1vi—Dy1—K1ix | 119.51 (12) | K1xiv—V1—K1iii | 83.89 (12) |
| O1xi—Dy1—K1ix | 127.58 (5) | K1vii—V1—K1iii | 118.88 (4) |
| O1iv—Dy1—K1ix | 52.42 (5) | O2—V1—K1xviii | 96.11 (12) |
| O1xii—Dy1—K1ix | 127.58 (5) | O1—V1—K1xviii | 59.72 (4) |
| O1ii—Dy1—K1ix | 52.42 (5) | O1vi—V1—K1xviii | 154.40 (15) |
| K1xiii—Dy1—K1ix | 75.58 (12) | O1xxiii—V1—K1xviii | 59.72 (4) |
| K1vii—Dy1—K1ix | 104.42 (12) | K1xiv—V1—K1xviii | 83.89 (12) |
| K1xiv—Dy1—K1ix | 180.0 | K1vii—V1—K1xviii | 118.88 (5) |
| O1x—Dy1—K1xv | 52.42 (5) | K1iii—V1—K1xviii | 118.88 (4) |
| O1vi—Dy1—K1xv | 127.58 (5) | O2—V1—Rb1xxiv | 60.209 (6) |
| O1xi—Dy1—K1xv | 119.51 (12) | O1—V1—Rb1xxiv | 49.28 (8) |
| O1iv—Dy1—K1xv | 60.49 (12) | O1vi—V1—Rb1xxiv | 125.09 (3) |
| O1xii—Dy1—K1xv | 52.42 (5) | O1xxiii—V1—Rb1xxiv | 125.09 (3) |
| O1ii—Dy1—K1xv | 127.58 (5) | K1xiv—V1—Rb1xxiv | 119.792 (6) |
| K1xiii—Dy1—K1xv | 104.42 (12) | K1vii—V1—Rb1xxiv | 156.32 (12) |
| K1vii—Dy1—K1xv | 75.58 (12) | K1iii—V1—Rb1xxiv | 67.75 (7) |
| K1xiv—Dy1—K1xv | 104.42 (12) | K1xviii—V1—Rb1xxiv | 67.75 (7) |
| K1ix—Dy1—K1xv | 75.58 (12) | O2—V1—Rb1xxv | 60.209 (6) |
| O1x—Dy1—K1iii | 127.58 (5) | O1—V1—Rb1xxv | 125.09 (3) |
| O1vi—Dy1—K1iii | 52.42 (5) | O1vi—V1—Rb1xxv | 125.09 (3) |
| O1xi—Dy1—K1iii | 60.49 (12) | O1xxiii—V1—Rb1xxv | 49.28 (8) |
| O1iv—Dy1—K1iii | 119.51 (12) | K1xiv—V1—Rb1xxv | 119.791 (6) |
| O1xii—Dy1—K1iii | 127.58 (5) | K1vii—V1—Rb1xxv | 67.76 (7) |
| O1ii—Dy1—K1iii | 52.42 (5) | K1iii—V1—Rb1xxv | 156.32 (12) |
| K1xiii—Dy1—K1iii | 75.58 (12) | K1xviii—V1—Rb1xxv | 67.76 (7) |
| K1vii—Dy1—K1iii | 104.42 (12) | Rb1xxiv—V1—Rb1xxv | 97.454 (8) |
| K1xiv—Dy1—K1iii | 75.58 (12) | O2—V1—Rb1 | 60.209 (6) |
| K1ix—Dy1—K1iii | 104.42 (12) | O1—V1—Rb1 | 125.09 (3) |
| K1xv—Dy1—K1iii | 180.0 | O1vi—V1—Rb1 | 49.28 (8) |
| O2—K1—O1xvi | 93.98 (15) | O1xxiii—V1—Rb1 | 125.09 (3) |
| O2—K1—O1xvii | 93.98 (15) | K1xiv—V1—Rb1 | 119.791 (6) |
| O1xvi—K1—O1xvii | 63.42 (7) | K1vii—V1—Rb1 | 67.76 (7) |
| O2—K1—O1xviii | 93.98 (15) | K1iii—V1—Rb1 | 67.76 (7) |
| O1xvi—K1—O1xviii | 56.26 (7) | K1xviii—V1—Rb1 | 156.32 (12) |
| O1xvii—K1—O1xviii | 119.52 (4) | Rb1xxiv—V1—Rb1 | 97.454 (8) |
| O2—K1—O1iii | 93.98 (15) | Rb1xxv—V1—Rb1 | 97.454 (8) |
| O1xvi—K1—O1iii | 119.52 (4) | O2—V1—Rb2 | 0.000 (1) |
| O1xvii—K1—O1iii | 56.26 (7) | O1—V1—Rb2 | 109.49 (8) |
| O1xviii—K1—O1iii | 171.3 (3) | O1vi—V1—Rb2 | 109.49 (8) |
| O2—K1—O1xix | 93.98 (15) | O1xxiii—V1—Rb2 | 109.49 (8) |
| O1xvi—K1—O1xix | 119.52 (4) | K1xiv—V1—Rb2 | 180.0 |
| O1xvii—K1—O1xix | 171.3 (3) | K1vii—V1—Rb2 | 96.11 (12) |
| O1xviii—K1—O1xix | 63.42 (7) | K1iii—V1—Rb2 | 96.11 (12) |
| O1iii—K1—O1xix | 119.52 (4) | K1xviii—V1—Rb2 | 96.11 (12) |
| O2—K1—O1i | 93.98 (15) | Rb1xxiv—V1—Rb2 | 60.209 (6) |
| O1xvi—K1—O1i | 171.3 (3) | Rb1xxv—V1—Rb2 | 60.209 (6) |
| O1xvii—K1—O1i | 119.52 (4) | Rb1—V1—Rb2 | 60.209 (6) |
| O1xviii—K1—O1i | 119.52 (4) | V1—O1—Dy1xxiv | 163.14 (14) |
| O1iii—K1—O1i | 63.42 (7) | V1—O1—K1xviii | 90.36 (6) |
| O1xix—K1—O1i | 56.26 (7) | Dy1xxiv—O1—K1xviii | 90.91 (9) |
| O2—K1—O1xx | 150.51 (7) | V1—O1—K1iii | 90.36 (6) |
| O1xvi—K1—O1xx | 61.46 (10) | Dy1xxiv—O1—K1iii | 90.91 (9) |
| O1xvii—K1—O1xx | 61.46 (10) | K1xviii—O1—K1iii | 171.3 (3) |
| O1xviii—K1—O1xx | 85.65 (13) | V1—O1—Rb1xxiv | 105.98 (10) |
| O1iii—K1—O1xx | 85.65 (13) | Dy1xxiv—O1—Rb1xxiv | 90.88 (6) |
| O1xix—K1—O1xx | 111.86 (19) | K1xviii—O1—Rb1xxiv | 85.72 (12) |
| O1i—K1—O1xx | 111.86 (19) | K1iii—O1—Rb1xxiv | 85.72 (12) |
| O2—K1—O1xxi | 150.51 (7) | V1—O1—K1xiv | 80.00 (10) |
| O1xvi—K1—O1xxi | 85.65 (13) | Dy1xxiv—O1—K1xiv | 83.14 (9) |
| O1xvii—K1—O1xxi | 111.86 (19) | K1xviii—O1—K1xiv | 94.35 (13) |
| O1xviii—K1—O1xxi | 61.46 (10) | K1iii—O1—K1xiv | 94.35 (13) |
| O1iii—K1—O1xxi | 111.86 (19) | Rb1xxiv—O1—K1xiv | 174.02 (9) |
| O1xix—K1—O1xxi | 61.46 (10) | V1—O2—Rb2 | 180.0 |
| O1i—K1—O1xxi | 85.65 (13) | V1—O2—K1 | 180.0 |
| O1xx—K1—O1xxi | 50.47 (12) | Rb2—O2—K1 | 0.000 (1) |
| O2—K1—O1xxii | 150.51 (7) | V1—O2—Rb1xxiv | 95.58 (5) |
| O1xvi—K1—O1xxii | 111.86 (19) | Rb2—O2—Rb1xxiv | 84.42 (5) |
| O1xvii—K1—O1xxii | 85.65 (13) | K1—O2—Rb1xxiv | 84.42 (5) |
| O1xviii—K1—O1xxii | 111.86 (19) | V1—O2—Rb1xxv | 95.58 (5) |
| O1iii—K1—O1xxii | 61.46 (10) | Rb2—O2—Rb1xxv | 84.42 (5) |
| O1xix—K1—O1xxii | 85.65 (13) | K1—O2—Rb1xxv | 84.42 (5) |
| O1i—K1—O1xxii | 61.46 (10) | Rb1xxiv—O2—Rb1xxv | 119.065 (18) |
| O1xx—K1—O1xxii | 50.47 (12) | V1—O2—Rb1 | 95.58 (5) |
| O1xxi—K1—O1xxii | 50.47 (12) | Rb2—O2—Rb1 | 84.42 (5) |
| O2—K1—V1xx | 180.0 | K1—O2—Rb1 | 84.42 (5) |
| O1xvi—K1—V1xx | 86.02 (15) | Rb1xxiv—O2—Rb1 | 119.065 (18) |
| O1xvii—K1—V1xx | 86.02 (15) | Rb1xxv—O2—Rb1 | 119.065 (18) |
| Cs1.52K1.48Gd(VO4)2 | |
| Mo | |
| Trigonal, | Cell parameters from 678 reflections |
| θ = 3.9–41.1° | |
| µ = 14.37 mm−1 | |
| Block, colourless | |
| 0.34 × 0.26 × 0.22 mm |
| Bruker X8 APEX diffractometer | 678 independent reflections |
| Radiation source: fine-focus sealed tube | 666 reflections with |
| Graphite monochromator | |
| φ and ω scans | θmax = 41.1°, θmin = 3.9° |
| Absorption correction: multi-scan (SADABS; Krause | |
| 14472 measured reflections |
| Refinement on | 0 restraints |
| Least-squares matrix: full | |
| (Δ/σ)max < 0.001 | |
| Δρmax = 0.63 e Å−3 | |
| Δρmin = −0.94 e Å−3 | |
| 678 reflections | Extinction correction: SHELXL2018 (Sheldrick, 2015 |
| 25 parameters | Extinction coefficient: 0.0022 (6) |
| 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. |
| Occ. (<1) | |||||
| Cs1 | 0.000000 | 0.000000 | 0.500000 | 0.02453 (5) | |
| Gd1 | 0.000000 | 0.000000 | 0.000000 | 0.00899 (4) | |
| K1 | 0.333333 | 0.666667 | 0.7877 (3) | 0.0113 (5) | 0.7404 (18) |
| Cs2 | 0.333333 | 0.666667 | 0.7867 (4) | 0.0230 (8) | 0.2597 (18) |
| V1 | 0.333333 | 0.666667 | 0.23977 (4) | 0.00899 (5) | |
| O1 | 0.17704 (10) | 0.82296 (10) | 0.16910 (16) | 0.0265 (2) | |
| O2 | 0.333333 | 0.666667 | 0.4470 (3) | 0.0317 (5) |
| Cs1 | 0.02979 (7) | 0.02979 (7) | 0.01402 (8) | 0.01489 (3) | 0.000 | 0.000 |
| Gd1 | 0.00627 (4) | 0.00627 (4) | 0.01444 (6) | 0.00313 (2) | 0.000 | 0.000 |
| K1 | 0.0091 (6) | 0.0091 (6) | 0.0156 (9) | 0.0046 (3) | 0.000 | 0.000 |
| Cs2 | 0.0200 (9) | 0.0200 (9) | 0.0288 (14) | 0.0100 (5) | 0.000 | 0.000 |
| V1 | 0.00756 (7) | 0.00756 (7) | 0.01186 (11) | 0.00378 (3) | 0.000 | 0.000 |
| O1 | 0.0244 (4) | 0.0244 (4) | 0.0379 (6) | 0.0177 (4) | −0.00613 (19) | 0.00613 (19) |
| O2 | 0.0404 (7) | 0.0404 (7) | 0.0144 (7) | 0.0202 (4) | 0.000 | 0.000 |
| Cs1—O1i | 3.2245 (13) | K1—O1xvii | 3.0377 (4) |
| Cs1—O1ii | 3.2245 (13) | K1—O1xviii | 3.0377 (4) |
| Cs1—O1iii | 3.2245 (13) | K1—O1iii | 3.0377 (4) |
| Cs1—O1iv | 3.2245 (13) | K1—O1xix | 3.0377 (4) |
| Cs1—O1v | 3.2245 (13) | K1—O1i | 3.0377 (4) |
| Cs1—O1vi | 3.2245 (13) | K1—V1vii | 3.4895 (2) |
| Cs1—O2vii | 3.5082 (3) | K1—V1iii | 3.4895 (2) |
| Cs1—O2viii | 3.5082 (3) | K1—V1xviii | 3.4895 (2) |
| Cs1—O2ix | 3.5082 (3) | K1—V1xx | 3.609 (3) |
| Cs1—O2 | 3.5083 (3) | Cs2—O2 | 2.712 (4) |
| Cs1—O2iii | 3.5083 (3) | Cs2—O1xvi | 3.0386 (4) |
| Cs1—O2iv | 3.5083 (2) | Cs2—O1xvii | 3.0386 (4) |
| Gd1—O1x | 2.2898 (10) | Cs2—O1xviii | 3.0386 (4) |
| Gd1—O1vi | 2.2898 (10) | Cs2—O1iii | 3.0386 (4) |
| Gd1—O1xi | 2.2898 (10) | Cs2—O1xix | 3.0386 (4) |
| Gd1—O1iv | 2.2898 (10) | Cs2—O1i | 3.0386 (4) |
| Gd1—O1xii | 2.2898 (10) | Cs2—O1xx | 3.462 (3) |
| Gd1—O1ii | 2.2898 (10) | Cs2—O1xxi | 3.462 (3) |
| Gd1—K1xiii | 3.8732 (12) | Cs2—O1xxii | 3.462 (3) |
| Gd1—K1vii | 3.8732 (12) | Cs2—V1vii | 3.4890 (2) |
| Gd1—K1xiv | 3.8731 (12) | Cs2—V1iii | 3.4890 (2) |
| Gd1—K1ix | 3.8731 (12) | V1—O2 | 1.654 (2) |
| Gd1—K1xv | 3.8732 (12) | V1—O1 | 1.7276 (10) |
| Gd1—K1iii | 3.8732 (12) | V1—O1vi | 1.7276 (10) |
| K1—O2 | 2.719 (3) | V1—O1xxiii | 1.7276 (10) |
| K1—O1xvi | 3.0377 (4) | ||
| O1i—Cs1—O1ii | 180.0 | O1xvi—K1—V1xx | 83.48 (6) |
| O1i—Cs1—O1iii | 59.57 (3) | O1xvii—K1—V1xx | 83.48 (6) |
| O1ii—Cs1—O1iii | 120.43 (3) | O1xviii—K1—V1xx | 83.48 (6) |
| O1i—Cs1—O1iv | 120.43 (3) | O1iii—K1—V1xx | 83.48 (6) |
| O1ii—Cs1—O1iv | 59.57 (3) | O1xix—K1—V1xx | 83.48 (6) |
| O1iii—Cs1—O1iv | 180.0 | O1i—K1—V1xx | 83.48 (6) |
| O1i—Cs1—O1v | 59.57 (3) | V1vii—K1—V1xx | 93.60 (4) |
| O1ii—Cs1—O1v | 120.43 (3) | V1iii—K1—V1xx | 93.60 (4) |
| O1iii—Cs1—O1v | 59.57 (3) | V1xviii—K1—V1xx | 93.60 (4) |
| O1iv—Cs1—O1v | 120.43 (3) | O2—K1—Gd1xxiv | 115.95 (4) |
| O1i—Cs1—O1vi | 120.43 (3) | O1xvi—K1—Gd1xxiv | 36.21 (2) |
| O1ii—Cs1—O1vi | 59.57 (3) | O1xvii—K1—Gd1xxiv | 36.21 (2) |
| O1iii—Cs1—O1vi | 120.43 (3) | O1xviii—K1—Gd1xxiv | 85.31 (3) |
| O1iv—Cs1—O1vi | 59.57 (3) | O1iii—K1—Gd1xxiv | 85.31 (3) |
| O1v—Cs1—O1vi | 180.0 | O1xix—K1—Gd1xxiv | 137.69 (7) |
| O1i—Cs1—O2vii | 48.07 (4) | O1i—K1—Gd1xxiv | 137.69 (7) |
| O1ii—Cs1—O2vii | 131.93 (4) | V1vii—K1—Gd1xxiv | 157.65 (8) |
| O1iii—Cs1—O2vii | 100.71 (3) | V1iii—K1—Gd1xxiv | 65.087 (12) |
| O1iv—Cs1—O2vii | 79.29 (3) | V1xviii—K1—Gd1xxiv | 65.087 (12) |
| O1v—Cs1—O2vii | 100.71 (3) | V1xx—K1—Gd1xxiv | 64.05 (4) |
| O1vi—Cs1—O2vii | 79.29 (3) | O2—Cs2—O1xvi | 96.67 (7) |
| O1i—Cs1—O2viii | 131.93 (4) | O2—Cs2—O1xvii | 96.67 (7) |
| O1ii—Cs1—O2viii | 48.07 (4) | O1xvi—Cs2—O1xvii | 63.63 (4) |
| O1iii—Cs1—O2viii | 79.29 (3) | O2—Cs2—O1xviii | 96.67 (7) |
| O1iv—Cs1—O2viii | 100.71 (3) | O1xvi—Cs2—O1xviii | 55.47 (4) |
| O1v—Cs1—O2viii | 79.29 (3) | O1xvii—Cs2—O1xviii | 118.67 (3) |
| O1vi—Cs1—O2viii | 100.71 (3) | O2—Cs2—O1iii | 96.67 (7) |
| O2vii—Cs1—O2viii | 180.0 | O1xvi—Cs2—O1iii | 118.67 (3) |
| O1i—Cs1—O2ix | 100.71 (3) | O1xvii—Cs2—O1iii | 55.47 (4) |
| O1ii—Cs1—O2ix | 79.29 (3) | O1xviii—Cs2—O1iii | 166.04 (13) |
| O1iii—Cs1—O2ix | 100.71 (3) | O2—Cs2—O1xix | 96.67 (7) |
| O1iv—Cs1—O2ix | 79.29 (3) | O1xvi—Cs2—O1xix | 118.67 (3) |
| O1v—Cs1—O2ix | 48.07 (4) | O1xvii—Cs2—O1xix | 166.04 (13) |
| O1vi—Cs1—O2ix | 131.93 (4) | O1xviii—Cs2—O1xix | 63.63 (4) |
| O2vii—Cs1—O2ix | 118.567 (13) | O1iii—Cs2—O1xix | 118.67 (3) |
| O2viii—Cs1—O2ix | 61.433 (14) | O2—Cs2—O1i | 96.67 (7) |
| O1i—Cs1—O2 | 79.29 (3) | O1xvi—Cs2—O1i | 166.04 (13) |
| O1ii—Cs1—O2 | 100.71 (3) | O1xvii—Cs2—O1i | 118.67 (3) |
| O1iii—Cs1—O2 | 79.29 (3) | O1xviii—Cs2—O1i | 118.67 (3) |
| O1iv—Cs1—O2 | 100.71 (3) | O1iii—Cs2—O1i | 63.63 (4) |
| O1v—Cs1—O2 | 131.93 (4) | O1xix—Cs2—O1i | 55.47 (4) |
| O1vi—Cs1—O2 | 48.07 (4) | O2—Cs2—O1xx | 151.86 (3) |
| O2vii—Cs1—O2 | 61.434 (13) | O1xvi—Cs2—O1xx | 60.03 (5) |
| O2viii—Cs1—O2 | 118.566 (13) | O1xvii—Cs2—O1xx | 60.03 (5) |
| O2ix—Cs1—O2 | 180.0 | O1xviii—Cs2—O1xx | 83.15 (6) |
| O1i—Cs1—O2iii | 100.71 (3) | O1iii—Cs2—O1xx | 83.15 (6) |
| O1ii—Cs1—O2iii | 79.29 (3) | O1xix—Cs2—O1xx | 108.15 (8) |
| O1iii—Cs1—O2iii | 48.07 (4) | O1i—Cs2—O1xx | 108.15 (8) |
| O1iv—Cs1—O2iii | 131.93 (4) | O2—Cs2—O1xxi | 151.86 (3) |
| O1v—Cs1—O2iii | 100.71 (3) | O1xvi—Cs2—O1xxi | 83.15 (6) |
| O1vi—Cs1—O2iii | 79.29 (3) | O1xvii—Cs2—O1xxi | 108.15 (8) |
| O2vii—Cs1—O2iii | 118.565 (14) | O1xviii—Cs2—O1xxi | 60.03 (5) |
| O2viii—Cs1—O2iii | 61.435 (13) | O1iii—Cs2—O1xxi | 108.15 (8) |
| O2ix—Cs1—O2iii | 118.565 (14) | O1xix—Cs2—O1xxi | 60.03 (5) |
| O2—Cs1—O2iii | 61.434 (13) | O1i—Cs2—O1xxi | 83.15 (6) |
| O1i—Cs1—O2iv | 79.29 (3) | O1xx—Cs2—O1xxi | 48.22 (5) |
| O1ii—Cs1—O2iv | 100.71 (3) | O2—Cs2—O1xxii | 151.86 (3) |
| O1iii—Cs1—O2iv | 131.93 (4) | O1xvi—Cs2—O1xxii | 108.15 (8) |
| O1iv—Cs1—O2iv | 48.07 (4) | O1xvii—Cs2—O1xxii | 83.15 (6) |
| O1v—Cs1—O2iv | 79.29 (3) | O1xviii—Cs2—O1xxii | 108.15 (8) |
| O1vi—Cs1—O2iv | 100.71 (3) | O1iii—Cs2—O1xxii | 60.03 (5) |
| O2vii—Cs1—O2iv | 61.435 (13) | O1xix—Cs2—O1xxii | 83.15 (6) |
| O2viii—Cs1—O2iv | 118.565 (14) | O1i—Cs2—O1xxii | 60.03 (5) |
| O2ix—Cs1—O2iv | 61.435 (13) | O1xx—Cs2—O1xxii | 48.22 (5) |
| O2—Cs1—O2iv | 118.566 (14) | O1xxi—Cs2—O1xxii | 48.22 (5) |
| O2iii—Cs1—O2iv | 180.0 | O2—Cs2—V1vii | 86.53 (5) |
| O1x—Gd1—O1vi | 180.00 (5) | O1xvi—Cs2—V1vii | 147.92 (2) |
| O1x—Gd1—O1xi | 88.78 (5) | O1xvii—Cs2—V1vii | 147.92 (2) |
| O1vi—Gd1—O1xi | 91.22 (5) | O1xviii—Cs2—V1vii | 92.44 (2) |
| O1x—Gd1—O1iv | 91.22 (5) | O1iii—Cs2—V1vii | 92.44 (2) |
| O1vi—Gd1—O1iv | 88.78 (5) | O1xix—Cs2—V1vii | 29.680 (19) |
| O1xi—Gd1—O1iv | 180.00 (6) | O1i—Cs2—V1vii | 29.680 (19) |
| O1x—Gd1—O1xii | 88.78 (5) | O1xx—Cs2—V1vii | 121.61 (8) |
| O1vi—Gd1—O1xii | 91.22 (5) | O1xxi—Cs2—V1vii | 79.51 (4) |
| O1xi—Gd1—O1xii | 88.78 (5) | O1xxii—Cs2—V1vii | 79.51 (4) |
| O1iv—Gd1—O1xii | 91.22 (5) | O2—Cs2—V1iii | 86.53 (5) |
| O1x—Gd1—O1ii | 91.22 (5) | O1xvi—Cs2—V1iii | 92.44 (2) |
| O1vi—Gd1—O1ii | 88.78 (5) | O1xvii—Cs2—V1iii | 29.680 (19) |
| O1xi—Gd1—O1ii | 91.22 (5) | O1xviii—Cs2—V1iii | 147.91 (2) |
| O1iv—Gd1—O1ii | 88.78 (5) | O1iii—Cs2—V1iii | 29.681 (19) |
| O1xii—Gd1—O1ii | 180.00 (6) | O1xix—Cs2—V1iii | 147.92 (2) |
| O1x—Gd1—K1xiii | 51.601 (16) | O1i—Cs2—V1iii | 92.44 (2) |
| O1vi—Gd1—K1xiii | 128.399 (17) | O1xx—Cs2—V1iii | 79.51 (4) |
| O1xi—Gd1—K1xiii | 51.602 (16) | O1xxi—Cs2—V1iii | 121.61 (8) |
| O1iv—Gd1—K1xiii | 128.398 (16) | O1xxii—Cs2—V1iii | 79.51 (4) |
| O1xii—Gd1—K1xiii | 117.93 (5) | V1vii—Cs2—V1iii | 119.638 (11) |
| O1ii—Gd1—K1xiii | 62.07 (5) | O2—V1—O1 | 109.06 (5) |
| O1x—Gd1—K1vii | 128.399 (17) | O2—V1—O1vi | 109.06 (5) |
| O1vi—Gd1—K1vii | 51.601 (16) | O1—V1—O1vi | 109.88 (5) |
| O1xi—Gd1—K1vii | 128.398 (16) | O2—V1—O1xxiii | 109.06 (5) |
| O1iv—Gd1—K1vii | 51.602 (16) | O1—V1—O1xxiii | 109.88 (5) |
| O1xii—Gd1—K1vii | 62.07 (5) | O1vi—V1—O1xxiii | 109.88 (5) |
| O1ii—Gd1—K1vii | 117.93 (5) | O2—V1—K1vii | 93.60 (4) |
| K1xiii—Gd1—K1vii | 180.0 | O1—V1—K1vii | 157.34 (6) |
| O1x—Gd1—K1xiv | 117.93 (5) | O1vi—V1—K1vii | 60.518 (16) |
| O1vi—Gd1—K1xiv | 62.07 (5) | O1xxiii—V1—K1vii | 60.518 (16) |
| O1xi—Gd1—K1xiv | 51.602 (16) | O2—V1—K1iii | 93.60 (4) |
| O1iv—Gd1—K1xiv | 128.398 (16) | O1—V1—K1iii | 60.517 (16) |
| O1xii—Gd1—K1xiv | 51.602 (16) | O1vi—V1—K1iii | 60.518 (16) |
| O1ii—Gd1—K1xiv | 128.398 (16) | O1xxiii—V1—K1iii | 157.34 (6) |
| K1xiii—Gd1—K1xiv | 102.28 (4) | K1vii—V1—K1iii | 119.610 (10) |
| K1vii—Gd1—K1xiv | 77.72 (4) | O2—V1—K1xviii | 93.60 (4) |
| O1x—Gd1—K1ix | 62.07 (5) | O1—V1—K1xviii | 60.517 (16) |
| O1vi—Gd1—K1ix | 117.93 (5) | O1vi—V1—K1xviii | 157.34 (6) |
| O1xi—Gd1—K1ix | 128.398 (16) | O1xxiii—V1—K1xviii | 60.518 (16) |
| O1iv—Gd1—K1ix | 51.602 (16) | K1vii—V1—K1xviii | 119.610 (10) |
| O1xii—Gd1—K1ix | 128.398 (16) | K1iii—V1—K1xviii | 119.609 (10) |
| O1ii—Gd1—K1ix | 51.602 (16) | O2—V1—K1xiv | 180.0 |
| K1xiii—Gd1—K1ix | 77.72 (4) | O1—V1—K1xiv | 70.94 (5) |
| K1vii—Gd1—K1ix | 102.28 (4) | O1vi—V1—K1xiv | 70.94 (5) |
| K1xiv—Gd1—K1ix | 180.0 | O1xxiii—V1—K1xiv | 70.94 (5) |
| O1x—Gd1—K1xv | 51.602 (16) | K1vii—V1—K1xiv | 86.40 (4) |
| O1vi—Gd1—K1xv | 128.398 (16) | K1iii—V1—K1xiv | 86.40 (4) |
| O1xi—Gd1—K1xv | 117.93 (5) | K1xviii—V1—K1xiv | 86.40 (4) |
| O1iv—Gd1—K1xv | 62.07 (5) | O2—V1—Cs1xxv | 59.187 (4) |
| O1xii—Gd1—K1xv | 51.602 (16) | O1—V1—Cs1xxv | 49.87 (5) |
| O1ii—Gd1—K1xv | 128.398 (16) | O1vi—V1—Cs1xxv | 124.970 (19) |
| K1xiii—Gd1—K1xv | 102.28 (4) | O1xxiii—V1—Cs1xxv | 124.970 (19) |
| K1vii—Gd1—K1xv | 77.72 (4) | K1vii—V1—Cs1xxv | 152.79 (5) |
| K1xiv—Gd1—K1xv | 102.28 (4) | K1iii—V1—Cs1xxv | 66.64 (3) |
| K1ix—Gd1—K1xv | 77.72 (4) | K1xviii—V1—Cs1xxv | 66.64 (3) |
| O1x—Gd1—K1iii | 128.398 (16) | K1xiv—V1—Cs1xxv | 120.814 (4) |
| O1vi—Gd1—K1iii | 51.602 (16) | O2—V1—Cs1xxvi | 59.187 (4) |
| O1xi—Gd1—K1iii | 62.07 (5) | O1—V1—Cs1xxvi | 124.969 (19) |
| O1iv—Gd1—K1iii | 117.93 (5) | O1vi—V1—Cs1xxvi | 124.970 (19) |
| O1xii—Gd1—K1iii | 128.398 (16) | O1xxiii—V1—Cs1xxvi | 49.87 (5) |
| O1ii—Gd1—K1iii | 51.602 (16) | K1vii—V1—Cs1xxvi | 66.65 (3) |
| K1xiii—Gd1—K1iii | 77.72 (4) | K1iii—V1—Cs1xxvi | 152.78 (5) |
| K1vii—Gd1—K1iii | 102.28 (4) | K1xviii—V1—Cs1xxvi | 66.65 (3) |
| K1xiv—Gd1—K1iii | 77.72 (4) | K1xiv—V1—Cs1xxvi | 120.813 (4) |
| K1ix—Gd1—K1iii | 102.28 (4) | Cs1xxv—V1—Cs1xxvi | 96.109 (5) |
| K1xv—Gd1—K1iii | 180.0 | O2—V1—Cs1 | 59.187 (4) |
| O2—K1—O1xvi | 96.52 (6) | O1—V1—Cs1 | 124.969 (19) |
| O2—K1—O1xvii | 96.52 (6) | O1vi—V1—Cs1 | 49.87 (5) |
| O1xvi—K1—O1xvii | 63.65 (4) | O1xxiii—V1—Cs1 | 124.970 (19) |
| O2—K1—O1xviii | 96.52 (6) | K1vii—V1—Cs1 | 66.65 (3) |
| O1xvi—K1—O1xviii | 55.49 (4) | K1iii—V1—Cs1 | 66.65 (3) |
| O1xvii—K1—O1xviii | 118.73 (2) | K1xviii—V1—Cs1 | 152.78 (5) |
| O2—K1—O1iii | 96.52 (6) | K1xiv—V1—Cs1 | 120.813 (4) |
| O1xvi—K1—O1iii | 118.73 (2) | Cs1xxv—V1—Cs1 | 96.109 (5) |
| O1xvii—K1—O1iii | 55.49 (4) | Cs1xxvi—V1—Cs1 | 96.109 (5) |
| O1xviii—K1—O1iii | 166.32 (11) | O2—V1—Cs2 | 0.0 |
| O2—K1—O1xix | 96.52 (6) | O1—V1—Cs2 | 109.06 (5) |
| O1xvi—K1—O1xix | 118.73 (2) | O1vi—V1—Cs2 | 109.06 (5) |
| O1xvii—K1—O1xix | 166.32 (11) | O1xxiii—V1—Cs2 | 109.06 (5) |
| O1xviii—K1—O1xix | 63.65 (4) | K1vii—V1—Cs2 | 93.60 (4) |
| O1iii—K1—O1xix | 118.73 (2) | K1iii—V1—Cs2 | 93.60 (4) |
| O2—K1—O1i | 96.52 (6) | K1xviii—V1—Cs2 | 93.60 (4) |
| O1xvi—K1—O1i | 166.32 (11) | K1xiv—V1—Cs2 | 180.0 |
| O1xvii—K1—O1i | 118.73 (2) | Cs1xxv—V1—Cs2 | 59.187 (4) |
| O1xviii—K1—O1i | 118.73 (2) | Cs1xxvi—V1—Cs2 | 59.187 (4) |
| O1iii—K1—O1i | 63.65 (4) | Cs1—V1—Cs2 | 59.187 (4) |
| O1xix—K1—O1i | 55.49 (4) | V1—O1—Gd1xxv | 162.94 (8) |
| O2—K1—V1vii | 86.40 (4) | V1—O1—K1xviii | 89.81 (3) |
| O1xvi—K1—V1vii | 147.94 (2) | Gd1xxv—O1—K1xviii | 92.19 (4) |
| O1xvii—K1—V1vii | 147.94 (2) | V1—O1—K1iii | 89.81 (3) |
| O1xviii—K1—V1vii | 92.45 (2) | Gd1xxv—O1—K1iii | 92.19 (4) |
| O1iii—K1—V1vii | 92.45 (2) | K1xviii—O1—K1iii | 166.32 (11) |
| O1xix—K1—V1vii | 29.676 (19) | V1—O1—Cs1xxv | 105.95 (5) |
| O1i—K1—V1vii | 29.676 (19) | Gd1xxv—O1—Cs1xxv | 91.12 (4) |
| O2—K1—V1iii | 86.40 (4) | K1xviii—O1—Cs1xxv | 83.48 (5) |
| O1xvi—K1—V1iii | 92.45 (2) | K1iii—O1—Cs1xxv | 83.48 (5) |
| O1xvii—K1—V1iii | 29.675 (19) | V1—O2—Cs2 | 180.0 |
| O1xviii—K1—V1iii | 147.94 (2) | V1—O2—K1 | 180.0 |
| O1iii—K1—V1iii | 29.676 (19) | Cs2—O2—K1 | 0.0 |
| O1xix—K1—V1iii | 147.94 (2) | V1—O2—Cs1xxv | 96.93 (3) |
| O1i—K1—V1iii | 92.45 (2) | Cs2—O2—Cs1xxv | 83.07 (3) |
| V1vii—K1—V1iii | 119.610 (10) | K1—O2—Cs1xxv | 83.07 (3) |
| O2—K1—V1xviii | 86.40 (4) | V1—O2—Cs1xxvi | 96.93 (3) |
| O1xvi—K1—V1xviii | 29.675 (19) | Cs2—O2—Cs1xxvi | 83.07 (3) |
| O1xvii—K1—V1xviii | 92.45 (2) | K1—O2—Cs1xxvi | 83.07 (3) |
| O1xviii—K1—V1xviii | 29.676 (19) | Cs1xxv—O2—Cs1xxvi | 118.566 (13) |
| O1iii—K1—V1xviii | 147.94 (2) | V1—O2—Cs1 | 96.93 (3) |
| O1xix—K1—V1xviii | 92.45 (2) | Cs2—O2—Cs1 | 83.07 (3) |
| O1i—K1—V1xviii | 147.94 (2) | K1—O2—Cs1 | 83.07 (3) |
| V1vii—K1—V1xviii | 119.610 (10) | Cs1xxv—O2—Cs1 | 118.566 (13) |
| V1iii—K1—V1xviii | 119.609 (10) | Cs1xxvi—O2—Cs1 | 118.566 (13) |
| O2—K1—V1xx | 180.0 |