The crystal structure of KScP2O7.

Single crystals of KScP2O7, potassium scandium diphosphate, were grown in a borate flux. The title compound crystallizes isotypically with KAlP2O7 in space-group type P21/c, Z = 4. The main building block is an {ScP2O11}9- unit, forming layers parallel to (001). These layers are stacked along [001] via common corners of octa-hedral and tetra-hedral units to span up large hepta-gonal cavities that host the potassium cations with a coordination number of 10. The P-O-P bridging angle increases with increasing size of the octa-hedrally coordinated M III cation, as do the K-O distances within a series of KM IIIP2O7 compounds (M III = Al to Y with ionic radii r = 0.538 to 0.90 Å). © Redhammer and Tippelt 2020.

Chemical context

Metal-phosphates with open framework structures raise large inter­est due to a rich crystal chemistry (Clearfield, 1988 ▸) and possible inter­esting applications, e.g. as non-linear optical materials, solid-state electrolytes, ionic conductors, battery materials or sensors (Hagerman & Poeppelmeier, 1995 ▸; Vītiņš et al., 2000 ▸). In the context of solid-state electrolytes, we recently investigated the Na-super ionic conducting NaSICON-type compounds Na3Sc2(PO4)3 (NSP) and Ag3Sc2(PO4)3 (ASP) in terms of their structural phase-transition sequences and ionic conductivities (Rettenwander et al., 2018 ▸; Ladenstein et al., 2020 ▸; Redhammer et al., 2020 ▸). To elucidate the role of the alkali metals on symmetry, we intended to synthesize the potassium analogue of NSP with flux-growth techniques. Using a method applied by Sljukic et al. (1967 ▸) for the synthesis of large crystals of NaSICON-type KZr2(PO4)3, however, did not yield the intended compound K3Sc2(PO4)3, but the title diphosphate KScP2O7 instead.

Vītiņš et al. (2000 ▸) reviewed that for such A I M IIIP2O7 (A = Li, Na, K, Rb, Cs, Tl; M = Al, Ga, Fe, In, Sc, …) compounds six different structure types can be distinguished. They confirm that structure type I, involving compounds with large A site cations, is the largest group, showing P21/c space-group symmetry. KAlP2O7 (Ng & Calvo, 1973 ▸) is regarded as the aristo-structure of group I with around 45 different compositions as compiled in the Inorganic Crystal Structure Database (ICSD; Zagorac et al., 2019 ▸). For K-containing compounds, further materials are KCrP2O7 (Gentil et al., 1997 ▸), KGaP2O7 (Genkin & Timofeeva, 1989 ▸), KFeP2O7 (Riou et al., 1988 ▸; Genkin & Timofeeva, 1989 ▸), KVP2O7 (Benhamada et al., 1991 ▸), KTiP2O7 (Zatovsky et al., 2000 ▸), KMoP2O7 (Leclaire et al., 1989 ▸; Chen et al., 1989 ▸), KInP2O7 (Zhang et al., 2004 ▸), KLuP2O7 (Yuan et al., 2007 ▸), KYbP2O7 (Horchani-Naifer & Férid, 2007 ▸), KErP2O7 (Chaker et al., 2016 ▸) and KYP2O7 (Yuan et al., 2007 ▸). Synthesis and lattice parameters of CeIII-doped polycrystalline KScP2O7 as well as the luminescence properties were reported recently by Zhang et al. (2016 ▸); however, no atomic coordinates were given.

In this contribution, we present the determination of the crystal structure of KScP2O7, not reported so far, and compare it with the series of other K-containing diphosphates.

Structural commentary

The title compound crystallizes in space group P21/c and is isostructural with KAlP2O7 (Ng & Calvo, 1973 ▸). It contains one distinct K and Sc atom site, two distinct P atom and seven different oxygen-atom positions, all of them on general position 4 e. The basic building unit is a pyrophosphate group, which is formed by two distinct PO4 tetra­hedra (Fig. 1 ▸). They share the O4 oxygen atom, and the bridging P1—O4 and P2—O4 bond lengths are distinctly longer [1.6128 (6) and 1.6076 (6) Å, respectively] than the three shorter terminal P—O bonds [ranging between 1.4944 (7) and 1.5207 (6) Å]. These latter distances are those to the oxygen atoms which are shared with the ScO6 octa­hedra. The tetra­hedral O—P—O angles involving the bridging oxygen atom O4 are generally smaller, those involving the terminal oxygen atoms distinctly larger than the ideal O—T—O angle of 109.5°. This – together with the difference in bond lengths between bridging and non-bridging T—O bonds – induces polyhedral distortion (especially for the tetra­hedral angle variance, TAV), which is distinctly larger for the P1 tetra­hedron. Likewise, the average bond length is slightly larger for the P1O4 tetra­hedron than for the P2O4 tetra­hedron (Table 1 ▸). When comparing average bond lengths and polyhedral distortion parameters of the series of KM IIIP2O7 structures (M = Al to Y), no clear variations with the ionic radius of the M cations can be found from the available data for tetra­hedral structure units and distortion parameters, and they remain almost constant. The parameters for KScP2O7 fit well into the data of the other KM IIIP2O7 structures. The tetra­hedral bridging angle P1—O4—P2 amounts to 125.80 (5)° and is distinctly larger than that of KAlP2O7 [123.2 (11)°]. On the other hand, here a clear trend of increasing bridging angle with increasing size of the M cation is evident, i.e. the pyrophosphate group is stretched to account for the increase in size of the M cations (Table 1 ▸).

Figure 1

The principal building unit of KScP2O7 shown with displacement ellipsoids at the 95% probability level. [Symmetry codes: (i) x,  − y,  + z; (ii) 1 − x, − + y,  − z; (iii) x,  − y, − + z; (iv) 2 − x, − + y,  − z].

Table 1

Selected structural and distortional parameters (Å, °) of KM IIIP2O7 compounds

Vol. = polyhedral volume (Å3), DI = distortion index, ECoN = effective coordination number, OQE = octa­hedral quadratic elongation, OAV = octa­hedral angle variance (°2), TQE = tetra­hedral quadratic elongation, TAV = tetra­hedral angle variance (°2). All calculations were performed using VESTA (Momma & Izumi 2011 ▸; for the mathematical meaning see the VESTA Handbook); ionic radii were taken from Shannon (1976 ▸).

M	Al	Cr	Ga	Fea	Feb	V	Ti	Mo	Sc	In	Lu	Yb	Er	Y
ionic radius	0.536	0.615	0.62	0.645	0.645	0.64	0.67	0.69	0.745	0.8	0.861	0.868	0.89	0.9
<K—O>	2.949	2.975	2.982	3.017	2.993	2.998	3.029	3.029	3.072	3.056	3.118	3.130	3.119	3.150
Vol.	44.03	45.21	45.23	50.08	45.73	46.03	47.21	47.63	49.40	48.45	52.04	52.11	52.09	53.25
DI	0.0442	0.0519	0.0484	0.0484	0.0535	0.0560	0.0596	0.0636	0.0620	0.0641	0.0695	0.0735	0.0813	0.0774
ECoN	8.84	8.38	8.54	8.58	8.29	8.22	7.89	7.51	7.66	7.29	7.09	6.63	6.80	6.40
<M—O>	1.889	1.973	1.964	2.021	1.991	2.000	2.036	2.091	2.085	2.124	2.199	2.207	2.301	2.266
Vol.	8.95	10.20	10.06	10.97	10.46	10.63	11.19	12.10	12.02	12.68	14.05	14.19	15.86	15.38
DI	0.0102	0.0091	0.0076	0.0313	0.0106	0.0154	0.0220	0.0086	0.0100	0.0073	0.0139	0.0116	0.0266	0.0074
OQE	1.0025	1.0031	1.0033	1.0032	1.0036	1.0036	1.0048	1.0045	1.0040	1.0047	1.0068	1.0070	1.0170	1.0060
OAV	7.97	10.31	11.42	6.47	11.79	10.66	12.98	15.40	13.52	16.38	22.62	23.79	54.07	20.97
ECoN	5.96	5.97	5.98	5.73	5.96	5.92	5.85	5.97	5.96	5.99	5.95	5.95	5.75	5.98
<P1—O>	1.536	1.542	1.540	1.537	1.537	1.540	1.540	1.536	1.537	1.538	1.545	1.531	1.494	1.518
Vol.	1.85	1.87	1.86	1.85	1.85	1.86	1.87	1.85	1.86	1.85	1.87	1.83	1.68	1.78
DI	0.0240	0.0241	0.0240	0.0124	0.0237	0.0245	0.0234	0.0256	0.0245	0.0281	0.0329	0.0264	0.0584	0.0326
TQE	1.0049	1.0053	1.0049	1.0042	1.0048	1.0047	1.0037	1.0052	1.0043	1.0059	1.0080	1.0043	1.0179	1.0074
TAV	19.55	21.29	19.79	17.39	18.95	18.34	14.44	20.41	16.80	22.82	27.35	16.12	37.83	24.70
ECoN	3.89	3.89	3.88	3.97	3.89	3.89	3.90	3.88	3.89	3.85	3.77	3.87	3.14	3.77
<P2—O>	1.531	1.535	1.535	1.530	1.531	1.535	1.536	1.534	1.535	1.530	1.546	1.535	1.509	1.529
Vol.	1.83	1.85	1.85	1.84	1.84	1.85	1.85	1.85	1.85	1.83	1.88	1.85	1.72	1.83
DI	0.0241	0.0242	0.0260	0.0088	0.0241	0.0227	0.0247	0.0231	0.0236	0.0272	0.0470	0.0237	0.0400	0.0351
TQE	1.0034	1.0032	1.0035	1.0011	1.0030	1.0026	1.0027	1.0027	1.0027	1.0034	1.0058	1.0024	1.0206	1.0038
TAV	12.54	11.68	12.48	4.49	10.67	9.18	9.12	9.60	9.48	10.99	9.51	7.94	71.43	4.61
ECoN	3.87	3.87	3.86	3.98	3.88	3.89	3.88	3.88	3.89	3.80	3.61	3.89	3.57	3.71
P1—O4—P2	123.18 (11)	123.68 (10)	123.8 (2)	n.d.	124.32 (10)	124.24	125.0 (2)	124.97 (15)	125.80 (5)	125.6 (5)	123.8 (9)	127.5 (3)	123.72 (7)	127.4 (6)

Notes: (a) data from Riou et al. (1988 ▸); (b) data from Genkin & Timofeeva (1989 ▸).

The terminal oxygen atoms of the pyrophosphate group share their corners with five neighbouring ScO6 octa­hedra. Following Leclaire et al. (1989 ▸), two phosphate tetra­hedra and one octa­hedron form the basic {ScP2O11}9– units (cf. Fig. 1 ▸), which are connected with units of the same kind via corner-sharing to make up a sheet parallel to (001), as depicted in Fig. 2 ▸. These layers are stacked along [001] in such a way that a ScO6 octa­hedron of one layer shares its O3iii and O6i corners (symmetry codes refer to Fig. 1 ▸) with one PO4 tetra­hedron each of the layer below and above.

Figure 2

(a) Layer of laterally inter­connected {ScP2O11}9− units, forming a layer parallel to (001), the KI cations are hosted in the channels extending along [001]; (b) the three-dimensional framework structure of KScP2O7, viewed along [010].

Generally, all corners of the octa­hedron are shared with neighbouring PO4 tetra­hedra, whereby all oxygen atoms except O4 directly connect the octa­hedron with a pyrophos­phate P2O7 group, and the O2ii and O5iv oxygen atoms join the octa­hedron with two PO4 tetra­hedra within the above-mentioned layer parallel to (001). Additionally, the O1, O5iv and O7 oxygen atoms (Fig. 1 ▸) are also bonded to one KI cation each. The average Sc—O bond length is 2.085 Å while individual bond lengths range between 2.0736 (7) and 2.1122 (6) Å with one shorter bond (Sc—O6i) of 2.0346 (7) Å. A similar behaviour with one significantly shorter M—O bond is also observed in other KM IIIP2O7 compounds and seems to be a more general feature. The Sc—O6i and the Sc—O3iii bonds, which point towards [001] and connect different (001) layers, both are the shortest within the ScO6 octa­hedron. Assuming that these two bonds are those to the axial oxygen atoms of the octa­hedron, the coordination polyhedron appears to be slightly compressed. Also, Ng & Calvo (1973 ▸) noted for KAlP2O7 that the axial bonds are considerably shorter that the equatorial ones within the (001) layer and – more generally speaking – this is also found in other KM IIIP2O7 compounds. The ScO6 octa­hedron in the title compound is only slightly distorted in terms of bond lengths and bond-angle variance (Table 1 ▸). It is worth noting that KAlP2O7 shows the most regular octa­hedral coordination of all KM IIIP2O7 structures compared here, and the distortion increases with increasing size of the octa­hedral cation as depicted in Fig. 3 ▸ a. The average bond lengths also scale well with the ionic radius of the M site cation and are positively correlated (Fig. 3 ▸ b).

Figure 3

Variation of the octa­hedral angle variance (OAV) (a) and the average M III—O bond lengths (b) as a function of the ionic radius of the M site cation across the series of KM IIIP2O7 compounds (M = Al to Y).

Large hepta­gonal cavities are formed in the skeleton of octa­hedral and tetra­hedral units that are made up from four tetra­hedrally and two octa­hedrally coordinated sites within the (001) layer. The stacking of the layers leads to channels running parallel to [001] where the potassium cations are hosted. They are tenfold coordinated with K—O bond lengths ranging between 2.7837 (7) Å and 3.3265 (9) Å, the average K—O bond length being 3.072 Å. As for , the average K—O bond length also increases with increasing size of the M site cation, i.e. the channel size increases also.

Using bond-valence energy landscape map (BVEL) calculations, an estimation of possible diffusion pathways of alkali ions in a compound can be facilitated. Using the program SoftBV (Chen & Adams, 2017 ▸; Chen et al., 2019 ▸) such calculations were performed on KScP2O7 and reveal two energy minima. The lowest lying minimum is indeed occupied by the KI cation, a second one is present at x, y, z = 0.271, 0.317, 0.438 (inter­stitial i1) and is unoccupied. A one-dimensional diffusion pathway is evident (Fig. 4 ▸), involving the i1 position, and is oriented parallel to [001]. An estimated activation energy of ∼0.3 eV would be needed to move a potassium ion from the regular K site to the inter­stitial i1 site; to move it from i1 to the next K1 site needs ∼1.3 eV. Inter­estingly, the percolation energy in e.g. FeIII, MoIII and InIII compounds of the KM IIIP2O7 series is distinctly higher with around 1.8 eV as estimated from BVEL maps. Generally, a partial substitution of trivalent cations by divalent ones might be of inter­est to increase the content of alkaline ions (here KI), which most probably could be found on the inter­stitial i1 site.

Figure 4

Bond-valence energy landscape map at levels of 1.5 eV above the minimum (yellow) viewed along [100]; the crystal structure of KScP2O7 is overlayed, the K sites lie within channels.

Synthesis and crystallization

The title compound was grown during attempts to synthesize NaSICON-type K3Sc2(PO4)3 adopting a flux growth protocol set up by Sljukic et al. (1967 ▸). Sc2O3 and KH2PO4 were mixed in stoichiometric qu­anti­ties (molar ratio 2:3) and B2O3 was added as a flux with a sixfold qu­antity of that of Sc2O3. The complete mixture was transferred to a platinum crucible, covered with a lid, and heated in a chamber furnace to 1473 K, held at this temperature for 24 h and then slowly cooled down to 1073 K at a rate of 3 K h−1. Between 1073 K and room temperature the cooling rate was 50 K h−1. The synthesis batch was immersed in hot water to dissolve the B2O3 and remaining K-phosphates. The residual contained single-phase KScP2O7 as checked by powder X-ray diffraction and showed single crystals of irregular to needle-like form with well-developed faces. The crystals are colorless and highly transparent with sizes up to 140 µm in lengths and ∼80 µm in diameter.

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2 ▸.

Table 2

Experimental details

Crystal data
Chemical formula	KScP2O7
M r	258
Crystal system, space group	Monoclinic, P21/c
Temperature (K)	293
a, b, c (Å)	7.4634 (1), 10.3902 (1), 8.3747 (1)
β (°)	106.49
V (Å3)	622.72 (1)
Z	4
Radiation type	Mo Kα
μ (mm−1)	2.35
Crystal size (mm)	0.16 × 0.09 × 0.08
Data collection
Diffractometer	Bruker SMART APEX CCD
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 ▸)
T min, T max	0.38, 0.52
No. of measured, independent and observed [I > 2σ(I)] reflections	20981, 2985, 2850
R int	0.021
(sin θ/λ)max (Å−1)	0.837
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.018, 0.049, 1.05
No. of reflections	2985
No. of parameters	101
Δρmax, Δρmin (e Å−3)	0.79, −0.66

Computer programs: APEX2 and SAINT (Bruker, 2012 ▸), SIR2014 (Burla et al., 2005 ▸), SHELXL2014/7 (Sheldrick, 2015 ▸), DIAMOND (Brandenburg, 2006 ▸), ORTEP for Windows and WinGX publication routines (Farrugia, 2012 ▸).

Crystal structure: contains datablock(s) global, I. DOI: 10.1107/S2056989020010427/wm5578sup1.cif

Structure factors: contains datablock(s) I. DOI: 10.1107/S2056989020010427/wm5578Isup2.hkl

CCDC reference: 2019936

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

KScP2O7	F(000) = 504
Mr = 258	Dx = 2.752 Mg m−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 20981 reflections
a = 7.4634 (1) Å	θ = 2.9–36.5°
b = 10.3902 (1) Å	µ = 2.35 mm−1
c = 8.3747 (1) Å	T = 293 K
β = 106.49°	Prismatic, colorless
V = 622.72 (1) Å3	0.16 × 0.09 × 0.08 mm
Z = 4

Bruker SMART APEX CCD diffractometer	2850 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.021
rotation, ω–scans at 4 different φ positions	θmax = 36.5°, θmin = 2.9°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −12→12
Tmin = 0.38, Tmax = 0.52	k = −17→17
20981 measured reflections	l = −13→13
2985 independent reflections

Refinement on F2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: structure-invariant direct methods
R[F2 > 2σ(F2)] = 0.018	w = 1/[σ2(Fo2) + (0.0257P)2 + 0.274P] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.049	(Δ/σ)max = 0.001
S = 1.05	Δρmax = 0.79 e Å−3
2985 reflections	Δρmin = −0.66 e Å−3
101 parameters	Extinction correction: SHELXL2014/7 (Sheldrick 2015), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 restraints	Extinction coefficient: 0.0429 (15)
0 constraints

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.

	x	y	z	Uiso*/Ueq
K1	0.82123 (3)	0.67829 (3)	0.94124 (3)	0.02342 (6)
Sc1	0.76534 (2)	0.09952 (2)	0.74255 (2)	0.00607 (4)
P1	0.55749 (3)	0.36164 (2)	0.80923 (2)	0.00673 (5)
P2	0.86703 (3)	0.40292 (2)	0.67637 (3)	0.00681 (5)
O1	0.54575 (9)	0.22058 (6)	0.76034 (9)	0.01132 (11)
O2	0.36433 (9)	0.42041 (6)	0.76741 (9)	0.01313 (11)
O3	0.67337 (11)	0.38889 (7)	0.98492 (9)	0.01712 (13)
O4	0.66159 (9)	0.43502 (6)	0.69104 (8)	0.01167 (11)
O5	0.99440 (9)	0.50481 (6)	0.77947 (8)	0.01003 (10)
O6	0.85616 (11)	0.40831 (7)	0.49554 (8)	0.01632 (13)
O7	0.92157 (9)	0.27011 (6)	0.75056 (8)	0.01088 (10)

	U11	U22	U33	U12	U13	U23
K1	0.02013 (10)	0.02973 (12)	0.01843 (10)	0.00408 (8)	0.00226 (7)	−0.00089 (8)
Sc1	0.00647 (6)	0.00539 (6)	0.00639 (6)	0.00013 (4)	0.00190 (4)	−0.00015 (4)
P1	0.00662 (8)	0.00633 (8)	0.00731 (8)	0.00074 (6)	0.00208 (6)	−0.00046 (6)
P2	0.00755 (8)	0.00703 (8)	0.00616 (8)	−0.00186 (6)	0.00246 (6)	−0.00017 (5)
O1	0.0091 (2)	0.0070 (2)	0.0185 (3)	0.00026 (18)	0.0050 (2)	−0.00208 (19)
O2	0.0086 (2)	0.0100 (2)	0.0214 (3)	0.00284 (19)	0.0052 (2)	−0.0002 (2)
O3	0.0209 (3)	0.0207 (3)	0.0073 (3)	0.0010 (3)	−0.0001 (2)	−0.0025 (2)
O4	0.0086 (2)	0.0124 (2)	0.0150 (3)	0.00151 (19)	0.0050 (2)	0.0054 (2)
O5	0.0103 (2)	0.0097 (2)	0.0107 (2)	−0.00398 (18)	0.00393 (19)	−0.00307 (18)
O6	0.0199 (3)	0.0229 (3)	0.0069 (2)	−0.0082 (2)	0.0049 (2)	−0.0016 (2)
O7	0.0098 (2)	0.0069 (2)	0.0159 (3)	−0.00059 (18)	0.0035 (2)	0.00091 (19)

K1—O5	2.7837 (7)	P1—O3	1.5068 (7)
K1—O7i	2.7966 (7)	P1—O2	1.5123 (7)
K1—O1ii	2.8141 (7)	P1—O1	1.5176 (6)
K1—O7iii	2.9876 (7)	P1—O4	1.6128 (6)
K1—O5i	3.0259 (7)	P1—K1vii	3.5569 (3)
K1—O2ii	3.1505 (7)	P2—O6	1.4944 (7)
K1—O3	3.2592 (8)	P2—O5	1.5178 (6)
K1—O4	3.2835 (7)	P2—O7	1.5207 (6)
K1—O2iv	3.2927 (7)	P2—O4	1.6076 (6)
K1—O6iii	3.3265 (9)	P2—K1i	3.4856 (3)
K1—P2i	3.4856 (3)	P2—K1viii	3.6237 (3)
K1—P1ii	3.5570 (3)	O1—K1vii	2.8141 (7)
Sc1—O6v	2.0346 (7)	O2—Sc1ii	2.0883 (6)
Sc1—O3vi	2.0736 (7)	O2—K1vii	3.1505 (7)
Sc1—O2vii	2.0884 (6)	O2—K1iv	3.2927 (7)
Sc1—O5viii	2.0989 (6)	O3—Sc1v	2.0736 (7)
Sc1—O1	2.1045 (6)	O5—Sc1iii	2.0990 (6)
Sc1—O7	2.1122 (6)	O5—K1i	3.0259 (7)
Sc1—K1viii	3.9059 (3)	O6—Sc1vi	2.0346 (7)
Sc1—K1vi	3.9333 (3)	O6—K1viii	3.3265 (9)
Sc1—K1i	4.1501 (3)	O7—K1i	2.7966 (7)
Sc1—K1vii	4.2870 (3)	O7—K1viii	2.9875 (7)
O5—K1—O7i	106.35 (2)	O2vii—Sc1—K1vi	56.82 (2)
O5—K1—O1ii	108.45 (2)	O5viii—Sc1—K1vi	49.513 (18)
O7i—K1—O1ii	145.07 (2)	O1—Sc1—K1vi	135.284 (19)
O5—K1—O7iii	59.145 (18)	O7—Sc1—K1vi	118.557 (19)
O7i—K1—O7iii	93.300 (18)	K1viii—Sc1—K1vi	70.210 (7)
O1ii—K1—O7iii	106.983 (19)	O6v—Sc1—K1i	52.43 (2)
O5—K1—O5i	78.29 (2)	O3vi—Sc1—K1i	126.74 (2)
O7i—K1—O5i	50.565 (17)	O2vii—Sc1—K1i	140.66 (2)
O1ii—K1—O5i	135.51 (2)	O5viii—Sc1—K1i	79.508 (19)
O7iii—K1—O5i	113.314 (18)	O1—Sc1—K1i	94.313 (18)
O5—K1—O2ii	116.03 (2)	O7—Sc1—K1i	37.741 (18)
O7i—K1—O2ii	115.93 (2)	K1viii—Sc1—K1i	66.889 (5)
O1ii—K1—O2ii	48.919 (17)	K1vi—Sc1—K1i	128.501 (4)
O7iii—K1—O2ii	72.254 (18)	O6v—Sc1—K1vii	112.70 (2)
O5i—K1—O2ii	164.277 (19)	O3vi—Sc1—K1vii	67.21 (2)
O5—K1—O3	71.10 (2)	O2vii—Sc1—K1vii	75.012 (19)
O7i—K1—O3	103.820 (19)	O5viii—Sc1—K1vii	150.317 (19)
O1ii—K1—O3	84.749 (19)	O1—Sc1—K1vii	34.402 (18)
O7iii—K1—O3	130.140 (19)	O7—Sc1—K1vii	110.455 (18)
O5i—K1—O3	55.064 (17)	K1viii—Sc1—K1vii	131.220 (7)
O2ii—K1—O3	133.582 (19)	K1vi—Sc1—K1vii	101.144 (6)
O5—K1—O4	47.582 (17)	K1i—Sc1—K1vii	128.415 (5)
O7i—K1—O4	140.014 (19)	O3—P1—O2	113.29 (4)
O1ii—K1—O4	67.811 (18)	O3—P1—O1	114.72 (4)
O7iii—K1—O4	94.293 (17)	O2—P1—O1	110.44 (4)
O5i—K1—O4	90.703 (17)	O3—P1—O4	105.51 (4)
O2ii—K1—O4	103.768 (18)	O2—P1—O4	105.11 (4)
O3—K1—O4	44.629 (17)	O1—P1—O4	106.97 (4)
O5—K1—O2iv	120.669 (19)	O3—P1—K1vii	144.71 (3)
O7i—K1—O2iv	72.463 (19)	O2—P1—K1vii	62.23 (3)
O1ii—K1—O2iv	87.172 (19)	O1—P1—K1vii	49.33 (3)
O7iii—K1—O2iv	165.347 (19)	O4—P1—K1vii	109.38 (3)
O5i—K1—O2iv	54.972 (17)	O3—P1—K1	56.74 (3)
O2ii—K1—O2iv	116.65 (2)	O2—P1—K1	95.62 (3)
O3—K1—O2iv	53.305 (18)	O1—P1—K1	153.20 (3)
O4—K1—O2iv	94.610 (18)	O4—P1—K1	58.24 (3)
O5—K1—O6iii	97.331 (19)	K1vii—P1—K1	152.503 (8)
O7i—K1—O6iii	55.891 (18)	O6—P2—O5	113.29 (4)
O1ii—K1—O6iii	121.365 (19)	O6—P2—O7	112.29 (4)
O7iii—K1—O6iii	46.342 (17)	O5—P2—O7	110.41 (4)
O5i—K1—O6iii	100.309 (18)	O6—P2—O4	106.93 (4)
O2ii—K1—O6iii	72.478 (18)	O5—P2—O4	105.59 (4)
O3—K1—O6iii	153.88 (2)	O7—P2—O4	107.91 (3)
O4—K1—O6iii	140.332 (18)	O6—P2—K1i	140.37 (3)
O2iv—K1—O6iii	122.924 (18)	O5—P2—K1i	59.96 (3)
O5—K1—P2i	90.537 (15)	O7—P2—K1i	51.21 (3)
O7i—K1—P2i	25.078 (13)	O4—P2—K1i	112.48 (3)
O1ii—K1—P2i	150.579 (16)	O6—P2—K1viii	66.61 (3)
O7iii—K1—P2i	102.011 (14)	O5—P2—K1viii	104.90 (3)
O5i—K1—P2i	25.736 (12)	O7—P2—K1viii	53.74 (3)
O2ii—K1—P2i	140.943 (16)	O4—P2—K1viii	148.68 (3)
O3—K1—P2i	80.358 (14)	K1i—P2—K1viii	77.363 (6)
O4—K1—P2i	115.250 (14)	O6—P2—K1	126.27 (3)
O2iv—K1—P2i	63.593 (13)	O5—P2—K1	42.96 (2)
O6iii—K1—P2i	76.323 (13)	O7—P2—K1	121.13 (3)
O5—K1—P1ii	117.439 (16)	O4—P2—K1	62.66 (3)
O7i—K1—P1ii	131.596 (16)	K1i—P2—K1	77.719 (8)
O1ii—K1—P1ii	24.144 (13)	K1viii—P2—K1	146.911 (7)
O7iii—K1—P1ii	92.076 (14)	P1—O1—Sc1	127.58 (4)
O5i—K1—P1ii	154.610 (15)	P1—O1—K1vii	106.53 (3)
O2ii—K1—P1ii	25.133 (12)	Sc1—O1—K1vii	120.60 (3)
O3—K1—P1ii	108.821 (15)	P1—O2—Sc1ii	140.31 (4)
O4—K1—P1ii	87.268 (13)	P1—O2—K1vii	92.64 (3)
O2iv—K1—P1ii	99.950 (13)	Sc1ii—O2—K1vii	124.31 (3)
O6iii—K1—P1ii	97.304 (14)	P1—O2—K1iv	106.05 (3)
P2i—K1—P1ii	151.985 (9)	Sc1ii—O2—K1iv	91.12 (2)
O6v—Sc1—O3vi	178.96 (3)	K1vii—O2—K1iv	87.202 (17)
O6v—Sc1—O2vii	91.12 (3)	P1—O3—Sc1v	162.86 (5)
O3vi—Sc1—O2vii	89.85 (3)	P1—O3—K1	100.52 (4)
O6v—Sc1—O5viii	91.86 (3)	Sc1v—O3—K1	92.33 (3)
O3vi—Sc1—O5viii	88.54 (3)	P2—O4—P1	125.80 (4)
O2vii—Sc1—O5viii	88.65 (3)	P2—O4—K1	91.56 (3)
O6v—Sc1—O1	89.20 (3)	P1—O4—K1	97.07 (3)
O3vi—Sc1—O1	90.26 (3)	P2—O5—Sc1iii	133.60 (4)
O2vii—Sc1—O1	100.03 (3)	P2—O5—K1	115.23 (3)
O5viii—Sc1—O1	171.24 (3)	Sc1iii—O5—K1	105.40 (2)
O6v—Sc1—O7	89.01 (3)	P2—O5—K1i	94.31 (3)
O3vi—Sc1—O7	90.06 (3)	Sc1iii—O5—K1i	98.65 (2)
O2vii—Sc1—O7	173.98 (3)	K1—O5—K1i	101.71 (2)
O5viii—Sc1—O7	85.32 (2)	P2—O6—Sc1vi	163.73 (5)
O1—Sc1—O7	86.00 (2)	P2—O6—K1viii	89.04 (3)
O6v—Sc1—K1viii	110.60 (2)	Sc1vi—O6—K1viii	98.58 (3)
O3vi—Sc1—K1viii	69.08 (2)	P2—O7—Sc1	131.85 (4)
O2vii—Sc1—K1viii	125.45 (2)	P2—O7—K1i	103.71 (3)
O5viii—Sc1—K1viii	43.401 (17)	Sc1—O7—K1i	114.72 (3)
O1—Sc1—K1viii	128.378 (19)	P2—O7—K1viii	102.03 (3)
O7—Sc1—K1viii	49.150 (18)	Sc1—O7—K1viii	98.52 (2)
O6v—Sc1—K1vi	125.03 (2)	K1i—O7—K1viii	100.37 (2)
O3vi—Sc1—K1vi	55.89 (2)