Crystal structure of Ag3Dy2(NO3)9 and qu­anti­tative comparison to isotypic compounds

Klein, W.

doi:10.1107/S2056989023004747

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ISSN: 2056-9890

Volume 79| Part 7| July 2023| Pages 600-604

https://doi.org/10.1107/S2056989023004747

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Crystal structure of Ag₃Dy₂(NO₃)₉ and quantitative comparison to isotypic compounds

Wilhelm Klein ^a ^*

^aTechnical University of Munich, School of Natural Sciences, Department of Chemistry, Lichtenbergstrasse 4, 85747 Garching, Germany
^*Correspondence e-mail: wilhelm.klein@tum.de

Edited by S. Parkin, University of Kentucky, USA (Received 4 April 2023; accepted 30 May 2023; online 2 June 2023)

Single crystals of Ag₃Dy₂(NO₃)₉ (trisilver didysprosium nonanitrate) were obtained from a mixture of AgNO₃ and Dy(NO₃)₃·5 H₂O. The new compound crystallizes in space group P4₁32 (No. 213) with a = 13.2004 (4) Å, V = 2300.2 (2) Å³, Z = 4. The Ag and Dy cations are coordinated by five and six bidentate nitrate anions, respectively. Ag₃Dy₂(NO₃)₉ is isostructural to several compounds that include alkali metals or ammonium and lanthanide cations, but silver and dysprosium are included for the first time and feature the smallest ion radii observed for this structure type to date. Crystal structures of isotypic compounds are compared.

Keywords: crystal structure; dysprosium; silver; nitrate.

CCDC reference: 2266445

1. Chemical context

Double nitrates of alkali metals and lanthanides of the composition A₃Ln₂(NO₃)₉ have been found to crystallize in the chiral space groups P4₁32 and P4₃32 (Wickleder, 2002 ). After the first finding of K₃Pr₂(NO₃)₉ by Carnall et al. (1973 ), this structure type has been observed in several compounds, to date with K (Carnall et al., 1973; Vigdorchik et al., 1992 ; Guillou et al., 1995 ; Gobichon et al., 1999 ), Rb (Vigdorchik et al., 1990 ; Manek & Meyer, 1993a ; Guillou et al., 1996 ), and NH₄ (Manek & Meyer, 1992 ) as 'A′ cations for the lighter lanthanides La–Sm, and also detached examples with Na at the 'A′ site (Stockhause & Meyer, 1997 ; Luo & Corruccini, 2004 ) and Eu (Manek & Meyer, 1992), Gd (Manek & Meyer, 1992; Luo & Corruccini, 2004), and even Bi (Goaz et al., 2012 ) at the lanthanide site have been reported. The compounds are typically synthesized by dissolving the lanthanide oxides or nitrates in melts of the respective alkali metal or ammonium nitrates under anhydrous atmosphere, while lanthanum and cerium compounds have been crystallized from solutions in H₂O or HNO₃ (Guillou et al., 1995, 1996; Gobichon et al., 1999). For the heavier lanthanides, usually another structure type with a slightly different composition, namely in an A/Ln ratio of 2:1 instead of 3:2, is observed under similar reaction conditions (Manek & Meyer, 1992, 1993a), and also for lithium, e.g. after the use of LiNO₃ as a starting material, compounds with 2:1 ratio seem to be favoured (Manek & Meyer, 1993b ).

In this work a new member of this group of compounds, Ag₃Dy₂(NO₃)₉, is presented, the first one containing Ag and Dy, which has been found to crystallize in the above-mentioned structure type.

2. Structural commentary

Similar to many related compounds, the title compound was obtained from a melt of nitrates, in this case silver nitrate and dysprosium nitrate pentahydrate. However, while for synthesis of related compounds, oxides are often used as lanthanide sources and the respective alkali metal nitrate or a eutectic combination of nitrates act as solvent as well as nitrate donor, in the present experimental setting the nitrates can be deployed in stoichiometric amounts. The crystals, which were found to be suitable for structure determination were obtained from a 2:1 mixture of Ag and Dy nitrates, i.e. a slight excess of AgNO₃, as described in the experimental section. The surplus Ag is present as remaining AgNO₃ as well as elemental silver after partial thermal or light-induced decomposition. So far, no hint of another compound with a 2:1 composition of metals in the Ag/Dy system, as could be expected for smaller lanthanides similar to the alkali metal or ammonium systems (Manek & Meyer, 1992, 1993a), has been observed.

Ag₃Dy₂(NO₃)₉ (Fig. 1) crystallizes in space group P4₁32 with most atoms at general positions except for Ag, N1 and O1 at 12d and Dy at 8c Wyckoff positions. The asymmetric unit comprises one Ag, one Dy, two N, and five O atoms. The Dy atom, being located on a threefold axis, is coordinated by six bidentate nitrate anions with Dy—O distances of 2.557 (11)–2.732 (11) Å (see Fig. 2a), the surrounding oxygen atoms form a distorted icosahedron (Fig. 2b). The polyhedra are connected to neighbouring icosahedra via common vertices, and inside this polyhedron the Dy atom is slightly off-centre, shown by formation of the shortest Dy—O distances to O3 and O4 as part of the same NO₃⁻ anion (the lower one in Fig. 2b), most probably driven by repulsion of next-neighbour Dy atoms. The silver atom is also coordinated by five nitrate ions in exclusively bidentate manner (Fig. 3). The Ag—O distances span quite a large range, so besides eight distances between 2.741 (11) and 3.004 (11) Å two relatively short distances of 2.383 (15) Å are found. These short bonds include oxygen atoms in almost opposite positions, which form an O—Ag—O angle of 154.7 (6)°, indicating the preferred formation of AgO₂ dumbbells even in an environment of quite rigid complex anions, for instance observed in Ag₄SiO₄ (Klein & Jansen, 2008 ), in contrast to a more spherical `alkali metal-like' coordination as in Ag₃SbO₄ (distorted rock salt structure; Klein & Jansen, 2010 ). Consequently, the Ag atom has its largest axis of the displacement ellipsoid perpendicular to the AgO₂ dumbbell direction (see Fig. 3), which also represents the largest extension of an anisotropic parameter of all atoms in this structure (see supporting information, U₂₂). The two independent nitrate ions are perfectly planar, with O—N—O angle sums of 360.00 and 359.79° around N1 and N2, respectively. Both the nitrate ions are situated between three bidentately coordinated metal atoms forming almost planar AgDy₂(NO₃) and Ag₂Dy(NO₃) units, respectively, as illustrated in Fig. 4. The longest N—O distances and the smallest O—N—O angles are found in the direction of coordinated Dy atoms, and in addition the Ag atom coordination, including a short Ag—O distance shows an O—N—O angle slightly below the mean value.

Figure 1
Unit cell of Ag₃Dy₂(NO₃)₉, view along the c axis, atomic displacement ellipsoids are drawn with a probability of 60%.

Figure 2
Twelvefold coordination of the Dy³⁺ ion by six bidentate nitrate ions in Ag₃Dy₂(NO₃)₉: (a) view along the threefold symmetry axis; (b) distorted icosahedron around Dy. Atoms are drawn at the 60% probability level. [Symmetry codes: (i) z + $[{1\over 4}]$ , −y + $[{1\over 4}]$ , x − $[{1\over 4}]$ ; (iv) x − $[{1\over 4}]$ , z + $[{1\over 4}]$ , −y + $[{1\over 4}]$ ; (v) −y + $[{1\over 4}]$ , x − $[{1\over 4}]$ , z + $[{1\over 4}]$ ; (vi) −y + $[{1\over 2}]$ , −z, x − $[{1\over 2}]$ ; (vii) x − $[{1\over 2}]$ ; −y + $[{1\over 2}]$ , −z; (viii) −z, x − $[{1\over 2}]$ , −y + $[{1\over 2}]$ .]

Figure 3
Coordination of the Ag⁺ cation by five bidentate nitrate anions. The shorter Ag—O bonds, which define the AgO₂ dumbbell, are emphasized, displacement ellipsoids are drawn at the 60% probability level. [Symmetry codes: (ii) y, z, x; (iii) x + $[{1\over 4}]$ , −z + $[{1\over 4}]$ , y − $[{1\over 4}]$ .]

Figure 4
Planar surrounding of the two independent nitrate anions: NO₃(1) (upper) coordinating two Dy and one Ag, view perpendicular to the twofold symmetry axis through Ag, N1, and O1; NO₃(2) (lower) coordinating one Dy and two Ag, the short Ag—O5 bond is drawn thicker than other Ag—O bonds. All atoms are shown at the 60% probability level. [Symmetry codes: (i) z + $[{1\over 4}]$ , −y + $[{1\over 4}]$ , x − $[{1\over 4}]$ ; (iv) x − $[{1\over 4}]$ , z + $[{1\over 4}]$ , −y + $[{1\over 4}]$ ; (ix) y + $[{1\over 4}]$ , −x + $[{1\over 4}]$ , z − $[{1\over 4}]$ ; (x) x + $[{1\over 2}]$ , −y + $[{1\over 2}]$ , −z.]

The appearance of this structure type for the combination Ag–Dy is somewhat remarkable. While silver as an atypical single-charged cation deforms its direct environment slightly to achieve a more convenient coordinative situation as explained above, dysprosium represents the heaviest lanthanide and, thus, the one with the smallest ionic radius observed in this structure type so far (Shannon, 1976 ), and a twelve-coordinate site seems to be unusual for this small lanthanide. This view is supported by the finding that compounds that include smaller lanthanide cations avoid to adopt this structure type in favour of another structure with a smaller coordination number and even a slightly different composition (A/Ln = 2:1; Manek & Meyer, 1992, 1993a). Additionally, this might be confirmed by the `underbonding' of the Dy cation, as the bond-valence sums (Brown & Altermatt, 1985 ) are calculated to be 2.51 valence units for the threefold positively charged ion, according to the parameters of Brese & O'Keeffe (1991 ).

The crystal structure has been quantitatively compared to isotypic structures by applying the program compstru (de la Flor et al., 2016 ), available at the Bilbao Crystallographic Server (Aroyo et al., 2006 ). With Ag₃Dy₂(NO₃)₉ as the reference structure, Table 1 lists the absolute distances between paired atoms as well as the arithmetic mean of the distance (d_av) between paired atoms, the degree of lattice deviation (S) and the measure of similarity (Δ). Generally, the low values for S and Δ indicate a close relationship between all phases, including the trend to increasing numbers at larger differences of lattice parameters from Na to Rb compounds. The differences of d_av, S, and Δ are of course determined in a higher degree by the more differing radii of the (more frequent) alkali metal cations than by those of the more similar lanthanide ions. Significantly, in all cases the largest displacements between atom pairs are observed for O5, i.e. the closest Ag-coordinating O atom, confirming the special bonding situation for Ag including the above-mentioned AgO₂ dumbbells. Consequently, the whole NO₃ anion, of which O5 is a part, is shifted slightly more than the atoms of the other anion. The Ag atom is also affected, as indicated by higher Ag—A displacements than those of the lanthanide cation pairs, while the coordination of the Ln cations remains similar (distortedly icosahedral, slightly off-centered), just accompanied by decreasing Ln—O distances with decreasing cation radii. An exception represents the, so far, only known Na structure, where the similarity as well as the relative displacements are about one order lower than for all other examples, indicating that the packing is distorted to a similar degree by the small Na cation as in the title compound by the Ag cation. However, the closest Ag—O distance is shorter than all Na—O distances in the related Na₃Nd₂(NO₃)₉.

Table 1
Structure comparison of Ag₃Dy₂(NO₃)₉ with Na₃Nd₂(NO₃)₉^a, K₃Ce₂(NO₃)₉^b, K₃Pr₂(NO₃)₉^c,g, Rb₃Ce₂(NO₃)₉^d, Rb₃Pr₂(NO₃)₉^e,g, and Rb₃Nd₂(NO₃)₉^f,g, by using the program Compstru (de la Flor et al., 2016)

Cubic lattice parameters (Å), absolute atomic displacements (Å), arithmetic mean displacements (d_av; Å), degree of lattice distortion (S), and measure of similarity (Δ)^h.

A =	Na	K	K	Rb	Rb	Rb
Ln =	Nd	Ce	Pr	Ce	Pr	Nd

a	13.1279	13.5975	13.52	13.8411	13.8091	13.759

A	0.0035	0.3157	0.3325	0.4725	0.4680	0.4729
Ln	0.0151	0.2318	0.2440	0.3670	0.3768	0.3885
N1	0.0261	0.1605	0.1997	0.1848	0.2296	0.2352
O1	0.0187	0.2072	0.2035	0.2576	0.2912	0.3080
O2	0.0170	0.1786	0.1821	0.2763	0.2582	0.2646
N2	0.0223	0.3350	0.3555	0.5195	0.4883	0.4907
O3	0.0577	0.3059	0.3072	0.4321	0.4278	0.4502
O4	0.0346	0.3302	0.3271	0.4027	0.4815	0.4732
O5	0.0577	0.4583	0.4839	0.6160	0.6490	0.6483

d_av	0.0320	0.2966	0.3080	0.4136	0.4280	0.4338
S	0.0032	0.0166	0.0135	0.0261	0.0249	0.0230
Δ	0.003	0.032	0.033	0.044	0.046	0.046
Notes: (a) Stockhause & Meyer (1997); (b) Guillou et al. (1995); (c) Carnall et al. (1973); (d) Guillou et al. (1996); (e) Manek & Meyer (1993a); (f) Vigdorchik et al. (1990); (g) K₃Pr₂(NO₃)₉, Rb₃Pr₂(NO₃)₉, and Rb₃Nd₂(NO₃)₉ were originally described in P4₃32 and were transformed into P4₁32; (h) atom displacements are calculated by applying the lattice parameter of Ag₃Dy₂(NO₃)₉ [a = 13.2004 (4) Å] to the structure models of the listed compounds.

3. Database survey

Several anhydrous rare-earth double nitrates of the composition A₃Ln₂(NO₃)₉ have been investigated, mainly including larger lanthanide elements and alkali metals of medium size or ammonium cations, as listed in the Chemical context. Obviously, all of them seem to crystallize in the above-mentioned structure type, however, for some of them only the cubic lattice parameter is given. To date, detailed structural data are available for K₃La₂(NO₃)₉ (Gobichon et al., 1999), K₃Ce₂(NO₃)₉ (Guillou et al., 1995), Rb₃Ce₂(NO₃)₉ (Guillou et al., 1996), K₃Pr₂(NO₃)₉ (Carnall et al., 1973), Rb₃Pr₂(NO₃)₉ (Manek & Meyer, 1993a), (NH₄)₃Pr₂(NO₃)₉ (Manek & Meyer, 1992), Na₃Nd₂(NO₃)₉ (Stockhause & Meyer, 1997), K₃Nd₂(NO₃)₉ (Vigdorchik et al., 1992), Rb₃Nd₂(NO₃)₉ (Vigdorchik et al., 1990), and K₃Bi₂(NO₃)₉ (Goaz et al., 2012).

4. Synthesis and crystallization

An alumina crucible was charged with 359 mg AgNO₃ (2.1 mmol; Merck; p.A.) and 495 mg Dy(NO₃)₃·5H₂O (1.1 mmol; Alfa Aesar; 99.99%). The mixture was melted together at 573 K for 72 h in an Ar atmosphere, and was cooled down to 453 K at a rate of 0.1 K min⁻¹. Within an amorphous yellow–grey matrix, pale-yellow plates were found that were hygroscopic. EDX measurements on several crystals confirm the presence of Ag and Dy as the only elements heavier than oxygen. For the X-ray data collection, crystals were immersed into perfluoroalkyl ether, which covers and acts as glue on a glass tip during the data collection at low temperatures.

5. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2. The structure was refined as an inversion twin.

Table 2
Experimental details

Crystal data
Chemical formula	Ag₃Dy₂(NO₃)₉
M_r	1206.70
Crystal system, space group	Cubic, P4₁32
Temperature (K)	223
a (Å)	13.2004 (4)
V (Å³)	2300.2 (2)
Z	4
Radiation type	Mo Kα
μ (mm⁻¹)	9.07
Crystal size (mm)	0.4 × 0.3 × 0.1

Data collection
Diffractometer	Stoe StadiVari
Absorption correction	Empirical (using intensity measurements) (X-AREA; Stoe & Cie, 2015 )
T_min, T_max	0.001, 0.215
No. of measured, independent and observed [I > 2σ(I)] reflections	37326, 763, 715
R_int	0.159
(sin θ/λ)_max (Å⁻¹)	0.617

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.045, 0.122, 1.18
No. of reflections	763
Δρ_max, Δρ_min (e Å⁻³)	2.01, −1.07
Absolute structure	Refined as an inversion twin
Absolute structure parameter	0.18 (6)
Computer programs: X-AREA (Stoe & Cie, 2015), SHELXS97and SHELX (Sheldrick, 2008 ), SHELXL2014/7 (Sheldrick, 2015 ), DIAMOND (Brandenburg & Putz (2018 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC reference: 2266445

Crystal structure: contains datablocks global, I. DOI: https://doi.org/10.1107/S2056989023004747/pk2686sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989023004747/pk2686Isup2.hkl

checkCIF report

Computing details top

Data collection: X-AREA (Stoe & Cie, 2015); cell refinement: X-AREA (Stoe & Cie, 2015); data reduction: X-AREA (Stoe & Cie, 2015); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2015); molecular graphics: DIAMOND 3.2k (Brandenburg & Putz (2018); software used to prepare material for publication: SHELX (Sheldrick, 2008) and publCIF (Westrip, 2010).

Trisilver Didysprosium nonanitrate top

Crystal data top

Ag₃Dy₂(NO₃)₉	Mo Kα radiation, λ = 0.71073 Å
M_r = 1206.70	Cell parameters from 63387 reflections
Cubic, P4₁32	θ = 2.2–30.7°
a = 13.2004 (4) Å	µ = 9.07 mm⁻¹
V = 2300.2 (2) Å³	T = 223 K
Z = 4	Plate, yellow
F(000) = 2208	0.4 × 0.3 × 0.1 mm
D_x = 3.485 Mg m⁻³

Data collection top

Stoe StadiVari diffractometer	763 independent reflections
Radiation source: Genix 3D HF Mo	715 reflections with I > 2σ(I)
Graded multilayer mirror monochromator	R_int = 0.159
Detector resolution: 5.81 pixels mm^-1	θ_max = 26.0°, θ_min = 2.2°
ω scans	h = −16→16
Absorption correction: empirical (using intensity measurements) (X-AREA; Stoe & Cie, 2015)	k = −16→16
T_min = 0.001, T_max = 0.215	l = −16→16
37326 measured reflections

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)] = 0.045	w = 1/[σ²(F_o²) + (0.0538P)² + 51.0589P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.122	(Δ/σ)_max < 0.001
S = 1.18	Δρ_max = 2.01 e Å⁻³
763 reflections	Δρ_min = −1.07 e Å⁻³
65 parameters	Absolute structure: Refined as an inversion twin
0 restraints	Absolute structure parameter: 0.18 (6)

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.

Refinement. Refined as a 2-component inversion twin.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Ag	0.42059 (11)	0.1250	0.17059 (11)	0.0411 (6)
Dy	0.03885 (6)	0.03885 (6)	0.03885 (6)	0.0233 (4)
N1	0.2541 (9)	0.1250	0.0041 (9)	0.014 (4)
O1	0.1852 (8)	0.1250	−0.0648 (8)	0.021 (3)
O2	0.2346 (8)	0.0854 (8)	0.0870 (8)	0.022 (2)
N2	0.3881 (11)	0.3676 (11)	0.1011 (10)	0.023 (3)
O3	0.4747 (8)	0.3304 (9)	0.0888 (9)	0.025 (2)
O4	0.3674 (8)	0.4493 (8)	0.0530 (9)	0.024 (2)
O5	0.3217 (10)	0.3253 (11)	0.1508 (9)	0.035 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ag	0.0260 (7)	0.0713 (17)	0.0260 (7)	−0.0052 (7)	−0.0006 (8)	0.0052 (7)
Dy	0.0233 (4)	0.0233 (4)	0.0233 (4)	0.0002 (3)	0.0002 (3)	0.0002 (3)
N1	0.015 (5)	0.011 (8)	0.015 (5)	0.000 (4)	−0.001 (7)	0.000 (4)
O1	0.022 (5)	0.017 (7)	0.022 (5)	−0.005 (4)	−0.003 (6)	0.005 (4)
O2	0.026 (6)	0.022 (5)	0.018 (5)	0.001 (4)	0.000 (5)	0.007 (4)
N2	0.019 (7)	0.031 (8)	0.018 (7)	−0.006 (6)	0.001 (5)	−0.004 (6)
O3	0.015 (5)	0.030 (6)	0.029 (6)	0.005 (5)	0.005 (5)	0.008 (5)
O4	0.022 (6)	0.017 (5)	0.033 (7)	0.001 (5)	−0.001 (5)	0.000 (5)
O5	0.036 (7)	0.043 (8)	0.027 (6)	−0.014 (6)	0.008 (6)	0.007 (6)

Geometric parameters (Å, º) top

Ag—O5ⁱ	2.383 (15)	Dy—O1ⁱ	2.626 (2)
Ag—O5ⁱⁱ	2.383 (15)	Dy—O1^vii	2.626 (2)
Ag—O2ⁱⁱⁱ	2.741 (11)	Dy—O1	2.626 (2)
Ag—O2	2.741 (11)	Dy—O2	2.732 (11)
Ag—O4ⁱⁱ	2.793 (11)	Dy—O2^vii	2.732 (11)
Ag—O4ⁱ	2.793 (11)	Dy—O2ⁱ	2.732 (11)
Ag—O5ⁱⁱⁱ	2.960 (15)	N1—O2	1.240 (14)
Ag—O5	2.960 (15)	N1—O2ⁱⁱⁱ	1.240 (14)
Ag—N2ⁱⁱ	2.972 (14)	N1—O1	1.29 (2)
Ag—N2ⁱ	2.972 (14)	O1—Dy^viii	2.626 (2)
Ag—O3	3.004 (11)	N2—O5	1.230 (17)
Ag—O3ⁱⁱⁱ	3.004 (11)	N2—O3	1.255 (18)
Dy—O3^iv	2.557 (11)	N2—O4	1.281 (18)
Dy—O3^v	2.557 (11)	N2—Ag^vii	2.972 (14)
Dy—O3^vi	2.557 (11)	O3—Dy^ix	2.557 (11)
Dy—O4^vi	2.572 (11)	O4—Dy^ix	2.572 (11)
Dy—O4^iv	2.572 (11)	O4—Ag^vii	2.793 (11)
Dy—O4^v	2.572 (11)	O5—Ag^vii	2.383 (15)

O5ⁱ—Ag—O5ⁱⁱ	154.7 (6)	O3^vi—Dy—O4^v	118.6 (3)
O5ⁱ—Ag—O2ⁱⁱⁱ	120.7 (4)	O4^vi—Dy—O4^v	70.6 (4)
O5ⁱⁱ—Ag—O2ⁱⁱⁱ	83.8 (4)	O4^iv—Dy—O4^v	70.6 (4)
O5ⁱ—Ag—O2	83.8 (4)	O3^iv—Dy—O1ⁱ	66.9 (4)
O5ⁱⁱ—Ag—O2	120.7 (4)	O3^v—Dy—O1ⁱ	67.4 (3)
O2ⁱⁱⁱ—Ag—O2	46.8 (4)	O3^vi—Dy—O1ⁱ	168.5 (4)
O5ⁱ—Ag—O4ⁱⁱ	109.2 (4)	O4^vi—Dy—O1ⁱ	139.4 (2)
O5ⁱⁱ—Ag—O4ⁱⁱ	48.8 (3)	O4^iv—Dy—O1ⁱ	112.0 (4)
O2ⁱⁱⁱ—Ag—O4ⁱⁱ	115.5 (3)	O4^v—Dy—O1ⁱ	72.6 (3)
O2—Ag—O4ⁱⁱ	162.3 (3)	O3^iv—Dy—O1^vii	168.5 (4)
O5ⁱ—Ag—O4ⁱ	48.8 (3)	O3^v—Dy—O1^vii	66.9 (4)
O5ⁱⁱ—Ag—O4ⁱ	109.2 (4)	O3^vi—Dy—O1^vii	67.4 (3)
O2ⁱⁱⁱ—Ag—O4ⁱ	162.3 (3)	O4^vi—Dy—O1^vii	72.6 (3)
O2—Ag—O4ⁱ	115.5 (3)	O4^iv—Dy—O1^vii	139.4 (2)
O4ⁱⁱ—Ag—O4ⁱ	82.1 (5)	O4^v—Dy—O1^vii	112.0 (4)
O5ⁱ—Ag—O5ⁱⁱⁱ	116.8 (5)	O1ⁱ—Dy—O1^vii	106.9 (3)
O5ⁱⁱ—Ag—O5ⁱⁱⁱ	73.3 (5)	O3^iv—Dy—O1	67.4 (3)
O2ⁱⁱⁱ—Ag—O5ⁱⁱⁱ	74.9 (3)	O3^v—Dy—O1	168.5 (4)
O2—Ag—O5ⁱⁱⁱ	64.8 (3)	O3^vi—Dy—O1	66.9 (4)
O4ⁱⁱ—Ag—O5ⁱⁱⁱ	116.5 (3)	O4^vi—Dy—O1	112.0 (4)
O4ⁱ—Ag—O5ⁱⁱⁱ	96.8 (3)	O4^iv—Dy—O1	72.6 (3)
O5ⁱ—Ag—O5	73.3 (5)	O4^v—Dy—O1	139.4 (2)
O5ⁱⁱ—Ag—O5	116.8 (5)	O1ⁱ—Dy—O1	106.9 (3)
O2ⁱⁱⁱ—Ag—O5	64.8 (3)	O1^vii—Dy—O1	106.9 (3)
O2—Ag—O5	74.9 (3)	O3^iv—Dy—O2	65.6 (4)
O4ⁱⁱ—Ag—O5	96.8 (3)	O3^v—Dy—O2	122.7 (4)
O4ⁱ—Ag—O5	116.5 (3)	O3^vi—Dy—O2	108.3 (3)
O5ⁱⁱⁱ—Ag—O5	136.1 (5)	O4^vi—Dy—O2	158.2 (3)
O5ⁱ—Ag—N2ⁱⁱ	133.8 (4)	O4^iv—Dy—O2	104.7 (3)
O5ⁱⁱ—Ag—N2ⁱⁱ	23.4 (4)	O4^v—Dy—O2	129.0 (4)
O2ⁱⁱⁱ—Ag—N2ⁱⁱ	99.1 (3)	O1ⁱ—Dy—O2	62.4 (2)
O2—Ag—N2ⁱⁱ	142.2 (4)	O1^vii—Dy—O2	103.1 (4)
O4ⁱⁱ—Ag—N2ⁱⁱ	25.4 (3)	O1—Dy—O2	47.8 (4)
O4ⁱ—Ag—N2ⁱⁱ	97.1 (3)	O3^iv—Dy—O2^vii	122.7 (4)
O5ⁱⁱⁱ—Ag—N2ⁱⁱ	94.4 (4)	O3^v—Dy—O2^vii	108.3 (3)
O5—Ag—N2ⁱⁱ	108.1 (3)	O3^vi—Dy—O2^vii	65.6 (4)
O5ⁱ—Ag—N2ⁱ	23.4 (4)	O4^vi—Dy—O2^vii	104.7 (3)
O5ⁱⁱ—Ag—N2ⁱ	133.8 (4)	O4^iv—Dy—O2^vii	129.0 (4)
O2ⁱⁱⁱ—Ag—N2ⁱ	142.2 (4)	O4^v—Dy—O2^vii	158.2 (3)
O2—Ag—N2ⁱ	99.1 (3)	O1ⁱ—Dy—O2^vii	103.1 (4)
O4ⁱⁱ—Ag—N2ⁱ	97.1 (3)	O1^vii—Dy—O2^vii	47.8 (4)
O4ⁱ—Ag—N2ⁱ	25.4 (3)	O1—Dy—O2^vii	62.4 (2)
O5ⁱⁱⁱ—Ag—N2ⁱ	108.1 (3)	O2—Dy—O2^vii	60.9 (4)
O5—Ag—N2ⁱ	94.4 (4)	O3^iv—Dy—O2ⁱ	108.3 (3)
N2ⁱⁱ—Ag—N2ⁱ	117.8 (5)	O3^v—Dy—O2ⁱ	65.6 (4)
O5ⁱ—Ag—O3	107.3 (4)	O3^vi—Dy—O2ⁱ	122.7 (4)
O5ⁱⁱ—Ag—O3	75.0 (4)	O4^vi—Dy—O2ⁱ	129.0 (4)
O2ⁱⁱⁱ—Ag—O3	66.5 (3)	O4^iv—Dy—O2ⁱ	158.2 (3)
O2—Ag—O3	103.9 (3)	O4^v—Dy—O2ⁱ	104.7 (3)
O4ⁱⁱ—Ag—O3	61.3 (3)	O1ⁱ—Dy—O2ⁱ	47.8 (4)
O4ⁱ—Ag—O3	127.5 (3)	O1^vii—Dy—O2ⁱ	62.4 (2)
O5ⁱⁱⁱ—Ag—O3	132.0 (3)	O1—Dy—O2ⁱ	103.1 (4)
O5—Ag—O3	42.9 (3)	O2—Dy—O2ⁱ	60.9 (4)
N2ⁱⁱ—Ag—O3	65.8 (3)	O2^vii—Dy—O2ⁱ	60.9 (4)
N2ⁱ—Ag—O3	119.9 (4)	O2—N1—O2ⁱⁱⁱ	122.9 (18)
O5ⁱ—Ag—O3ⁱⁱⁱ	75.0 (4)	O2—N1—O1	118.5 (9)
O5ⁱⁱ—Ag—O3ⁱⁱⁱ	107.3 (4)	O2ⁱⁱⁱ—N1—O1	118.5 (9)
O2ⁱⁱⁱ—Ag—O3ⁱⁱⁱ	103.9 (3)	N1—O1—Dy	98.7 (3)
O2—Ag—O3ⁱⁱⁱ	66.5 (3)	N1—O1—Dy^viii	98.7 (3)
O4ⁱⁱ—Ag—O3ⁱⁱⁱ	127.5 (3)	Dy—O1—Dy^viii	162.6 (6)
O4ⁱ—Ag—O3ⁱⁱⁱ	61.3 (3)	N1—O2—Dy	94.9 (9)
O5ⁱⁱⁱ—Ag—O3ⁱⁱⁱ	42.9 (3)	N1—O2—Ag	95.1 (9)
O5—Ag—O3ⁱⁱⁱ	132.0 (3)	Dy—O2—Ag	169.6 (5)
N2ⁱⁱ—Ag—O3ⁱⁱⁱ	119.9 (4)	O5—N2—O3	122.7 (15)
N2ⁱ—Ag—O3ⁱⁱⁱ	65.8 (3)	O5—N2—O4	119.7 (14)
O3—Ag—O3ⁱⁱⁱ	170.1 (5)	O3—N2—O4	117.4 (13)
O3^iv—Dy—O3^v	116.77 (16)	O5—N2—Ag^vii	50.3 (9)
O3^iv—Dy—O3^vi	116.77 (16)	O3—N2—Ag^vii	170.4 (11)
O3^v—Dy—O3^vi	116.77 (16)	O4—N2—Ag^vii	69.4 (8)
O3^iv—Dy—O4^vi	118.6 (3)	N2—O3—Dy^ix	97.0 (9)
O3^v—Dy—O4^vi	76.0 (4)	N2—O3—Ag	95.2 (9)
O3^vi—Dy—O4^vi	50.0 (3)	Dy^ix—O3—Ag	157.7 (5)
O3^iv—Dy—O4^iv	50.0 (3)	N2—O4—Dy^ix	95.6 (8)
O3^v—Dy—O4^iv	118.6 (3)	N2—O4—Ag^vii	85.1 (8)
O3^vi—Dy—O4^iv	76.0 (4)	Dy^ix—O4—Ag^vii	170.9 (5)
O4^vi—Dy—O4^iv	70.6 (4)	N2—O5—Ag^vii	106.3 (11)
O3^iv—Dy—O4^v	76.0 (4)	N2—O5—Ag	98.0 (11)
O3^v—Dy—O4^v	50.0 (3)	Ag^vii—O5—Ag	148.6 (5)

Symmetry codes: (i) y, z, x; (ii) x+1/4, −z+1/4, y−1/4; (iii) z+1/4, −y+1/4, x−1/4; (iv) −y+1/2, −z, x−1/2; (v) −z, x−1/2, −y+1/2; (vi) x−1/2, −y+1/2, −z; (vii) z, x, y; (viii) y+1/4, −x+1/4, z−1/4; (ix) x+1/2, −y+1/2, −z.

Structure comparison of Ag₃Dy₂(NO₃)₉ with Na₃Nd₂(NO₃)₉^a, K₃Ce₂(NO₃)₉^b, K₃Pr₂(NO₃)₉^c^,^g, Rb₃Ce₂(NO₃)₉^d, Rb₃Pr₂(NO₃)₉^e^,^g, and Rb₃Nd₂(NO₃)₉^f^,^g, by using the program Compstru (de la Flor et al., 2016) top

Cubic lattice parameters (Å), absolute atomic displacements (Å), arithmetic mean displacements (d_av; Å), degree of lattice distortion (S), and measure of similarity (Δ)^h.

A =	Na	K	K	Rb	Rb	Rb
Ln =	Nd	Ce	Pr	Ce	Pr	Nd

a	13.1279	13.5975	13.52	13.8411	13.8091	13.759

A	0.0035	0.3157	0.3325	0.4725	0.4680	0.4729
Ln	0.0151	0.2318	0.2440	0.3670	0.3768	0.3885
N1	0.0261	0.1605	0.1997	0.1848	0.2296	0.2352
O1	0.0187	0.2072	0.2035	0.2576	0.2912	0.3080
O2	0.0170	0.1786	0.1821	0.2763	0.2582	0.2646
N2	0.0223	0.3350	0.3555	0.5195	0.4883	0.4907
O3	0.0577	0.3059	0.3072	0.4321	0.4278	0.4502
O4	0.0346	0.3302	0.3271	0.4027	0.4815	0.4732
O5	0.0577	0.4583	0.4839	0.6160	0.6490	0.6483

d_av	0.0320	0.2966	0.3080	0.4136	0.4280	0.4338
S	0.0032	0.0166	0.0135	0.0261	0.0249	0.0230
Δ	0.003	0.032	0.033	0.044	0.046	0.046

Notes: (a) Stockhause & Meyer (1997); (b) Guillou et al. (1995); (c) Carnall et al. (1973); (d) Guillou et al. (1996); (e) Manek & Meyer (1993a); (f) Vigdorchik et al. (1990); (g) K₃Pr₂(NO₃)₉, Rb₃Pr₂(NO₃)₉, and Rb₃Nd₂(NO₃)₉ were originally described in P4₃32 and were transformed into P4₁32; (h) atom displacements are calculated by applying the lattice parameter of Ag₃Dy₂(NO₃)₉ [a = 13.2004 (4) Å] to the structure models of the listed compounds.

Acknowledgements

Maria Müller is gratefully acknowledged for the EDX measurements.

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