New triple molybdate Rb2AgIn(MoO4)3: synthesis, framework crystal structure and ion-transport behaviour

Spiridonova, T.S.; Solodovnikov, S.F.; Savina, A.A.; Kadyrova, Y.M.; Solodovnikova, Z.A.; Yudin, V.N.; Stefanovich, S.Y.; Khaikina, E.G.

doi:10.1107/S2053229618014717

New triple molybdate Rb₂AgIn(MoO₄)₃: synthesis, framework crystal structure and ion-transport behaviour

T. S. Spiridonova, S. F. Solodovnikov, A. A. Savina, Y. M. Kadyrova, Z. A. Solodovnikova, V. N. Yudin, S. Y. Stefanovich and E. G. Khaikina

A new triple molybdate, Rb₂Ag_1+3xIn_1–x(MoO₄)₃ (0 ≤ x ≤ 0.02), was found in the course of a study of the system Rb₂MoO₄–Ag₂MoO₄–In₂(MoO₄)₃ and was synthesized as both powders and single crystals by solid-state reactions and spontaneous crystallization from melts. The structure of Rb₂Ag_1+3xIn_1–x(MoO₄)₃ (x ≈ 0.004) is of a new type crystallizing in the centrosymmetric space group R $\overline{3}$ c [a = 10.3982 (9), c = 38.858 (4) Å, Z = 12 and R = 0.0225] and contains (In,Ag)O₆ octahedra and distorted Ag1O₆ trigonal prisms linked by common faces to form [Ag(In,Ag)O₉] dimers connected to each other via MoO₄ tetrahedra into an open three-dimensional (3D) framework. Between two adjacent [Ag(In,Ag)O₉] dimers along the c axis, an extra Ag2O₆ trigonal prism with about 1% occupancy was found. The Ag1O₆ and Ag2O₆ prisms are located at levels of z ≈ 1/12, 1/4, 5/12, 7/12, 3/4 and 11/12, and can facilitate two-dimensional ionic conductivity. The 12-coordinate Rb atoms are in the framework cavities. The structure of Rb₂AgIn(MoO₄)₃ is a member of the series of rhombohedral 3D framework molybdate structure types with a ≈ 9–10 Å and long c axes, which contain rods of face-shared filled and empty coordination polyhedra around threefold axes. Electrical conductivity of ceramics is measured by impedance spectroscopy. Rb₂AgIn(MoO₄)₃ undergoes a `blurred' first-order phase transition at 535 K with increasing electrical conductivity up to 1.1 × 10⁻² S cm⁻¹ at 720 K. Thus, the compound may be of interest for developing new materials with high ionic conductivity at elevated temperatures.

Keywords: rubidium; silver; indium; triple molybdate; crystal structure; powder X-ray diffraction; ionic conductivity.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S2053229618014717/ly3077sup1.cif Contains datablocks global, I
	Structure factor file (CIF format) https://doi.org/10.1107/S2053229618014717/ly3077Isup2.hkl Contains datablock I
	Portable Document Format (PDF) file https://doi.org/10.1107/S2053229618014717/ly3077sup3.pdf XRD data

CCDC reference: 1873827

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2017 (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 2008).

(I) top

Crystal data top

Ag_1.01InMo₃O₁₂Rb₂	D_x = 4.787 Mg m⁻³
M_r = 874.15	Melting point: 831 K
Trigonal, R3c:H	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -R 3 2"c	Cell parameters from 12966 reflections
a = 10.3982 (15) Å	θ = 3.9–30.6°
c = 38.858 (8) Å	µ = 14.51 mm⁻¹
V = 3638.6 (13) Å³	T = 293 K
Z = 12	Fragment, colourless
F(000) = 4708	0.07 × 0.05 × 0.04 mm

Data collection top

Bruker–Nonius X8 APEX CCD diffractometer	976 reflections with I > 2σ(I)
\ f scans, frame data integration	R_int = 0.061
Absorption correction: multi-scan (SADABS; Bruker, 2004)	θ_max = 30.6°, θ_min = 3.9°
T_min = 0.430, T_max = 0.594	h = −14→14
12966 measured reflections	k = −14→14
1212 independent reflections	l = −51→55

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.023	w = 1/[σ²(F_o²) + (0.0287P)²] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.057	(Δ/σ)_max = 0.002
S = 1.01	Δρ_max = 1.10 e Å⁻³
1212 reflections	Δρ_min = −1.45 e Å⁻³
63 parameters	Extinction correction: SHELXL2017 (Sheldrick, 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
1 restraint	Extinction coefficient: 0.000094 (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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Rb1	0.000000	0.000000	0.000000	0.01629 (18)
Rb2	0.29504 (7)	0.29504 (7)	0.250000	0.02853 (15)
Mo	0.33406 (3)	0.33038 (3)	0.36161 (2)	0.00961 (9)
Ag1	0.000000	0.000000	0.08654 (2)	0.01801 (13)
Ag2	0.000000	0.000000	0.250000	0.030 (18)*	0.012 (2)
In	0.000000	0.000000	0.32843 (2)	0.00931 (11)	0.9971 (6)
Ag3	0.000000	0.000000	0.32843 (2)	0.00931 (11)	0.0029 (6)
O1	0.3172 (3)	0.4917 (3)	0.37040 (7)	0.0162 (5)
O2	0.3992 (3)	0.3458 (3)	0.32006 (7)	0.0186 (5)
O3	0.1532 (3)	0.1658 (3)	0.36428 (6)	0.0155 (5)
O4	0.4626 (3)	0.3313 (3)	0.39077 (7)	0.0174 (5)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Rb1	0.0131 (2)	0.0131 (2)	0.0226 (5)	0.00657 (12)	0.000	0.000
Rb2	0.0406 (3)	0.0406 (3)	0.0158 (3)	0.0290 (3)	−0.00108 (10)	0.00108 (10)
Mo	0.00968 (15)	0.00929 (15)	0.00920 (16)	0.00425 (11)	−0.00177 (9)	−0.00045 (9)
Ag1	0.02011 (18)	0.02011 (18)	0.0138 (3)	0.01005 (9)	0.000	0.000
In	0.00919 (14)	0.00919 (14)	0.0096 (2)	0.00459 (7)	0.000	0.000
Ag3	0.00919 (14)	0.00919 (14)	0.0096 (2)	0.00459 (7)	0.000	0.000
O1	0.0221 (13)	0.0134 (12)	0.0151 (13)	0.0105 (11)	0.0004 (10)	0.0005 (9)
O2	0.0210 (13)	0.0235 (13)	0.0119 (13)	0.0115 (11)	0.0007 (10)	0.0013 (10)
O3	0.0138 (12)	0.0155 (12)	0.0125 (12)	0.0037 (10)	−0.0002 (9)	−0.0019 (9)
O4	0.0161 (12)	0.0228 (13)	0.0144 (13)	0.0106 (11)	−0.0040 (9)	−0.0005 (10)

Geometric parameters (Å, º) top

Rb1—O2ⁱ	2.895 (3)	Mo—O2	1.727 (3)
Rb1—O2ⁱⁱ	2.895 (3)	Mo—O4	1.748 (2)
Rb1—O2ⁱⁱⁱ	2.895 (3)	Mo—O1	1.804 (2)
Rb1—O2^iv	2.895 (3)	Mo—O3	1.805 (2)
Rb1—O2^v	2.895 (3)	Ag1—O4^vi	2.396 (2)
Rb1—O2^vi	2.895 (3)	Ag1—O4ⁱⁱ	2.396 (2)
Rb1—O4^v	3.072 (3)	Ag1—O4^iv	2.396 (2)
Rb1—O4^vi	3.072 (3)	Ag1—O3^vii	2.533 (2)
Rb1—O4ⁱ	3.073 (3)	Ag1—O3^xiv	2.533 (2)
Rb1—O4ⁱⁱ	3.073 (3)	Ag1—O3^xv	2.533 (2)
Rb1—O4ⁱⁱⁱ	3.073 (3)	Ag2—O1^viii	2.503 (3)
Rb1—O4^iv	3.073 (3)	Ag2—O1^xvi	2.503 (3)
Rb2—O2^vii	2.880 (3)	Ag2—O1^xvii	2.503 (3)
Rb2—O2	2.880 (3)	Ag2—O1^x	2.503 (3)
Rb2—O1^viii	3.095 (3)	Ag2—O1^xi	2.503 (3)
Rb2—O1^ix	3.095 (3)	Ag2—In^vii	3.0473 (7)
Rb2—O4^x	3.183 (3)	Ag2—In	3.0475 (8)
Rb2—O4^xi	3.183 (3)	In—O1^ix	2.143 (2)
Rb2—O1^xi	3.336 (2)	In—O1^xvii	2.143 (2)
Rb2—O1^x	3.336 (2)	In—O1^x	2.143 (2)
Rb2—O4^xii	3.525 (3)	In—O3	2.169 (2)
Rb2—O4^xiii	3.525 (3)	In—O3^xviii	2.169 (2)
Rb2—O3^ix	3.565 (2)	In—O3^xix	2.169 (2)

O2ⁱ—Rb1—O2ⁱⁱ	180.00 (14)	O1^x—Rb2—O4^xii	108.52 (6)
O2ⁱ—Rb1—O2ⁱⁱⁱ	116.90 (3)	O2^vii—Rb2—O4^xiii	54.78 (7)
O2ⁱⁱ—Rb1—O2ⁱⁱⁱ	63.10 (3)	O2—Rb2—O4^xiii	94.21 (7)
O2ⁱ—Rb1—O2^iv	63.10 (3)	O1^viii—Rb2—O4^xiii	126.13 (6)
O2ⁱⁱ—Rb1—O2^iv	116.90 (3)	O1^ix—Rb2—O4^xiii	128.05 (6)
O2ⁱⁱⁱ—Rb1—O2^iv	180.00 (10)	O4^x—Rb2—O4^xiii	113.45 (3)
O2ⁱ—Rb1—O2^v	116.90 (3)	O4^xi—Rb2—O4^xiii	65.86 (8)
O2ⁱⁱ—Rb1—O2^v	63.10 (3)	O1^xi—Rb2—O4^xiii	108.52 (6)
O2ⁱⁱⁱ—Rb1—O2^v	116.90 (3)	O1^x—Rb2—O4^xiii	159.60 (6)
O2^iv—Rb1—O2^v	63.10 (3)	O4^xii—Rb2—O4^xiii	51.76 (8)
O2ⁱ—Rb1—O2^vi	63.10 (3)	O2^vii—Rb2—O3^ix	111.56 (7)
O2ⁱⁱ—Rb1—O2^vi	116.90 (3)	O2—Rb2—O3^ix	63.79 (7)
O2ⁱⁱⁱ—Rb1—O2^vi	63.10 (3)	O1^viii—Rb2—O3^ix	142.64 (6)
O2^iv—Rb1—O2^vi	116.90 (3)	O1^ix—Rb2—O3^ix	51.89 (6)
O2^v—Rb1—O2^vi	180.00 (14)	O4^x—Rb2—O3^ix	125.96 (6)
O2ⁱ—Rb1—O4^v	119.69 (7)	O4^xi—Rb2—O3^ix	53.92 (6)
O2ⁱⁱ—Rb1—O4^v	60.31 (7)	O1^xi—Rb2—O3^ix	91.00 (6)
O2ⁱⁱⁱ—Rb1—O4^v	116.05 (7)	O1^x—Rb2—O3^ix	99.64 (6)
O2^iv—Rb1—O4^v	63.95 (7)	O4^xii—Rb2—O3^ix	89.15 (6)
O2^v—Rb1—O4^v	56.90 (7)	O4^xiii—Rb2—O3^ix	77.07 (6)
O2^vi—Rb1—O4^v	123.10 (7)	O2—Mo—O4	110.01 (12)
O2ⁱ—Rb1—O4^vi	60.31 (7)	O2—Mo—O1	107.85 (12)
O2ⁱⁱ—Rb1—O4^vi	119.69 (7)	O4—Mo—O1	107.54 (11)
O2ⁱⁱⁱ—Rb1—O4^vi	63.95 (7)	O2—Mo—O3	108.43 (12)
O2^iv—Rb1—O4^vi	116.05 (7)	O4—Mo—O3	113.53 (11)
O2^v—Rb1—O4^vi	123.10 (7)	O1—Mo—O3	109.33 (11)
O2^vi—Rb1—O4^vi	56.90 (7)	O4^vi—Ag1—O4ⁱⁱ	99.53 (8)
O4^v—Rb1—O4^vi	180.00 (16)	O4^vi—Ag1—O4^iv	99.53 (8)
O2ⁱ—Rb1—O4ⁱ	56.89 (7)	O4ⁱⁱ—Ag1—O4^iv	99.53 (8)
O2ⁱⁱ—Rb1—O4ⁱ	123.11 (7)	O4^vi—Ag1—O3^vii	133.09 (8)
O2ⁱⁱⁱ—Rb1—O4ⁱ	119.69 (7)	O4ⁱⁱ—Ag1—O3^vii	77.25 (8)
O2^iv—Rb1—O4ⁱ	60.31 (7)	O4^iv—Ag1—O3^vii	127.32 (8)
O2^v—Rb1—O4ⁱ	116.05 (7)	O4^vi—Ag1—O3^xiv	77.26 (8)
O2^vi—Rb1—O4ⁱ	63.95 (7)	O4ⁱⁱ—Ag1—O3^xiv	127.32 (8)
O4^v—Rb1—O4ⁱ	73.07 (7)	O4^iv—Ag1—O3^xiv	133.09 (8)
O4^vi—Rb1—O4ⁱ	106.93 (7)	O3^vii—Ag1—O3^xiv	69.28 (9)
O2ⁱ—Rb1—O4ⁱⁱ	123.11 (7)	O4^vi—Ag1—O3^xv	127.32 (8)
O2ⁱⁱ—Rb1—O4ⁱⁱ	56.89 (7)	O4ⁱⁱ—Ag1—O3^xv	133.09 (8)
O2ⁱⁱⁱ—Rb1—O4ⁱⁱ	60.31 (7)	O4^iv—Ag1—O3^xv	77.25 (8)
O2^iv—Rb1—O4ⁱⁱ	119.69 (7)	O3^vii—Ag1—O3^xv	69.28 (9)
O2^v—Rb1—O4ⁱⁱ	63.95 (7)	O3^xiv—Ag1—O3^xv	69.28 (9)
O2^vi—Rb1—O4ⁱⁱ	116.05 (7)	O1^ix—Ag2—O1^viii	133.22 (11)
O4^v—Rb1—O4ⁱⁱ	106.93 (7)	O1^ix—Ag2—O1^xvi	145.53 (11)
O4^vi—Rb1—O4ⁱⁱ	73.07 (7)	O1^viii—Ag2—O1^xvi	74.10 (9)
O4ⁱ—Rb1—O4ⁱⁱ	180.00 (12)	O1^ix—Ag2—O1^xvii	74.10 (9)
O2ⁱ—Rb1—O4ⁱⁱⁱ	116.05 (7)	O1^viii—Ag2—O1^xvii	145.53 (11)
O2ⁱⁱ—Rb1—O4ⁱⁱⁱ	63.95 (7)	O1^xvi—Ag2—O1^xvii	92.21 (11)
O2ⁱⁱⁱ—Rb1—O4ⁱⁱⁱ	56.89 (7)	O1^ix—Ag2—O1^x	74.10 (9)
O2^iv—Rb1—O4ⁱⁱⁱ	123.11 (7)	O1^viii—Ag2—O1^x	92.21 (11)
O2^v—Rb1—O4ⁱⁱⁱ	119.69 (7)	O1^xvi—Ag2—O1^x	133.22 (11)
O2^vi—Rb1—O4ⁱⁱⁱ	60.31 (7)	O1^xvii—Ag2—O1^x	74.10 (9)
O4^v—Rb1—O4ⁱⁱⁱ	73.07 (7)	O1^ix—Ag2—O1^xi	92.21 (11)
O4^vi—Rb1—O4ⁱⁱⁱ	106.93 (7)	O1^viii—Ag2—O1^xi	74.10 (9)
O4ⁱ—Rb1—O4ⁱⁱⁱ	73.07 (7)	O1^xvi—Ag2—O1^xi	74.10 (9)
O4ⁱⁱ—Rb1—O4ⁱⁱⁱ	106.93 (7)	O1^xvii—Ag2—O1^xi	133.22 (11)
O2ⁱ—Rb1—O4^iv	63.95 (7)	O1^x—Ag2—O1^xi	145.53 (11)
O2ⁱⁱ—Rb1—O4^iv	116.05 (7)	O1^ix—In—O1^xvii	89.43 (10)
O2ⁱⁱⁱ—Rb1—O4^iv	123.11 (7)	O1^ix—In—O1^x	89.43 (10)
O2^iv—Rb1—O4^iv	56.89 (7)	O1^xvii—In—O1^x	89.43 (10)
O2^v—Rb1—O4^iv	60.31 (7)	O1^ix—In—O3	89.15 (10)
O2^vi—Rb1—O4^iv	119.69 (7)	O1^xvii—In—O3	171.90 (9)
O4^v—Rb1—O4^iv	106.93 (7)	O1^x—In—O3	98.53 (10)
O4^vi—Rb1—O4^iv	73.07 (7)	O1^ix—In—O3^xviii	171.89 (9)
O4ⁱ—Rb1—O4^iv	106.93 (7)	O1^xvii—In—O3^xviii	98.53 (10)
O4ⁱⁱ—Rb1—O4^iv	73.07 (7)	O1^x—In—O3^xviii	89.15 (9)
O4ⁱⁱⁱ—Rb1—O4^iv	180.00 (11)	O3—In—O3^xviii	83.17 (10)
O2^vii—Rb2—O2	147.51 (11)	O1^ix—In—O3^xix	98.53 (10)
O2^vii—Rb2—O1^viii	73.47 (7)	O1^xvii—In—O3^xix	89.15 (10)
O2—Rb2—O1^viii	131.26 (7)	O1^x—In—O3^xix	171.89 (9)
O2^vii—Rb2—O1^ix	131.26 (7)	O3—In—O3^xix	83.17 (10)
O2—Rb2—O1^ix	73.47 (7)	O3^xviii—In—O3^xix	83.17 (10)
O1^viii—Rb2—O1^ix	95.84 (9)	Mo—O1—In^ix	132.54 (14)
O2^vii—Rb2—O4^x	117.11 (7)	Mo—O1—Ag2^ix	144.02 (13)
O2—Rb2—O4^x	62.67 (7)	In^ix—O1—Ag2^ix	81.58 (8)
O1^viii—Rb2—O4^x	75.49 (6)	Mo—O1—Rb2^ix	104.00 (10)
O1^ix—Rb2—O4^x	104.99 (6)	In^ix—O1—Rb2^ix	109.94 (9)
O2^vii—Rb2—O4^xi	62.67 (7)	Ag2^ix—O1—Rb2^ix	65.47 (6)
O2—Rb2—O4^xi	117.11 (7)	Mo—O1—Rb2^xii	95.18 (9)
O1^viii—Rb2—O4^xi	104.99 (6)	In^ix—O1—Rb2^xii	102.02 (8)
O1^ix—Rb2—O4^xi	75.49 (6)	Ag2^ix—O1—Rb2^xii	61.45 (5)
O4^x—Rb2—O4^xi	179.31 (9)	Rb2^ix—O1—Rb2^xii	111.39 (8)
O2^vii—Rb2—O1^xi	66.84 (7)	Mo—O2—Rb2	140.60 (13)
O2—Rb2—O1^xi	141.58 (7)	Mo—O2—Rb1^xx	99.80 (11)
O1^viii—Rb2—O1^xi	55.79 (8)	Rb2—O2—Rb1^xx	116.23 (9)
O1^ix—Rb2—O1^xi	68.13 (8)	Mo—O3—In	136.03 (13)
O4^x—Rb2—O1^xi	128.52 (6)	Mo—O3—Ag1^vii	133.73 (12)
O4^xi—Rb2—O1^xi	52.10 (6)	In—O3—Ag1^vii	88.95 (8)
O2^vii—Rb2—O1^x	141.58 (7)	Mo—O3—Rb2^ix	88.09 (8)
O2—Rb2—O1^x	66.83 (7)	In—O3—Rb2^ix	120.70 (9)
O1^viii—Rb2—O1^x	68.13 (8)	Ag1^vii—O3—Rb2^ix	72.08 (6)
O1^ix—Rb2—O1^x	55.79 (8)	Mo—O4—Ag1^xx	167.77 (14)
O4^x—Rb2—O1^x	52.10 (6)	Mo—O4—Rb1^xx	93.02 (10)
O4^xi—Rb2—O1^x	128.52 (6)	Ag1^xx—O4—Rb1^xx	74.75 (7)
O1^xi—Rb2—O1^x	91.56 (9)	Mo—O4—Rb2^xii	101.83 (10)
O2^vii—Rb2—O4^xii	94.21 (7)	Ag1^xx—O4—Rb2^xii	81.31 (7)
O2—Rb2—O4^xii	54.78 (7)	Rb1^xx—O4—Rb2^xii	103.19 (7)
O1^viii—Rb2—O4^xii	128.05 (6)	Mo—O4—Rb2^x	107.77 (10)
O1^ix—Rb2—O4^xii	126.13 (6)	Ag1^xx—O4—Rb2^x	74.20 (6)
O4^x—Rb2—O4^xii	65.86 (8)	Rb1^xx—O4—Rb2^x	95.75 (7)
O4^xi—Rb2—O4^xii	113.45 (3)	Rb2^xii—O4—Rb2^x	143.76 (8)
O1^xi—Rb2—O4^xii	159.60 (6)

Symmetry codes: (i) x−y−1/3, x−2/3, −z+1/3; (ii) −x+y+1/3, −x+2/3, z−1/3; (iii) y−1/3, −x+y+1/3, −z+1/3; (iv) −y+1/3, x−y−1/3, z−1/3; (v) −x+2/3, −y+1/3, −z+1/3; (vi) x−2/3, y−1/3, z−1/3; (vii) y, x, −z+1/2; (viii) −y+2/3, −x+1/3, z−1/6; (ix) −x+1/3, −y+2/3, −z+2/3; (x) x−y+1/3, x−1/3, −z+2/3; (xi) x−1/3, x−y+1/3, z−1/6; (xii) y+1/3, −x+y+2/3, −z+2/3; (xiii) −x+y+2/3, y+1/3, z−1/6; (xiv) −x, −x+y, −z+1/2; (xv) x−y, −y, −z+1/2; (xvi) −x+y−1/3, y−2/3, z−1/6; (xvii) y−2/3, −x+y−1/3, −z+2/3; (xviii) −x+y, −x, z; (xix) −y, x−y, z; (xx) x+2/3, y+1/3, z+1/3.

Selected interatomic distances (Å) for Rb₂Ag_1+3xIn_1-x(MoO₄)₃ top

Mo tetrahedron		Rb1 polyhedron
Mo—O2	1.727 (3)	Rb1—O2^iv	2.894 (3) (× 6)
Mo—O4	1.748 (2)	Rb1—O4^iv	3.073 (3) (× 6)
Mo—O1	1.805 (2)	<Rb1—O>	2.9835
Mo—O3	1.805 (2)
<Mo1—O>	1.771	Rb2 polyhedron
		Rb2—O2	2.880 (3) (× 2)
(In,Ag) octahedron		Rb2—O1ⁱ	3.095 (3) (× 2)
In—O1ⁱ	2.143 (2) (× 3)	Rb2—O4^v	3.183 (3) (× 2)
In—O3	2.169 (2) (× 6)	Rb2—O1^v	3.335 (3) (× 2)
<(In,Ag)—O>	2.156	Rb2—O4^vi	3.525 (3) (× 2)
		Rb2—O3ⁱ	3.565 (2) (× 2)
Ag1 trigonal prism		<Rb2—O>	3.236
Ag1—O4ⁱⁱ	2.396 (2) (× 3)
Ag1—O3ⁱⁱⁱ	2.533 (2) (× 3)	Shortest cation–cation distances
<Ag1—O>	2.465	(In,Ag)—Ag2	3.0474 (7)
		Ag2—Rb2	3.0677 (9)
Ag2 trigonal prism		(In,Ag)—Ag1ⁱⁱⁱ	3.3043 (9)
Ag2—O1ⁱ	2.503 (3) (× 6)

Symmetry codes: (i) -x+1/3, -y+2/3, -z+2/3; (ii) x-2/3, y-1/3, z-1/3; (iii) y, x, -z+1/2; (iv) -x+2/3, -y+1/3, -z+1/3; (v) x-y+1/3, x-1/3, -z+2/3; (vi) y+1/3, -x+y+2/3, -z+2/3.

Rhombohedral structure types of complex molybdates and related compounds with a ~ 9–10 Å and long c periods top

Structure	Space group	Z	a (Å)	c (Å)	Polyhedral rod
Ba₉Sc₂(SiO₄)₆^a	R3	3	9.872	21.938	···BaO12–ScO₆–BaO₉squareO6···
Na_0.625Zn_0.625Sc_1.375(MoO₄)₃^b	R3c	6	9.526	23.392	···NaO6–(Sc,Zn)O₆–[squareO₆](p)···
Cs₇Na₅Yb₂(MoO₄)₉^c	R32	3	10.511	36.358	···[NaO₆](p)–CsO₉–CsO₉–NaO₆(p)–YbO₆–
K₅(Mg_0.5Zr_1.5)(MoO₄)₆^d	R3c	6	10.576	37.511	···(Zr,Mg)O₆–KO₉–squareO₆(p)–(Zr,Mg)O₆–squareO₆(p)–KO₉–(Zr,Mg)O₆···
K₅Pb_0.5Hf_1.5(MoO₄)₆^e	R3	6	10.739	37.933	···HfO₆–squareO₆(p)–KO₉–HfO₆–KO₁₂–PbO6···
Rb₂Ag₁₊₃_xIn_1?_x(MoO₄)₃^f	R3c	12	10.398	38.858	···RbO12–AgO₆(p)–(In,Ag)O₆–[square,AgO₆](p)···
Cs₂NaBi(MoO₄)₃^g	R3c	12	10.644	40.952	···CsO₁₂–squareO₆(p)–BiO₆–NaO₆(p)–BiO₆–NaO₆(p)–CsO₁₂···
Ca₃(VO₄)₂^h	R3c	21	10.809	38.028	···PO₄–(Ca_0.5square_0.5)O₁₂–squareO₆–CaO₆–squareO₁₀–PO₄···
Nd₂Zr₃(MoO₄)₉ⁱ	R3c	6	9.804	58.467	···ZrO6–squareO₆(p)–ZrO₆–squareO₆(p)–NdO₉–[squareO₆](p)···

References: (a) Wang et al. (1994); (b) Lazoryak & Efremov (1987) (NASICON type); (c) Basovich et al. (2011); (d) Klevtsova et al. (1994); (e) Bazarov et al. (2005); (f) this work; (g) Savina et al. (2015); (h) Gopal & Calvo (1973) (isostructural with β-Ca₃(VO₄)₂ and whitlokite); (i) Klevtsova et al. (2000).

Independent parts of the polyhedral rods are shown. Centrosymmetric polyhedra are underlined, polyhedra on twofold axes are in square brackets, trigonal prisms are marked with the letter p.

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