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The triple molybdates K3–xNa1+xM4(MoO4)6 (M = Ni, Mg, Co) and K3+xLi1–xMg4(MoO4)6 were found upon studying the corresponding ternary molybdate systems, and their structures, thermal stability and electrical conductiviplusmnty were investigated. The com­pounds crystallize in the space group R3c and are isostructural with the sodium-ion conductor II-Na3Fe2(AsO4)3 and yurmarinite, Na7(Fe3+, Mg, Cu)4(AsO4)6; their basic structural units are flat polyhedral clusters of the central M1O6 octahedron sharing edges with three surrounding M2O6 octahedra, which combine with single NaO6 octahedra and bridging MoO4 tetrahedra to form open three-dimensional (3D) frameworks where the cavities are partially occupied by disordered potassium (sodium) ions. The split alkali-ion positions in K3–xNa1+xM4(MoO4)6 (M = Ni, Mg, Co) give their structural formulae as [(K,Na)0.50.5)]6(Na)[M1][M2]3(MoO4)6, whereas the lithium-containing com­pound (K0.50.5)6(Mg0.89K0.11)(Li0.89Mg0.11)Mg3(MoO4)6 shows an unexpected (Mg, K) isomorphism, which is similar to (Mn, K) and (Co, K) substitutions in isostructural K3+xLi1–xM4(MoO4)6 (M = Mn, Co). The crystal chemistry of the title com­pounds and related arsenates, phosphates and molybdates was considered, and the connections of the cationic distributions with potential 3D ionic conductivity were shown by means of calculating the bond valence sum (BVS) maps for the Na+, Li+ and K+ ions. Electrical conductivity measurements gave relatively low values for the triple molybdates [σ = 4.8 × 10−6 S cm−1 at 390°C for K3NaCo4(MoO4)6 and 5 × 10−7 S cm−1 at 400°C for K3LiMg4(MoO4)6] com­pared with II-Na3Fe2(AsO4)3 (σ = 8.3 × 10−4 S cm−1 at 300°C). This may be explained by a low concentration of sodium or lithium ions and the blocking of their transport by large potassium ions.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S2052520620010677/je5031sup1.cif
Contains datablocks global, I, II, III, IV, V, VI

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520620010677/je5031Isup2.hkl
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520620010677/je5031IIsup3.hkl
Contains datablock II

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520620010677/je5031IIIsup4.hkl
Contains datablock III

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520620010677/je5031IVsup5.hkl
Contains datablock IV

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520620010677/je5031Vsup6.hkl
Contains datablock V

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520620010677/je5031VIsup7.hkl
Contains datablock VI

CCDC references: 2021110; 2021111; 2021112; 2021113; 2021114; 2021115

Computing details top

For all structures, data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); program(s) used to solve structure: SHELXL2017/1 (Sheldrick, 2017); program(s) used to refine structure: SHELXL2017/1 (Sheldrick, 2017); molecular graphics: DIAMOND (Brandenburg, 2008).

(I) top
Crystal data top
K3NaNi4·6(MoO4)Dx = 3.812 Mg m3
Mr = 1334.77Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 9130 reflections
a = 14.2790 (2) Åθ = 2.6–31.1°
c = 19.7589 (4) ŵ = 6.94 mm1
V = 3488.90 (12) Å3T = 296 K
Z = 6Fragment, yellow
F(000) = 37440.06 × 0.04 × 0.04 mm
Data collection top
Bruker-Nonius X8 APEX CCD
diffractometer
1192 reflections with I > 2σ(I)
\ f scans, frame data integrationRint = 0.035
Absorption correction: multi-scan
SADABS (Bruker, 2005)
θmax = 31.1°, θmin = 2.6°
Tmin = 0.724, Tmax = 0.758h = 1720
9130 measured reflectionsk = 1719
1256 independent reflectionsl = 2827
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.024 w = 1/[σ2(Fo2) + (0.0077P)2 + 33.3386P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.051(Δ/σ)max = 0.008
S = 1.29Δρmax = 0.57 e Å3
1257 reflectionsΔρmin = 0.80 e Å3
76 parametersExtinction correction: SHELXL-2017/1 (Sheldrick 2017), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
7 restraintsExtinction coefficient: 0.000140 (14)
Special details top

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Mo0.18717 (2)0.00775 (2)0.35438 (2)0.01308 (8)
Ni10.0000000.0000000.2500000.00923 (17)
Ni20.21298 (4)0.21298 (4)0.2500000.01184 (12)
Na10.0000000.0000000.5000000.0334 (9)
K10.2596 (3)0.2417 (2)0.4415 (2)0.0301 (7)0.4259 (14)
K20.3037 (13)0.2613 (15)0.4267 (9)0.035 (5)0.0741 (14)
O10.1564 (2)0.0291 (2)0.43533 (13)0.0325 (6)
O20.26368 (19)0.05718 (19)0.35748 (13)0.0224 (5)
O30.26770 (18)0.13297 (19)0.31356 (12)0.0207 (5)
O40.06282 (17)0.07414 (17)0.30770 (11)0.0141 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mo0.01283 (13)0.01344 (13)0.01335 (12)0.00685 (10)0.00340 (8)0.00136 (8)
Ni10.0081 (2)0.0081 (2)0.0116 (4)0.00403 (12)0.0000.000
Ni20.00910 (18)0.00910 (18)0.0164 (2)0.00386 (19)0.00085 (9)0.00085 (9)
Na10.0392 (14)0.0392 (14)0.0218 (18)0.0196 (7)0.0000.000
K10.045 (2)0.0192 (12)0.0278 (13)0.0170 (14)0.0111 (13)0.0065 (9)
K20.047 (16)0.021 (7)0.038 (16)0.018 (9)0.030 (12)0.016 (8)
O10.0322 (15)0.0445 (17)0.0193 (12)0.0180 (13)0.0026 (10)0.0111 (11)
O20.0190 (11)0.0167 (11)0.0342 (13)0.0109 (9)0.0079 (9)0.0019 (9)
O30.0137 (10)0.0149 (10)0.0318 (12)0.0058 (9)0.0043 (9)0.0037 (9)
O40.0142 (10)0.0127 (9)0.0171 (10)0.0080 (8)0.0036 (8)0.0004 (8)
Geometric parameters (Å, º) top
Mo—O11.726 (3)K1—K20.620 (17)
Mo—O21.752 (2)K1—K2xi1.45 (2)
Mo—O31.765 (2)K1—K1xi2.072 (6)
Mo—O41.815 (2)K1—O12.632 (4)
Ni1—O42.043 (2)K1—O2xii2.675 (5)
Ni1—O4i2.043 (2)K1—O3xi2.821 (5)
Ni1—O4ii2.043 (2)K1—O3xii2.871 (4)
Ni1—O4iii2.043 (2)K1—O1viii2.945 (4)
Ni1—O4iv2.043 (2)K1—O2vi2.958 (5)
Ni1—O4v2.043 (2)K1—O33.000 (5)
Ni2—O2vi2.017 (2)K1—O4i3.504 (5)
Ni2—O2vii2.017 (2)K1—O1i3.598 (5)
Ni2—O4iv2.063 (2)K2—K2xi0.83 (4)
Ni2—O4i2.063 (2)K2—O2xii2.612 (17)
Ni2—O3iii2.094 (2)K2—O3xi2.693 (18)
Ni2—O32.094 (2)K2—O2vi2.735 (18)
Na1—O1viii2.422 (3)K2—O32.772 (17)
Na1—O1v2.422 (3)K2—O12.910 (18)
Na1—O1ix2.422 (3)K2—O3xii3.171 (19)
Na1—O1i2.422 (3)K2—O1xi3.460 (19)
Na1—O1x2.422 (3)K2—O1viii3.499 (19)
Na1—O12.422 (3)
O1—Mo—O2110.03 (13)K2—O1—K1ix99.3 (4)
O1—Mo—O3109.80 (13)Mo—O1—K2xi83.4 (3)
O2—Mo—O3106.82 (11)Na1—O1—K2xi119.1 (3)
O1—Mo—O4109.36 (12)K1—O1—K2xi22.8 (3)
O2—Mo—O4110.17 (10)K2—O1—K2xi11.4 (5)
O3—Mo—O4110.63 (10)K1ix—O1—K2xi99.0 (3)
O4—Ni1—O4i91.89 (8)Mo—O1—K2ix119.1 (3)
O4—Ni1—O4ii84.94 (12)Na1—O1—K2ix91.8 (3)
O4i—Ni1—O4ii175.47 (12)K1—O1—K2ix103.1 (4)
O4—Ni1—O4iii175.47 (12)K2—O1—K2ix101.9 (3)
O4i—Ni1—O4iii91.45 (12)K1ix—O1—K2ix4.9 (3)
O4ii—Ni1—O4iii91.89 (8)K2xi—O1—K2ix100.7 (3)
O4—Ni1—O4iv91.45 (12)Mo—O1—K1v85.42 (12)
O4i—Ni1—O4iv84.94 (12)Na1—O1—K1v74.64 (9)
O4ii—Ni1—O4iv91.89 (8)K1—O1—K1v170.94 (13)
O4iii—Ni1—O4iv91.89 (8)K2—O1—K1v177.6 (4)
O4—Ni1—O4v91.89 (8)K1ix—O1—K1v80.72 (11)
O4i—Ni1—O4v91.89 (8)K2xi—O1—K1v166.2 (4)
O4ii—Ni1—O4v91.45 (12)K2ix—O1—K1v77.9 (3)
O4iii—Ni1—O4v84.94 (12)Mo—O1—K1xi78.62 (11)
O4iv—Ni1—O4v175.47 (12)Na1—O1—K1xi124.94 (11)
O2vi—Ni2—O2vii92.13 (14)K1—O1—K1xi28.63 (9)
O2vi—Ni2—O4iv175.65 (9)K2—O1—K1xi17.2 (4)
O2vii—Ni2—O4iv91.99 (9)K1ix—O1—K1xi98.72 (10)
O2vi—Ni2—O4i91.99 (9)K2xi—O1—K1xi5.8 (3)
O2vii—Ni2—O4i175.65 (9)K2ix—O1—K1xi100.0 (3)
O4iv—Ni2—O4i83.93 (11)K1v—O1—K1xi160.42 (8)
O2vi—Ni2—O3iii93.89 (10)Mo—O1—K2v81.3 (3)
O2vii—Ni2—O3iii92.97 (10)Na1—O1—K2v77.3 (3)
O4iv—Ni2—O3iii84.49 (9)K1—O1—K2v172.6 (3)
O4i—Ni2—O3iii88.15 (9)K2—O1—K2v173.8 (6)
O2vi—Ni2—O392.97 (10)K1ix—O1—K2v84.1 (3)
O2vii—Ni2—O393.89 (10)K2xi—O1—K2v163.18 (13)
O4iv—Ni2—O388.15 (9)K2ix—O1—K2v81.1 (3)
O4i—Ni2—O384.49 (9)K1v—O1—K2v4.3 (3)
O3iii—Ni2—O3170.10 (13)K1xi—O1—K2v157.5 (3)
O1viii—Na1—O1v180.00 (13)Mo—O2—Ni2xiii146.55 (16)
O1viii—Na1—O1ix94.73 (9)Mo—O2—K2xiv105.2 (4)
O1v—Na1—O1ix85.27 (9)Ni2xiii—O2—K2xiv101.6 (4)
O1viii—Na1—O1i85.27 (9)Mo—O2—K1xiv98.95 (12)
O1v—Na1—O1i94.73 (9)Ni2xiii—O2—K1xiv102.81 (12)
O1ix—Na1—O1i180.00 (10)K2xiv—O2—K1xiv13.4 (4)
O1viii—Na1—O1x94.73 (9)Mo—O2—K2xiii111.6 (4)
O1v—Na1—O1x85.27 (9)Ni2xiii—O2—K2xiii100.0 (4)
O1ix—Na1—O1x94.73 (9)K2xiv—O2—K2xiii17.8 (8)
O1i—Na1—O1x85.27 (9)K1xiv—O2—K2xiii31.1 (4)
O1viii—Na1—O185.27 (9)Mo—O2—K1xiii114.31 (13)
O1v—Na1—O194.73 (9)Ni2xiii—O2—K1xiii98.87 (12)
O1ix—Na1—O185.27 (9)K2xiv—O2—K1xiii29.4 (4)
O1i—Na1—O194.73 (9)K1xiv—O2—K1xiii42.79 (12)
O1x—Na1—O1180.0K2xiii—O2—K1xiii11.7 (4)
O1—K1—O2xii140.20 (18)Mo—O2—K1v74.13 (9)
O1—K1—O3xi79.80 (12)Ni2xiii—O2—K1v88.75 (10)
O2xii—K1—O3xi65.65 (12)K2xiv—O2—K1v156.7 (4)
O1—K1—O3xii134.48 (14)K1xiv—O2—K1v166.35 (14)
O2xii—K1—O3xii61.09 (10)K2xiii—O2—K1v140.3 (4)
O3xi—K1—O3xii122.73 (15)K1xiii—O2—K1v128.91 (10)
O1—K1—O1viii71.83 (13)Mo—O2—K1ix81.30 (10)
O2xii—K1—O1viii83.08 (13)Ni2xiii—O2—K1ix65.33 (8)
O3xi—K1—O1viii80.42 (13)K2xiv—O2—K1ix138.8 (4)
O3xii—K1—O1viii74.01 (10)K1xiv—O2—K1ix126.98 (11)
O1—K1—O2vi113.36 (17)K2xiii—O2—K1ix153.4 (4)
O2xii—K1—O2vi105.12 (13)K1xiii—O2—K1ix160.76 (10)
O3xi—K1—O2vi134.93 (13)K1v—O2—K1ix64.42 (7)
O3xii—K1—O2vi79.82 (11)Mo—O3—Ni2126.52 (12)
O1viii—K1—O2vi144.27 (15)Mo—O3—K2xi109.7 (4)
O1—K1—O360.53 (10)Ni2—O3—K2xi97.0 (4)
O2xii—K1—O3140.23 (13)Mo—O3—K296.5 (4)
O3xi—K1—O397.76 (12)Ni2—O3—K296.9 (4)
O3xii—K1—O3137.07 (17)K2xi—O3—K217.5 (8)
O1viii—K1—O3131.70 (13)Mo—O3—K1xi119.13 (13)
O2vi—K1—O360.06 (10)Ni2—O3—K1xi96.21 (11)
O1—K1—O4i66.73 (11)K2xi—O3—K1xi12.6 (4)
O2xii—K1—O4i151.82 (14)K2—O3—K1xi30.1 (4)
O3xi—K1—O4i141.77 (13)Mo—O3—K1xiv91.87 (12)
O3xii—K1—O4i94.57 (12)Ni2—O3—K1xiv124.13 (14)
O1viii—K1—O4i104.80 (11)K2xi—O3—K1xiv106.7 (4)
O2vi—K1—O4i53.21 (9)K2—O3—K1xiv119.7 (3)
O3—K1—O4i50.17 (9)K1xi—O3—K1xiv97.10 (13)
O1—K1—O1i67.74 (13)Mo—O3—K187.99 (11)
O2xii—K1—O1i124.09 (13)Ni2—O3—K195.83 (11)
O3xi—K1—O1i133.86 (12)K2xi—O3—K128.9 (4)
O3xii—K1—O1i69.24 (9)K2—O3—K111.5 (4)
O1viii—K1—O1i59.19 (10)K1xi—O3—K141.56 (11)
O2vi—K1—O1i89.07 (12)K1xiv—O3—K1127.98 (15)
O3—K1—O1i93.92 (12)Mo—O3—K2xiv85.5 (3)
O4i—K1—O1i48.00 (8)Ni2—O3—K2xiv122.8 (3)
O2xii—K2—O3xi68.4 (4)K2xi—O3—K2xiv116.5 (7)
O2xii—K2—O2vi113.7 (7)K2—O3—K2xiv128.6 (5)
O3xi—K2—O2vi159.1 (8)K1xi—O3—K2xiv107.3 (3)
O2xii—K2—O3164.9 (8)K1xiv—O3—K2xiv10.3 (3)
O3xi—K2—O3106.8 (7)K1—O3—K2xiv135.7 (3)
O2vi—K2—O365.6 (4)Mo—O3—K2xiii78.9 (3)
O2xii—K2—O1129.2 (7)Ni2—O3—K2xiii119.8 (3)
O3xi—K2—O177.2 (5)K2xi—O3—K2xiii127.2 (5)
O2vi—K2—O1111.8 (5)K2—O3—K2xiii137.8 (6)
O3—K2—O160.3 (4)K1xi—O3—K2xiii118.4 (3)
O2xii—K2—O3xii57.5 (4)K1xiv—O3—K2xiii21.6 (3)
O3xi—K2—O3xii116.6 (6)K1—O3—K2xiii143.0 (3)
O2vi—K2—O3xii78.2 (5)K2xiv—O3—K2xiii11.3 (5)
O3—K2—O3xii133.5 (6)Mo—O3—K1xiii75.00 (10)
O1—K2—O3xii113.1 (6)Ni2—O3—K1xiii117.44 (11)
O2xii—K2—O1xi99.7 (5)K2xi—O3—K1xiii133.6 (3)
O3xi—K2—O1xi53.6 (3)K2—O3—K1xiii142.9 (4)
O2vi—K2—O1xi106.7 (6)K1xi—O3—K1xiii125.14 (11)
O3—K2—O1xi67.3 (4)K1xiv—O3—K1xiii28.34 (9)
O1—K2—O1xi87.8 (5)K1—O3—K1xiii146.60 (10)
O3xii—K2—O1xi155.5 (5)K2xiv—O3—K1xiii18.0 (4)
O2xii—K2—O1viii73.7 (4)K2xiii—O3—K1xiii6.8 (3)
O3xi—K2—O1viii72.6 (4)Mo—O4—Ni1119.42 (11)
O2vi—K2—O1viii128.2 (6)Mo—O4—Ni2v135.65 (11)
O3—K2—O1viii119.3 (6)Ni1—O4—Ni2v95.56 (9)
O1—K2—O1viii60.8 (4)Mo—O4—K1v87.10 (9)
O3xii—K2—O1viii63.1 (3)Ni1—O4—K1v138.49 (10)
O1xi—K2—O1viii122.9 (5)Ni2v—O4—K1v82.54 (8)
Mo—O1—Na1138.85 (15)Mo—O4—K2v94.6 (3)
Mo—O1—K1101.66 (15)Ni1—O4—K2v136.6 (3)
Na1—O1—K196.31 (12)Ni2v—O4—K2v73.2 (3)
Mo—O1—K292.6 (4)K1v—O4—K2v9.4 (3)
Na1—O1—K2107.8 (4)Mo—O4—K2xv102.9 (3)
K1—O1—K211.5 (4)Ni1—O4—K2xv133.2 (3)
Mo—O1—K1ix123.68 (16)Ni2v—O4—K2xv62.2 (3)
Na1—O1—K1ix88.62 (11)K1v—O4—K2xv20.4 (3)
K1—O1—K1ix99.65 (11)K2v—O4—K2xv11.0 (6)
Symmetry codes: (i) y, xy, z; (ii) x, x+y, z+1/2; (iii) y, x, z+1/2; (iv) xy, y, z+1/2; (v) x+y, x, z; (vi) y+1/3, x+y+2/3, z+2/3; (vii) x+y+2/3, y+1/3, z1/6; (viii) xy, x, z+1; (ix) y, x+y, z+1; (x) x, y, z+1; (xi) x+2/3, x+y+1/3, z+5/6; (xii) y+1/3, x+2/3, z+1/6; (xiii) xy+1/3, x1/3, z+2/3; (xiv) y+2/3, x+1/3, z1/6; (xv) y1/3, x2/3, z+5/6.
(II) top
Crystal data top
K2.51Na1.49Ni4·6(MoO4)Dx = 3.784 Mg m3
Mr = 1326.84Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 13749 reflections
a = 14.2719 (2) Åθ = 2.6–2.7°
c = 19.8063 (4) ŵ = 6.85 mm1
V = 3493.80 (14) Å3T = 296 K
Z = 6Fragment, yellow
F(000) = 37210.07 × 0.07 × 0.06 mm
Data collection top
Bruker-Nonius X8 APEX CCD
diffractometer
1062 reflections with I > 2σ(I)
\ f scans, frame data integrationRint = 0.027
Absorption correction: multi-scan
SADABS (Bruker, 2005)
θmax = 29.7°, θmin = 2.6°
Tmin = 0.625, Tmax = 0.663h = 1919
13749 measured reflectionsk = 1919
1111 independent reflectionsl = 2727
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.014 w = 1/[σ2(Fo2) + (0.0124P)2 + 12.1272P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.033(Δ/σ)max = 0.025
S = 1.16Δρmax = 0.67 e Å3
1106 reflectionsΔρmin = 0.43 e Å3
86 parametersExtinction correction: SHELXL-2017/1 (Sheldrick 2017), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
7 restraintsExtinction coefficient: 0.000093 (12)
Special details top

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Mo0.18781 (2)0.00850 (2)0.35417 (2)0.01230 (6)
Ni10.0000000.0000000.2500000.00785 (11)
Ni20.21317 (2)0.21317 (2)0.2500000.01112 (8)
Na10.0000000.0000000.5000000.0341 (5)
K10.2579 (5)0.2401 (6)0.4432 (6)0.0253 (10)0.2611 (16)
K20.2791 (12)0.2517 (12)0.4342 (10)0.063 (5)0.1578 (16)
Na20.249 (2)0.2275 (17)0.4731 (10)0.043 (5)0.0810 (16)
O10.15739 (15)0.03009 (16)0.43513 (9)0.0355 (4)
O20.26437 (12)0.05662 (12)0.35708 (9)0.0236 (3)
O30.26868 (12)0.13385 (12)0.31374 (8)0.0220 (3)
O40.06333 (11)0.07385 (11)0.30776 (7)0.0136 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mo0.01203 (8)0.01256 (8)0.01260 (9)0.00636 (6)0.00403 (5)0.00181 (5)
Ni10.00661 (14)0.00661 (14)0.0103 (3)0.00331 (7)0.0000.000
Ni20.00843 (11)0.00843 (11)0.01552 (17)0.00348 (12)0.00094 (6)0.00094 (6)
Na10.0392 (8)0.0392 (8)0.0241 (12)0.0196 (4)0.0000.000
K10.0359 (14)0.0168 (14)0.024 (2)0.0137 (11)0.0049 (16)0.0058 (16)
K20.128 (12)0.034 (5)0.040 (9)0.052 (7)0.051 (9)0.021 (5)
Na20.062 (11)0.044 (10)0.018 (8)0.023 (9)0.002 (10)0.014 (8)
O10.0328 (9)0.0511 (11)0.0188 (8)0.0180 (9)0.0023 (7)0.0130 (8)
O20.0207 (7)0.0183 (7)0.0343 (9)0.0116 (6)0.0100 (6)0.0003 (6)
O30.0149 (6)0.0165 (7)0.0325 (8)0.0064 (6)0.0050 (6)0.0041 (6)
O40.0138 (6)0.0120 (6)0.0164 (7)0.0075 (5)0.0048 (5)0.0015 (5)
Geometric parameters (Å, º) top
Mo—O11.7287 (17)K1—O3xii2.862 (8)
Mo—O21.7539 (15)K1—O1ix2.912 (9)
Mo—O31.7633 (15)K1—O2vi2.989 (12)
Mo—O41.8150 (13)K1—O33.021 (11)
Ni1—O4i2.0468 (13)K1—O4i3.520 (12)
Ni1—O4ii2.0468 (13)K1—O1i3.591 (7)
Ni1—O4iii2.0468 (13)K2—Na20.86 (3)
Ni1—O4iv2.0468 (13)K2—K2xi1.51 (3)
Ni1—O4v2.0468 (13)K2—Na2xi2.26 (3)
Ni1—O42.0468 (13)K2—O2xii2.620 (18)
Ni2—O2vi2.0190 (15)K2—O12.744 (15)
Ni2—O2vii2.0190 (15)K2—O3xi2.757 (17)
Ni2—O4iv2.0693 (13)K2—O2vi2.818 (19)
Ni2—O4i2.0693 (13)K2—O32.881 (19)
Ni2—O3iii2.0975 (15)K2—O3xii2.976 (16)
Ni2—O32.0975 (15)K2—O1ix3.207 (19)
Na1—O1viii2.4323 (18)K2—O4i3.569 (17)
Na1—O1i2.4323 (18)K2—O1xi3.724 (15)
Na1—O1ix2.4324 (18)K2—O1i3.846 (14)
Na1—O1v2.4324 (18)Na2—O1ix2.37 (2)
Na1—O12.4324 (18)Na2—O2xii2.50 (2)
Na1—O1x2.4324 (18)Na2—O3xi2.53 (3)
K1—K20.32 (2)Na2—O12.555 (19)
K1—Na20.61 (2)Na2—O3xii2.86 (2)
K1—K2xi1.824 (13)Na2—Na2xi3.05 (5)
K1—K1xi2.139 (13)Na2—O2ix3.48 (2)
K1—Na2xi2.57 (3)Na2—O33.493 (18)
K1—O12.602 (8)Na2—O1i3.58 (3)
K1—O2xii2.663 (11)Na2—O2vi3.58 (2)
K1—O3xi2.798 (11)
O1—Mo—O2110.03 (9)Na1—O1—K2viii89.9 (3)
O1—Mo—O3109.61 (9)Na2—O1—K2viii89.7 (6)
O2—Mo—O3106.70 (7)K1—O1—K2viii100.7 (5)
O1—Mo—O4109.48 (7)K2—O1—K2viii101.3 (3)
O2—Mo—O4109.93 (6)K1viii—O1—K2viii2.1 (5)
O3—Mo—O4111.05 (7)Mo—O1—Na2v95.7 (4)
O4i—Ni1—O4ii175.80 (8)Na2viii—O1—Na2v70.6 (5)
O4i—Ni1—O4iii91.29 (8)Na1—O1—Na2v67.0 (4)
O4ii—Ni1—O4iii91.80 (5)Na2—O1—Na2v148.6 (8)
O4i—Ni1—O4iv85.26 (7)K1—O1—Na2v161.1 (5)
O4ii—Ni1—O4iv91.80 (5)K2—O1—Na2v166.8 (6)
O4iii—Ni1—O4iv91.80 (5)K1viii—O1—Na2v73.3 (3)
O4i—Ni1—O4v91.80 (5)K2viii—O1—Na2v72.7 (4)
O4ii—Ni1—O4v91.29 (8)Mo—O1—K1v86.0 (2)
O4iii—Ni1—O4v85.26 (7)Na2viii—O1—K1v76.6 (6)
O4iv—Ni1—O4v175.80 (8)Na1—O1—K1v73.84 (16)
O4i—Ni1—O491.80 (5)Na2—O1—K1v158.3 (6)
O4ii—Ni1—O485.26 (7)K1—O1—K1v169.5 (3)
O4iii—Ni1—O4175.80 (8)K2—O1—K1v175.6 (4)
O4iv—Ni1—O491.29 (8)K1viii—O1—K1v80.0 (2)
O4v—Ni1—O491.80 (5)K2viii—O1—K1v79.2 (4)
O2vi—Ni2—O2vii92.27 (9)Na2v—O1—K1v9.8 (3)
O2vi—Ni2—O4iv175.80 (6)Mo—O1—K2xi81.0 (3)
O2vii—Ni2—O4iv91.81 (6)Na2viii—O1—K2xi101.0 (7)
O2vi—Ni2—O4i91.81 (6)Na1—O1—K2xi122.4 (3)
O2vii—Ni2—O4i175.80 (6)Na2—O1—K2xi36.4 (5)
O4iv—Ni2—O4i84.12 (7)K1—O1—K2xi26.7 (3)
O2vi—Ni2—O3iii94.16 (6)K2—O1—K2xi20.7 (5)
O2vii—Ni2—O3iii92.28 (7)K1viii—O1—K2xi99.2 (4)
O4iv—Ni2—O3iii84.70 (6)K2viii—O1—K2xi99.4 (3)
O4i—Ni2—O3iii88.40 (6)Na2v—O1—K2xi168.4 (4)
O2vi—Ni2—O392.28 (7)K1v—O1—K2xi163.7 (4)
O2vii—Ni2—O394.16 (6)Mo—O1—K2v83.1 (3)
O4iv—Ni2—O388.40 (6)Na2viii—O1—K2v78.4 (8)
O4i—Ni2—O384.70 (6)Na1—O1—K2v75.9 (3)
O3iii—Ni2—O3170.71 (8)Na2—O1—K2v161.1 (5)
O1viii—Na1—O1i180.00 (7)K1—O1—K2v171.5 (3)
O1viii—Na1—O1ix94.67 (6)K2—O1—K2v176.8 (3)
O1i—Na1—O1ix85.33 (6)K1viii—O1—K2v82.0 (3)
O1viii—Na1—O1v85.33 (6)K2viii—O1—K2v81.1 (3)
O1i—Na1—O1v94.67 (6)Na2v—O1—K2v12.7 (5)
O1ix—Na1—O1v180.00 (8)K1v—O1—K2v2.9 (5)
O1viii—Na1—O185.33 (6)K2xi—O1—K2v161.54 (9)
O1i—Na1—O194.67 (6)Mo—O2—Ni2xiii146.10 (11)
O1ix—Na1—O185.33 (6)Mo—O2—Na2xiv101.4 (6)
O1v—Na1—O194.67 (6)Ni2xiii—O2—Na2xiv94.6 (6)
O1viii—Na1—O1x94.67 (6)Mo—O2—K2xiv101.4 (3)
O1i—Na1—O1x85.33 (6)Ni2xiii—O2—K2xiv103.3 (4)
O1ix—Na1—O1x94.67 (6)Na2xiv—O2—K2xiv19.2 (7)
O1v—Na1—O1x85.33 (6)Mo—O2—K1xiv99.00 (18)
O1—Na1—O1x180.0Ni2xiii—O2—K1xiv102.8 (2)
O1—K1—O2xii141.3 (5)Na2xiv—O2—K1xiv13.2 (5)
O1—K1—O3xi80.2 (2)K2xiv—O2—K1xiv6.8 (5)
O2xii—K1—O3xi65.8 (3)Mo—O2—K2xiii113.2 (3)
O1—K1—O3xii135.5 (2)Ni2xiii—O2—K2xiii100.0 (3)
O2xii—K1—O3xii61.3 (2)Na2xiv—O2—K2xiii49.7 (6)
O3xi—K1—O3xii123.2 (4)K2xiv—O2—K2xiii32.0 (6)
O1—K1—O1ix73.2 (2)K1xiv—O2—K2xiii38.8 (3)
O2xii—K1—O1ix83.5 (3)Mo—O2—K1xiii114.46 (19)
O3xi—K1—O1ix81.2 (3)Ni2xiii—O2—K1xiii99.22 (19)
O3xii—K1—O1ix74.1 (2)Na2xiv—O2—K1xiii54.9 (5)
O1—K1—O2vi112.7 (4)K2xiv—O2—K1xiii37.2 (4)
O2xii—K1—O2vi104.3 (2)K1xiv—O2—K1xiii44.0 (2)
O3xi—K1—O2vi133.8 (2)K2xiii—O2—K1xiii5.2 (4)
O3xii—K1—O2vi79.6 (2)Mo—O2—Na2viii77.1 (4)
O1ix—K1—O2vi144.6 (3)Ni2xiii—O2—Na2viii69.0 (5)
O1—K1—O360.4 (2)Na2xiv—O2—Na2viii115.8 (6)
O2xii—K1—O3138.9 (2)K2xiv—O2—Na2viii134.8 (5)
O3xi—K1—O397.6 (2)K1xiv—O2—Na2viii128.2 (4)
O3xii—K1—O3136.2 (4)K2xiii—O2—Na2viii162.4 (5)
O1ix—K1—O3133.0 (3)K1xiii—O2—Na2viii165.4 (5)
O2vi—K1—O359.2 (2)Mo—O2—Na2xiii112.5 (3)
O1—K1—O4i66.8 (2)Ni2xiii—O2—Na2xiii101.3 (3)
O2xii—K1—O4i151.1 (3)Na2xiv—O2—Na2xiii56.9 (9)
O3xi—K1—O4i141.9 (3)K2xiv—O2—Na2xiii38.9 (4)
O3xii—K1—O4i94.3 (3)K1xiv—O2—Na2xiii45.7 (6)
O1ix—K1—O4i105.6 (2)K2xiii—O2—Na2xiii7.3 (6)
O2vi—K1—O4i52.9 (2)K1xiii—O2—Na2xiii2.8 (3)
O3—K1—O4i50.12 (19)Na2viii—O2—Na2xiii168.2 (5)
O1—K1—O1i68.43 (17)Mo—O2—K1v73.91 (13)
O2xii—K1—O1i124.8 (3)Ni2xiii—O2—K1v88.27 (15)
O3xi—K1—O1i135.1 (3)Na2xiv—O2—K1v174.7 (6)
O3xii—K1—O1i69.25 (14)K2xiv—O2—K1v162.8 (3)
O1ix—K1—O1i59.84 (12)K1xiv—O2—K1v167.4 (3)
O2vi—K1—O1i88.9 (3)K2xiii—O2—K1v134.1 (4)
O3—K1—O1i94.1 (3)K1xiii—O2—K1v129.05 (16)
O4i—K1—O1i48.02 (13)Na2viii—O2—K1v61.2 (4)
O2xii—K2—O1135.7 (8)Na2xiii—O2—K1v126.9 (4)
O2xii—K2—O3xi67.0 (4)Mo—O2—K1viii80.82 (10)
O1—K2—O3xi78.5 (4)Ni2xiii—O2—K1viii65.36 (9)
O2xii—K2—O2vi110.4 (5)Na2xiv—O2—K1viii113.7 (5)
O1—K2—O2vi113.8 (6)K2xiv—O2—K1viii133.0 (4)
O3xi—K2—O2vi145.5 (6)K1xiv—O2—K1viii126.5 (2)
O2xii—K2—O3150.9 (6)K2xiii—O2—K1viii158.8 (4)
O1—K2—O360.9 (4)K1xiii—O2—K1viii161.47 (14)
O3xi—K2—O3101.9 (5)Na2viii—O2—K1viii4.0 (4)
O2vi—K2—O362.8 (4)Na2xiii—O2—K1viii164.2 (3)
O2xii—K2—O3xii60.2 (4)K1v—O2—K1viii63.47 (18)
O1—K2—O3xii124.3 (5)Mo—O2—K2v76.1 (2)
O3xi—K2—O3xii120.5 (7)Ni2xiii—O2—K2v88.2 (3)
O2vi—K2—O3xii80.5 (4)Na2xiv—O2—K2v177.2 (7)
O3—K2—O3xii137.5 (6)K2xiv—O2—K2v159.4 (6)
O2xii—K2—O1ix78.6 (5)K1xiv—O2—K2v165.0 (2)
O1—K2—O1ix66.8 (4)K2xiii—O2—K2v129.9 (2)
O3xi—K2—O1ix76.7 (5)K1xiii—O2—K2v124.8 (3)
O2vi—K2—O1ix137.8 (5)Na2viii—O2—K2v65.1 (5)
O3—K2—O1ix126.6 (5)Na2xiii—O2—K2v122.7 (6)
O3xii—K2—O1ix68.4 (4)K1v—O2—K2v4.3 (3)
O2xii—K2—O4i150.6 (6)K1viii—O2—K2v67.3 (3)
O1—K2—O4i64.8 (3)Mo—O3—Ni2126.06 (8)
O3xi—K2—O4i141.4 (5)Mo—O3—Na2xi130.3 (4)
O2vi—K2—O4i53.2 (3)Ni2—O3—Na2xi91.8 (4)
O3—K2—O4i50.2 (3)Mo—O3—K2xi115.1 (4)
O3xii—K2—O4i91.3 (4)Ni2—O3—K2xi96.8 (4)
O1ix—K2—O4i98.4 (4)Na2xi—O3—K2xi18.2 (7)
O2xii—K2—O1xi92.8 (4)Mo—O3—K1xi119.8 (2)
O1—K2—O1xi84.5 (4)Ni2—O3—K1xi96.5 (2)
O3xi—K2—O1xi49.5 (2)Na2xi—O3—K1xi11.9 (4)
O2vi—K2—O1xi97.9 (5)K2xi—O3—K1xi6.5 (5)
O3—K2—O1xi62.1 (3)Mo—O3—Na2xiv88.7 (5)
O3xii—K2—O1xi149.5 (5)Ni2—O3—Na2xiv134.6 (4)
O1ix—K2—O1xi123.4 (5)Na2xi—O3—Na2xiv82.9 (10)
O4i—K2—O1xi112.3 (5)K2xi—O3—Na2xiv91.8 (6)
O2xii—K2—O1i117.3 (6)K1xi—O3—Na2xiv87.4 (5)
O1—K2—O1i63.2 (3)Mo—O3—K1xiv91.9 (2)
O3xi—K2—O1i126.3 (6)Ni2—O3—K1xiv124.5 (3)
O2vi—K2—O1i86.5 (4)Na2xi—O3—K1xiv89.9 (6)
O3—K2—O1i91.2 (4)K2xi—O3—K1xiv101.2 (3)
O3xii—K2—O1i64.5 (3)K1xi—O3—K1xiv96.2 (3)
O1ix—K2—O1i54.8 (2)Na2xiv—O3—K1xiv12.3 (4)
O4i—K2—O1i45.75 (18)Mo—O3—K291.9 (3)
O1xi—K2—O1i146.0 (5)Ni2—O3—K296.1 (3)
O1ix—Na2—O2xii99.7 (6)Na2xi—O3—K248.7 (6)
O1ix—Na2—O3xi98.7 (8)K2xi—O3—K231.0 (6)
O2xii—Na2—O3xi72.4 (7)K1xi—O3—K237.4 (3)
O1ix—Na2—O184.0 (7)Na2xiv—O3—K2112.6 (5)
O2xii—Na2—O1158.7 (12)K1xiv—O3—K2124.4 (3)
O3xi—Na2—O186.4 (7)Mo—O3—K2xiv88.9 (3)
O1ix—Na2—O3xii82.9 (7)Ni2—O3—K2xiv123.2 (4)
O2xii—Na2—O3xii63.1 (4)Na2xi—O3—K2xiv95.6 (6)
O3xi—Na2—O3xii135.0 (8)K2xi—O3—K2xiv107.0 (6)
O1—Na2—O3xii138.0 (11)K1xi—O3—K2xiv102.0 (3)
O1ix—Na2—O2ix54.5 (4)Na2xiv—O3—K2xiv16.9 (6)
O2xii—Na2—O2ix55.4 (4)K1xiv—O3—K2xiv5.8 (4)
O3xi—Na2—O2ix57.7 (4)K2—O3—K2xiv129.5 (5)
O1—Na2—O2ix113.7 (8)Mo—O3—K187.27 (16)
O3xii—Na2—O2ix90.1 (4)Ni2—O3—K196.4 (2)
O1ix—Na2—O3135.6 (8)Na2xi—O3—K154.2 (6)
O2xii—Na2—O3124.5 (9)K2xi—O3—K136.4 (3)
O3xi—Na2—O391.9 (6)K1xi—O3—K142.9 (2)
O1—Na2—O353.6 (3)Na2xiv—O3—K1115.5 (5)
O3xii—Na2—O3118.2 (7)K1xiv—O3—K1127.6 (4)
O2ix—Na2—O3149.2 (8)K2—O3—K15.5 (4)
O1ix—Na2—O1i63.6 (6)K2xiv—O3—K1132.4 (3)
O2xii—Na2—O1i131.4 (8)Mo—O3—Na280.8 (4)
O3xi—Na2—O1i150.4 (8)Ni2—O3—Na2102.4 (4)
O1—Na2—O1i69.0 (6)Na2xi—O3—Na258.3 (9)
O3xii—Na2—O1i69.4 (6)K2xi—O3—Na240.2 (4)
O2ix—Na2—O1i116.6 (7)K1xi—O3—Na246.6 (5)
O3—Na2—O1i86.7 (5)Na2xiv—O3—Na2112.4 (6)
O1ix—Na2—O2vi141.0 (11)K1xiv—O3—Na2124.7 (4)
O2xii—Na2—O2vi92.8 (7)K2—O3—Na211.0 (5)
O3xi—Na2—O2vi120.2 (8)K2xiv—O3—Na2128.9 (7)
O1—Na2—O2vi97.3 (5)K1—O3—Na27.0 (4)
O3xii—Na2—O2vi70.1 (5)Mo—O3—K2xiii76.3 (2)
O2ix—Na2—O2vi148.1 (7)Ni2—O3—K2xiii118.3 (3)
O3—Na2—O2vi49.6 (3)Na2xi—O3—K2xiii116.1 (6)
O1i—Na2—O2vi80.5 (5)K2xi—O3—K2xiii126.9 (4)
Mo—O1—Na2viii118.3 (6)K1xi—O3—K2xiii122.3 (2)
Mo—O1—Na1138.64 (9)Na2xiv—O3—K2xiii35.2 (5)
Na2viii—O1—Na192.1 (5)K1xiv—O3—K2xiii26.3 (3)
Mo—O1—Na2115.7 (5)K2—O3—K2xiii144.2 (4)
Na2viii—O1—Na293.1 (3)K2xiv—O3—K2xiii20.5 (4)
Na1—O1—Na287.6 (6)K1—O3—K2xiii145.0 (4)
Mo—O1—K1102.7 (3)Na2—O3—K2xiii139.4 (4)
Na2viii—O1—K1103.8 (8)Mo—O4—Ni1119.40 (7)
Na1—O1—K195.72 (16)Mo—O4—Ni2v135.89 (7)
Na2—O1—K113.7 (5)Ni1—O4—Ni2v95.31 (6)
Mo—O1—K297.4 (4)Mo—O4—K1v87.00 (13)
Na2viii—O1—K2104.1 (6)Ni1—O4—K1v138.16 (14)
Na1—O1—K2101.7 (4)Ni2v—O4—K1v83.19 (13)
Na2—O1—K218.3 (7)Mo—O4—K2v90.7 (3)
K1—O1—K26.1 (5)Ni1—O4—K2v137.9 (3)
Mo—O1—K1viii124.0 (2)Ni2v—O4—K2v78.1 (3)
Na2viii—O1—K1viii6.1 (7)K1v—O4—K2v5.1 (4)
Na1—O1—K1viii88.2 (2)Mo—O4—Na2v83.2 (4)
Na2—O1—K1viii88.3 (6)Ni1—O4—Na2v135.9 (3)
K1—O1—K1viii99.5 (2)Ni2v—O4—Na2v90.1 (4)
K2—O1—K1viii100.3 (5)K1v—O4—Na2v7.1 (3)
Mo—O1—K2viii121.9 (3)K2v—O4—Na2v12.0 (5)
Na2viii—O1—K2viii4.1 (6)
Symmetry codes: (i) y, xy, z; (ii) x, x+y, z+1/2; (iii) y, x, z+1/2; (iv) xy, y, z+1/2; (v) x+y, x, z; (vi) y+1/3, x+y+2/3, z+2/3; (vii) x+y+2/3, y+1/3, z1/6; (viii) y, x+y, z+1; (ix) xy, x, z+1; (x) x, y, z+1; (xi) x+2/3, x+y+1/3, z+5/6; (xii) y+1/3, x+2/3, z+1/6; (xiii) xy+1/3, x1/3, z+2/3; (xiv) y+2/3, x+1/3, z1/6.
(III) top
Crystal data top
K3NaMg4·6(MoO4)Dx = 3.315 Mg m3
Mr = 1197.17Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 10553 reflections
a = 14.4528 (2) Åθ = 2.6–28.3°
c = 19.8894 (3) ŵ = 3.79 mm1
V = 3597.96 (11) Å3T = 296 K
Z = 6Fragment, colourless
F(000) = 33600.06 × 0.04 × 0.03 mm
Data collection top
Bruker-Nonius X8 APEX CCD
diffractometer
932 reflections with I > 2σ(I)
\ f scans, frame data integrationRint = 0.030
Absorption correction: multi-scan
SADABS (Bruker, 2005)
θmax = 28.3°, θmin = 2.6°
Tmin = 0.834, Tmax = 0.893h = 1919
10553 measured reflectionsk = 1817
1001 independent reflectionsl = 2626
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.015 w = 1/[σ2(Fo2) + (0.0111P)2 + 7.1525P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.034(Δ/σ)max = 0.004
S = 1.20Δρmax = 0.39 e Å3
1001 reflectionsΔρmin = 0.46 e Å3
76 parametersExtinction correction: SHELXL-2017/1 (Sheldrick 2017), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
7 restraintsExtinction coefficient: 0.000180 (16)
Special details top

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Mo0.18653 (2)0.00666 (2)0.35467 (2)0.01349 (7)
Mg10.0000000.0000000.2500000.0106 (3)
Mg20.21486 (7)0.21486 (7)0.2500000.0130 (2)
Na10.0000000.0000000.5000000.0274 (5)
K10.2565 (3)0.2400 (3)0.44331 (17)0.0263 (6)0.4237 (14)
K20.281 (2)0.252 (2)0.4288 (10)0.050 (6)0.0763 (14)
O10.15435 (14)0.02413 (15)0.43545 (8)0.0337 (4)
O20.26341 (12)0.05651 (12)0.35676 (8)0.0234 (4)
O30.26436 (12)0.13186 (12)0.31610 (8)0.0219 (3)
O40.06533 (11)0.07261 (11)0.30737 (7)0.0146 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mo0.01417 (11)0.01354 (11)0.01332 (10)0.00735 (8)0.00376 (6)0.00154 (6)
Mg10.0087 (5)0.0087 (5)0.0144 (7)0.0043 (2)0.0000.000
Mg20.0107 (3)0.0107 (3)0.0165 (5)0.0045 (4)0.00126 (17)0.00126 (17)
Na10.0312 (8)0.0312 (8)0.0198 (11)0.0156 (4)0.0000.000
K10.0407 (10)0.0197 (9)0.0197 (17)0.0160 (8)0.0064 (10)0.0028 (10)
K20.122 (18)0.026 (7)0.006 (7)0.038 (10)0.010 (8)0.004 (5)
O10.0363 (10)0.0428 (11)0.0180 (8)0.0167 (9)0.0023 (7)0.0085 (7)
O20.0209 (8)0.0194 (8)0.0329 (9)0.0122 (7)0.0084 (6)0.0010 (6)
O30.0155 (8)0.0170 (8)0.0307 (8)0.0062 (6)0.0056 (6)0.0021 (6)
O40.0150 (7)0.0125 (7)0.0169 (7)0.0074 (6)0.0036 (5)0.0009 (5)
Geometric parameters (Å, º) top
Mo—O11.7259 (16)Na1—K13.767 (3)
Mo—O21.7562 (16)Na1—K1v3.767 (3)
Mo—O31.7586 (15)Na1—K1viii3.767 (3)
Mo—O41.8053 (14)K1—K20.42 (2)
Mg1—O4i2.0701 (13)K1—K2xi1.80 (2)
Mg1—O4ii2.0701 (13)K1—K1xi2.195 (6)
Mg1—O4iii2.0701 (13)K1—O2xii2.697 (4)
Mg1—O4iv2.0701 (13)K1—O12.707 (4)
Mg1—O4v2.0701 (13)K1—O3xi2.848 (4)
Mg1—O42.0701 (13)K1—O1viii2.902 (3)
Mg2—O2vi2.0367 (16)K1—O3xii2.936 (4)
Mg2—O2vii2.0367 (16)K1—O33.006 (4)
Mg2—O4iv2.1163 (15)K1—O2vi3.009 (4)
Mg2—O4i2.1163 (16)K1—O1i3.544 (4)
Mg2—O32.1302 (15)K1—O4i3.554 (4)
Mg2—O3iii2.1303 (15)K2—K2xi1.41 (5)
Na1—O1viii2.4430 (18)K2—O2xii2.71 (3)
Na1—O1v2.4430 (18)K2—O2vi2.74 (2)
Na1—O1ix2.4430 (18)K2—O32.77 (2)
Na1—O1i2.4430 (18)K2—O3xi2.84 (3)
Na1—O1x2.4430 (18)K2—O12.86 (2)
Na1—O12.4431 (18)K2—O3xii3.11 (3)
Na1—K1ix3.767 (3)K2—O1viii3.31 (2)
Na1—K1i3.767 (3)K2—O4i3.55 (3)
Na1—K1x3.767 (3)
O1—Mo—O2109.93 (8)O3—K2—O160.7 (5)
O1—Mo—O3109.63 (8)O3xi—K2—O178.0 (6)
O2—Mo—O3107.44 (7)O2xii—K2—O3xii57.8 (5)
O1—Mo—O4109.33 (7)O2vi—K2—O3xii81.0 (7)
O2—Mo—O4110.36 (6)O3—K2—O3xii140.6 (10)
O3—Mo—O4110.13 (6)O3xi—K2—O3xii117.5 (7)
O4i—Mg1—O4ii177.09 (8)O1—K2—O3xii122.9 (8)
O4i—Mg1—O4iii89.60 (8)O2xii—K2—O1viii76.8 (5)
O4ii—Mg1—O4iii92.54 (5)O2vi—K2—O1viii138.1 (10)
O4i—Mg1—O4iv85.39 (8)O3—K2—O1viii124.1 (8)
O4ii—Mg1—O4iv92.54 (5)O3xi—K2—O1viii75.1 (5)
O4iii—Mg1—O4iv92.54 (5)O1—K2—O1viii64.3 (4)
O4i—Mg1—O4v92.54 (5)O3xii—K2—O1viii67.9 (5)
O4ii—Mg1—O4v89.60 (8)O2xii—K2—O4i149.6 (10)
O4iii—Mg1—O4v85.39 (8)O2vi—K2—O4i54.8 (4)
O4iv—Mg1—O4v177.09 (8)O3—K2—O4i51.2 (4)
O4i—Mg1—O492.54 (5)O3xi—K2—O4i142.3 (9)
O4ii—Mg1—O485.39 (8)O1—K2—O4i66.0 (5)
O4iii—Mg1—O4177.09 (8)O3xii—K2—O4i92.2 (7)
O4iv—Mg1—O489.60 (8)O1viii—K2—O4i97.7 (6)
O4v—Mg1—O492.54 (5)Mo—O1—Na1139.63 (9)
O2vi—Mg2—O2vii93.08 (10)Mo—O1—K1101.00 (10)
O2vi—Mg2—O4iv174.99 (7)Na1—O1—K193.85 (9)
O2vii—Mg2—O4iv91.91 (5)Mo—O1—K293.6 (4)
O2vi—Mg2—O4i91.91 (5)Na1—O1—K2101.5 (5)
O2vii—Mg2—O4i174.99 (7)K1—O1—K28.0 (5)
O4iv—Mg2—O4i83.10 (8)Mo—O1—K1ix124.79 (12)
O2vi—Mg2—O392.96 (6)Na1—O1—K1ix89.19 (9)
O2vii—Mg2—O396.01 (6)K1—O1—K1ix98.24 (9)
O4iv—Mg2—O386.96 (6)K2—O1—K1ix100.4 (5)
O4i—Mg2—O383.28 (6)Mo—O1—K2ix123.3 (5)
O2vi—Mg2—O3iii96.01 (6)Na1—O1—K2ix90.2 (4)
O2vii—Mg2—O3iii92.96 (6)K1—O1—K2ix99.7 (5)
O4iv—Mg2—O3iii83.28 (6)K2—O1—K2ix101.7 (4)
O4i—Mg2—O3iii86.96 (6)K1ix—O1—K2ix1.8 (5)
O3—Mg2—O3iii166.95 (10)Mo—O1—K1v87.60 (8)
O1viii—Na1—O1v180.00 (8)Na1—O1—K1v75.48 (7)
O1viii—Na1—O1ix94.92 (5)K1—O1—K1v169.33 (10)
O1v—Na1—O1ix85.08 (5)K2—O1—K1v176.4 (6)
O1viii—Na1—O1i85.08 (5)K1ix—O1—K1v81.67 (8)
O1v—Na1—O1i94.92 (5)K2ix—O1—K1v80.5 (5)
O1ix—Na1—O1i180.00 (6)Mo—O2—Mg2xiii145.54 (10)
O1viii—Na1—O1x94.92 (5)Mo—O2—K1xiv99.77 (10)
O1v—Na1—O1x85.08 (5)Mg2xiii—O2—K1xiv102.15 (10)
O1ix—Na1—O1x94.92 (5)Mo—O2—K2xiv102.4 (6)
O1i—Na1—O1x85.08 (5)Mg2xiii—O2—K2xiv103.3 (6)
O1viii—Na1—O185.08 (5)K1xiv—O2—K2xiv8.8 (5)
O1v—Na1—O194.92 (5)Mo—O2—K2xiii115.2 (5)
O1ix—Na1—O185.08 (5)Mg2xiii—O2—K2xiii98.4 (5)
O1i—Na1—O194.92 (5)K1xiv—O2—K2xiii38.5 (5)
O1x—Na1—O1180.0K2xiv—O2—K2xiii29.9 (10)
O2xii—K1—O1141.42 (14)Mo—O2—K1xiii115.55 (10)
O2xii—K1—O3xi65.99 (9)Mg2xiii—O2—K1xiii98.71 (10)
O1—K1—O3xi80.35 (11)K1xiv—O2—K1xiii44.84 (12)
O2xii—K1—O1viii84.50 (11)K2xiv—O2—K1xiii36.1 (4)
O1—K1—O1viii72.07 (10)K2xiii—O2—K1xiii6.4 (6)
O3xi—K1—O1viii81.74 (10)Mo—O3—Mg2128.79 (8)
O2xii—K1—O3xii60.22 (10)Mo—O3—K295.9 (4)
O1—K1—O3xii136.60 (12)Mg2—O3—K295.3 (5)
O3xi—K1—O3xii122.93 (14)Mo—O3—K2xi115.6 (5)
O1viii—K1—O3xii75.80 (9)Mg2—O3—K2xi97.0 (5)
O2xii—K1—O3139.12 (12)K2—O3—K2xi29.0 (9)
O1—K1—O359.53 (9)Mo—O3—K1xi122.20 (10)
O3xi—K1—O396.16 (12)Mg2—O3—K1xi95.12 (10)
O1viii—K1—O3131.08 (14)K2—O3—K1xi37.2 (5)
O3xii—K1—O3137.41 (13)K2xi—O3—K1xi8.4 (5)
O2xii—K1—O2vi103.20 (12)Mo—O3—K1xiv91.40 (9)
O1—K1—O2vi113.40 (14)Mg2—O3—K1xiv121.77 (9)
O3xi—K1—O2vi131.68 (11)K2—O3—K1xiv123.9 (6)
O1viii—K1—O2vi146.17 (13)K2xi—O3—K1xiv100.2 (5)
O3xii—K1—O2vi79.73 (10)K1xi—O3—K1xiv94.35 (13)
O3—K1—O2vi60.33 (7)Mo—O3—K189.81 (9)
O2xii—K1—O1i125.09 (13)Mg2—O3—K196.67 (9)
O1—K1—O1i68.83 (10)K2—O3—K16.9 (5)
O3xi—K1—O1i136.77 (11)K2xi—O3—K135.6 (4)
O1viii—K1—O1i60.70 (8)K1xi—O3—K143.95 (11)
O3xii—K1—O1i70.28 (8)K1xiv—O3—K1127.51 (11)
O3—K1—O1i93.58 (10)Mo—O3—K2xiv88.7 (5)
O2vi—K1—O1i89.25 (9)Mg2—O3—K2xiv119.1 (4)
O2xii—K1—O4i150.63 (14)K2—O3—K2xiv130.9 (7)
O1—K1—O4i67.30 (9)K2xi—O3—K2xiv107.4 (9)
O3xi—K1—O4i141.66 (15)K1xi—O3—K2xiv101.5 (4)
O1viii—K1—O4i105.95 (10)K1xiv—O3—K2xiv7.2 (4)
O3xii—K1—O4i95.14 (10)K1—O3—K2xiv134.2 (3)
O3—K1—O4i50.10 (7)Mo—O4—Mg1120.62 (7)
O2vi—K1—O4i53.34 (7)Mo—O4—Mg2v135.84 (7)
O1i—K1—O4i47.90 (6)Mg1—O4—Mg2v95.76 (6)
O2xii—K2—O2vi110.2 (8)Mo—O4—K2v91.2 (4)
O2xii—K2—O3153.9 (10)Mg1—O4—K2v136.5 (4)
O2vi—K2—O366.4 (5)Mg2v—O4—K2v75.4 (3)
O2xii—K2—O3xi65.9 (6)Mo—O4—K1v86.14 (7)
O2vi—K2—O3xi146.5 (9)Mg1—O4—K1v137.12 (9)
O3—K2—O3xi101.9 (9)Mg2v—O4—K1v82.16 (6)
O2xii—K2—O1132.4 (8)K2v—O4—K1v6.7 (4)
O2vi—K2—O1117.0 (9)
Symmetry codes: (i) y, xy, z; (ii) x, x+y, z+1/2; (iii) y, x, z+1/2; (iv) xy, y, z+1/2; (v) x+y, x, z; (vi) y+1/3, x+y+2/3, z+2/3; (vii) x+y+2/3, y+1/3, z1/6; (viii) xy, x, z+1; (ix) y, x+y, z+1; (x) x, y, z+1; (xi) x+2/3, x+y+1/3, z+5/6; (xii) y+1/3, x+2/3, z+1/6; (xiii) xy+1/3, x1/3, z+2/3; (xiv) y+2/3, x+1/3, z1/6.
(IV) top
Crystal data top
K2.88Mg4Na1.12·6(MoO4)Dx = 3.298 Mg m3
Mr = 1195.26Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 11402 reflections
a = 14.4673 (5) Åθ = 2.6–33.3°
c = 19.9186 (9) ŵ = 3.76 mm1
V = 3610.5 (3) Å3T = 296 K
Z = 6Fragment, colourless
F(000) = 3354.30.06 × 0.06 × 0.05 mm
Data collection top
Bruker-Nonius X8 APEX CCD
diffractometer
1326 reflections with I > 2σ(I)
\ f scans, frame data integrationRint = 0.048
Absorption correction: multi-scan
SADABS (Bruker, 2005)
θmax = 33.3°, θmin = 2.6°
Tmin = 0.798, Tmax = 0.829h = 1722
11402 measured reflectionsk = 2221
1561 independent reflectionsl = 3016
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.021 w = 1/[σ2(Fo2) + (0.0169P)2 + 1.2304P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.044(Δ/σ)max = 0.005
S = 1.04Δρmax = 0.71 e Å3
1552 reflectionsΔρmin = 0.71 e Å3
81 parametersExtinction correction: SHELXL-2017/1 (Sheldrick 2017), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
7 restraintsExtinction coefficient: 0.000166 (19)
Special details top

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Mo0.18616 (2)0.00683 (2)0.35501 (2)0.01160 (6)
Mg10.0000000.0000000.2500000.0090 (3)
Mg20.21506 (7)0.21506 (7)0.2500000.01157 (18)
Na10.0000000.0000000.5000000.0298 (5)
K10.2546 (4)0.2392 (5)0.4430 (4)0.0216 (11)0.2781 (16)
K20.2622 (8)0.2446 (9)0.4397 (5)0.051 (3)0.2021 (16)
Na20.247 (6)0.214 (5)0.469 (3)0.030 (15)*0.0198 (15)
O10.15319 (13)0.02320 (15)0.43567 (8)0.0310 (4)
O20.26296 (12)0.05624 (12)0.35715 (8)0.0225 (3)
O30.26435 (12)0.13271 (12)0.31727 (7)0.0201 (3)
O40.06579 (11)0.07220 (11)0.30708 (7)0.0135 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mo0.01121 (9)0.01207 (9)0.01189 (8)0.00610 (7)0.00308 (5)0.00137 (5)
Mg10.0076 (4)0.0076 (4)0.0118 (7)0.0038 (2)0.0000.000
Mg20.0093 (3)0.0093 (3)0.0146 (4)0.0035 (3)0.00073 (16)0.00073 (16)
Na10.0334 (8)0.0334 (8)0.0224 (11)0.0167 (4)0.0000.000
K10.0286 (16)0.0147 (19)0.022 (2)0.0116 (13)0.0013 (15)0.0043 (15)
K20.094 (6)0.029 (4)0.037 (4)0.035 (4)0.041 (4)0.014 (3)
O10.0296 (9)0.0418 (11)0.0172 (7)0.0145 (9)0.0005 (6)0.0079 (7)
O20.0202 (8)0.0195 (8)0.0322 (9)0.0133 (6)0.0077 (6)0.0002 (6)
O30.0143 (7)0.0159 (7)0.0282 (8)0.0062 (6)0.0028 (6)0.0040 (6)
O40.0136 (7)0.0113 (6)0.0164 (6)0.0068 (5)0.0040 (5)0.0008 (5)
Geometric parameters (Å, º) top
Mo—O11.7255 (15)K1—O2xii2.724 (7)
Mo—O21.7558 (15)K1—O3xi2.853 (7)
Mo—O31.7611 (15)K1—O1viii2.897 (6)
Mo—O41.8057 (13)K1—O3xii2.947 (6)
Mg1—O42.0697 (13)K1—O32.980 (6)
Mg1—O4i2.0697 (13)K1—O2vi3.020 (8)
Mg1—O4ii2.0697 (13)K1—O1ii3.510 (6)
Mg1—O4iii2.0697 (13)K1—O4ii3.546 (7)
Mg1—O4iv2.0697 (13)K2—Na20.70 (7)
Mg1—O4v2.0697 (13)K2—K2xi2.00 (2)
Mg2—O2vi2.0399 (16)K2—Na2xi2.50 (7)
Mg2—O2vii2.0399 (16)K2—O2xii2.695 (11)
Mg2—O4iii2.1221 (15)K2—O12.775 (11)
Mg2—O4ii2.1221 (15)K2—O3xi2.840 (11)
Mg2—O3iv2.1384 (14)K2—O32.935 (10)
Mg2—O32.1384 (14)K2—O2vi2.943 (11)
Na1—O1viii2.4337 (17)K2—O3xii2.969 (10)
Na1—O1v2.4337 (17)K2—O1viii3.007 (11)
Na1—O1ix2.4337 (17)K2—O4ii3.559 (11)
Na1—O1ii2.4337 (17)K2—O1ii3.599 (11)
Na1—O1x2.4337 (17)Na2—O1viii2.40 (7)
Na1—O12.4337 (17)Na2—O12.48 (6)
K1—K20.118 (16)Na2—O3xi2.52 (7)
K1—Na20.61 (7)Na2—O2xii2.70 (6)
K1—K2xi2.120 (7)Na2—Na2xi3.01 (15)
K1—K1xi2.235 (10)Na2—O3xii3.13 (6)
K1—Na2xi2.61 (7)Na2—O33.30 (7)
K1—O12.711 (7)Na2—O1ii3.53 (7)
O1—Mo—O2109.81 (8)Na2—O1—K1v160.6 (17)
O1—Mo—O3109.53 (8)K1—O1—K1v169.41 (18)
O2—Mo—O3107.55 (7)K2—O1—K1v171.4 (3)
O1—Mo—O4109.51 (7)K1ix—O1—K1v82.19 (16)
O2—Mo—O4110.14 (6)K2ix—O1—K1v82.1 (3)
O3—Mo—O4110.28 (7)Mo—O1—Na2v97.7 (12)
O4—Mg1—O4i85.45 (7)Na2ix—O1—Na2v71.5 (14)
O4—Mg1—O4ii92.71 (5)Na1—O1—Na2v67.1 (11)
O4i—Mg1—O4ii177.43 (8)Na2—O1—Na2v151 (3)
O4—Mg1—O4iii89.17 (8)K1—O1—Na2v160.1 (12)
O4i—Mg1—O4iii92.71 (5)K2—O1—Na2v162.2 (12)
O4ii—Mg1—O4iii85.46 (7)K1ix—O1—Na2v78.0 (10)
O4—Mg1—O4iv177.43 (8)K2ix—O1—Na2v78.1 (10)
O4i—Mg1—O4iv92.71 (5)K1v—O1—Na2v9.9 (11)
O4ii—Mg1—O4iv89.17 (8)Mo—O1—K2v86.65 (19)
O4iii—Mg1—O4iv92.71 (5)Na2ix—O1—K2v75.7 (16)
O4—Mg1—O4v92.71 (5)Na1—O1—K2v76.97 (19)
O4i—Mg1—O4v89.17 (8)Na2—O1—K2v161.8 (16)
O4ii—Mg1—O4v92.71 (5)K1—O1—K2v170.4 (2)
O4iii—Mg1—O4v177.43 (8)K2—O1—K2v172.4 (3)
O4iv—Mg1—O4v85.46 (7)K1ix—O1—K2v82.8 (2)
O2vi—Mg2—O2vii92.81 (10)K2ix—O1—K2v82.7 (2)
O2vi—Mg2—O4iii175.01 (7)K1v—O1—K2v1.2 (3)
O2vii—Mg2—O4iii92.16 (6)Na2v—O1—K2v11.2 (12)
O2vi—Mg2—O4ii92.16 (6)Mo—O1—K2xi77.64 (17)
O2vii—Mg2—O4ii175.01 (7)Na2ix—O1—K2xi103.1 (15)
O4iii—Mg2—O4ii82.87 (8)Na1—O1—K2xi122.14 (18)
O2vi—Mg2—O3iv96.19 (6)Na2—O1—K2xi35.7 (16)
O2vii—Mg2—O3iv92.65 (6)K1—O1—K2xi28.64 (17)
O4iii—Mg2—O3iv83.11 (6)K2—O1—K2xi26.6 (3)
O4ii—Mg2—O3iv87.27 (6)K1ix—O1—K2xi97.2 (2)
O2vi—Mg2—O392.65 (6)K2ix—O1—K2xi97.0 (2)
O2vii—Mg2—O396.19 (6)K1v—O1—K2xi161.9 (3)
O4iii—Mg2—O387.27 (6)Na2v—O1—K2xi169.9 (10)
O4ii—Mg2—O383.11 (6)K2v—O1—K2xi160.87 (7)
O3iv—Mg2—O3167.16 (9)Mo—O2—Mg2xiii145.84 (10)
O1viii—Na1—O1v180.00 (8)Mo—O2—K2xiv100.1 (2)
O1viii—Na1—O1ix94.83 (5)Mg2xiii—O2—K2xiv102.6 (2)
O1v—Na1—O1ix85.17 (5)Mo—O2—Na2xiv104.9 (14)
O1viii—Na1—O1ii85.17 (5)Mg2xiii—O2—Na2xiv91.8 (14)
O1v—Na1—O1ii94.83 (5)K2xiv—O2—Na2xiv14.9 (15)
O1ix—Na1—O1ii180.0Mo—O2—K1xiv99.57 (15)
O1viii—Na1—O1x94.83 (5)Mg2xiii—O2—K1xiv102.08 (17)
O1v—Na1—O1x85.17 (5)K2xiv—O2—K1xiv2.4 (3)
O1ix—Na1—O1x94.83 (5)Na2xiv—O2—K1xiv12.9 (15)
O1ii—Na1—O1x85.17 (5)Mo—O2—K2xiii115.2 (2)
O1viii—Na1—O185.17 (5)Mg2xiii—O2—K2xiii98.6 (2)
O1v—Na1—O194.83 (5)K2xiv—O2—K2xiii41.4 (4)
O1ix—Na1—O185.17 (5)Na2xiv—O2—K2xiii52.4 (15)
O1ii—Na1—O194.83 (5)K1xiv—O2—K2xiii43.72 (17)
O1x—Na1—O1180.0Mo—O2—K1xiii115.83 (14)
O1—K1—O2xii141.0 (3)Mg2xiii—O2—K1xiii98.15 (13)
O1—K1—O3xi80.4 (2)K2xiv—O2—K1xiii43.09 (19)
O2xii—K1—O3xi65.59 (16)Na2xiv—O2—K1xiii54.0 (15)
O1—K1—O1viii71.84 (17)K1xiv—O2—K1xiii45.44 (18)
O2xii—K1—O1viii84.41 (19)K2xiii—O2—K1xiii1.7 (3)
O3xi—K1—O1viii81.8 (2)Mo—O2—Na2ix76.6 (11)
O1—K1—O3xii136.93 (19)Mg2xiii—O2—Na2ix69.2 (11)
O2xii—K1—O3xii59.87 (13)K2xiv—O2—Na2ix132.7 (10)
O3xi—K1—O3xii122.3 (2)Na2xiv—O2—Na2ix119.4 (16)
O1viii—K1—O3xii75.89 (13)K1xiv—O2—Na2ix130.2 (10)
O1—K1—O359.82 (13)K2xiii—O2—Na2ix166.2 (11)
O2xii—K1—O3138.54 (19)K1xiii—O2—Na2ix166.4 (11)
O3xi—K1—O395.56 (16)Mo—O2—Na2xiii116.5 (9)
O1viii—K1—O3131.2 (2)Mg2xiii—O2—Na2xiii97.5 (9)
O3xii—K1—O3138.3 (3)K2xiv—O2—Na2xiii43.6 (11)
O1—K1—O2vi114.0 (2)Na2xiv—O2—Na2xiii54 (2)
O2xii—K1—O2vi102.9 (2)K1xiv—O2—Na2xiii45.9 (11)
O3xi—K1—O2vi130.61 (18)K2xiii—O2—Na2xiii2.4 (11)
O1viii—K1—O2vi147.1 (2)K1xiii—O2—Na2xiii0.8 (10)
O3xii—K1—O2vi80.27 (19)Na2ix—O2—Na2xiii165.9 (13)
O3—K1—O2vi60.49 (14)Mo—O2—K1v73.12 (11)
O1—K1—O1ii68.98 (15)Mg2xiii—O2—K1v88.90 (10)
O2xii—K1—O1ii125.25 (17)K2xiv—O2—K1v166.3 (2)
O3xi—K1—O1ii137.2 (2)Na2xiv—O2—K1v177.2 (15)
O1viii—K1—O1ii60.99 (11)K1xiv—O2—K1v167.9 (2)
O3xii—K1—O1ii70.72 (12)K2xiii—O2—K1v130.2 (2)
O3—K1—O1ii94.13 (18)K1xiii—O2—K1v128.55 (12)
O2vi—K1—O1ii89.95 (19)Na2ix—O2—K1v58.4 (10)
O1—K1—O4ii67.73 (15)Na2xiii—O2—K1v128.2 (11)
O2xii—K1—O4ii150.7 (3)Mo—O2—K2v74.13 (17)
O3xi—K1—O4ii141.7 (2)Mg2xiii—O2—K2v88.70 (16)
O1viii—K1—O4ii106.56 (17)K2xiv—O2—K2v165.4 (3)
O3xii—K1—O4ii95.82 (19)Na2xiv—O2—K2v178.9 (15)
O3—K1—O4ii50.42 (11)K1xiv—O2—K2v167.28 (19)
O2vi—K1—O4ii53.62 (13)K2xiii—O2—K2v128.55 (18)
O1ii—K1—O4ii48.25 (9)K1xiii—O2—K2v126.9 (2)
O2xii—K2—O1139.0 (4)Na2ix—O2—K2v59.9 (10)
O2xii—K2—O3xi66.1 (2)Na2xiii—O2—K2v126.6 (12)
O1—K2—O3xi79.6 (3)K1v—O2—K2v1.7 (2)
O2xii—K2—O3142.8 (4)Mo—O2—K1ix80.01 (9)
O1—K2—O359.8 (2)Mg2xiii—O2—K1ix65.92 (8)
O3xi—K2—O396.8 (3)K2xiv—O2—K1ix128.0 (3)
O2xii—K2—O2vi105.6 (4)Na2xiv—O2—K1ix114.3 (15)
O1—K2—O2vi114.5 (4)K1xiv—O2—K1ix125.56 (12)
O3xi—K2—O2vi134.6 (4)K2xiii—O2—K1ix160.8 (3)
O3—K2—O2vi61.9 (2)K1xiii—O2—K1ix161.32 (10)
O2xii—K2—O3xii59.9 (2)Na2ix—O2—K1ix5.6 (10)
O1—K2—O3xii132.9 (4)Na2xiii—O2—K1ix160.9 (10)
O3xi—K2—O3xii122.0 (4)K1v—O2—K1ix63.57 (14)
O3—K2—O3xii139.5 (4)K2v—O2—K1ix64.98 (17)
O2vi—K2—O3xii81.2 (3)Mo—O3—Mg2128.53 (8)
O2xii—K2—O1viii82.8 (3)Mo—O3—Na2xi129.7 (15)
O1—K2—O1viii69.3 (3)Mg2—O3—Na2xi94.7 (14)
O3xi—K2—O1viii80.1 (3)Mo—O3—K2xi121.7 (2)
O3—K2—O1viii128.6 (4)Mg2—O3—K2xi95.6 (2)
O2vi—K2—O1viii145.0 (4)Na2xi—O3—K2xi13.3 (17)
O3xii—K2—O1viii73.9 (2)Mo—O3—K1xi123.08 (13)
O2xii—K2—O4ii151.8 (4)Mg2—O3—K1xi95.64 (14)
O1—K2—O4ii67.0 (2)Na2xi—O3—K1xi11.0 (16)
O3xi—K2—O4ii141.6 (4)K2xi—O3—K1xi2.4 (3)
O3—K2—O4ii50.48 (17)Mo—O3—K292.1 (2)
O2vi—K2—O4ii53.91 (18)Mg2—O3—K296.6 (2)
O3xii—K2—O4ii95.2 (3)Na2xi—O3—K253.9 (17)
O1viii—K2—O4ii103.8 (3)K2xi—O3—K240.6 (4)
O2xii—K2—O1ii123.0 (3)K1xi—O3—K242.95 (17)
O1—K2—O1ii67.0 (2)Mo—O3—K1xiv91.70 (14)
O3xi—K2—O1ii133.7 (4)Mg2—O3—K1xiv120.57 (16)
O3—K2—O1ii93.1 (3)Na2xi—O3—K1xiv84.9 (16)
O2vi—K2—O1ii89.5 (3)K2xi—O3—K1xiv95.86 (15)
O3xii—K2—O1ii69.2 (2)K1xi—O3—K1xiv93.8 (2)
O1viii—K2—O1ii59.00 (19)K2—O3—K1xiv127.3 (2)
O4ii—K2—O1ii47.51 (14)Mo—O3—K2xiv90.5 (2)
O1viii—Na2—O185 (2)Mg2—O3—K2xiv120.1 (2)
O1viii—Na2—O3xi100 (2)Na2xi—O3—K2xiv87.1 (15)
O1—Na2—O3xi92 (2)K2xi—O3—K2xiv98.1 (4)
O1viii—Na2—O2xii95 (2)K1xi—O3—K2xiv96.08 (15)
O1—Na2—O2xii162 (3)K2—O3—K2xiv129.3 (3)
O3xi—Na2—O2xii70.6 (17)K1xiv—O3—K2xiv2.3 (3)
O1viii—Na2—O3xii80.0 (18)Mo—O3—K190.21 (14)
O1—Na2—O3xii139 (3)Mg2—O3—K197.09 (16)
O3xi—Na2—O3xii128 (2)Na2xi—O3—K156.0 (17)
O2xii—Na2—O3xii57.7 (11)K2xi—O3—K142.64 (17)
O1viii—Na2—O3139 (2)K1xi—O3—K145.0 (2)
O1—Na2—O356.9 (12)K2—O3—K12.1 (3)
O3xi—Na2—O395 (2)K1xiv—O3—K1128.3 (2)
O2xii—Na2—O3125 (3)K2xiv—O3—K1130.3 (2)
O3xii—Na2—O3119 (2)Mo—O3—Na2xiv89.8 (12)
O1viii—Na2—O1ii64.3 (16)Mg2—O3—Na2xiv128.9 (12)
O1—Na2—O1ii70.8 (16)Na2xi—O3—Na2xiv78 (3)
O3xi—Na2—O1ii157 (3)K2xi—O3—Na2xiv87.6 (13)
O2xii—Na2—O1ii125 (2)K1xi—O3—Na2xiv85.8 (14)
O3xii—Na2—O1ii68.6 (13)K2—O3—Na2xiv116.6 (13)
O3—Na2—O1ii88.5 (15)K1xiv—O3—Na2xiv11.0 (13)
O1viii—Na2—O2viii52.4 (13)K2xiv—O3—Na2xiv12.8 (14)
O1—Na2—O2viii115 (2)K1—O3—Na2xiv117.5 (14)
O3xi—Na2—O2viii58.2 (13)Mo—O3—Na281.6 (12)
O2xii—Na2—O2viii53.9 (11)Mg2—O3—Na2105.6 (11)
O3xii—Na2—O2viii84.5 (14)Na2xi—O3—Na260 (3)
O3—Na2—O2viii153 (2)K2xi—O3—Na247.4 (12)
O1ii—Na2—O2viii114.4 (19)K1xi—O3—Na249.6 (12)
Mo—O1—Na2ix121.1 (16)K2—O3—Na211.0 (12)
Mo—O1—Na1140.03 (9)K1xiv—O3—Na2124.2 (12)
Na2ix—O1—Na190.0 (15)K2xiv—O3—Na2125.9 (13)
Mo—O1—Na2111.5 (17)K1—O3—Na29.5 (11)
Na2ix—O1—Na294.3 (9)Na2xiv—O3—Na2113.2 (19)
Na1—O1—Na288.0 (16)Mo—O3—K2xiii73.50 (16)
Mo—O1—K1100.42 (15)Mg2—O3—K2xiii115.34 (15)
Na2ix—O1—K1105.6 (16)Na2xi—O3—K2xiii113.9 (15)
Na1—O1—K193.50 (11)K2xi—O3—K2xiii124.5 (3)
Na2—O1—K112.5 (16)K1xi—O3—K2xiii122.56 (18)
Mo—O1—K298.5 (2)K2—O3—K2xiii147.4 (2)
Na2ix—O1—K2105.9 (15)K1xiv—O3—K2xiii28.96 (17)
Na1—O1—K295.6 (2)K2xiv—O3—K2xiii26.7 (3)
Na2—O1—K213.9 (16)K1—O3—K2xiii147.3 (2)
K1—O1—K22.1 (3)Na2xiv—O3—K2xiii37.0 (13)
Mo—O1—K1ix125.13 (16)Na2—O3—K2xiii139.1 (11)
Na2ix—O1—K1ix7.6 (16)Mo—O4—Mg1120.81 (7)
Na1—O1—K1ix89.05 (14)Mo—O4—Mg2v136.13 (7)
Na2—O1—K1ix86.7 (16)Mg1—O4—Mg2v95.84 (6)
K1—O1—K1ix98.06 (12)Mo—O4—K1v85.60 (9)
K2—O1—K1ix98.5 (3)Mg1—O4—K1v136.90 (12)
Mo—O1—K2ix124.3 (2)Mg2v—O4—K1v82.19 (10)
Na2ix—O1—K2ix7.3 (16)Mo—O4—K2v86.78 (17)
Na1—O1—K2ix89.9 (2)Mg1—O4—K2v137.17 (19)
Na2—O1—K2ix87.0 (16)Mg2v—O4—K2v80.31 (17)
K1—O1—K2ix98.3 (3)K1v—O4—K2v1.9 (3)
K2—O1—K2ix98.68 (19)Mo—O4—Na2v84.1 (10)
K1ix—O1—K2ix0.9 (3)Mg1—O4—Na2v132.0 (9)
Mo—O1—K1v87.90 (14)Mg2v—O4—Na2v88.4 (11)
Na2ix—O1—K1v75.1 (15)K1v—O4—Na2v7.6 (10)
Na1—O1—K1v75.91 (13)K2v—O4—Na2v9.4 (11)
Symmetry codes: (i) x, x+y, z+1/2; (ii) y, xy, z; (iii) xy, y, z+1/2; (iv) y, x, z+1/2; (v) x+y, x, z; (vi) y+1/3, x+y+2/3, z+2/3; (vii) x+y+2/3, y+1/3, z1/6; (viii) xy, x, z+1; (ix) y, x+y, z+1; (x) x, y, z+1; (xi) x+2/3, x+y+1/3, z+5/6; (xii) y+1/3, x+2/3, z+1/6; (xiii) xy+1/3, x1/3, z+2/3; (xiv) y+2/3, x+1/3, z1/6.
(V) top
Crystal data top
K3NaCo4·6(MoO4)Dx = 3.703 Mg m3
Mr = 1335.65Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 8646 reflections
a = 14.4638 (1) Åθ = 2.6–33.1°
c = 19.8369 (3) ŵ = 6.36 mm1
V = 3593.93 (9) Å3T = 296 K
Z = 6Fragment, blue
F(000) = 37200.05 × 0.05 × 0.03 mm
Data collection top
Bruker-Nonius X8 APEX CCD
diffractometer
1436 reflections with I > 2σ(I)
\ f scans, frame data integrationRint = 0.022
Absorption correction: multi-scan
SADABS (Bruker, 2005)
θmax = 33.1°, θmin = 2.6°
Tmin = 0.735, Tmax = 0.826h = 1722
8646 measured reflectionsk = 2218
1535 independent reflectionsl = 3022
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.015 w = 1/[σ2(Fo2) + (0.0161P)2 + 6.9365P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.037(Δ/σ)max = 0.004
S = 1.14Δρmax = 0.53 e Å3
1534 reflectionsΔρmin = 0.87 e Å3
76 parametersExtinction correction: SHELXL-2017/1 (Sheldrick 2017), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
7 restraintsExtinction coefficient: 0.00012 (2)
Special details top

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Mo0.18671 (2)0.00704 (2)0.35520 (2)0.01455 (5)
Co10.0000000.0000000.2500000.01144 (8)
Co20.21416 (2)0.21416 (2)0.2500000.01388 (6)
Na10.0000000.0000000.5000000.0319 (4)
K10.2573 (2)0.2410 (2)0.44224 (17)0.0270 (5)0.3501 (14)
K20.2682 (9)0.2456 (8)0.4377 (5)0.069 (3)0.1499 (14)
O10.15458 (12)0.02484 (12)0.43627 (7)0.0335 (3)
O20.26342 (10)0.05645 (9)0.35690 (7)0.0246 (2)
O30.26572 (9)0.13284 (9)0.31640 (7)0.0233 (2)
O40.06507 (9)0.07307 (9)0.30783 (6)0.01682 (19)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mo0.01466 (6)0.01531 (6)0.01417 (7)0.00786 (4)0.00291 (4)0.00140 (4)
Co10.01007 (11)0.01007 (11)0.0142 (2)0.00504 (5)0.0000.000
Co20.01178 (9)0.01178 (9)0.01683 (13)0.00494 (9)0.00090 (5)0.00090 (5)
Na10.0359 (6)0.0359 (6)0.0239 (9)0.0179 (3)0.0000.000
K10.0370 (8)0.0188 (9)0.0253 (10)0.0141 (6)0.0053 (7)0.0042 (7)
K20.141 (8)0.042 (4)0.044 (4)0.060 (5)0.059 (4)0.026 (3)
O10.0341 (7)0.0440 (8)0.0189 (6)0.0170 (6)0.0003 (5)0.0077 (5)
O20.0226 (5)0.0209 (5)0.0336 (7)0.0134 (4)0.0075 (5)0.0013 (5)
O30.0177 (5)0.0185 (5)0.0318 (6)0.0075 (4)0.0042 (4)0.0034 (4)
O40.0166 (4)0.0148 (4)0.0198 (5)0.0084 (4)0.0048 (4)0.0013 (4)
Geometric parameters (Å, º) top
Mo—O11.7288 (14)K1—K1xi2.157 (5)
Mo—O21.7589 (12)K1—O2xii2.699 (4)
Mo—O31.7691 (12)K1—O12.712 (3)
Mo—O41.8117 (11)K1—O3xi2.841 (4)
Co1—O4i2.0769 (10)K1—O1ix2.910 (3)
Co1—O4ii2.0769 (10)K1—O3xii2.930 (3)
Co1—O4iii2.0769 (10)K1—O32.981 (4)
Co1—O4iv2.0769 (10)K1—O2vi2.982 (4)
Co1—O4v2.0769 (10)K1—O4i3.530 (4)
Co1—O42.0770 (10)K1—O1i3.563 (3)
Co2—O2vi2.0417 (12)K1—O2i3.990 (4)
Co2—O2vii2.0417 (12)K1—O2ix4.063 (4)
Co2—O4iv2.1085 (11)K2—K2xi1.83 (2)
Co2—O4i2.1085 (11)K2—O2xii2.680 (9)
Co2—O32.1335 (12)K2—O12.765 (10)
Co2—O3iii2.1335 (12)K2—O3xi2.799 (10)
Na1—O1viii2.4336 (15)K2—O32.897 (10)
Na1—O1i2.4336 (15)K2—O2vi2.902 (10)
Na1—O1ix2.4336 (15)K2—O3xii3.003 (10)
Na1—O1v2.4336 (15)K2—O1ix3.059 (11)
Na1—O12.4336 (15)K2—O4i3.554 (9)
Na1—O1x2.4337 (15)K2—O1i3.698 (11)
K1—K20.163 (14)K2—O1xi3.950 (11)
K1—K2xi1.995 (10)
O1—Mo—O2110.28 (7)O3xi—K2—O1xi46.32 (17)
O1—Mo—O3109.57 (7)O3—K2—O1xi60.3 (2)
O2—Mo—O3107.08 (6)O2vi—K2—O1xi94.7 (3)
O1—Mo—O4109.28 (6)O3xii—K2—O1xi145.7 (3)
O2—Mo—O4109.90 (5)O1ix—K2—O1xi122.9 (3)
O3—Mo—O4110.70 (6)O4i—K2—O1xi111.1 (3)
O4i—Co1—O4ii176.81 (6)O1i—K2—O1xi146.9 (3)
O4i—Co1—O4iii89.92 (6)Mo—O1—Na1139.19 (8)
O4ii—Co1—O4iii92.43 (4)Mo—O1—K1100.32 (9)
O4i—Co1—O4iv85.31 (6)Na1—O1—K194.65 (7)
O4ii—Co1—O4iv92.43 (4)Mo—O1—K297.6 (2)
O4iii—Co1—O4iv92.43 (4)Na1—O1—K297.9 (2)
O4i—Co1—O4v92.43 (4)K1—O1—K23.2 (3)
O4ii—Co1—O4v89.92 (6)Mo—O1—K1viii124.39 (10)
O4iii—Co1—O4v85.31 (6)Na1—O1—K1viii89.81 (8)
O4iv—Co1—O4v176.81 (6)K1—O1—K1viii98.96 (7)
O4i—Co1—O492.43 (4)K2—O1—K1viii99.2 (2)
O4ii—Co1—O485.31 (6)Mo—O1—K2viii123.3 (2)
O4iii—Co1—O4176.81 (6)Na1—O1—K2viii90.52 (18)
O4iv—Co1—O489.92 (6)K1—O1—K2viii100.0 (2)
O4v—Co1—O492.43 (4)K2—O1—K2viii100.17 (18)
O2vi—Co2—O2vii92.42 (7)K1viii—O1—K2viii1.3 (2)
O2vi—Co2—O4iv175.60 (5)Mo—O1—K1v86.81 (8)
O2vii—Co2—O4iv91.92 (5)Na1—O1—K1v75.74 (7)
O2vi—Co2—O4i91.92 (5)K1—O1—K1v170.36 (9)
O2vii—Co2—O4i175.60 (5)K2—O1—K1v173.5 (3)
O4iv—Co2—O4i83.74 (6)K1viii—O1—K1v82.02 (8)
O2vi—Co2—O392.63 (5)K2viii—O1—K1v81.1 (2)
O2vii—Co2—O395.38 (5)Mo—O1—K2v85.44 (16)
O4iv—Co2—O387.66 (5)Na1—O1—K2v76.56 (16)
O4i—Co2—O383.71 (5)K1—O1—K2v170.98 (19)
O2vi—Co2—O3iii95.38 (5)K2—O1—K2v174.0 (3)
O2vii—Co2—O3iii92.63 (5)K1viii—O1—K2v83.20 (18)
O4iv—Co2—O3iii83.71 (5)K2viii—O1—K2v82.28 (18)
O4i—Co2—O3iii87.66 (5)K1v—O1—K2v1.5 (2)
O3—Co2—O3iii168.42 (6)Mo—O1—K2xi78.47 (15)
O1viii—Na1—O1i180.00 (6)Na1—O1—K2xi122.30 (16)
O1viii—Na1—O1ix95.47 (5)K1—O1—K2xi27.65 (16)
O1i—Na1—O1ix84.53 (5)K2—O1—K2xi24.4 (3)
O1viii—Na1—O1v84.53 (5)K1viii—O1—K2xi97.64 (17)
O1i—Na1—O1v95.47 (5)K2viii—O1—K2xi98.20 (18)
O1ix—Na1—O1v180.00 (7)K1v—O1—K2xi161.9 (2)
O1viii—Na1—O184.54 (5)K2v—O1—K2xi161.06 (7)
O1i—Na1—O195.46 (5)Mo—O1—K1xi77.25 (7)
O1ix—Na1—O184.54 (5)Na1—O1—K1xi123.63 (7)
O1v—Na1—O195.46 (5)K1—O1—K1xi28.99 (7)
O1viii—Na1—O1x95.47 (5)K2—O1—K1xi25.8 (2)
O1i—Na1—O1x84.53 (5)K1viii—O1—K1xi97.80 (8)
O1ix—Na1—O1x95.46 (5)K2viii—O1—K1xi98.3 (2)
O1v—Na1—O1x84.54 (5)K1v—O1—K1xi160.60 (5)
O1—Na1—O1x180.0K2v—O1—K1xi159.7 (2)
O2xii—K1—O3xi66.01 (8)K2xi—O1—K1xi1.36 (19)
O1—K1—O3xi79.65 (10)Mo—O2—Co2xiii145.58 (8)
O2xii—K1—O1ix84.29 (10)Mo—O2—K2xiv101.4 (2)
O1—K1—O1ix71.12 (8)Co2xiii—O2—K2xiv102.3 (2)
O3xi—K1—O1ix81.46 (10)Mo—O2—K1xiv99.75 (9)
O2xii—K1—O3xii60.38 (8)Co2xiii—O2—K1xiv102.39 (9)
O1—K1—O3xii135.56 (10)K2xiv—O2—K1xiv3.5 (3)
O3xi—K1—O3xii122.79 (12)Mo—O2—K2xiii115.52 (19)
O1ix—K1—O3xii75.06 (8)Co2xiii—O2—K2xiii98.45 (19)
O2xii—K1—O3139.43 (10)K2xiv—O2—K2xiii38.1 (5)
O1—K1—O360.05 (8)K1xiv—O2—K2xiii41.5 (2)
O3xi—K1—O395.88 (10)Mo—O2—K1xiii115.81 (9)
O1ix—K1—O3130.65 (11)Co2xiii—O2—K1xiii98.40 (8)
O3xii—K1—O3138.34 (14)K2xiv—O2—K1xiii40.8 (2)
O2xii—K1—O2vi103.70 (11)K1xiv—O2—K1xiii44.29 (10)
O1—K1—O2vi114.19 (12)K2xiii—O2—K1xiii2.8 (3)
O3xi—K1—O2vi132.37 (9)Mo—O2—K1v73.37 (6)
O1ix—K1—O2vi145.81 (12)Co2xiii—O2—K1v88.69 (6)
O3xii—K1—O2vi80.25 (9)K2xiv—O2—K1v165.4 (2)
O3—K1—O2vi60.86 (7)K1xiv—O2—K1v167.33 (11)
O2xii—K1—O4i151.19 (13)K2xiii—O2—K1v131.4 (2)
O1—K1—O4i67.53 (8)K1xiii—O2—K1v128.65 (6)
O3xi—K1—O4i141.50 (12)Mo—O2—K2v74.33 (15)
O1ix—K1—O4i105.15 (8)Co2xiii—O2—K2v88.84 (14)
O3xii—K1—O4i95.21 (9)K2xiv—O2—K2v163.8 (3)
O3—K1—O4i50.68 (6)K1xiv—O2—K2v166.04 (14)
O2vi—K1—O4i53.74 (6)K2xiii—O2—K2v129.25 (16)
O2xii—K1—O1i124.58 (10)K1xiii—O2—K2v126.50 (18)
O1—K1—O1i68.52 (8)K1v—O2—K2v2.17 (19)
O3xi—K1—O1i135.61 (10)Mo—O2—K1viii80.10 (6)
O1ix—K1—O1i59.75 (6)Co2xiii—O2—K1viii65.58 (5)
O3xii—K1—O1i69.86 (7)K2xiv—O2—K1viii129.2 (3)
O3—K1—O1i94.19 (9)K1xiv—O2—K1viii126.01 (8)
O2vi—K1—O1i89.76 (9)K2xiii—O2—K1viii159.3 (2)
O4i—K1—O1i48.05 (5)K1xiii—O2—K1viii160.86 (6)
O2xii—K1—O2i107.88 (10)K1v—O2—K1viii64.14 (6)
O1—K1—O2i104.68 (10)K2v—O2—K1viii66.14 (16)
O3xi—K1—O2i172.86 (12)Mo—O2—K2viii82.18 (16)
O1ix—K1—O2i94.48 (8)Co2xiii—O2—K2viii63.49 (16)
O3xii—K1—O2i50.19 (6)K2xiv—O2—K2viii129.2 (2)
O3—K1—O2i91.22 (9)K1xiv—O2—K2viii126.14 (17)
O2vi—K1—O2i51.35 (6)K2xiii—O2—K2viii157.9 (2)
O4i—K1—O2i45.24 (5)K1xiii—O2—K2viii159.24 (19)
O1i—K1—O2i44.08 (5)K1v—O2—K2viii64.33 (15)
O2xii—K1—O2ix46.48 (7)K2v—O2—K2viii66.3 (2)
O1—K1—O2ix96.12 (10)K1viii—O2—K2viii2.10 (19)
O3xi—K1—O2ix49.34 (6)Mo—O3—Co2127.70 (6)
O1ix—K1—O2ix44.78 (6)Mo—O3—K2xi119.7 (2)
O3xii—K1—O2ix78.76 (8)Co2—O3—K2xi96.2 (2)
O3—K1—O2ix142.87 (11)Mo—O3—K1xi122.07 (9)
O2vi—K1—O2ix149.67 (10)Co2—O3—K1xi95.64 (8)
O4i—K1—O2ix149.93 (7)K2xi—O3—K1xi3.2 (3)
O1i—K1—O2ix103.16 (7)Mo—O3—K292.1 (2)
O2i—K1—O2ix123.93 (8)Co2—O3—K296.43 (19)
O2xii—K2—O1138.4 (4)K2xi—O3—K237.5 (4)
O2xii—K2—O3xi66.9 (2)K1xi—O3—K240.7 (2)
O1—K2—O3xi79.5 (3)Mo—O3—K1xiv91.50 (8)
O2xii—K2—O3145.6 (5)Co2—O3—K1xiv121.78 (9)
O1—K2—O360.6 (2)K2xi—O3—K1xiv97.94 (19)
O3xi—K2—O398.7 (3)K1xi—O3—K1xiv95.61 (11)
O2xii—K2—O2vi106.4 (3)K2—O3—K1xiv126.7 (2)
O1—K2—O2vi115.1 (3)Mo—O3—K190.05 (8)
O3xi—K2—O2vi138.3 (4)Co2—O3—K196.34 (8)
O3—K2—O2vi62.8 (2)K2xi—O3—K140.2 (2)
O2xii—K2—O3xii59.6 (2)K1xi—O3—K143.41 (9)
O1—K2—O3xii129.7 (4)K2—O3—K12.7 (3)
O3xi—K2—O3xii121.7 (3)K1xiv—O3—K1128.60 (11)
O3—K2—O3xii138.9 (3)Mo—O3—K2xiv89.9 (2)
O2vi—K2—O3xii80.4 (2)Co2—O3—K2xiv121.31 (18)
O2xii—K2—O1ix81.8 (3)K2xi—O3—K2xiv100.8 (4)
O1—K2—O1ix68.2 (2)K1xi—O3—K2xiv98.43 (19)
O3xi—K2—O1ix79.6 (2)K2—O3—K2xiv129.2 (3)
O3—K2—O1ix128.0 (4)K1xiv—O3—K2xiv2.8 (3)
O2vi—K2—O1ix141.8 (4)K1—O3—K2xiv131.0 (2)
O3xii—K2—O1ix71.9 (2)Mo—O3—K2xiii74.45 (14)
O2xii—K2—O4i150.7 (4)Co2—O3—K2xiii116.55 (14)
O1—K2—O4i66.7 (2)K2xi—O3—K2xiii124.8 (2)
O3xi—K2—O4i142.4 (3)K1xi—O3—K2xiii122.64 (16)
O3—K2—O4i50.80 (15)K2—O3—K2xiii146.1 (2)
O2vi—K2—O4i53.91 (15)K1xiv—O3—K2xiii27.26 (15)
O3xii—K2—O4i93.4 (3)K1—O3—K2xiii146.69 (16)
O1ix—K2—O4i101.4 (3)K2xiv—O3—K2xiii24.5 (3)
O2xii—K2—O1i120.4 (3)Mo—O4—Co1120.22 (6)
O1—K2—O1i65.9 (2)Mo—O4—Co2v136.21 (6)
O3xi—K2—O1i131.6 (4)Co1—O4—Co2v95.48 (5)
O3—K2—O1i92.8 (3)Mo—O4—K1v86.66 (6)
O2vi—K2—O1i88.4 (2)Co1—O4—K1v137.44 (7)
O3xii—K2—O1i67.2 (2)Co2v—O4—K1v82.02 (5)
O1ix—K2—O1i57.0 (2)Mo—O4—K2v88.78 (18)
O4i—K2—O1i46.88 (13)Co1—O4—K2v137.05 (16)
O2xii—K2—O1xi90.2 (3)Co2v—O4—K2v79.43 (19)
O1—K2—O1xi83.2 (3)K1v—O4—K2v2.6 (2)
Symmetry codes: (i) y, xy, z; (ii) x, x+y, z+1/2; (iii) y, x, z+1/2; (iv) xy, y, z+1/2; (v) x+y, x, z; (vi) y+1/3, x+y+2/3, z+2/3; (vii) x+y+2/3, y+1/3, z1/6; (viii) y, x+y, z+1; (ix) xy, x, z+1; (x) x, y, z+1; (xi) x+2/3, x+y+1/3, z+5/6; (xii) y+1/3, x+2/3, z+1/6; (xiii) xy+1/3, x1/3, z+2/3; (xiv) y+2/3, x+1/3, z1/6.
(VI) top
Crystal data top
K3.11Li0.89Mg4·6(MoO4)Dx = 3.352 Mg m3
Mr = 1184.71Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3cCell parameters from 12163 reflections
a = 14.3541 (2) Åθ = 2.6–33.1°
c = 19.7338 (4) ŵ = 3.87 mm1
V = 3521.22 (12) Å3T = 296 K
Z = 6Fragment, colourless
F(000) = 33230.14 × 0.08 × 0.06 mm
Data collection top
Bruker-Nonius X8 APEX CCD
diffractometer
1356 reflections with I > 2σ(I)
\ f scans, frame data integrationRint = 0.027
Absorption correction: multi-scan
SADABS (Bruker, 2005)
θmax = 33.1°, θmin = 2.6°
Tmin = 0.697, Tmax = 0.793h = 2022
12163 measured reflectionsk = 2212
1502 independent reflectionsl = 2730
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.018 w = 1/[σ2(Fo2) + (0.0144P)2 + 19.5824P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.042(Δ/σ)max = 0.013
S = 1.06Δρmax = 1.54 e Å3
1501 reflectionsΔρmin = 1.48 e Å3
77 parametersExtinction correction: SHELXL-2017/1 (Sheldrick 2017), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
1 restraintExtinction coefficient: 0.000104 (17)
Special details top

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Mo0.17938 (2)0.00765 (2)0.35913 (2)0.01155 (5)
Mg10.0000000.0000000.2500000.0165 (16)0.112 (9)
Li10.0000000.0000000.2500000.0165 (16)0.888 (9)
Mg20.21366 (6)0.21366 (6)0.2500000.01093 (16)
Mg30.0000000.0000000.5000000.0154 (4)0.888 (9)
K30.0000000.0000000.5000000.0154 (4)0.112 (9)
K10.25444 (19)0.2466 (2)0.44311 (18)0.0245 (4)0.4561 (14)
K20.382 (2)0.311 (3)0.4004 (18)0.030 (5)0.0440 (14)
O10.13373 (14)0.02087 (14)0.43942 (8)0.0258 (3)
O20.25663 (13)0.05555 (13)0.36431 (9)0.0241 (3)
O30.26204 (11)0.13543 (12)0.32224 (8)0.0176 (3)
O40.06674 (11)0.07315 (11)0.30737 (7)0.0142 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mo0.01206 (8)0.01108 (8)0.01089 (8)0.00531 (6)0.00325 (5)0.00035 (5)
Mg10.015 (2)0.015 (2)0.019 (3)0.0075 (10)0.0000.000
Li10.015 (2)0.015 (2)0.019 (3)0.0075 (10)0.0000.000
Mg20.0094 (3)0.0094 (3)0.0125 (4)0.0037 (3)0.00088 (15)0.00088 (15)
Mg30.0179 (5)0.0179 (5)0.0104 (7)0.0089 (3)0.0000.000
K30.0179 (5)0.0179 (5)0.0104 (7)0.0089 (3)0.0000.000
K10.0300 (11)0.0176 (10)0.0264 (9)0.0124 (9)0.0083 (8)0.0076 (7)
K20.038 (13)0.033 (12)0.032 (13)0.027 (12)0.018 (10)0.015 (9)
O10.0292 (8)0.0289 (8)0.0137 (7)0.0104 (7)0.0008 (6)0.0044 (6)
O20.0221 (7)0.0199 (7)0.0337 (9)0.0131 (6)0.0092 (6)0.0023 (6)
O30.0137 (6)0.0144 (6)0.0220 (7)0.0050 (5)0.0017 (5)0.0033 (5)
O40.0152 (6)0.0126 (6)0.0153 (6)0.0073 (5)0.0057 (5)0.0031 (5)
Geometric parameters (Å, º) top
Mo—O21.7519 (16)K1—K1xi2.222 (4)
Mo—O11.7606 (16)K1—O2xii2.776 (4)
Mo—O31.7680 (14)K1—O12.810 (3)
Mo—O41.7685 (14)K1—O3xi2.830 (4)
Mg1—O4i2.0755 (13)K1—O32.902 (4)
Mg1—O4ii2.0755 (13)K1—O3xii2.908 (4)
Mg1—O4iii2.0755 (13)K1—O1viii2.973 (3)
Mg1—O42.0755 (13)K1—O2vi3.115 (4)
Mg1—O4iv2.0755 (13)K1—O1iii3.424 (3)
Mg1—O4v2.0756 (13)K1—O4iii3.508 (4)
Mg2—O2vi2.0346 (16)K1—O2iii3.760 (4)
Mg2—O2vii2.0346 (16)K2—K2xi1.37 (5)
Mg2—O4iv2.0821 (15)K2—O2vi2.70 (4)
Mg2—O4iii2.0821 (15)K2—O32.71 (4)
Mg2—O3v2.1342 (14)K2—O3xi2.76 (4)
Mg2—O32.1343 (14)K2—O2xii2.92 (4)
Mg3—O12.1514 (17)K2—O1xi3.04 (3)
Mg3—O1viii2.1514 (17)K2—O3vi3.08 (4)
Mg3—O1ii2.1514 (17)K2—O1vii3.36 (3)
Mg3—O1ix2.1514 (17)K2—O4xiii3.62 (3)
Mg3—O1iii2.1514 (17)K2—O1xiii3.80 (3)
Mg3—O1x2.1514 (17)K2—O3xii3.92 (3)
K1—K2xi0.43 (3)K2—O2xiii3.94 (3)
K1—K21.79 (3)
O2—Mo—O1111.68 (9)O4xiii—K2—O3xii99.5 (8)
O2—Mo—O3106.92 (7)O1xiii—K2—O3xii126.2 (9)
O1—Mo—O3110.59 (8)O2vi—K2—O2xiii106.8 (11)
O2—Mo—O4107.57 (7)O3—K2—O2xiii163.6 (10)
O1—Mo—O4108.84 (7)O3xi—K2—O2xiii90.8 (9)
O3—Mo—O4111.21 (7)O2xii—K2—O2xiii52.7 (6)
O4i—Mg1—O4ii88.79 (8)O1xi—K2—O2xiii92.1 (7)
O4i—Mg1—O4iii177.46 (8)O3vi—K2—O2xiii49.6 (5)
O4ii—Mg1—O4iii93.08 (5)O1vii—K2—O2xiii84.7 (6)
O4i—Mg1—O485.11 (7)O4xiii—K2—O2xiii43.9 (4)
O4ii—Mg1—O493.07 (5)O1xiii—K2—O2xiii44.1 (3)
O4iii—Mg1—O493.07 (5)O3xii—K2—O2xiii82.1 (7)
O4i—Mg1—O4iv93.08 (5)Mo—O1—Mg3147.07 (10)
O4ii—Mg1—O4iv177.46 (8)Mo—O1—K195.71 (9)
O4iii—Mg1—O4iv85.10 (7)Mg3—O1—K197.99 (8)
O4—Mg1—O4iv88.80 (8)Mo—O1—K1ix115.39 (11)
O4i—Mg1—O4v93.08 (5)Mg3—O1—K1ix93.30 (8)
O4ii—Mg1—O4v85.11 (7)K1—O1—K1ix94.30 (8)
O4iii—Mg1—O4v88.80 (8)Mo—O1—K2xi89.6 (7)
O4—Mg1—O4v177.46 (8)Mg3—O1—K2xi105.1 (6)
O4iv—Mg1—O4v93.08 (5)K1—O1—K2xi7.1 (6)
O2vi—Mg2—O2vii87.41 (10)K1ix—O1—K2xi93.7 (7)
O2vi—Mg2—O4iv175.39 (6)Mo—O1—K2xiv112.7 (6)
O2vii—Mg2—O4iv94.08 (6)Mg3—O1—K2xiv95.3 (6)
O2vi—Mg2—O4iii94.08 (6)K1—O1—K2xiv96.5 (7)
O2vii—Mg2—O4iii175.39 (6)K1ix—O1—K2xiv3.3 (6)
O4iv—Mg2—O4iii84.77 (8)K2xi—O1—K2xiv95.6 (7)
O2vi—Mg2—O3v93.79 (7)Mo—O1—K1ii86.14 (8)
O2vii—Mg2—O3v94.53 (7)Mg3—O1—K1ii81.62 (8)
O4iv—Mg2—O3v81.75 (6)K1—O1—K1ii176.97 (14)
O4iii—Mg2—O3v89.73 (6)K1ix—O1—K1ii82.73 (8)
O2vi—Mg2—O394.53 (7)K2xi—O1—K1ii172.6 (6)
O2vii—Mg2—O393.79 (7)K2xiv—O1—K1ii80.5 (6)
O4iv—Mg2—O389.73 (6)Mo—O1—K2xv83.2 (5)
O4iii—Mg2—O381.75 (6)Mg3—O1—K2xv83.6 (5)
O3v—Mg2—O3168.48 (9)K1—O1—K2xv178.3 (6)
O1—Mg3—O1viii87.89 (6)K1ix—O1—K2xv85.0 (6)
O1—Mg3—O1ii92.11 (6)K2xi—O1—K2xv171.3 (6)
O1viii—Mg3—O1ii180.0K2xiv—O1—K2xv82.7 (6)
O1—Mg3—O1ix87.89 (6)K1ii—O1—K2xv3.2 (6)
O1viii—Mg3—O1ix92.11 (6)Mo—O1—K275.6 (5)
O1ii—Mg3—O1ix87.89 (6)Mg3—O1—K2121.5 (4)
O1—Mg3—O1iii92.11 (6)K1—O1—K223.5 (5)
O1viii—Mg3—O1iii87.89 (6)K1ix—O1—K291.8 (6)
O1ii—Mg3—O1iii92.11 (6)K2xi—O1—K216.5 (7)
O1ix—Mg3—O1iii180.00 (7)K2xiv—O1—K292.9 (6)
O1—Mg3—O1x180.0K1ii—O1—K2156.6 (5)
O1viii—Mg3—O1x92.11 (6)K2xv—O1—K2154.8 (2)
O1ii—Mg3—O1x87.89 (6)Mo—O2—Mg2xvi152.83 (11)
O1ix—Mg3—O1x92.11 (6)Mo—O2—K2xvi101.3 (7)
O1iii—Mg3—O1x87.89 (6)Mg2xvi—O2—K2xvi99.4 (8)
O2xii—K1—O1139.29 (15)Mo—O2—K1xvii97.88 (10)
O2xii—K1—O3xi66.22 (9)Mg2xvi—O2—K1xvii99.87 (10)
O1—K1—O3xi82.63 (10)K2xvi—O2—K1xvii8.8 (6)
O2xii—K1—O3140.95 (9)Mo—O2—K2xvii110.7 (7)
O1—K1—O361.01 (8)Mg2xvi—O2—K2xvii95.8 (7)
O3xi—K1—O392.08 (10)K2xvi—O2—K2xvii27.8 (10)
O2xii—K1—O3xii59.62 (8)K1xvii—O2—K2xvii36.6 (5)
O1—K1—O3xii130.98 (9)Mo—O2—K1xvi112.65 (9)
O3xi—K1—O3xii123.25 (12)Mg2xvi—O2—K1xvi94.37 (8)
O3—K1—O3xii141.82 (15)K2xvi—O2—K1xvi35.0 (5)
O2xii—K1—O1viii88.31 (11)K1xvii—O2—K1xvi43.84 (8)
O1—K1—O1viii62.11 (8)K2xvii—O2—K1xvi7.2 (5)
O3xi—K1—O1viii84.39 (10)Mo—O2—K1ii75.95 (7)
O3—K1—O1viii122.99 (11)Mg2xvi—O2—K1ii90.90 (7)
O3xii—K1—O1viii78.56 (8)K2xvi—O2—K1ii158.5 (6)
O2xii—K1—O2vi106.29 (10)K1xvii—O2—K1ii165.33 (11)
O1—K1—O2vi113.64 (12)K2xvii—O2—K1ii132.9 (6)
O3xi—K1—O2vi128.29 (9)K1xvi—O2—K1ii125.91 (7)
O3—K1—O2vi61.07 (8)Mo—O2—K1ix82.91 (7)
O3xii—K1—O2vi83.81 (10)Mg2xvi—O2—K1ix70.03 (6)
O1viii—K1—O2vi147.20 (12)K2xvi—O2—K1ix133.8 (6)
O2xii—K1—O1iii127.38 (11)K1xvii—O2—K1ix125.62 (8)
O1—K1—O1iii58.62 (8)K2xvii—O2—K1ix156.8 (7)
O3xi—K1—O1iii132.76 (11)K1xvi—O2—K1ix160.70 (7)
O3—K1—O1iii91.39 (9)K1ii—O2—K1ix67.44 (7)
O3xii—K1—O1iii75.53 (7)Mo—O2—K2xv79.1 (5)
O1viii—K1—O1iii55.11 (6)Mg2xvi—O2—K2xv90.1 (5)
O2vi—K1—O1iii93.84 (10)K2xvi—O2—K2xv153.7 (10)
O2xii—K1—O4iii153.70 (13)K1xvii—O2—K2xv161.5 (5)
O1—K1—O4iii65.25 (8)K2xvii—O2—K2xv127.3 (6)
O3xi—K1—O4iii138.35 (12)K1xvi—O2—K2xv120.3 (4)
O3—K1—O4iii49.90 (7)K1ii—O2—K2xv5.8 (4)
O3xii—K1—O4iii98.20 (10)K1ix—O2—K2xv72.5 (5)
O1viii—K1—O4iii101.64 (8)Mo—O2—K2xiv88.7 (4)
O2vi—K1—O4iii53.72 (7)Mg2xvi—O2—K2xiv64.2 (4)
O1iii—K1—O4iii48.90 (5)K2xvi—O2—K2xiv133.0 (6)
O2xii—K1—O2iii109.94 (10)K1xvii—O2—K2xiv125.3 (5)
O1—K1—O2iii99.81 (9)K2xvii—O2—K2xiv153.1 (5)
O3xi—K1—O2iii175.62 (12)K1xvi—O2—K2xiv155.9 (4)
O3—K1—O2iii92.28 (10)K1ii—O2—K2xiv68.5 (5)
O3xii—K1—O2iii52.46 (6)K1ix—O2—K2xiv5.8 (4)
O1viii—K1—O2iii93.51 (8)K2xv—O2—K2xiv73.2 (6)
O2vi—K1—O2iii54.09 (7)Mo—O3—Mg2126.49 (8)
O1iii—K1—O2iii47.45 (6)Mo—O3—K2121.0 (7)
O4iii—K1—O2iii45.84 (5)Mg2—O3—K296.4 (8)
O2vi—K2—O368.9 (9)Mo—O3—K2xi99.0 (6)
O2vi—K2—O3xi157.2 (11)Mg2—O3—K2xi98.2 (7)
O3—K2—O3xi97.9 (12)K2—O3—K2xi28.9 (10)
O2vi—K2—O2xii114.2 (11)Mo—O3—K1xi126.69 (9)
O3—K2—O2xii143.7 (11)Mg2—O3—K1xi95.78 (9)
O3xi—K2—O2xii65.2 (8)K2—O3—K1xi8.5 (5)
O2vi—K2—O1xi131.6 (12)K2xi—O3—K1xi37.4 (5)
O3—K2—O1xi80.5 (9)Mo—O3—K192.40 (8)
O3xi—K2—O1xi59.8 (7)Mg2—O3—K198.51 (9)
O2xii—K2—O1xi112.7 (12)K2—O3—K137.1 (6)
O2vi—K2—O3vi58.2 (7)K2xi—O3—K18.2 (5)
O3—K2—O3vi121.2 (13)K1xi—O3—K145.58 (8)
O3xi—K2—O3vi140.3 (13)Mo—O3—K1xvii92.92 (8)
O2xii—K2—O3vi84.3 (9)Mg2—O3—K1xvii116.33 (10)
O1xi—K2—O3vi116.5 (8)K2—O3—K1xvii102.5 (6)
O2vi—K2—O1vii82.0 (9)K2xi—O3—K1xvii125.4 (6)
O3—K2—O1vii79.1 (8)K1xi—O3—K1xvii95.28 (10)
O3xi—K2—O1vii114.7 (10)K1—O3—K1xvii131.13 (12)
O2xii—K2—O1vii136.8 (10)Mo—O3—K2xvi87.9 (6)
O1xi—K2—O1vii55.3 (4)Mg2—O3—K2xvi115.4 (7)
O3vi—K2—O1vii70.5 (6)K2—O3—K2xvi109.9 (10)
O2vi—K2—O4xiii150.7 (13)K2xi—O3—K2xvi132.0 (10)
O3—K2—O4xiii138.3 (12)K1xi—O3—K2xvi102.8 (5)
O3xi—K2—O4xiii49.0 (6)K1—O3—K2xvi137.1 (5)
O2xii—K2—O4xiii53.5 (6)K1xvii—O3—K2xvi7.5 (5)
O1xi—K2—O4xiii61.8 (6)Mo—O3—K2xvii76.3 (5)
O3vi—K2—O4xiii92.8 (8)Mg2—O3—K2xvii111.6 (6)
O1vii—K2—O4xiii92.2 (6)K2—O3—K2xvii127.5 (9)
O2vi—K2—O1xiii116.7 (10)K2xi—O3—K2xvii146.2 (10)
O3—K2—O1xiii122.4 (9)K1xi—O3—K2xvii120.6 (5)
O3xi—K2—O1xiii86.0 (8)K1—O3—K2xvii148.9 (6)
O2xii—K2—O1xiii89.7 (8)K1xvii—O3—K2xvii25.4 (5)
O1xi—K2—O1xiii52.4 (4)K2xvi—O3—K2xvii17.8 (7)
O3vi—K2—O1xiii68.1 (5)Mo—O4—Mg1119.02 (7)
O1vii—K2—O1xiii48.8 (3)Mo—O4—Mg2ii140.92 (8)
O4xiii—K2—O1xiii45.4 (4)Mg1—O4—Mg2ii95.06 (6)
O2vi—K2—O3xii72.3 (7)Mo—O4—K1ii83.41 (6)
O3—K2—O3xii110.5 (8)Mg1—O4—K1ii138.16 (8)
O3xi—K2—O3xii96.7 (8)Mg2ii—O4—K1ii82.80 (6)
O2xii—K2—O3xii46.0 (4)Mo—O4—K2xv88.8 (5)
O1xi—K2—O3xii155.8 (12)Mg1—O4—K2xv137.7 (6)
O3vi—K2—O3xii77.1 (7)Mg2ii—O4—K2xv76.2 (4)
O1vii—K2—O3xii146.1 (11)K1ii—O4—K2xv6.6 (5)
Symmetry codes: (i) x, x+y, z+1/2; (ii) x+y, x, z; (iii) y, xy, z; (iv) xy, y, z+1/2; (v) y, x, z+1/2; (vi) y+1/3, x+y+2/3, z+2/3; (vii) x+y+2/3, y+1/3, z1/6; (viii) xy, x, z+1; (ix) y, x+y, z+1; (x) x, y, z+1; (xi) x+2/3, x+y+1/3, z+5/6; (xii) y+1/3, x+2/3, z+1/6; (xiii) y+2/3, x+1/3, z+5/6; (xiv) x+y+1/3, y1/3, z+1/6; (xv) y1/3, x2/3, z+5/6; (xvi) xy+1/3, x1/3, z+2/3; (xvii) y+2/3, x+1/3, z1/6.
 

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