Potassium gadolinium polyphosphate, KGd(PO₃)₄

Potassium gadolinium polyphosphate, KGd(PO₃)₄, was synthesized using the flux method. The atomic arrangement consists of an infinite long-chain polyphosphate organization. Two types of chains, with a period of eight PO₄ tetrahedra, run along the [101] direction. The Gd atoms have an eightfold coordination, while the K atoms have nine O-atom neighbours.

S1. Comment

The present structure investigation was performed as part of a research program in condensed phosphates with general formula M^IM^III(PO₃)₄, where M^I is a monovalent cation and M^III is a trivalent cation. The common chemical features of these polyphosphates indicate that they are stable under normal conditions of temperature and humidity (Hong, 1975a; Hong, 1975b; Koizumi, 1976; Jaouadi et al., 2003; Palkina et al., 1977, 1978, 1979; Tarasenkova et al., 1985). These compounds can be kept for many years in a perfect state of crystallinity, they are not water soluble, as may be inferred from their estimated molecular weights, and they all produce glasses when heated to their melting points (Durif, 1995). The literature dealing with these compounds was rather confusing for a long time, but it is currently well established that the M^IM^III(PO₃)₄ compounds can be classified into seven different types, which are usually denoted by Roman numerals I to VII. This nomenclature, first proposed by Palkina et al. (1981), is today generally accepted. In addition, many of these compounds are isotypic and some of them are polymorphic. Only the cyclic condensed phosphate KGdP₄O₁₂ (Ettis et al., 2003) has been elaborated in the ternary K₂O—Gd₂O₃—P₂O₅ system and, up to now, the types of polyphosphates existing in this ternary system have been unknown.

Our attempt to prepare new single crystals from a phosphoric acid, gadolinium oxide and potassium dihydrogenophosphate was successful. In fact, this study allowed us to find a new form of polyphosphate, KGd(PO₃)₄ (type IV), whose chemical preparation and crystal structure are presented here. The basic structural units are helical ribbons formed by corner-sharing of PO₄ tetrahedra. The ribbons (two per unit cell) run along the [101] direction with a period of eight tetrahedra. Every two chains deduct? themselves by 2₁ symmetry (Fig. 1). These chains are joined to one another by GdO₈ dodecahedra, forming a three-dimensional framework structure and delimiting tunnels in which the K⁺ cations are located (Fig. 2).

In such a polyphosphate chain, the P—O distances may be divided into linking or bridging P—O(L_ij) and exterior P—O(E_ij) distance [where O(L_ij) denotes the O atom that links atom P_i with atom P_j, and O(E_ij) denotes the j^th O atom exterior to the chain and bonded to atom P_i (Averbuch-Pouchot et al., 1976)]. It is important to note that the linking distances, P—O(L_ij), which range from 1.593 to 1.614 Å, are longer than the P—O(E_ij) distances, which range from 1.485 to 1.496 Å. The P—O—P angles range from 124.84 to 133.77 °. Furthemore, three different types of O—P—O angles coexist in the PO₄ tetrahedra. The O(L)—P—O(L) angles (mean 99.21°) correspond to the largest P—O bonds, the O(L)—P—O(E) angles have the values expected for a regular tetrahedron and the O(E)—P—O(E) angles correspond to the shortest P—O distances (mean 119.04°), probably induced by the mutual repulsion of the nonbridging O atoms(see Table 2). Nevertheless, the calculated mean distortion indices (Baur, 1974) corresponding to the different angles and distances in the independent PO₄ tetrahedra [DI(P—O) = 0.0377, DI(O—P—O) = 0.0376 and DI(O—O) = 0.0138] show ?that the distortion of the P—O distances is greater then that of the O—O distances. The PO₄ tetrahedra therefore have local C₁ symmetry rather than the ideal −43m symmetry (Baur, 1974).

All external O atoms of the PO₄ tetrahedra are involved in the coordination of the Gd atoms, with Gd—O distances ranging from 2.322 to 2.492 Å (Table 2). These atoms form irregular GdO₈ dodecahedra, separated from one another (Fig. 5a), the shortest Gd···Gd distance being 6.316 Å. Such a configuration? is also common around lanthanide cations, and thus the existence of isotypic compounds M^ILn(PO₃)₄ is not surprising. These dodecahedra are regrouped two-by-two according to? the [001] and [101] directions (Fig. 3). The coordination polyhedra of the potassium cation are formed by nine O atoms, two of them bridging O atoms (Fig. 5 b). These polyhedra are very irregular, as seen in other polyphosphates (Palkina et al., 1977); in fact, the K—O distance ranges from 2.779 to 3.353 Å (Table 2). KO₉ polyhedra are bound between them? to form chains parallel to the [010] direction (Fig. 4). By comparison with the coordination around the Li⁺ and Na⁺ ions in the structures LiNd(PO₃)₄ (Hong, 1975) and NaNd(PO₃)₄ (Koizumi, 1976), respectively, it can be noted that the coordination number decreases from nine for KO₉ polyhedra in the title structure to six for the NaO₆ octahedra in NaNd(PO₃)₄ and four for the LiO₄ tetrahedra in LiNd(PO₃)₄. This result can be explained on the basis of the radii of the monovalent cation, as r(K⁺) > r(Na⁺) > r(Li⁺); therefore, as the number of O atoms per cation in the chemical formula is constant, it is clear that we pass from an open structure of coordination tetrahedra sharing only vertices in LiNd(PO₃)₄ to a compact framework sharing all edges in KGd(PO₃)₄ (type IV). If the anionic configuration of KGd(PO₃)₄ is compared with that of NH₄Y(PO₃)₄ (Beucher et al., 1988), a decrease in the complexity of the chain is seen as the size of the trivalent cation increases; in particular, there is a decrease in the period from 16 to eight tetrahedra. This complication of the chain shape has already been observed in other types of polyphosphates, M^ILn(PO₃)₄ (Palkina, 1982)·It should be related more precisely to an increase in the difference between the sizes of the monovalent cations and the trivalent ones.

S2. Experimental

Crystals of KGd(PO₃)₄ were prepared using the flux method. H₃PO₄ (2.8 g), KH₂PO₄ (3.2 g) and Gd₂O₃ (0.4 g) were mixed in a Pt crucible, preheated to 473 K and kept at this temperature for 4 h. The temperature was then inceased to 823 K. Two days later, the temperature was reduced to 323 K at a rate of 40° d⁻¹. After double washing in boiling water and with nitric acid to eliminate the remaining oxide, Gd₂O₃, colourless hexagonal crystals of KGd(PO₃)₄ were formed.

Computing details

Data collection: CAD-4 Software (Enraf-Nonius, 1989); cell refinement: CAD-4 Software; data reduction: MolEN (Fair, 1990); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Larson, 1996); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. A projection of the structure of KGd(PO3)4 along the b axis. Red circles represent P atoms. For clarity, K and Gd atoms have been omitted.
	Fig. 2. A projection of the structure of KGd(PO3)4 along the a axis. Large and middle-size circles represent K and Gd atoms, respectively.
	Fig. 3. A projection of the structure of KGd(PO3)4 along the b axis. PO4 tetrahedra have been omitted.
	Fig. 4. A projection of the structure of KGd(PO3)4 along the c axis. PO4 tetrahedra have been omitted.
	Fig. 5. O-atom coordination around the K and Gd cations (50% probability displacement ellipsoids)·[Symmetry codes: (a) 1/2 − x,y − 1/2,3/2 − z; (b) 1/2 − x,y − 1/2,5/2 − z; (c) −x,-y,2 − z; (e) x − 1/2,1/2 − y,z − 1/2; (h) 1/2 + x,-y − 1/2,1/2 + z.]

Potassium gadolinium polyphosphate

Crystal data

GdO12P4·K	F(000) = 956
Mr = 512.23	Dx = 3.486 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yn	Cell parameters from 25 reflections
a = 10.412 (2) Å	θ = 11–15°
b = 8.996 (2) Å	µ = 7.94 mm^−1
c = 10.836 (2) Å	T = 293 K
β = 105.94 (1)°	Hexagonal, colourless
V = 975.9 (3) Å^3	0.36 × 0.21 × 0.14 mm
Z = 4

Data collection

Enraf–Nonius CAD-4 diffractometer	2058 reflections with I > 2σ(I)'
Radiation source: fine-focus sealed tube	Rint = 0.017
Graphite monochromator	θmax = 27.0°, θmin = 2.4°
θ/2θ scans	h = 0→13
Absorption correction: empirical (using intensity measurements) ψ scan (North et al., 1968)	k = 0→11
Tmin = 0.149, Tmax = 0.329	l = −13→13
2233 measured reflections	2 standard reflections every 60 min
2119 independent reflections	intensity decay: 1.3%

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: heavy-atom method
R[F^2 > 2σ(F^2)] = 0.018	Secondary atom site location: difference Fourier map
wR(F^2) = 0.046	w = 1/[σ^2(Fo^2) + (0.0187P)^2 + 2.8091P] where P = (Fo^2 + 2Fc^2)/3
S = 1.24	(Δ/σ)max = 0.001
2119 reflections	Δρmax = 0.79 e Å^−3
164 parameters	Δρmin = −1.08 e Å^−3

Special details

Experimental. Data were corrected for Lorentz-polarization effects and an empirical absorption correction (ψ scan; North et al., 1968) was applied. The structure was solved in the P 1 2₁/n 1 space group by the Patterson method (Gd and K) and subsequent difference Fourier syntheses (all other atoms).

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Gd	−0.000118 (16)	0.228200 (18)	0.815525 (15)	0.00652 (8)
K	0.29451 (10)	−0.42810 (13)	1.04311 (9)	0.0302 (2)
P1	0.03972 (9)	−0.17043 (9)	0.85859 (8)	0.00733 (18)
P2	0.25049 (8)	−0.02288 (9)	0.76926 (8)	0.00739 (18)
P3	0.32330 (9)	0.10578 (10)	1.01953 (8)	0.00760 (17)
P4	0.35386 (9)	−0.09521 (10)	1.23991 (8)	0.00764 (18)
OL14	−0.0236 (3)	−0.2920 (3)	0.7506 (2)	0.0119 (5)
OL34	0.3311 (3)	−0.0502 (3)	1.0933 (2)	0.0129 (5)
OE22	0.1455 (2)	0.0883 (3)	0.7080 (2)	0.0113 (5)
OL12	0.1840 (2)	−0.1543 (3)	0.8323 (2)	0.0114 (5)
OE11	0.0645 (3)	−0.2387 (3)	0.9883 (3)	0.0131 (5)
OE12	−0.0394 (3)	−0.0310 (3)	0.8238 (3)	0.0132 (5)
OL23	0.3577 (2)	0.0469 (3)	0.8923 (2)	0.0100 (5)
OE21	0.3284 (3)	−0.0904 (3)	0.6868 (2)	0.0120 (5)
OE31	0.4311 (3)	0.2075 (3)	1.0911 (2)	0.0127 (5)
OE32	0.1825 (2)	0.1592 (3)	0.9827 (2)	0.0137 (5)
OE41	0.2374 (3)	−0.1819 (3)	1.2543 (3)	0.0155 (5)
OE42	0.3977 (3)	0.0359 (3)	1.3250 (2)	0.0128 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Gd	0.00751 (11)	0.00571 (12)	0.00645 (11)	0.00052 (6)	0.00207 (7)	0.00081 (6)
K	0.0279 (5)	0.0459 (7)	0.0172 (5)	0.0032 (5)	0.0067 (4)	−0.0050 (4)
P1	0.0088 (4)	0.0056 (4)	0.0081 (4)	−0.0006 (3)	0.0031 (3)	−0.0002 (3)
P2	0.0083 (4)	0.0072 (4)	0.0073 (4)	0.0001 (3)	0.0034 (3)	0.0000 (3)
P3	0.0086 (4)	0.0080 (4)	0.0059 (4)	−0.0004 (3)	0.0011 (3)	0.0004 (3)
P4	0.0088 (4)	0.0060 (4)	0.0074 (4)	−0.0001 (3)	0.0012 (3)	0.0006 (3)
OL14	0.0136 (13)	0.0123 (13)	0.0115 (13)	−0.0054 (11)	0.0056 (10)	−0.0048 (10)
OL34	0.0185 (13)	0.0095 (13)	0.0086 (12)	−0.0025 (11)	0.0008 (10)	0.0034 (10)
OE22	0.0124 (12)	0.0125 (13)	0.0093 (12)	0.0036 (10)	0.0029 (10)	0.0023 (10)
OL12	0.0115 (12)	0.0088 (12)	0.0155 (13)	−0.0007 (10)	0.0058 (10)	0.0005 (10)
OE11	0.0142 (14)	0.0164 (14)	0.0091 (13)	0.0020 (11)	0.0041 (11)	0.0019 (10)
OE12	0.0106 (12)	0.0086 (13)	0.0216 (14)	0.0016 (10)	0.0063 (11)	0.0014 (11)
OL23	0.0091 (12)	0.0115 (13)	0.0098 (12)	−0.0019 (10)	0.0035 (10)	−0.0012 (10)
OE21	0.0138 (13)	0.0131 (13)	0.0113 (12)	0.0008 (11)	0.0064 (10)	−0.0024 (10)
OE31	0.0135 (13)	0.0143 (13)	0.0105 (13)	−0.0030 (11)	0.0034 (10)	−0.0025 (11)
OE32	0.0110 (13)	0.0199 (15)	0.0097 (12)	0.0054 (11)	0.0014 (10)	0.0010 (11)
OE41	0.0108 (13)	0.0154 (14)	0.0190 (14)	−0.0018 (11)	0.0029 (11)	0.0064 (12)
OE42	0.0195 (14)	0.0069 (12)	0.0135 (13)	−0.0015 (11)	0.0069 (11)	−0.0017 (10)

Geometric parameters (Å, º)

Gd—OE32	2.322 (3)	P2—OE21	1.491 (3)
Gd—OE12	2.373 (3)	P2—OE22	1.496 (3)
Gd—OE42^i	2.389 (3)	P2—OL23	1.613 (3)
Gd—OE11^ii	2.400 (3)	P2—OL12	1.614 (3)
Gd—OE31^i	2.409 (3)	P2—K^iii	3.3959 (14)
Gd—OE41^ii	2.413 (3)	P3—OE32	1.489 (3)
Gd—OE21^iii	2.426 (3)	P3—OE31	1.490 (3)
Gd—OE22	2.492 (3)	P3—OL23	1.606 (3)
Gd—K^iv	4.1361 (13)	P3—OL34	1.606 (3)
Gd—K^ii	4.1899 (12)	P4—OE41	1.485 (3)
K—OE42^v	2.779 (3)	P4—OE42	1.489 (3)
K—OE11	2.865 (3)	P4—OL34	1.593 (3)
K—OE21^vi	2.867 (3)	P4—OL14^vii	1.609 (3)
K—OE22^vi	2.958 (3)	P4—K^viii	3.4885 (14)
K—OE12^vii	3.081 (3)	OL14—P4^iv	1.609 (3)
K—OL14^vii	3.198 (3)	OL14—K^iv	3.198 (3)
K—OE41^v	3.247 (3)	OE22—K^iii	2.958 (3)
K—OL12	3.342 (3)	OE11—Gd^ii	2.400 (3)
K—OE41	3.353 (3)	OE12—K^iv	3.081 (3)
K—P2^vi	3.3959 (14)	OE21—Gd^vi	2.426 (3)
K—P4^v	3.4885 (15)	OE21—K^iii	2.867 (3)
K—P4	3.6296 (15)	OE31—Gd^ix	2.409 (3)
P1—OE11	1.490 (3)	OE41—Gd^ii	2.413 (3)
P1—OE12	1.491 (3)	OE41—K^viii	3.247 (3)
P1—OL14	1.605 (3)	OE42—Gd^ix	2.389 (3)
P1—OL12	1.610 (3)	OE42—K^viii	2.779 (3)
P1—K^iv	3.7679 (15)
OE32—Gd—OE12	79.65 (9)	OE12^vii—K—P4^v	61.01 (5)
OE32—Gd—OE42^i	118.90 (9)	OL14^vii—K—P4^v	94.55 (6)
OE12—Gd—OE42^i	141.97 (9)	OE41^v—K—P4^v	25.15 (5)
OE32—Gd—OE11^ii	71.80 (9)	OL12—K—P4^v	130.19 (6)
OE12—Gd—OE11^ii	84.94 (9)	OE41—K—P4^v	68.30 (5)
OE42^i—Gd—OE11^ii	72.00 (9)	P2^vi—K—P4^v	126.74 (4)
OE32—Gd—OE31^i	143.55 (9)	OE42^v—K—P4	79.89 (6)
OE12—Gd—OE31^i	105.53 (9)	OE11—K—P4	68.21 (6)
OE42^i—Gd—OE31^i	79.49 (9)	OE21^vi—K—P4	153.35 (7)
OE11^ii—Gd—OE31^i	143.77 (9)	OE22^vi—K—P4	117.03 (6)
OE32—Gd—OE41^ii	138.34 (9)	OE12^vii—K—P4	63.87 (5)
OE12—Gd—OE41^ii	70.73 (9)	OL14^vii—K—P4	26.30 (5)
OE42^i—Gd—OE41^ii	74.75 (9)	OE41^v—K—P4	102.44 (6)
OE11^ii—Gd—OE41^ii	76.91 (9)	OL12—K—P4	76.39 (5)
OE31^i—Gd—OE41^ii	74.34 (9)	OE41—K—P4	24.15 (5)
OE32—Gd—OE21^iii	74.93 (9)	P2^vi—K—P4	138.37 (4)
OE12—Gd—OE21^iii	142.80 (9)	P4^v—K—P4	89.71 (3)
OE42^i—Gd—OE21^iii	75.00 (9)	OE11—P1—OE12	121.70 (15)
OE11^ii—Gd—OE21^iii	111.63 (9)	OE11—P1—OL14	109.69 (15)
OE31^i—Gd—OE21^iii	81.00 (9)	OE12—P1—OL14	107.54 (15)
OE41^ii—Gd—OE21^iii	143.79 (9)	OE11—P1—OL12	106.00 (15)
OE32—Gd—OE22	75.92 (9)	OE12—P1—OL12	110.92 (14)
OE12—Gd—OE22	69.81 (9)	OL14—P1—OL12	98.54 (14)
OE42^i—Gd—OE22	143.53 (8)	OE11—P1—K	46.71 (11)
OE11^ii—Gd—OE22	141.97 (8)	OE12—P1—K	159.15 (11)
OE31^i—Gd—OE22	72.52 (8)	OL14—P1—K	93.29 (11)
OE41^ii—Gd—OE22	117.91 (9)	OL12—P1—K	65.42 (10)
OE21^iii—Gd—OE22	77.90 (9)	OE11—P1—K^iv	148.39 (11)
OE32—Gd—K^iv	122.30 (7)	OE12—P1—K^iv	51.93 (11)
OE12—Gd—K^iv	47.55 (7)	OL14—P1—K^iv	57.22 (10)
OE42^i—Gd—K^iv	117.47 (7)	OL12—P1—K^iv	104.52 (10)
OE11^ii—Gd—K^iv	116.25 (7)	K—P1—K^iv	148.25 (3)
OE31^i—Gd—K^iv	58.96 (7)	OE21—P2—OE22	117.25 (15)
OE41^ii—Gd—K^iv	51.64 (7)	OE21—P2—OL23	106.70 (14)
OE21^iii—Gd—K^iv	132.05 (6)	OE22—P2—OL23	111.23 (14)
OE22—Gd—K^iv	66.31 (6)	OE21—P2—OL12	108.82 (14)
OE32—Gd—K^ii	110.74 (7)	OE22—P2—OL12	109.34 (14)
OE12—Gd—K^ii	104.87 (6)	OL23—P2—OL12	102.44 (13)
OE42^i—Gd—K^ii	39.08 (6)	OE21—P2—K^iii	56.88 (11)
OE11^ii—Gd—K^ii	41.32 (6)	OE22—P2—K^iii	60.39 (10)
OE31^i—Gd—K^ii	102.80 (6)	OL23—P2—K^iii	126.95 (10)
OE41^ii—Gd—K^ii	53.12 (7)	OL12—P2—K^iii	130.39 (10)
OE21^iii—Gd—K^ii	109.28 (6)	OE32—P3—OE31	119.15 (16)
OE22—Gd—K^ii	171.03 (6)	OE32—P3—OL23	108.14 (14)
K^iv—Gd—K^ii	104.735 (18)	OE31—P3—OL23	109.61 (14)
OE42^v—K—OE11	59.81 (8)	OE32—P3—OL34	109.08 (15)
OE42^v—K—OE21^vi	100.07 (8)	OE31—P3—OL34	110.44 (15)
OE11—K—OE21^vi	88.54 (8)	OL23—P3—OL34	98.41 (14)
OE42^v—K—OE22^vi	147.44 (8)	OE41—P4—OE42	118.09 (16)
OE11—K—OE22^vi	98.93 (8)	OE41—P4—OL34	109.65 (15)
OE21^vi—K—OE22^vi	51.90 (7)	OE42—P4—OL34	110.64 (15)
OE42^v—K—OE12^vii	76.49 (8)	OE41—P4—OL14^vii	108.38 (15)
OE11—K—OE12^vii	119.10 (8)	OE42—P4—OL14^vii	110.65 (15)
OE21^vi—K—OE12^vii	142.42 (8)	OL34—P4—OL14^vii	97.45 (14)
OE22^vi—K—OE12^vii	135.33 (8)	OE41—P4—K^viii	68.29 (12)
OE42^v—K—OL14^vii	94.68 (8)	OE42—P4—K^viii	50.10 (10)
OE11—K—OL14^vii	94.44 (8)	OL34—P4—K^viii	126.21 (11)
OE21^vi—K—OL14^vii	164.35 (8)	OL14^vii—P4—K^viii	135.42 (10)
OE22^vi—K—OL14^vii	112.46 (8)	OE41—P4—K	67.44 (12)
OE12^vii—K—OL14^vii	46.86 (7)	OE42—P4—K	172.26 (11)
OE42^v—K—OE41^v	49.34 (7)	OL34—P4—K	70.67 (10)
OE11—K—OE41^v	108.87 (8)	OL14^vii—P4—K	61.70 (10)
OE21^vi—K—OE41^v	97.19 (8)	K^viii—P4—K	135.73 (3)
OE22^vi—K—OE41^v	138.04 (8)	P1—OL14—P4^iv	129.86 (17)
OE12^vii—K—OE41^v	51.85 (7)	P1—OL14—K^iv	97.81 (12)
OL14^vii—K—OE41^v	96.37 (7)	P4^iv—OL14—K^iv	92.00 (12)
OE42^v—K—OL12	106.02 (7)	P4—OL34—P3	133.77 (18)
OE11—K—OL12	46.25 (7)	P2—OE22—Gd	126.48 (14)
OE21^vi—K—OL12	78.09 (7)	P2—OE22—K^iii	93.53 (12)
OE22^vi—K—OL12	56.94 (7)	Gd—OE22—K^iii	139.87 (10)
OE12^vii—K—OL12	139.26 (8)	P1—OL12—P2	132.11 (17)
OL14^vii—K—OL12	92.90 (7)	P1—OL12—K	88.59 (10)
OE41^v—K—OL12	154.22 (7)	P2—OL12—K	136.22 (13)
OE42^v—K—OE41	55.82 (7)	P1—OE11—Gd^ii	143.24 (16)
OE11—K—OE41	56.90 (7)	P1—OE11—K	111.05 (14)
OE21^vi—K—OE41	143.97 (8)	Gd^ii—OE11—K	105.11 (9)
OE22^vi—K—OE41	135.79 (8)	P1—OE12—Gd	138.33 (15)
OE12^vii—K—OE41	64.00 (7)	P1—OE12—K^iv	105.67 (13)
OL14^vii—K—OE41	44.99 (7)	Gd—OE12—K^iv	97.80 (9)
OE41^v—K—OE41	86.15 (3)	P3—OL23—P2	124.84 (16)
OL12—K—OE41	83.54 (7)	P2—OE21—Gd^vi	143.49 (16)
OE42^v—K—P2^vi	124.17 (7)	P2—OE21—K^iii	97.30 (12)
OE11—K—P2^vi	93.67 (6)	Gd^vi—OE21—K^iii	119.20 (10)
OE21^vi—K—P2^vi	25.82 (5)	P3—OE31—Gd^ix	130.20 (15)
OE22^vi—K—P2^vi	26.08 (5)	P3—OE32—Gd	146.13 (16)
OE12^vii—K—P2^vi	147.20 (6)	P4—OE41—Gd^ii	148.49 (16)
OL14^vii—K—P2^vi	138.53 (6)	P4—OE41—K^viii	86.55 (13)
OE41^v—K—P2^vi	119.05 (6)	Gd^ii—OE41—K^viii	92.71 (9)
OL12—K—P2^vi	64.93 (5)	P4—OE41—K	88.41 (12)
OE41—K—P2^vi	147.60 (6)	Gd^ii—OE41—K	91.72 (9)
OE42^v—K—P4^v	24.28 (5)	K^viii—OE41—K	174.96 (9)
OE11—K—P4^v	84.06 (6)	P4—OE42—Gd^ix	137.85 (15)
OE21^vi—K—P4^v	101.04 (6)	P4—OE42—K^viii	105.62 (13)
OE22^vi—K—P4^v	152.37 (6)	Gd^ix—OE42—K^viii	108.11 (9)

Symmetry codes: (i) x−1/2, −y+1/2, z−1/2; (ii) −x, −y, −z+2; (iii) −x+1/2, y+1/2, −z+3/2; (iv) x−1/2, −y−1/2, z−1/2; (v) −x+1/2, y−1/2, −z+5/2; (vi) −x+1/2, y−1/2, −z+3/2; (vii) x+1/2, −y−1/2, z+1/2; (viii) −x+1/2, y+1/2, −z+5/2; (ix) x+1/2, −y+1/2, z+1/2.