A disordered cerium(IV) phosphate with a tunnel structure, K₄CeZr(PO₄)₄

Tetra­potassium cerium(IV) zirconium tetra­kis­(mono­phos­phate) crystallizes in the tetra­gonal system (space group I4₁/amd). A complex disorder in K₄CeZr(PO₄)₄ involves the mixing of Ce and Zr atoms on a single site with m2 symmetry and the splitting of P- and O-atom positions, equivalent to a rotation of the phosphate groups, to yield eight- and sixfold coordination environments around Ce and Zr, respectively. The K atoms are located in tunnels running parallel to the a and b axes.

S1. Comment

Cerium is only the lanthanide that forms compounds in the tetravalent as well as the trivalent oxidation state. Its chemical behavior as a tetravalent metal is similar to those of Zr, Hf, Th, U, Np and Pu. Such properties can be explained by the similar ionic radii and electron configurations of these elements (the presence of the f electrons). At the same time, there are only a few phosphates containing Ce^IV that have been synthesized at high temperature. At high temperatures, many Ce phosphates decompose to yield CePO₄ (monazite) as a main product, owing to its chemical stability (Leonardos, 1974) and its elevated melting temperature in excess of 2223 K (Ueda & Korekawa, 1955). Another stable compound containing cerium is CeP₂O₇ (Völlenkle et al., 1963), which is easily prepared by the high-temperature recrystallization of the precipitate obtained by the mixing of Ce^IV sulfate and sodium pyrophosphate aqueous solutions. The Ce^IV phosphate Ce^IV(PO₄)(HPO₄)_0.5(H₂O)_0.5 can also be synthesized from CeO₂, H₃PO₄ and H₂O (Nazaraly et al., 2005). Finally, Cd_0.5Ce^IV₂(PO₄)₃ can be prepared by solid-state reaction at 1373 K (Orlova et al., 2005). The latter compound is isostructural to monazite, with Cd and Ce atoms randomly occupying the same crystallographic site.

We present here the structure determination of a new mixed orthophosphate containing tetravalent cerium, K₄CeZr(PO₄)₄, (I). The projection of the structure of (I) on to the bc plane shows the three-dimensional character of the [CeZr(PO₄)₄]_∞ framework (Fig. 1). The structure can be described as a combination of [ZrO₆] octahedra, [CeO₈] dodecahedra and [PO₄] tetrahedra linked together by sharing corners and edges. The rigid framework contains tunnels running along the a and b directions, in which the K⁺ cations are located.

A complex disorder involving the phosphate groups is observed in (I). The P positions are split equally over two sites, PA (8e site, 50% occupancy) and PB (16h site, 25% occupancy). The O1 (16h) position is fully occupied but the other O atoms are disordered over three sites, O2A (16h, 50% occupancy), O2B (8e, 50% occupancy) and O3 (16h, 25% occupancy) (Fig. 2). The disorder appears as a result of the mixed Ce/Zr occupancy and of their different sizes and bonding requirements. Three types of M—O distances are observed in (I): 1.998 (11), 2.141 (4) and 2.491 (6) Å. The latter distance is rather long for Zr^IV atoms by comparison with K₂Zr(PO₄)₂, with Zr—O distances of 2.060 (6) and 2.072 (3) Å (Doerffel & Liebertz, 1990). In Cd_0.5Ce^IV₂(PO₄)₃ (Orlova et al., 2005), the Ce—O distances are in the range 2.40 (1)–2.87 (1) Å for nine-coordinated Ce^IV atoms.

Four phosphate groups coordinate the M (= Ce or Zr) atom via O1 atoms forming an equatorial square-planar arrangement with M—O1 distances equal to 2.141 (4) Å. For M = Ce, the coordination is completed with four O2A atoms (Fig. 3a). A similar oxygen environment can be found for Zr in ZrSiO₄ (Siegel or Siggel & Jansen, 1990). for M = Zr, the coordination is completed by two O2B atoms (Fig. 3b). Thus, Ce is eight-coordinated and Zr is six-coordinated. The O2B and O3 positions result from a rotation of 32.3 (6)° of the PO₄ tetrahedron around the O1—O1^I edge (Fig. 2). Bond valence sum (BVS) calculations confirm the six- and eightfold coordinations of the Zr and Ce atoms, respectively. The BVS around Zr is equal to 4.00 (4 Zr—O1 bonds with BV = 0.576 and 2 Zr—O2B bonds with BV = 0.848), while the BVS around Ce is equal to 4.09 (4 Ce—O1 bonds with BV = 0.737 and 4 Ce—O2A bonds with BV = 0.286) (Brese & O'Keeffe, 1991; Brown, 2002).

The potassium cations are located in tunnels running in two orthogonal directions parallel to the a and b axes with diameters of approximately 4 Å. Their oxygen environment depends on the orientation of the disordered PO₄ group, which yields a wide range of K—O distances (2.532–3.087 Å). The BVS calculation gives a value of 1.1 taking into account the partial occupancies of the O sites. The K⁺ ions are at a distance of 3.3520 (6) Å from one another and ionic conductivity may be expected on the basis of the large tunnel dimensions.

S2. Experimental

The title compound can be obtained easily using the self-flux technique in air. However, ZrO₂ has low solubility in phosphate fluxes and ZrF₄ was used as a starting Zr compound. CeF₃ was used for the same reason.

In a first step, a mixture of 4.52 g of KPO₃ and 3.4 g of K₄P₂O₇ was melted in a platinum crucible at 1273 K for 1 h with stirring. It was then cooled quickly to 1173 K and a ground mixture of ZrF₄ and CeF₃ was added. The temperature of the crucible was kept constant for 30 min and then cooled at a rate of 25 K h⁻¹ to 913 K and the molten glass was poured out. After cooling to room temperature and rinsing in hot deionized water, a mixture of yellow crystals of (I) (0.1–0.15 mm in size) and CePO₄ powder was recovered. This mixture was separated by sedimentation in water. Crystals of (I) were dried at 400 K in air and sieved.

The purity of (I) was checked using powder X-ray diffraction (DRON-3 Ni-filtered Cu Kα radiation). CePO₄ and other crystalline impurities were not detected. The ICP determination of K, Ce and Zr in (I) yielded an atomic ratio of the elements of 3.95:0.97:0.98. Further analysis for K, Ce, Zr and P was performed by energy dispersive spectroscopy; the analysis yielded atomic ratios equal to 3.9:1.05:1.03:4. The presence of fluorine was checked by the following procedure: the sample was melted with NaOH at 800 K in a gold crucible and washed with hot deionized water. Nitric acid was then added to the crucible. Fluoride ions were precipitated as PbClF and the chloride content was estimated by Volhard's method, from which the fluoride content was calculated (Vogel, 1962). No fluorine was detected in (I).

By the same technique, we also synthesized K₄CeHf(PO₄)₄, but with smaller crystal dimensions (unpublished work).

S3. Refinement

The Ce and Zr atomic coordinates and displacement parameters were constrained and their occupancies were refined. After the final refinement cycles, the P and O atoms were found to have high values of U_eq and the convergence factors were also high. Three peaks were assigned as extra P and O positions according to the anion geometry. The occupancies of the P and O sites were calculated from the compound stoichiometry and fixed.

Computing details

Data collection: CrysAlis CCD (Oxford Diffraction, 2005); cell refinement: CrysAlis CCD; data reduction: CrysAlis RED (Oxford Diffraction, 2005); program(s) used to solve structure: SIR2004 (Burla et al., 2005); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: WinGX (Farrugia, 1999).

Figures

	Fig. 1. Projection of (I) on to the bc plane. CeO8 and ZrO6 polyhedra are shown with light grey shading, PO4 tetrahedra with dark grey shading and K atoms as light grey circles.
	Fig. 2. View of the disorder in the [PO4] tetrahedron (50% probability displacement ellipsoids). [Symmetry codes: (i) −x, 3/2 − y, z.]
	Fig. 3. Oxygen environment and structural arrangement around the Ce (a) and Zr (b) atoms (50% probability displacement ellipsoids). [Symmetry codes: (i) −x, 3/2 − y, z; (ii) −x, 1/2 + y, 1 − z; (iii) −1/4 + y, 3/4 − x, 1/4 + z; (iv) 1/4 − y, 3/4 + x, 1/4 + z; (v) x, 1 − y, 1 − z; (vi) −3/4 + y, 3/4 + x, 5/4 − z; (vii) 3/4 − y, 3/4 − x, 5/4 − z.]

Tetrapotassium cerium(IV) zirconium tetrakis(monophosphate)

Crystal data

K4CeZr(PO4)4	Dx = 3.330 Mg m^−3
Mr = 767.62	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I41/amd	Cell parameters from 320 reflections
Hall symbol: -I 4bd 2	θ = 15–25°
a = 6.7039 (9) Å	µ = 5.24 mm^−1
c = 17.065 (3) Å	T = 293 K
V = 766.9 (2) Å^3	Tetragonal bipyramid, light yellow
Z = 2	0.16 × 0.13 × 0.12 mm
F(000) = 725

Data collection

Oxford Diffraction XCalibur-3 diffractometer	327 independent reflections
Radiation source: fine-focus sealed tube	292 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.034
ϕ and ω scans	θmax = 30.0°, θmin = 3.3°
Absorption correction: multi-scan (Blessing, 1995)	h = −7→9
Tmin = 0.442, Tmax = 0.501	k = −9→6
3037 measured reflections	l = −23→24

Refinement

Refinement on F^2	2 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.029	Secondary atom site location: difference Fourier map
wR(F^2) = 0.080	w = 1/[σ^2(Fo^2) + (0.062P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 1.03	(Δ/σ)max < 0.001
327 reflections	Δρmax = 0.59 e Å^−3
41 parameters	Δρmin = −0.86 e Å^−3

Special details

Experimental. The purity of (I) was checked using powder X-ray diffraction (DRON-3 Ni-filtered Cu Kα radiation λ=1.54178). CePO₄ and other crystalline impurities were not detected. The ICP determination of K, Ce and Zr in (I) was performed on a `Spectroflame Modula ICP' (`Sectro', Germany) instrument. The atomic ratio of the elements in (I) was found to be 3.95:0.97:0.98. Further analysis for K, Ce, Zr and P was performed by energy dispersive spectroscopy using a Link Isis analyzer mounted on a Philips XL 30 FE 6 scanning electron microscope. The analysis yielded atomic ratios equal to 3.9:1.05:1.03:4.

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.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr	0	0.75	0.625	0.0232 (2)	0.493 (3)
Ce	0	0.75	0.625	0.0232 (2)	0.509 (4)
K	0.25	0.75	0.25	0.0566 (6)
PA	0	0.75	0.4415 (5)	0.0193 (12)	0.5
PB	0.0646 (16)	0.75	0.4245 (6)	0.0269 (17)	0.25
O1	0	0.5685 (5)	0.3842 (2)	0.0376 (10)
O2A	0.1788 (9)	0.75	0.4971 (4)	0.0283 (14)	0.5
O2B	0	0.75	0.5079 (6)	0.044 (3)	0.5
O3	0.302 (3)	0.75	0.4205 (11)	0.050 (4)	0.25

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Zr	0.0160 (3)	0.0160 (3)	0.0375 (4)	0	0	0
Ce	0.0160 (3)	0.0160 (3)	0.0375 (4)	0	0	0
K	0.0371 (11)	0.0611 (13)	0.0715 (13)	0	0.0037 (10)	0
PA	0.018 (4)	0.020 (2)	0.020 (4)	0	0	0
PB	0.043 (6)	0.015 (2)	0.022 (4)	0	−0.005 (3)	0
O1	0.052 (3)	0.0204 (17)	0.0403 (19)	0	0	−0.0021 (14)
O2A	0.022 (3)	0.040 (4)	0.022 (3)	0	−0.002 (2)	0
O2B	0.064 (8)	0.046 (7)	0.022 (4)	0	0	0
O3	0.056 (11)	0.031 (8)	0.063 (10)	0	−0.012 (9)	0

Geometric parameters (Å, º)

Ce—O1^i	2.141 (4)	K—O3	2.930 (19)
Ce—O1^ii	2.141 (4)	K—O1	3.087 (3)
Ce—O1^iii	2.141 (4)	K—O1^xviii	3.087 (3)
Ce—O1^iv	2.141 (4)	K—O1^v	3.087 (3)
Ce—O2A^v	2.491 (6)	K—O1^xvii	3.087 (3)
Ce—O2A^vi	2.491 (6)	K—K^v	3.3520 (6)
Ce—O2A	2.491 (6)	PA—O2A	1.529 (8)
Ce—O2A^vii	2.491 (6)	PA—O2A^v	1.529 (8)
Zr—O2B^vii	1.998 (11)	PA—O1	1.561 (7)
Zr—O2B	1.998 (11)	PA—O1^v	1.561 (7)
Zr—O1^i	2.141 (4)	PA—K^v	3.672 (8)
Zr—O1^iv	2.141 (4)	PB—PB^v	0.87 (2)
Zr—O1^ii	2.141 (4)	PB—O1	1.464 (8)
Zr—O1^iii	2.141 (4)	PB—O1^v	1.464 (8)
Zr—K^viii	4.3122 (5)	PB—O2B	1.488 (14)
Zr—K^ix	4.3122 (5)	PB—O3	1.59 (2)
Zr—K^x	4.3122 (5)	PB—K^xiii	3.604 (11)
Zr—K^xi	4.3122 (5)	PB—K^xvi	3.604 (11)
Zr—K^xii	4.3122 (5)	PB—K^v	3.649 (13)
Zr—K^xiii	4.3122 (5)	O1—PB^v	1.464 (8)
K—O3^xiv	2.532 (14)	O1—Ce^iv	2.141 (4)
K—O3^xiii	2.532 (14)	O1—Zr^iv	2.141 (4)
K—O3^xv	2.532 (14)	O1—K^v	3.087 (3)
K—O3^xvi	2.532 (14)	O2A—K^xiii	2.729 (5)
K—O2A^xiv	2.729 (5)	O2A—K^xvi	2.729 (5)
K—O2A^xiii	2.729 (5)	O2B—PB^v	1.488 (14)
K—O2A^xv	2.729 (5)	O3—K^xiii	2.532 (14)
K—O2A^xvi	2.729 (5)	O3—K^xvi	2.532 (14)
K—O3^xvii	2.930 (19)
O2B^vii—Zr—O2B	180.0000 (10)	O3^xvi—K—O3	52.3 (6)
O2B^vii—Zr—O1^i	85.81 (9)	O2A^xiv—K—O3	95.3 (3)
O2B—Zr—O1^i	94.19 (9)	O2A^xiii—K—O3	84.7 (3)
O2B^vii—Zr—O1^iv	94.19 (9)	O2A^xv—K—O3	95.3 (3)
O2B—Zr—O1^iv	85.81 (9)	O2A^xvi—K—O3	84.7 (3)
O1^i—Zr—O1^iv	90.306 (14)	O3^xvii—K—O3	180.000 (3)
O2B^vii—Zr—O1^ii	85.81 (9)	O3^xiv—K—O1^xviii	75.8 (3)
O2B—Zr—O1^ii	94.19 (9)	O3^xiii—K—O1^xviii	104.2 (3)
O1^i—Zr—O1^ii	171.62 (19)	O3^xv—K—O1^xviii	99.7 (4)
O1^iv—Zr—O1^ii	90.306 (15)	O3^xvi—K—O1^xviii	80.3 (4)
O2B^vii—Zr—O1^iii	94.19 (9)	O2A^xiv—K—O1^xviii	90.51 (12)
O2B—Zr—O1^iii	85.81 (9)	O2A^xiii—K—O1^xviii	89.49 (12)
O1^i—Zr—O1^iii	90.306 (15)	O2A^xv—K—O1^xviii	129.11 (14)
O1^iv—Zr—O1^iii	171.62 (19)	O2A^xvi—K—O1^xviii	50.89 (14)
O1^ii—Zr—O1^iii	90.306 (14)	O3^xvii—K—O1^xviii	47.8 (3)
O2B^vii—Zr—K^viii	60.351 (6)	O3—K—O1^xviii	132.2 (3)
O2B—Zr—K^viii	119.649 (6)	O3^xiv—K—O1^v	104.2 (3)
O1^i—Zr—K^viii	64.93 (5)	O3^xiii—K—O1^v	75.8 (3)
O1^iv—Zr—K^viii	144.23 (7)	O3^xv—K—O1^v	80.3 (4)
O1^ii—Zr—K^viii	110.58 (5)	O3^xvi—K—O1^v	99.7 (4)
O1^iii—Zr—K^viii	42.35 (8)	O2A^xiv—K—O1^v	89.49 (12)
O2B^vii—Zr—K^ix	119.649 (6)	O2A^xiii—K—O1^v	90.51 (12)
O2B—Zr—K^ix	60.351 (6)	O2A^xv—K—O1^v	50.89 (14)
O1^i—Zr—K^ix	144.23 (7)	O2A^xvi—K—O1^v	129.11 (14)
O1^iv—Zr—K^ix	64.93 (5)	O3^xvii—K—O1^v	132.2 (3)
O1^ii—Zr—K^ix	42.35 (8)	O3—K—O1^v	47.8 (3)
O1^iii—Zr—K^ix	110.58 (5)	O1^xviii—K—O1^v	180
K^viii—Zr—K^ix	148.097 (2)	O2A—PA—O2A^v	103.3 (7)
O2B^vii—Zr—K^x	60.351 (6)	O2A—PA—O1	112.88 (14)
O2B—Zr—K^x	119.649 (6)	O2A^v—PA—O1	112.88 (14)
O1^i—Zr—K^x	110.58 (5)	O2A—PA—O1^v	112.88 (14)
O1^iv—Zr—K^x	144.23 (7)	O2A^v—PA—O1^v	112.88 (14)
O1^ii—Zr—K^x	64.93 (5)	O1—PA—O1^v	102.4 (6)
O1^iii—Zr—K^x	42.35 (8)	O2A—PA—K^v	155.5 (4)
K^viii—Zr—K^x	45.743 (3)	O2A^v—PA—K^v	101.2 (3)
K^ix—Zr—K^x	104.165 (5)	O1—PA—K^v	56.1 (3)
O2B^vii—Zr—K^xi	119.649 (6)	O1^v—PA—K^v	56.1 (3)
O2B—Zr—K^xi	60.351 (6)	O2A—PA—K	101.2 (3)
O1^i—Zr—K^xi	144.23 (7)	O2A^v—PA—K	155.5 (4)
O1^iv—Zr—K^xi	110.58 (5)	O1—PA—K	56.1 (3)
O1^ii—Zr—K^xi	42.35 (8)	O1^v—PA—K	56.1 (3)
O1^iii—Zr—K^xi	64.93 (5)	K^v—PA—K	54.31 (13)
K^viii—Zr—K^xi	104.165 (5)	PB^v—PB—O1	72.8 (4)
K^ix—Zr—K^xi	45.743 (3)	PB^v—PB—O1^v	72.8 (4)
K^x—Zr—K^xi	68.929 (10)	O1—PB—O1^v	112.5 (8)
O2B^vii—Zr—K^xii	60.351 (6)	PB^v—PB—O2B	73.1 (5)
O2B—Zr—K^xii	119.649 (6)	O1—PB—O2B	111.3 (4)
O1^i—Zr—K^xii	110.58 (5)	O1^v—PB—O2B	111.3 (4)
O1^iv—Zr—K^xii	42.35 (8)	PB^v—PB—O3	177.5 (8)
O1^ii—Zr—K^xii	64.93 (5)	O1—PB—O3	106.0 (5)
O1^iii—Zr—K^xii	144.23 (7)	O1^v—PB—O3	106.0 (5)
K^viii—Zr—K^xii	120.703 (12)	O2B—PB—O3	109.4 (11)
K^ix—Zr—K^xii	68.929 (10)	PB^v—PB—K	112.7 (2)
K^x—Zr—K^xii	102.032 (8)	O1—PB—K	71.3 (3)
K^xi—Zr—K^xii	104.165 (5)	O1^v—PB—K	71.3 (3)
O2B^vii—Zr—K^xiii	119.649 (6)	O2B—PB—K	174.3 (7)
O2B—Zr—K^xiii	60.351 (6)	O3—PB—K	64.9 (8)
O1^i—Zr—K^xiii	42.35 (8)	PB^v—PB—K^xiii	144.08 (10)
O1^iv—Zr—K^xiii	110.58 (5)	O1—PB—K^xiii	142.6 (5)
O1^ii—Zr—K^xiii	144.23 (7)	O1^v—PB—K^xiii	91.2 (3)
O1^iii—Zr—K^xiii	64.93 (5)	O2B—PB—K^xiii	83.9 (5)
K^viii—Zr—K^xiii	68.929 (10)	K—PB—K^xiii	91.0 (2)
K^ix—Zr—K^xiii	120.702 (12)	PB^v—PB—K^xvi	144.08 (10)
K^x—Zr—K^xiii	104.165 (5)	O1—PB—K^xvi	91.2 (3)
K^xi—Zr—K^xiii	102.032 (8)	O1^v—PB—K^xvi	142.6 (5)
K^xii—Zr—K^xiii	148.097 (2)	O2B—PB—K^xvi	83.9 (5)
O3^xiv—K—O3^xiii	180.0 (10)	K—PB—K^xvi	91.0 (2)
O3^xiv—K—O3^xv	63.2 (8)	K^xiii—PB—K^xvi	55.43 (18)
O3^xiii—K—O3^xv	116.8 (8)	PB^v—PB—K^v	54.69 (13)
O3^xiv—K—O3^xvi	116.8 (8)	O1—PB—K^v	56.3 (4)
O3^xiii—K—O3^xvi	63.2 (8)	O1^v—PB—K^v	56.3 (4)
O3^xv—K—O3^xvi	180.0 (7)	O2B—PB—K^v	127.8 (6)
O3^xiv—K—O2A^xiv	34.0 (5)	O3—PB—K^v	122.8 (8)
O3^xiii—K—O2A^xiv	146.0 (5)	K—PB—K^v	57.96 (18)
O3^xv—K—O2A^xiv	89.8 (4)	K^xiii—PB—K^v	139.45 (18)
O3^xvi—K—O2A^xiv	90.2 (4)	K^xvi—PB—K^v	139.45 (18)
O3^xiv—K—O2A^xiii	146.0 (5)	PB—O1—Ce^iv	149.7 (4)
O3^xiii—K—O2A^xiii	34.0 (5)	PB^v—O1—Ce^iv	149.7 (5)
O3^xv—K—O2A^xiii	90.2 (4)	PA—O1—Ce^iv	145.4 (3)
O3^xvi—K—O2A^xiii	89.8 (4)	PB—O1—Zr^iv	149.7 (4)
O2A^xiv—K—O2A^xiii	180.0 (3)	PB^v—O1—Zr^iv	149.7 (5)
O3^xiv—K—O2A^xv	89.8 (4)	PA—O1—Zr^iv	145.4 (3)
O3^xiii—K—O2A^xv	90.2 (4)	PB—O1—K^v	100.5 (4)
O3^xv—K—O2A^xv	34.0 (5)	PB^v—O1—K^v	82.0 (3)
O3^xvi—K—O2A^xv	146.0 (5)	PA—O1—K^v	99.0 (3)
O2A^xiv—K—O2A^xv	104.18 (16)	Ce^iv—O1—K^v	109.81 (11)
O2A^xiii—K—O2A^xv	75.82 (16)	Zr^iv—O1—K^v	109.81 (11)
O3^xiv—K—O2A^xvi	90.2 (4)	PB—O1—K	82.0 (3)
O3^xiii—K—O2A^xvi	89.8 (4)	PB^v—O1—K	100.5 (4)
O3^xv—K—O2A^xvi	146.0 (5)	PA—O1—K	99.0 (3)
O3^xvi—K—O2A^xvi	34.0 (5)	Ce^iv—O1—K	109.81 (11)
O2A^xiv—K—O2A^xvi	75.82 (16)	Zr^iv—O1—K	109.81 (11)
O2A^xiii—K—O2A^xvi	104.18 (16)	K^v—O1—K	65.76 (7)
O2A^xv—K—O2A^xvi	180.0000 (10)	PA—O2A—K^xiii	129.0 (3)
O3^xiv—K—O3^xvii	52.3 (6)	PA—O2A—K^xvi	129.0 (3)
O3^xiii—K—O3^xvii	127.7 (6)	K^xiii—O2A—K^xvi	75.78 (16)
O3^xv—K—O3^xvii	52.3 (6)	PB—O2B—Zr	163.1 (5)
O3^xvi—K—O3^xvii	127.7 (6)	PB^v—O2B—Zr	163.1 (5)
O2A^xiv—K—O3^xvii	84.7 (3)	PB—O3—K^xiii	120.0 (8)
O2A^xiii—K—O3^xvii	95.3 (3)	PB—O3—K^xvi	120.0 (8)
O2A^xv—K—O3^xvii	84.7 (3)	K^xiii—O3—K^xvi	82.9 (6)
O2A^xvi—K—O3^xvii	95.3 (3)	PB—O3—K	85.6 (9)
O3^xiv—K—O3	127.7 (6)	K^xiii—O3—K	126.5 (5)
O3^xiii—K—O3	52.3 (6)	K^xvi—O3—K	126.5 (5)
O3^xv—K—O3	127.7 (6)

Symmetry codes: (i) y−1/4, x+3/4, z+1/4; (ii) −y+1/4, −x+3/4, z+1/4; (iii) x, y+1/2, −z+1; (iv) −x, −y+1, −z+1; (v) −x, −y+3/2, z; (vi) y−3/4, x+3/4, −z+5/4; (vii) −y+3/4, −x+3/4, −z+5/4; (viii) −x+1/2, −y+2, z+1/2; (ix) y−5/4, x+1/4, −z+3/4; (x) x−1/2, y+1/2, z+1/2; (xi) −y+1/4, −x+5/4, −z+3/4; (xii) x−1/2, y−1/2, z+1/2; (xiii) −y+5/4, −x+5/4, −z+3/4; (xiv) y−3/4, x+1/4, z−1/4; (xv) −y+3/4, −x+5/4, z−1/4; (xvi) y−1/4, x+1/4, −z+3/4; (xvii) −x+1/2, −y+3/2, −z+1/2; (xviii) x+1/2, y, −z+1/2.