Synthesis and crystal structure of a new magnesium phosphate Na₃RbMg₇(PO₄)₆

Trisodium rubidium hepta­magnesium hexakis(ortho­phosphate) exhibits a new structure type, with MgO_x (x = 5 and 6) polyhedra linked directly to each other through common corners or edges and reinforced by corner-sharing with PO₄ tetra­hedra. The resulting anionic three-dimensional framework leads to the formation of channels in which the Na⁺ cations are located, while the Rb⁺ cations are located in large inter­stitial cavities.

Abstract

A new magnesium phosphate, Na₃RbMg₇(PO₄)₆ [tris­odium rubidium hepta­magnesium hexakis(ortho­phosphate)], has been synthesized as single crystals by the flux method and exhibits a new structure type. Its original structure is built up from MgO_x (x = 5 and 6) polyhedra linked directly to each other through common corners or edges and reinforced by corner-sharing with PO₄ tetra­hedra. The resulting anionic three-dimensional framework leads to the formation of channels along the [010] direction, in which the Na⁺ cations are located, while the Rb⁺ cations are located in large inter­stitial cavities.

Chemical context  

Magnesium phosphates are of increasing inter­est because of their potential applications as host materials for optically active rare earth ions (Seo, 2013 ▸; Kim et al., 2013 ▸; Boukhris et al., 2015 ▸). Moreover, these materials are very attractive in terms of basic research because they exhibit a rich structural chemistry due to their polymorphism (Ait Benhamou et al., 2010 ▸; Orlova et al., 2015 ▸).

Among the variety of magnesium monophosphates synthesized and characterized up to now, only four compounds belong to the system Na₃PO₄–Mg₃(PO₄)₂, namely NaMgPO₄, NaMg₄(PO₄)₃, Na₂Mg₅(PO₄)₄ and Na₄Mg(PO₄)₂ (Imura & Kawahara, 1997 ▸; Ben Amara et al., 1983 ▸; Yamakawa et al., 1994 ▸; Ghorbel et al., 1974 ▸). NaMgPO₄ compound crystallizes in the ortho­rhom­bic system with space group P2₁2₁2₁. Its structure involves MgO₆ and MgO₅ polyhedra linked by the monophosphate groups that form a three-dimensional framework. NaMg₄(PO₄)₃ is also ortho­rhom­bic, space group Pnma. Its structure is built up from three kinds of MgO₅ units sharing edges and corners and linked to each other by the PO₄ tetra­hedra, leading to a three-dimensional framework. Na₂Mg₅(PO₄)₄, synthesized under pressure, crystallizes in the triclinic system. Its structure results from a three-dimensional framework of MgO₆ and MgO₅ polyhedra connected either directly via common corners or by means of the phosphate groups. Na₄Mg(PO₄)₂ exhibits two polymorphs, which were only identified by their powder diffraction patterns.

Starting from these compounds, suitable replacements of magnesium and/or sodium by large cations induces their transformation into several structural types for different Mg/P atomic ratios. NaMMg(PO₄)₂ (M = Ca, Sr and Ba) compounds are related to the glaserite-type structure (Alkemper & Fuess, 1998 ▸; Boukhris et al., 2012 ▸, 2013 ▸). They adopt an anionic two-dimensional network with different symmetries as a function of the size of the M ²⁺ cation. For an atomic ratio M:P of 7:6, magnesium phosphate compounds adopt a three-dimensional network related to the fillowite-type structure, as observed in Na₄Ca₄Mg₂₁(PO₄)₁₈, Na₂CaMg₇(PO₄)₆ and Na_2.5Y_0.5Mg₇(PO₄)₆ (Domanskii et al., 1982 ▸; McCoy et al., 1994 ▸; Jerbi et al., 2010a ▸). All of them crystallize with trigonal symmetry (space group R ) and differ only by their cationic distributions. Three-dimensional anionic networks includes also original structures such as those observed in Na₁₈Ca₁₃Mg₅(PO₄)₁₈, NaCa₉Mg(PO₄)₇, Na₇ LnMg₁₃(PO₄)₁₂ (Ln = La, Eu, Nd) (Yamakawa et al., 1994 ▸; Morozov et al., 1997 ▸; Jerbi et al., 2010b ▸, 2012 ▸).

As a contribution to the investigation of the above-mentioned systems, we report here the structural characterization of a new magnesium phosphate Na₃RbMg₇(PO₄)₆, which is, to our knowledge, the first magnesium phosphate revealing an original structure for an atomic ratio Mg/P equal to 7/6.

Structural commentary  

To the best of our knowledge, Na₃RbMg₇(PO₄)₆ exhibits a new structure type. A projection along the [010] direction of its structure (Fig. 1 ▸) clearly evidences the three-dimensional character of its anionic framework, which is built up from five different polyhedra MgO_x (x = 5, 6) and three kinds of PO₄ tetra­hedra connected together by sharing edges and corners. The Na⁺ cations are located within channels running along the [010] direction while the Rb⁺ cations are found in the large inter­stitial cavities.

Figure 1.

A view of the Na₃RbMg₇(PO₄)₆ structure along [010]. Colour key: MgO_x (x = 5 and 6; blue polyhedra), PO₄ (purple polyhedra), Rb (green spheres) and Na (yellow spheres).

A projection of the structure on the (012) plane (Fig. 2 ▸) shows that it can also be described on the basis of three kinds of rows (A, B and C) running parallel to the [100] direction. The first row (A; Fig. 3 ▸), consists of units with edge-sharing between one Na1O₈ and two Na2O₆ polyhedra. Such units alternate with Mg1O₅ polyhedra, leading to the sequence –Mg1–Na2–Na1–Na2–. The second row (B) consists of corner-sharing P2O₄, P3O₄, Mg4O₆ and Mg5O₅ polyhedra, forming the sequence –P3–Mg4–P2–Mg5–. Rows B and B′ are symmetrical with respect to the inversion centre located on the A row. The last row (C) includes units with corner-sharing between P1O₄ tetra­hedra and Mg₂O₁₀ dimers, which consist of edge-sharing MgiO₆ (i = 2, 3) octa­hedra. These units alternate with RbO₁₂ polyhedra to form a –P1–[Mg2,Mg3]–P1–Rb– sequence. These rows, connected to each other through common corners or edges, occur with a sequence of ABCB′.

Figure 2.

A view down the b axis, showing ABCB’ rows made of PO₄ tetra­hedra and Mg, Na and Rb atoms.

Figure 3.

A view of parallel rows of ABC polyhedra.

There are five distinct Mg sites. The Mg1 atom is displaced slightly from the inversion center, statistically occupying two symmetry-related positions. As a consequence, the Mg1O₆ polyhedron exhibits two distances that are long [2.241 (5) Å] compared to the other Mg1—O distances, which vary from 1.969 (10) to 2.030 (10) Å. Thus, this environment can be considered as [4 + 1]. The average value of 2.005 (10) Å calculated from the four short distances is slightly higher but consistent with that of 1.930 (2) Å reported for the tetra-coordinated Mg²⁺ cation in KMgPO₄ (Wallez et al.,1998 ▸). Sites Mg2 and Mg3 are located on twofold rotation axes and have slightly distorted octa­hedral environments with Mg—O distances varying from 2.052 (3) to 2.202 (2) Å for Mg2 and from 2.042 (2) to 2.169 (2) Å for Mg3. The corresponding average values of 2.123 and 2.103 Å, respectively, are in a good agreement with that of 2.14 Å observed for hexa-coordinated Mg²⁺ ions in Mg₃(PO₄)₂ (Jaulmes et al., 1997 ▸). Site Mg4 is [5 + 1]-coordinated, with five short distances varying from 1.981 (3) to 2.050 (3) Å and a sixth longer distance of 2.5734 (3) Å. A similar environment has already been observed in Mg₃(PO₄)₂ (Jaulmes et al., 1997 ▸). Site Mg5 is five-coordinated with Mg—O distances ranging from 2.020 (3) to 2.148 (3) Å. The corresponding mean distance of 2.07 Å is close to that of 2.08 Å observed for Mg²⁺ with the same coordination in NaMg₄(PO₄)₃ (Ben Amara et al., 1983 ▸). The P—O distances within the PO₄ tetra­hedra are in the range of 1.518 (2)–1.552 (2) Å with an overall mean value of 1.539 Å, very close to that of 1.537 Å predicted by Baur (1974 ▸) for monophosphate groups.

The environments of the alkali cations are shown in Fig. 4 ▸. Those of the two crystallographic distinct Na sites were determined assuming a maximum sodium–oxygen distance L _max of 3.13 Å, as suggested by Donnay & Allmann (1970 ▸). As in the case of the Mg1 atom, the sodium atom Na1 is also moved slightly away from the inversion center and statistically occupying two symmetry-related positions. This moving probably occurs to accommodate the environment of the Na1 site, which then consists of eight oxygen atoms with Na—O distances varying from 2.303 (7) to 2.963 (6) Å. Na2 is bound to only six oxygen atoms, with Na2—O distances in the range 2.246 (3)–2.962 (3) Å. The Rb⁺ ion is located on a twofold rotation axis and occupies a single site whose environment was determined assuming all Rb—O distances to be shorter than the shortest distance between Rb⁺ and its nearest cation. This environment then consists of twelve oxygen atoms with Rb—O distances ranging from 2.923 (3) to 3.517 (2) Å.

Figure 4.

The environment of the (a) Na1⁺, (b) Na2⁺ and (c) Rb⁺ cations, showing displacement ellipsoids drawn at the 50% probability level.

Synthesis and crystallization  

Single crystals of Na₃RbMg₇(PO₄)₆ were grown in a flux of sodium molybdate, Na₂MoO₄, with a P:Mo atomic ratio of 2:1. Appropriate amounts of the starting reactants (NH₄)H₂PO₄, Na₂CO₃, Rb₂CO₃, (MgCO₃)₄Mg(OH)₂·5H₂O and Na₂MoO₄·2H₂O were dissolved in nitric acid and the obtained solution was evaporated to dryness. The residue was homogenized by grinding in an agate mortar, and subsequently heated in a platinum crucible for 24 h at 673 K and then for 12 h at 873 K. After being reground, the sample was melted for 2 h at 1273 K and then cooled slowly down to room temperature at a rate of 10 K h⁻¹. The solidified melt was washed with boiling water to dissolve the flux. Colourless, irregularly shaped crystals were extracted from the final product.

Refinement  

Crystal data, data collection and structure refinement details are summarized in Table 1 ▸. The refinement was performed on the basis of electric neutrality and similar works. The atomic positions are determined by comparison with the refinements reported by Jerbi et al. (2010a ▸) and McCoy et al. (1994 ▸).

Table 1. Experimental details.

Crystal data
Chemical formula	Na3RbMg7(PO4)6
M r	894.43
Crystal system, space group	Monoclinic, C2/c
Temperature (K)	293
a, b, c (Å)	12.734 (3), 10.685 (3), 15.498 (5)
β (°)	112.83 (2)
V (Å3)	1943.5 (10)
Z	4
Radiation type	Mo Kα
μ (mm−1)	3.47
Crystal size (mm)	0.16 × 0.10 × 0.07
Data collection
Diffractometer	Enraf–Nonius Turbo CAD-4
Absorption correction	Part of the refinement model (ΔF) (Parkin et al., 1995 ▸)
T min, T max	0.377, 0.485
No. of measured, independent and observed [I > 2σ(I)] reflections	2333, 2333, 1968
R int	0.020
(sin θ/λ)max (Å−1)	0.660
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.036, 0.100, 1.07
No. of reflections	2333
No. of parameters	196
Δρmax, Δρmin (e Å−3)	0.87, −1.49

Computer programs: CAD-4 EXPRESS (Enraf–Nonius, 1994 ▸), XCAD4 (Harms & Wocadlo, 1995 ▸), SIR92 (Altomare et al., 1993 ▸), SHELXL2014 (Sheldrick, 2015 ▸), DIAMOND (Brandenburg et al., 1999 ▸) and WinGX (Farrugia, 2012 ▸).

Supplementary Material

CCDC reference: 1546558

Additional supporting information: crystallographic information; 3D view; checkCIF report

supplementary crystallographic information

Crystal data

Mg7Na3O24P6Rb	F(000) = 1744
Mr = 894.43	Dx = 3.057 Mg m−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 12.734 (3) Å	Cell parameters from 25 reflections
b = 10.685 (3) Å	θ = 7.5–10.8°
c = 15.498 (5) Å	µ = 3.47 mm−1
β = 112.83 (2)°	T = 293 K
V = 1943.5 (10) Å3	Prism, colourless
Z = 4	0.16 × 0.10 × 0.07 mm

Data collection

Enraf–Nonius Turbo CAD-4 diffractometer	Rint = 0.020
non–profiled ω/2τ scans	θmax = 28.0°, θmin = 2.6°
Absorption correction: part of the refinement model (ΔF) (Parkin et al., 1995)	h = −16→15
Tmin = 0.377, Tmax = 0.485	k = 0→14
2333 measured reflections	l = 0→20
2333 independent reflections	2 standard reflections every 60 min
1968 reflections with I > 2σ(I)	intensity decay: −2%

Refinement

Refinement on F2	196 parameters
Least-squares matrix: full	0 restraints
R[F2 > 2σ(F2)] = 0.036	w = 1/[σ2(Fo2) + (0.0549P)2 + 7.6361P] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.100	(Δ/σ)max < 0.001
S = 1.07	Δρmax = 0.87 e Å−3
2333 reflections	Δρmin = −1.49 e Å−3

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb	0.5000	0.74607 (5)	0.7500	0.02406 (16)
Na1	0.2552 (5)	0.7550 (6)	0.0226 (3)	0.0279 (12)	0.5
Na2	−0.01858 (14)	0.76242 (14)	0.98277 (13)	0.0226 (4)
Mg1	0.2487 (8)	0.2471 (9)	0.0142 (4)	0.0098 (10)	0.5
Mg2	0.0000	0.58859 (15)	0.7500	0.0071 (3)
Mg3	0.5000	0.62142 (14)	0.2500	0.0059 (3)
Mg4	0.18422 (9)	0.54259 (10)	0.12717 (7)	0.0065 (2)
Mg5	0.19042 (9)	0.99696 (11)	0.14183 (7)	0.0081 (2)
P1	0.28980 (7)	0.76938 (7)	0.27439 (6)	0.00668 (18)
O11	0.41297 (19)	0.7658 (2)	0.27801 (17)	0.0097 (5)
O12	0.25429 (18)	0.9074 (2)	0.27435 (15)	0.0084 (4)
O13	0.2043 (2)	0.7106 (3)	0.18543 (18)	0.0164 (5)
O14	0.2884 (2)	0.6963 (2)	0.36018 (17)	0.0146 (5)
P2	0.41165 (6)	0.50005 (7)	0.08098 (5)	0.00531 (18)
O21	0.53692 (18)	0.5150 (2)	0.15135 (15)	0.0084 (4)
O22	0.38853 (19)	0.5698 (2)	0.98959 (16)	0.0113 (5)
O23	0.34627 (19)	0.5654 (2)	0.13363 (15)	0.0085 (4)
O24	0.38345 (19)	0.3619 (2)	0.06370 (17)	0.0119 (5)
P3	0.09357 (6)	0.50198 (7)	0.92791 (5)	0.00484 (18)
O31	−0.03126 (18)	0.4851 (2)	0.86059 (16)	0.0100 (5)
O32	0.10990 (18)	0.6126 (2)	0.99444 (15)	0.0103 (5)
O33	0.15211 (18)	0.5301 (2)	0.85956 (16)	0.0109 (5)
O34	0.1418 (2)	0.3884 (2)	0.99025 (18)	0.0136 (5)

Atomic displacement parameters (Ų)

	U11	U22	U33	U12	U13	U23
Rb	0.0278 (3)	0.0250 (3)	0.0200 (3)	0.000	0.0099 (2)	0.000
Na1	0.0132 (16)	0.0218 (17)	0.050 (4)	−0.0034 (12)	0.014 (3)	0.009 (3)
Na2	0.0180 (8)	0.0166 (7)	0.0412 (10)	−0.0006 (6)	0.0202 (7)	−0.0027 (6)
Mg1	0.0043 (9)	0.0081 (11)	0.015 (3)	0.0002 (8)	0.001 (2)	−0.001 (3)
Mg2	0.0052 (7)	0.0109 (7)	0.0054 (7)	0.000	0.0021 (5)	0.000
Mg3	0.0044 (7)	0.0099 (7)	0.0050 (6)	0.000	0.0037 (5)	0.000
Mg4	0.0035 (5)	0.0114 (5)	0.0052 (5)	−0.0010 (4)	0.0024 (4)	0.0014 (4)
Mg5	0.0036 (5)	0.0166 (6)	0.0055 (5)	0.0009 (4)	0.0033 (4)	−0.0002 (4)
P1	0.0030 (3)	0.0093 (4)	0.0098 (4)	−0.0003 (3)	0.0046 (3)	−0.0010 (3)
O11	0.0045 (10)	0.0115 (11)	0.0158 (11)	0.0007 (8)	0.0070 (9)	0.0000 (9)
O12	0.0059 (10)	0.0106 (11)	0.0097 (11)	0.0019 (8)	0.0042 (9)	−0.0004 (8)
O13	0.0076 (11)	0.0216 (13)	0.0179 (12)	−0.0027 (10)	0.0026 (9)	−0.0117 (11)
O14	0.0149 (12)	0.0142 (12)	0.0203 (13)	0.0005 (10)	0.0129 (10)	0.0051 (10)
P2	0.0029 (4)	0.0105 (4)	0.0038 (4)	−0.0006 (3)	0.0028 (3)	−0.0011 (3)
O21	0.0027 (10)	0.0169 (11)	0.0056 (10)	−0.0002 (8)	0.0017 (8)	−0.0028 (8)
O22	0.0098 (11)	0.0191 (12)	0.0060 (10)	−0.0007 (9)	0.0043 (9)	0.0011 (9)
O23	0.0065 (10)	0.0139 (11)	0.0072 (10)	0.0000 (8)	0.0049 (8)	−0.0026 (9)
O24	0.0081 (11)	0.0112 (11)	0.0165 (12)	−0.0023 (9)	0.0049 (9)	−0.0042 (9)
P3	0.0025 (4)	0.0090 (4)	0.0040 (4)	0.0005 (3)	0.0024 (3)	0.0008 (3)
O31	0.0027 (10)	0.0181 (12)	0.0089 (11)	−0.0016 (9)	0.0018 (8)	−0.0003 (9)
O32	0.0091 (11)	0.0144 (11)	0.0082 (11)	0.0003 (9)	0.0041 (9)	−0.0034 (9)
O33	0.0044 (10)	0.0232 (12)	0.0066 (10)	0.0001 (9)	0.0037 (8)	0.0014 (9)
O34	0.0093 (11)	0.0141 (11)	0.0197 (12)	0.0061 (9)	0.0080 (9)	0.0088 (10)

Geometric parameters (Å, º)

Rb—O24i	2.923 (3)	Mg2—O33xvi	2.115 (2)
Rb—O24ii	2.923 (3)	Mg2—O33	2.115 (2)
Rb—O13iii	3.163 (3)	Mg2—O31	2.202 (2)
Rb—O13iv	3.163 (3)	Mg2—O31xvi	2.202 (2)
Rb—O31v	3.186 (2)	Mg3—O11	2.042 (2)
Rb—O31vi	3.186 (2)	Mg3—O11xvii	2.042 (2)
Rb—O21i	3.301 (2)	Mg3—O21	2.100 (2)
Rb—O21ii	3.301 (2)	Mg3—O21xvii	2.100 (2)
Rb—O14iii	3.452 (3)	Mg3—O23xvii	2.169 (2)
Rb—O14iv	3.452 (3)	Mg3—O23	2.169 (2)
Rb—O12iv	3.517 (2)	Mg4—O13	1.981 (3)
Rb—O12iii	3.517 (2)	Mg4—O12xv	2.026 (3)
Na1—O32vii	2.303 (7)	Mg4—O23	2.041 (2)
Na1—O32iv	2.318 (7)	Mg4—O32vii	2.043 (3)
Na1—O22iv	2.573 (7)	Mg4—O31xviii	2.050 (2)
Na1—O23	2.620 (7)	Mg4—O34vii	2.573 (3)
Na1—O22vii	2.782 (7)	Mg5—O22iv	2.020 (3)
Na1—O13	2.878 (5)	Mg5—O21xix	2.026 (2)
Na1—O33iv	2.886 (6)	Mg5—O33iv	2.034 (2)
Na1—O23viii	2.963 (6)	Mg5—O12	2.121 (3)
Na2—O32	2.246 (3)	Mg5—O14xx	2.148 (3)
Na2—O24ix	2.340 (3)	P1—O13	1.521 (3)
Na2—O22x	2.365 (3)	P1—O12	1.542 (2)
Na2—O34xi	2.396 (3)	P1—O11	1.548 (2)
Na2—O14xii	2.495 (3)	P1—O14	1.548 (2)
Na2—O11xii	2.962 (3)	P2—O24	1.518 (2)
Mg1—O34vii	1.969 (10)	P2—O22vii	1.524 (2)
Mg1—O24	2.004 (10)	P2—O23	1.541 (2)
Mg1—O24xiii	2.017 (10)	P2—O21	1.552 (2)
Mg1—O34xiv	2.030 (10)	P3—O34	1.524 (2)
Mg1—O14xv	2.241 (4)	P3—O32	1.528 (2)
Mg2—O11iv	2.052 (3)	P3—O31	1.537 (2)
Mg2—O11xii	2.052 (3)	P3—O33	1.543 (2)
O24i—Rb—O24ii	133.51 (9)	O24ix—Na2—O22x	92.29 (10)
O24i—Rb—O13iii	84.83 (7)	O32—Na2—O34xi	90.71 (10)
O24ii—Rb—O13iii	101.86 (7)	O24ix—Na2—O34xi	71.97 (10)
O24i—Rb—O13iv	101.86 (7)	O22x—Na2—O34xi	159.77 (12)
O24ii—Rb—O13iv	84.83 (7)	O32—Na2—O14xii	131.25 (11)
O13iii—Rb—O13iv	163.19 (10)	O24ix—Na2—O14xii	75.82 (9)
O24i—Rb—O31v	136.57 (6)	O22x—Na2—O14xii	114.69 (10)
O24ii—Rb—O31v	84.63 (6)	O34xi—Na2—O14xii	74.54 (9)
O13iii—Rb—O31v	110.05 (7)	O32—Na2—O11xii	85.19 (9)
O13iv—Rb—O31v	54.74 (6)	O24ix—Na2—O11xii	128.61 (10)
O24i—Rb—O31vi	84.63 (6)	O22x—Na2—O11xii	99.52 (9)
O24ii—Rb—O31vi	136.57 (6)	O34xi—Na2—O11xii	100.27 (10)
O13iii—Rb—O31vi	54.74 (6)	O14xii—Na2—O11xii	53.75 (8)
O13iv—Rb—O31vi	110.05 (7)	O34vii—Mg1—O24	91.7 (4)
O31v—Rb—O31vi	73.42 (9)	O34vii—Mg1—O24xiii	88.6 (4)
O24i—Rb—O21i	47.00 (6)	O24—Mg1—O24xiii	166.9 (2)
O24ii—Rb—O21i	90.86 (6)	O34vii—Mg1—O34xiv	167.0 (2)
O13iii—Rb—O21i	72.22 (6)	O24—Mg1—O34xiv	87.2 (4)
O13iv—Rb—O21i	123.54 (6)	O24xiii—Mg1—O34xiv	89.6 (4)
O31v—Rb—O21i	175.28 (6)	O34vii—Mg1—O14xv	89.2 (3)
O31vi—Rb—O21i	110.99 (6)	O24—Mg1—O14xv	104.7 (3)
O24i—Rb—O21ii	90.86 (6)	O24xiii—Mg1—O14xv	88.4 (3)
O24ii—Rb—O21ii	47.00 (6)	O34xiv—Mg1—O14xv	103.6 (3)
O13iii—Rb—O21ii	123.54 (6)	O11iv—Mg2—O11xii	81.37 (14)
O13iv—Rb—O21ii	72.22 (7)	O11iv—Mg2—O33xvi	117.11 (10)
O31v—Rb—O21ii	110.99 (6)	O11xii—Mg2—O33xvi	89.56 (10)
O31vi—Rb—O21ii	175.28 (6)	O11iv—Mg2—O33	89.56 (10)
O21i—Rb—O21ii	64.66 (8)	O11xii—Mg2—O33	117.11 (10)
O24i—Rb—O14iii	126.45 (6)	O33xvi—Mg2—O33	145.64 (16)
O24ii—Rb—O14iii	63.05 (6)	O11iv—Mg2—O31	145.19 (10)
O13iii—Rb—O14iii	44.16 (6)	O11xii—Mg2—O31	86.60 (9)
O13iv—Rb—O14iii	131.70 (6)	O33xvi—Mg2—O31	95.21 (10)
O31v—Rb—O14iii	85.51 (6)	O33—Mg2—O31	67.21 (9)
O31vi—Rb—O14iii	78.00 (6)	O11iv—Mg2—O31xvi	86.60 (9)
O21i—Rb—O14iii	93.70 (6)	O11xii—Mg2—O31xvi	145.19 (10)
O21ii—Rb—O14iii	103.71 (6)	O33xvi—Mg2—O31xvi	67.21 (9)
O24i—Rb—O14iv	63.05 (6)	O33—Mg2—O31xvi	95.20 (9)
O24ii—Rb—O14iv	126.45 (6)	O31—Mg2—O31xvi	119.70 (14)
O13iii—Rb—O14iv	131.70 (6)	O11—Mg3—O11xvii	81.88 (14)
O13iv—Rb—O14iv	44.16 (6)	O11—Mg3—O21	149.00 (10)
O31v—Rb—O14iv	78.00 (6)	O11xvii—Mg3—O21	87.76 (9)
O31vi—Rb—O14iv	85.51 (6)	O11—Mg3—O21xvii	87.76 (9)
O21i—Rb—O14iv	103.71 (6)	O11xvii—Mg3—O21xvii	149.00 (10)
O21ii—Rb—O14iv	93.70 (6)	O21—Mg3—O21xvii	114.43 (14)
O14iii—Rb—O14iv	159.44 (9)	O11—Mg3—O23xvii	114.89 (10)
O24i—Rb—O12iv	67.45 (6)	O11xvii—Mg3—O23xvii	89.77 (9)
O24ii—Rb—O12iv	90.89 (6)	O21—Mg3—O23xvii	94.09 (9)
O13iii—Rb—O12iv	150.50 (6)	O21xvii—Mg3—O23xvii	68.28 (9)
O13iv—Rb—O12iv	42.77 (6)	O11—Mg3—O23	89.77 (9)
O31v—Rb—O12iv	97.43 (6)	O11xvii—Mg3—O23	114.89 (10)
O31vi—Rb—O12iv	128.18 (6)	O21—Mg3—O23	68.28 (9)
O21i—Rb—O12iv	81.20 (5)	O21xvii—Mg3—O23	94.09 (9)
O21ii—Rb—O12iv	50.59 (5)	O23xvii—Mg3—O23	147.97 (14)
O14iii—Rb—O12iv	153.49 (6)	O13—Mg4—O12xv	111.06 (11)
O14iv—Rb—O12iv	43.24 (6)	O13—Mg4—O23	85.41 (10)
O24i—Rb—O12iii	90.89 (6)	O12xv—Mg4—O23	87.74 (10)
O24ii—Rb—O12iii	67.45 (6)	O13—Mg4—O32vii	93.13 (12)
O13iii—Rb—O12iii	42.77 (6)	O12xv—Mg4—O32vii	155.80 (11)
O13iv—Rb—O12iii	150.50 (6)	O23—Mg4—O32vii	94.02 (10)
O31v—Rb—O12iii	128.18 (6)	O13—Mg4—O31xviii	92.75 (11)
O31vi—Rb—O12iii	97.43 (6)	O12xv—Mg4—O31xviii	86.03 (10)
O21i—Rb—O12iii	50.59 (5)	O23—Mg4—O31xviii	172.38 (11)
O21ii—Rb—O12iii	81.20 (5)	O32vii—Mg4—O31xviii	93.46 (10)
O14iii—Rb—O12iii	43.24 (6)	O13—Mg4—O34vii	154.80 (11)
O14iv—Rb—O12iii	153.49 (6)	O12xv—Mg4—O34vii	93.48 (10)
O12iv—Rb—O12iii	124.43 (8)	O23—Mg4—O34vii	90.10 (9)
O32vii—Na1—O32iv	163.38 (18)	O32vii—Mg4—O34vii	62.42 (9)
O32vii—Na1—O22iv	88.3 (2)	O31xviii—Mg4—O34vii	94.64 (9)
O32iv—Na1—O22iv	94.9 (3)	O22iv—Mg5—O21xix	89.44 (10)
O32vii—Na1—O23	74.4 (2)	O22iv—Mg5—O33iv	92.64 (10)
O32iv—Na1—O23	112.8 (3)	O21xix—Mg5—O33iv	175.75 (11)
O22iv—Na1—O23	137.03 (19)	O22iv—Mg5—O12	132.14 (11)
O32vii—Na1—O22vii	89.9 (2)	O21xix—Mg5—O12	89.48 (10)
O32iv—Na1—O22vii	83.2 (2)	O33iv—Mg5—O12	86.38 (10)
O22iv—Na1—O22vii	166.37 (17)	O22iv—Mg5—O14xx	110.57 (11)
O23—Na1—O22vii	54.84 (15)	O21xix—Mg5—O14xx	92.12 (10)
Na1viii—Na1—O13	150.6 (12)	O33iv—Mg5—O14xx	90.63 (10)
O32vii—Na1—O13	67.64 (15)	O12—Mg5—O14xx	117.28 (10)
O32iv—Na1—O13	129.0 (2)	O13—P1—O12	106.71 (14)
O22iv—Na1—O13	77.79 (16)	O13—P1—O11	112.40 (14)
O23—Na1—O13	59.29 (12)	O12—P1—O11	108.47 (12)
O22vii—Na1—O13	113.9 (2)	O13—P1—O14	109.11 (15)
O32vii—Na1—O33iv	138.3 (2)	O12—P1—O14	112.44 (13)
O32iv—Na1—O33iv	56.44 (15)	O11—P1—O14	107.79 (13)
O22iv—Na1—O33iv	64.67 (16)	O24—P2—O22vii	111.34 (14)
O23—Na1—O33iv	103.37 (17)	O24—P2—O23	113.25 (13)
O22vii—Na1—O33iv	123.6 (2)	O22vii—P2—O23	108.74 (13)
O13—Na1—O33iv	75.63 (12)	O24—P2—O21	109.41 (13)
O32vii—Na1—O23viii	102.1 (2)	O22vii—P2—O21	112.20 (13)
O32iv—Na1—O23viii	67.63 (16)	O23—P2—O21	101.56 (12)
O22iv—Na1—O23viii	52.91 (14)	O34—P3—O32	105.79 (14)
O23—Na1—O23viii	168.2 (2)	O34—P3—O31	113.15 (14)
O22vii—Na1—O23viii	114.48 (15)	O32—P3—O31	112.52 (13)
O13—Na1—O23viii	130.4 (2)	O34—P3—O33	114.02 (13)
O33iv—Na1—O23viii	86.8 (2)	O32—P3—O33	109.69 (14)
O32—Na2—O24ix	143.52 (12)	O31—P3—O33	101.82 (13)
O32—Na2—O22x	95.11 (10)

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