Ce20Mg19Zn81: a new structure type with a giant cubic cell

Pavlyuk, V.; Solokha, P.; Zelinska, O.; Paul-Boncour, V.; Nowik-Zając, A.

doi:10.1107/S0108270108015862

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Ce₂₀Mg₁₉Zn₈₁: a new structure type with a giant cubic cell

V. Pavlyuk, P. Solokha, O. Zelinska, V. Paul-Boncour and A. Nowik-Zajac

Icosacerium nonadecamagnesium henoctacontazinc, Ce₂₀Mg₁₉Zn₈₁, synthesized by fritting of the pure elements with subsequent arc melting, crystallizes with an unusually large cubic unit cell [space group F $\overline{4}$ 3m, a = 21.1979 (8) Å] and represents a new structure type among the technologically important family of ternary rare earth-transition metal-magnesium intermetallics. The majority of atoms (two Ce and five Zn) display .3m site symmetry, two Ce and one Mg atom occupy three 2.mm positions, one Mg and one Zn have $\overline{4}$ 3m site symmetry, one Mg and three Zn atoms sit in ..m positions, and one Zn atom is in a general position. The Ce₂₀Mg₁₉Zn₈₁ structure can be described using the geometric concept of nested polyhedral units, by which it consists of four different polyhedral units, viz. A (Zn+Zn₄+Zn₄+Zn₁₂+Ce₆), B (Mg+Zn₁₂+Ce₄+Zn₂₄+Ce₄), C (Zn₄+Zn₁₂+Mg₆) and D (Zn₄+Zn₄+Mg₁₂+Ce₆), with the outer construction unit being an octahedron or tetrahedron. All interatomic distances in the structure indicate metallic-type bonding.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270108015862/sq3145sup1.cif Contains datablocks global, I
	Structure factor file (CIF format) https://doi.org/10.1107/S0108270108015862/sq3145Isup2.hkl Contains datablock I

Comment top

Ternary compounds containing a rare earth (RE), a transition metal (M) and magnesium represent a growing class of materials which attract attention due to their physical properties and applications as modern light-weight alloys and hydrogen storage materials. The crystal structures, physical properties and hydrogenation behaviour of these materials have been reviewed (Rodewald et al., 2007). The appearance of numerous quasicrystals has also been observed in these systems (Steurer & Deloudi, 2008). The Ce–Mg–Zn ternary system was first reported by Melnyk et al. (1978). The isothermal section of the phase diagram was partially constructed up to 60 at.% of Zn and 50 at.% of Ce at 573 K. Four new ternary compounds with preliminary compositions ~ CeMg₇Zn₁₂, \sim Ce(Mg_0.5-0.85Zn_0.5-0.15)₉, ~CeMg₃Zn₅, and Ce₂Mg₃Zn₃ were reported in this region. The last compound was found to crystallize with a cubic unit cell (a = 7.064 Å), whereas the crystal structures of the first three compounds remain unknown. We decided to explore the rest of the phase diagram starting from the Zn-rich corner.

The most transition metal-rich phases known in the literature so far are REMg₂M₉ and REMgM₄. The first series adopts either a rhombohedral PuNi₃ type (space group R3m; Kadir et al., 1997) or a hexagonal TbCu₉Mg₂ type (space group P6₃/mmc) structure (Solokha et al., 2006). The second series crystallizes with the cubic MgCu₄Sn structure type (space group F3m), an ordered version of the Laves phase relative [related?] structure AuBe₅ (Kadir et al., 2002; Sarrao et al., 1999). Many of these REMgM₄ alloys have been studied intensively for hydrogen storage purposes (Wang, Zhou, Cheng et al., 2004 or Wang, Zhou, Gu et al., 2004 ?; Xu et al., 2005). They show excellent discharge capacities of the order of 400 mAh g^-1 and can keep their discharge stability over 50 cycles. The influence of different factors (e.g. mechanical alloying, or rare earth or transition metal substitution) on the discharge characteristics of these alloys has also been investigated (Wang , Zhou, Cheng et al., 2004 or Wang, Zhou, Gu et al., 2004 ?; Zhang et al., 2005; Li et al., 2005). Here, we present the results of a crystallographic study of a new transition metal-rich compound, Ce₂₀Mg₁₉Zn₈₁.

The crystal structure of this compound is fairly complicated, with a cubic unit cell containing 480 atoms. The projection of the unit cell of Ce₂₀Mg₁₉Zn₈₁ and the coordination polyhedra of the atoms are shown in Fig. 1. The number of neighbour atoms correlates well with the sizes of the central atoms. The largest Ce atoms are enclosed in 16-, 17- and 18-vertex polyhedra. Mg atoms are characterized by Frank–Kasper or pseudo-Frank–Kasper polyhedra, having coordination number (CN) 15 or 16. Atom Zn1 is surrounded by 14 neighbours in the form of a distorted rhombododecahedron (CN 14). The remaining Zn atoms (Zn2–Zn10) have icosahedral symmetry with CN 10–13. The shortest interatomic distances (Table 1) are in the ranges typical for intermetallic compounds of these elements and indicate metallic-type bonding. The structure can be assigned to the class No. 5 (CN 12 for the smallest atom, icosahedron as a coordination polyhedron), according to the classification scheme of Krypyakevich (1977).

Chabot et al. (1981) proposed the geometric concept of nested polyhedral units for the description of complicated cubic structures. According to this concept, seven different polyhedral units were proposed as basic units, with the outermost polyhedron always being a cubo-octahedron. With respect to the spatial arrangement of nested polyhedral units, cubic structures were divided into two groups with isolated and linked units, respectively. The crystal structure of Ce₂₀Mg₁₉Zn₈₁ can also be described by means of isolated polyhedral units, although the construction units here are different from those proposed earlier. We can distinguish four different units, A, B, C and D (Fig. 2a). Unit A (27 atoms) consists of a central atom (C) surrounded by a small inner tetrahedron (IT) and a larger outer tetrahedron (OT). Further away from the centre are a cubo-octahedron (CO) and an octahedron (OH). The B unit (45 atoms) includes the following elements: (C)–(TT)–(IT)–(TCO)–(OT).As the construction elements of the B nested unit, a truncated tetrahedron (TT) and a truncated cubo-octahedron (TCO) also occur. The C unit (22 atoms) includes (T)–(CO)–(OH), and the D unit (26 atoms) is characterized by an (IT)–(OT)–(CO)–(OH) sequence.

If we compare the A and D units we can see that they are almost the same and only differ by one atom, which centres the A unit. Both these units correspond to the γ-brass basic unit with or without a central atom. Unit C is related to the Ti₂Ni structure type with a slightly different sequence of geometric forms. The B unit cannot be fully described by the Chabot concept. Instead, we can apply here the ideas of Bodak et al. (2006), who proposed the description of complicated cubic structures starting from four `arystotypes', namely diamond, Cu, CsCl and W, from the example of cubic rare earth-containing compounds. On this basis, we can assume that the B unit is a `hybrid' of α-Mn and face-centred cubic (fcc) Cu units in which the internal part (C–TT–IT) is the same as in α-Mn and the external part (TCO) is identical to that in fcc Cu (Fig. 2b). The number of atoms in the unit cell is equal to the sum of the atoms in each unit: (4 × 27) + (4 × 22) + (4 × 26) + (4 × 45) = 480 (Pearson code cF480). Taking the nested polyhedral units as `pseudo-atoms', we can also consider Ce₂₀Mg₁₉Zn₈₁ to belong to the LiMgPdSn structure type (F43m, cF16).

Experimental top

To avoid losses of magnesium and zinc due to their vapour pressure at higher temperatures, the alloys were prepared in two steps. First, powders of the pure metals with a stoichiometry Ce:Mg:Zn = 1:1:4 were pressed into a pellet, enclosed in an evacuated silica ampoule (internal pressure 10^-5 – 10 ^-6 Pa) and placed in a resistance furnace with a thermocouple controller. The heating process was carried out in a consecutive order, increasing the temperature from 673 to 1073 K over 6 d. The alloy was then annealed at this temperature for 4 h and slowly cooled down to room temperature. In the second step, the pellet was remelted in an arc furnace under an argon atmosphere at least three times in order to ensure homogeneity. The total weight loss after the melting procedures was less than 2 wt.%. The brittle sample was stable in air, showing a metallic lustre. Wavelength-dispersive spectrometry and electron probe microanalysis (CAMECA SX100 analyser) were used to control [determine?] the number of phases and their content in the sample. Various point analyses on this phase were in good agreement with the ideal composition determined by the single-crystal X-ray data (an average result is 17.6 at.% Ce, 14.7 at.% Mg and 67.7 at.% Zn). Irregularly shaped single crystals, exhibiting metallic lustre, were isolated by mechanical fragmentation from the alloys.

Computing details top

Data collection: CrysAlis CCD (Oxford Diffraction, 2004); cell refinement: CrysAlis CCD (Oxford Diffraction, 2004); data reduction: CrysAlis RED (Oxford Diffraction, 2005); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top

	Fig. 1. A projection of the Ce₂₀Mg₁₉Zn₈₁ unit cell and the coordination polyhedra of the atoms. Ce, Mg and Zn atoms are drawn as black, dark-grey and light-grey circles, respectively.
	Fig. 2. (a) The nested polyhedral units as construction elements of Ce₂₀Mg₁₉Zn₈₁. (b) The B unit as a `hybrid' of α-Mn and fcc Cu structural fragments.

Icosacerium nonadecamagnesium henoctacontazinc top

Crystal data top

Ce₂₀Mg₁₉Zn₈₁	D_x = 5.969 Mg m⁻³
M_r = 8559.26	Mo Kα radiation, λ = 0.71073 Å
Cubic, F43m	Cell parameters from 544 reflections
Hall symbol: F -4 2 3	θ = 3.8–26.3°
a = 21.1979 (8) Å	µ = 29.39 mm⁻¹
V = 9525.3 (6) Å³	T = 295 K
Z = 4	Irregularly shaped, metallic dark grey
F(000) = 15272	0.11 × 0.09 × 0.07 mm

Data collection top

Oxford Diffraction Xcalibur diffractometer	544 independent reflections
Radiation source: fine-focus sealed tube	388 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.034
Detector resolution: 0 pixels mm^-1	θ_max = 26.3°, θ_min = 3.8°
ω scans	h = −15→15
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2005)	k = 0→18
T_min = 0.056, T_max = 0.122	l = 3→26
1009 measured reflections

Refinement top

Refinement on F²	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0544P)²] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.044	(Δ/σ)_max < 0.001
wR(F²) = 0.101	Δρ_max = 1.63 e Å⁻³
S = 1.01	Δρ_min = −1.89 e Å⁻³
544 reflections	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
73 parameters	Extinction coefficient: 0.000081 (14)
0 restraints	Absolute structure: Flack (1983), with how many Friedel pairs?
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.3 (2)

Crystal data top

Ce₂₀Mg₁₉Zn₈₁	Z = 4
M_r = 8559.26	Mo Kα radiation
Cubic, F43m	µ = 29.39 mm⁻¹
a = 21.1979 (8) Å	T = 295 K
V = 9525.3 (6) Å³	0.11 × 0.09 × 0.07 mm

Data collection top

Oxford Diffraction Xcalibur diffractometer	544 independent reflections
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2005)	388 reflections with I > 2σ(I)
T_min = 0.056, T_max = 0.122	R_int = 0.034
1009 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.044	0 restraints
wR(F²) = 0.101	Δρ_max = 1.63 e Å⁻³
S = 1.01	Δρ_min = −1.89 e Å⁻³
544 reflections	Absolute structure: Flack (1983), with how many Friedel pairs?
73 parameters	Absolute structure parameter: 0.3 (2)

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. 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 (Å²) top

	x	y	z	U_iso*/U_eq
Ce1	0.39743 (11)	0.39743 (11)	0.39743 (11)	0.0322 (10)
Ce2	0.15367 (10)	0.15367 (10)	0.15367 (10)	0.0333 (10)
Ce3	0.17469 (15)	0.0000	0.0000	0.0363 (8)
Ce4	−0.03469 (16)	0.2500	0.2500	0.0341 (7)
Mg1	0.2500	0.2500	0.2500	0.036 (10)
Mg2	0.3314 (7)	0.0000	0.0000	0.040 (4)
Mg3	0.1049 (5)	0.1049 (5)	−0.2255 (7)	0.050 (4)
Zn1	0.0000	0.0000	0.0000	0.045 (4)
Zn2	0.0776 (3)	0.0776 (3)	−0.0776 (3)	0.059 (3)
Zn3	0.2005 (3)	0.2005 (3)	−0.2005 (3)	0.074 (3)
Zn4	0.1718 (2)	0.3282 (2)	−0.1718 (2)	0.045 (2)
Zn5	0.0452 (2)	0.4548 (2)	−0.0452 (2)	0.0348 (19)
Zn6	0.0708 (2)	0.0708 (2)	0.0708 (2)	0.0374 (19)
Zn7	0.20822 (16)	0.20822 (16)	0.3834 (2)	0.0443 (13)
Zn8	0.14745 (15)	0.14745 (15)	0.0018 (3)	0.0371 (11)
Zn9	0.14003 (19)	0.35997 (19)	−0.0455 (3)	0.0669 (17)
Zn10	0.03414 (15)	0.11980 (15)	0.26195 (15)	0.0393 (9)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ce1	0.0322 (10)	0.0322 (10)	0.0322 (10)	0.0015 (10)	0.0015 (10)	0.0015 (10)
Ce2	0.0333 (10)	0.0333 (10)	0.0333 (10)	0.0029 (10)	0.0029 (10)	0.0029 (10)
Ce3	0.0403 (18)	0.0344 (10)	0.0344 (10)	0.000	0.000	−0.0036 (16)
Ce4	0.0469 (19)	0.0278 (9)	0.0278 (9)	0.000	0.000	−0.0008 (14)
Mg1	0.036 (10)	0.036 (10)	0.036 (10)	0.000	0.000	0.000
Mg2	0.022 (9)	0.049 (7)	0.049 (7)	0.000	0.000	−0.031 (11)
Mg3	0.044 (5)	0.044 (5)	0.061 (9)	−0.001 (7)	0.018 (5)	0.018 (5)
Zn1	0.045 (4)	0.045 (4)	0.045 (4)	0.000	0.000	0.000
Zn2	0.059 (3)	0.059 (3)	0.059 (3)	0.031 (4)	−0.031 (4)	−0.031 (4)
Zn3	0.074 (3)	0.074 (3)	0.074 (3)	0.003 (4)	−0.003 (4)	−0.003 (4)
Zn4	0.045 (2)	0.045 (2)	0.045 (2)	0.003 (2)	0.003 (2)	−0.003 (2)
Zn5	0.0348 (19)	0.0348 (19)	0.0348 (19)	−0.001 (2)	−0.001 (2)	0.001 (2)
Zn6	0.0374 (19)	0.0374 (19)	0.0374 (19)	0.003 (2)	0.003 (2)	0.003 (2)
Zn7	0.0442 (18)	0.0442 (18)	0.044 (3)	0.003 (2)	0.0069 (17)	0.0069 (17)
Zn8	0.0389 (15)	0.0389 (15)	0.033 (2)	0.0114 (19)	0.0052 (16)	0.0052 (16)
Zn9	0.073 (3)	0.073 (3)	0.054 (4)	0.027 (3)	−0.0068 (19)	0.0068 (19)
Zn10	0.0401 (18)	0.0391 (17)	0.039 (2)	0.0089 (15)	−0.0053 (15)	0.0001 (14)

Geometric parameters (Å, º) top

Ce1—Zn7ⁱ	3.181 (6)	Zn1—Zn6^xxxii	2.598 (8)
Ce1—Zn7ⁱⁱ	3.181 (6)	Zn1—Zn6^xxiv	2.598 (8)
Ce1—Zn7ⁱⁱⁱ	3.181 (6)	Zn1—Zn6^xvii	2.598 (8)
Ce1—Zn10^iv	3.238 (4)	Zn1—Zn2^xxxii	2.850 (12)
Ce1—Zn10ⁱⁱⁱ	3.238 (4)	Zn1—Zn2^xxiv	2.850 (12)
Ce1—Zn10ⁱ	3.238 (4)	Zn1—Zn2	2.850 (12)
Ce1—Zn10^v	3.238 (4)	Zn1—Zn2^xvii	2.850 (12)
Ce1—Zn10^vi	3.238 (4)	Zn2—Zn8	2.686 (6)
Ce1—Zn10ⁱⁱ	3.238 (4)	Zn2—Zn8^xxvi	2.686 (6)
Ce1—Zn9^vii	3.334 (5)	Zn2—Zn8^xviii	2.686 (6)
Ce1—Zn9^viii	3.334 (5)	Zn2—Ce3^xxx	3.106 (7)
Ce1—Zn9^ix	3.334 (5)	Zn2—Ce3^x	3.106 (7)
Ce2—Zn6	3.044 (9)	Zn2—Zn6^xvii	3.152 (7)
Ce2—Zn8^x	3.225 (6)	Zn2—Zn6^xxiv	3.152 (7)
Ce2—Zn8^xi	3.225 (6)	Zn2—Zn6	3.152 (7)
Ce2—Zn8	3.225 (6)	Zn2—Mg3^xviii	3.241 (16)
Ce2—Zn7^ix	3.244 (3)	Zn3—Zn4	2.842 (8)
Ce2—Zn7^xii	3.244 (3)	Zn3—Zn4^xxvii	2.842 (8)
Ce2—Zn7^viii	3.244 (3)	Zn3—Zn4ⁱⁱ	2.842 (8)
Ce2—Zn7^xiii	3.244 (3)	Zn3—Mg3^xviii	2.914 (16)
Ce2—Zn7^xiv	3.244 (3)	Zn3—Mg3^xxvi	2.914 (16)
Ce2—Zn7^vii	3.244 (3)	Zn3—Zn3ⁱⁱ	2.968 (9)
Ce2—Zn10^xv	3.493 (3)	Zn3—Zn3^xxvii	2.968 (9)
Ce2—Zn10^xvi	3.493 (3)	Zn3—Zn3^xxxiii	2.968 (9)
Ce3—Zn6^xvii	3.059 (3)	Zn4—Zn3ⁱⁱ	2.842 (8)
Ce3—Zn6	3.059 (3)	Zn4—Zn3^xxvii	2.842 (8)
Ce3—Zn2^xvii	3.106 (7)	Zn4—Zn9^xxxiv	2.840 (9)
Ce3—Zn2	3.106 (7)	Zn4—Zn9^xxxv	2.840 (9)
Ce3—Zn8^xi	3.179 (3)	Zn4—Zn9	2.840 (9)
Ce3—Zn8	3.179 (3)	Zn4—Mg3^xviii	2.959 (13)
Ce3—Zn8^xviii	3.179 (3)	Zn4—Mg3^xxxvi	2.959 (13)
Ce3—Zn8^xvii	3.179 (3)	Zn4—Mg3^xxvii	2.959 (13)
Ce3—Zn10^x	3.224 (3)	Zn5—Zn5^xxxvii	2.713 (12)
Ce3—Zn10^xix	3.224 (3)	Zn5—Zn5^xxxviii	2.713 (12)
Ce3—Zn10^xx	3.224 (3)	Zn5—Zn5^xxiv	2.713 (12)
Ce3—Zn10^xxi	3.224 (3)	Zn5—Zn9	2.842 (8)
Ce4—Zn10^xxii	3.132 (3)	Zn5—Zn9^xxxv	2.841 (8)
Ce4—Zn10^xiv	3.132 (3)	Zn5—Zn9^xxxiv	2.842 (8)
Ce4—Zn10	3.132 (3)	Zn5—Mg2^xxxix	2.945 (14)
Ce4—Zn10^xvi	3.132 (3)	Zn5—Mg2^x	2.945 (14)
Ce4—Zn8ⁱⁱⁱ	3.170 (4)	Zn5—Mg2ⁱⁱ	2.945 (14)
Ce4—Zn8^x	3.170 (4)	Zn5—Ce1^xl	3.574 (4)
Ce4—Zn9^x	3.305 (6)	Zn5—Ce1^vii	3.574 (4)
Ce4—Zn9ⁱⁱⁱ	3.305 (6)	Zn5—Ce1^xli	3.574 (4)
Ce4—Zn7^xii	3.443 (6)	Zn6—Zn8^x	2.724 (6)
Ce4—Zn7^ix	3.443 (6)	Zn6—Zn8^xi	2.724 (6)
Ce4—Mg3^xxiii	3.456 (11)	Zn6—Zn8	2.724 (6)
Ce4—Mg3^xxiv	3.456 (11)	Zn6—Ce3^xi	3.058 (3)
Mg1—Zn7ⁱⁱ	3.092 (5)	Zn6—Ce3^x	3.058 (3)
Mg1—Zn7^xii	3.092 (5)	Zn6—Zn2^xxiv	3.152 (7)
Mg1—Zn7^ix	3.092 (5)	Zn6—Zn2^xvii	3.152 (7)
Mg1—Zn7ⁱ	3.092 (5)	Zn7—Zn7ⁱⁱ	2.505 (10)
Mg1—Zn7^viii	3.092 (5)	Zn7—Zn10^viii	2.640 (5)
Mg1—Zn7ⁱⁱⁱ	3.092 (5)	Zn7—Zn10^xlii	2.640 (5)
Mg1—Zn7	3.092 (5)	Zn7—Zn7^xii	2.746 (8)
Mg1—Zn7^xiii	3.092 (5)	Zn7—Zn7^viii	2.746 (8)
Mg1—Zn7^xi	3.092 (5)	Zn7—Ce1ⁱⁱ	3.181 (6)
Mg1—Zn7^xiv	3.092 (5)	Zn7—Ce2^xiv	3.244 (3)
Mg1—Zn7^vii	3.092 (5)	Zn7—Ce2^vii	3.244 (3)
Mg1—Zn7^x	3.092 (5)	Zn7—Ce4ⁱ	3.443 (5)
Mg2—Zn5^xxv	2.945 (14)	Zn8—Zn10^xi	2.589 (4)
Mg2—Zn5ⁱⁱ	2.945 (14)	Zn8—Zn10^xix	2.589 (4)
Mg2—Zn10^x	3.024 (8)	Zn8—Mg3^xviii	2.944 (10)
Mg2—Zn10^xix	3.024 (8)	Zn8—Mg3^xxvi	2.945 (10)
Mg2—Zn10^xx	3.024 (8)	Zn8—Ce4^xi	3.170 (4)
Mg2—Zn10^xxi	3.024 (8)	Zn8—Ce3^x	3.179 (3)
Mg2—Zn9^xxv	3.179 (5)	Zn9—Zn10^xliii	2.712 (5)
Mg2—Zn9ⁱⁱ	3.179 (5)	Zn9—Zn10^xi	2.712 (5)
Mg2—Zn9^xi	3.179 (5)	Zn9—Zn9^xxxv	2.833 (10)
Mg2—Zn9^xviii	3.179 (5)	Zn9—Zn9^xxxiv	2.833 (10)
Mg2—Ce1^xiv	3.378 (7)	Zn9—Mg2^x	3.179 (5)
Mg3—Zn3	2.914 (16)	Zn9—Mg2ⁱⁱ	3.179 (5)
Mg3—Zn8^xxvi	2.944 (10)	Zn9—Mg3^xviii	3.203 (14)
Mg3—Zn8^xviii	2.945 (10)	Zn9—Mg3^xxxvi	3.203 (14)
Mg3—Zn4^xxvii	2.959 (13)	Zn9—Ce4^xi	3.305 (6)
Mg3—Zn10^xxiv	3.063 (10)	Zn9—Ce1^vii	3.334 (5)
Mg3—Zn10^xxviii	3.064 (10)	Zn10—Zn10^xv	2.568 (6)
Mg3—Zn9^xxix	3.203 (14)	Zn10—Zn8^x	2.589 (4)
Mg3—Zn9^xxvi	3.203 (14)	Zn10—Zn7^xii	2.640 (5)
Mg3—Zn2	3.241 (16)	Zn10—Zn9^x	2.712 (5)
Mg3—Ce3^xxx	3.325 (13)	Zn10—Mg2^xi	3.024 (8)
Mg3—Ce4^xxxi	3.456 (11)	Zn10—Mg3^xxiv	3.063 (10)
Mg3—Ce4^xx	3.456 (11)	Zn10—Ce3^xi	3.224 (3)
Zn1—Zn6	2.598 (8)	Zn10—Ce1ⁱⁱ	3.238 (4)

Zn7ⁱ—Ce1—Zn7ⁱⁱ	51.14 (16)	Zn6^xvii—Zn1—Zn2^xxiv	180.00 (16)
Zn7ⁱ—Ce1—Zn7ⁱⁱⁱ	51.14 (16)	Zn2^xxxii—Zn1—Zn2^xxiv	109.5
Zn7ⁱⁱ—Ce1—Zn7ⁱⁱⁱ	51.14 (16)	Zn6—Zn1—Zn2	70.53 (16)
Zn7ⁱ—Ce1—Zn10^iv	71.36 (8)	Zn6^xxxii—Zn1—Zn2	180.00 (16)
Zn7ⁱⁱ—Ce1—Zn10^iv	48.56 (9)	Zn6^xxiv—Zn1—Zn2	70.53 (16)
Zn7ⁱⁱⁱ—Ce1—Zn10^iv	98.80 (14)	Zn6^xvii—Zn1—Zn2	70.53 (16)
Zn7ⁱ—Ce1—Zn10ⁱⁱⁱ	48.56 (9)	Zn2^xxxii—Zn1—Zn2	109.5
Zn7ⁱⁱ—Ce1—Zn10ⁱⁱⁱ	71.36 (8)	Zn2^xxiv—Zn1—Zn2	109.5
Zn7ⁱⁱⁱ—Ce1—Zn10ⁱⁱⁱ	98.80 (14)	Zn6—Zn1—Zn2^xvii	70.53 (16)
Zn10^iv—Ce1—Zn10ⁱⁱⁱ	46.72 (11)	Zn6^xxxii—Zn1—Zn2^xvii	70.53 (16)
Zn7ⁱ—Ce1—Zn10ⁱ	98.80 (14)	Zn6^xxiv—Zn1—Zn2^xvii	180.00 (16)
Zn7ⁱⁱ—Ce1—Zn10ⁱ	48.56 (9)	Zn6^xvii—Zn1—Zn2^xvii	70.53 (16)
Zn7ⁱⁱⁱ—Ce1—Zn10ⁱ	71.36 (8)	Zn2^xxxii—Zn1—Zn2^xvii	109.5
Zn10^iv—Ce1—Zn10ⁱ	66.38 (11)	Zn2^xxiv—Zn1—Zn2^xvii	109.5
Zn10ⁱⁱⁱ—Ce1—Zn10ⁱ	110.35 (8)	Zn2—Zn1—Zn2^xvii	109.5
Zn7ⁱ—Ce1—Zn10^v	98.80 (14)	Zn8—Zn2—Zn8^xxvi	112.8 (2)
Zn7ⁱⁱ—Ce1—Zn10^v	71.36 (8)	Zn8—Zn2—Zn8^xviii	112.8 (2)
Zn7ⁱⁱⁱ—Ce1—Zn10^v	48.56 (9)	Zn8^xxvi—Zn2—Zn8^xviii	112.8 (2)
Zn10^iv—Ce1—Zn10^v	110.35 (8)	Zn8—Zn2—Zn1	105.9 (3)
Zn10ⁱⁱⁱ—Ce1—Zn10^v	141.44 (17)	Zn8^xxvi—Zn2—Zn1	105.9 (3)
Zn10ⁱ—Ce1—Zn10^v	46.72 (11)	Zn8^xviii—Zn2—Zn1	105.9 (3)
Zn7ⁱ—Ce1—Zn10^vi	48.56 (9)	Zn8—Zn2—Ce3^xxx	177.3 (5)
Zn7ⁱⁱ—Ce1—Zn10^vi	98.80 (14)	Zn8^xxvi—Zn2—Ce3^xxx	66.10 (16)
Zn7ⁱⁱⁱ—Ce1—Zn10^vi	71.36 (8)	Zn8^xviii—Zn2—Ce3^xxx	66.10 (16)
Zn10^iv—Ce1—Zn10^vi	110.35 (8)	Zn1—Zn2—Ce3^xxx	76.8 (2)
Zn10ⁱⁱⁱ—Ce1—Zn10^vi	66.38 (11)	Zn8—Zn2—Ce3^x	66.10 (16)
Zn10ⁱ—Ce1—Zn10^vi	141.44 (17)	Zn8^xxvi—Zn2—Ce3^x	66.10 (16)
Zn10^v—Ce1—Zn10^vi	110.35 (8)	Zn8^xviii—Zn2—Ce3^x	177.3 (5)
Zn7ⁱ—Ce1—Zn10ⁱⁱ	71.36 (8)	Zn1—Zn2—Ce3^x	76.8 (2)
Zn7ⁱⁱ—Ce1—Zn10ⁱⁱ	98.80 (14)	Ce3^xxx—Zn2—Ce3^x	114.91 (17)
Zn7ⁱⁱⁱ—Ce1—Zn10ⁱⁱ	48.56 (9)	Zn8—Zn2—Ce3	66.10 (16)
Zn10^iv—Ce1—Zn10ⁱⁱ	141.44 (17)	Zn8^xxvi—Zn2—Ce3	177.3 (5)
Zn10ⁱⁱⁱ—Ce1—Zn10ⁱⁱ	110.35 (8)	Zn8^xviii—Zn2—Ce3	66.10 (16)
Zn10ⁱ—Ce1—Zn10ⁱⁱ	110.35 (8)	Zn1—Zn2—Ce3	76.8 (2)
Zn10^v—Ce1—Zn10ⁱⁱ	66.38 (11)	Ce3^xxx—Zn2—Ce3	114.91 (17)
Zn10^vi—Ce1—Zn10ⁱⁱ	46.72 (11)	Ce3^x—Zn2—Ce3	114.91 (17)
Zn7ⁱ—Ce1—Zn9^vii	118.23 (11)	Zn8—Zn2—Zn6^xvii	123.12 (18)
Zn7ⁱⁱ—Ce1—Zn9^vii	75.69 (13)	Zn8^xxvi—Zn2—Zn6^xvii	123.12 (18)
Zn7ⁱⁱⁱ—Ce1—Zn9^vii	118.23 (11)	Zn8^xviii—Zn2—Zn6^xvii	54.93 (17)
Zn10^iv—Ce1—Zn9^vii	48.71 (8)	Zn1—Zn2—Zn6^xvii	51.0 (2)
Zn10ⁱⁱⁱ—Ce1—Zn9^vii	90.10 (6)	Ce3^xxx—Zn2—Zn6^xvii	58.50 (11)
Zn10ⁱ—Ce1—Zn9^vii	48.71 (8)	Ce3^x—Zn2—Zn6^xvii	127.8 (5)
Zn10^v—Ce1—Zn9^vii	90.10 (6)	Ce3—Zn2—Zn6^xvii	58.51 (11)
Zn10^vi—Ce1—Zn9^vii	156.19 (6)	Zn8—Zn2—Zn6^xxiv	123.12 (18)
Zn10ⁱⁱ—Ce1—Zn9^vii	156.19 (6)	Zn8^xxvi—Zn2—Zn6^xxiv	54.93 (17)
Zn7ⁱ—Ce1—Zn9^viii	75.69 (13)	Zn8^xviii—Zn2—Zn6^xxiv	123.12 (18)
Zn7ⁱⁱ—Ce1—Zn9^viii	118.23 (11)	Zn1—Zn2—Zn6^xxiv	51.0 (2)
Zn7ⁱⁱⁱ—Ce1—Zn9^viii	118.23 (11)	Ce3^xxx—Zn2—Zn6^xxiv	58.50 (11)
Zn10^iv—Ce1—Zn9^viii	90.10 (6)	Ce3^x—Zn2—Zn6^xxiv	58.50 (11)
Zn10ⁱⁱⁱ—Ce1—Zn9^viii	48.71 (8)	Ce3—Zn2—Zn6^xxiv	127.8 (5)
Zn10ⁱ—Ce1—Zn9^viii	156.19 (6)	Zn6^xvii—Zn2—Zn6^xxiv	84.6 (4)
Zn10^v—Ce1—Zn9^viii	156.19 (6)	Zn8—Zn2—Zn6	54.93 (17)
Zn10^vi—Ce1—Zn9^viii	48.71 (8)	Zn8^xxvi—Zn2—Zn6	123.12 (18)
Zn10ⁱⁱ—Ce1—Zn9^viii	90.10 (6)	Zn8^xviii—Zn2—Zn6	123.12 (18)
Zn9^vii—Ce1—Zn9^viii	113.06 (9)	Zn1—Zn2—Zn6	51.0 (2)
Zn7ⁱ—Ce1—Zn9^ix	118.23 (11)	Ce3^xxx—Zn2—Zn6	127.8 (5)
Zn7ⁱⁱ—Ce1—Zn9^ix	118.23 (11)	Ce3^x—Zn2—Zn6	58.50 (11)
Zn7ⁱⁱⁱ—Ce1—Zn9^ix	75.69 (13)	Ce3—Zn2—Zn6	58.51 (11)
Zn10^iv—Ce1—Zn9^ix	156.19 (6)	Zn6^xvii—Zn2—Zn6	84.6 (4)
Zn10ⁱⁱⁱ—Ce1—Zn9^ix	156.19 (6)	Zn6^xxiv—Zn2—Zn6	84.6 (4)
Zn10ⁱ—Ce1—Zn9^ix	90.10 (6)	Zn8—Zn2—Mg3	114.2 (5)
Zn10^v—Ce1—Zn9^ix	48.71 (8)	Zn8^xxvi—Zn2—Mg3	58.69 (19)
Zn10^vi—Ce1—Zn9^ix	90.10 (6)	Zn8^xviii—Zn2—Mg3	58.69 (19)
Zn10ⁱⁱ—Ce1—Zn9^ix	48.71 (8)	Zn1—Zn2—Mg3	139.9 (3)
Zn9^vii—Ce1—Zn9^ix	113.06 (9)	Ce3^xxx—Zn2—Mg3	63.1 (3)
Zn9^viii—Ce1—Zn9^ix	113.06 (9)	Ce3^x—Zn2—Mg3	119.3 (2)
Zn6—Ce2—Zn8^x	51.42 (10)	Ce3—Zn2—Mg3	119.3 (2)
Zn6—Ce2—Zn8^xi	51.42 (10)	Zn6^xvii—Zn2—Mg3	103.4 (2)
Zn8^x—Ce2—Zn8^xi	85.22 (14)	Zn6^xxiv—Zn2—Mg3	103.4 (2)
Zn6—Ce2—Zn8	51.42 (10)	Zn6—Zn2—Mg3	169.1 (5)
Zn8^x—Ce2—Zn8	85.22 (14)	Zn8—Zn2—Mg3^xviii	58.69 (19)
Zn8^xi—Ce2—Zn8	85.22 (14)	Zn8^xxvi—Zn2—Mg3^xviii	58.69 (19)
Zn6—Ce2—Zn7^ix	125.95 (10)	Zn8^xviii—Zn2—Mg3^xviii	114.2 (5)
Zn8^x—Ce2—Zn7^ix	79.03 (11)	Zn1—Zn2—Mg3^xviii	139.9 (3)
Zn8^xi—Ce2—Zn7^ix	154.90 (9)	Ce3^xxx—Zn2—Mg3^xviii	119.3 (2)
Zn8—Ce2—Zn7^ix	112.51 (8)	Ce3^x—Zn2—Mg3^xviii	63.1 (3)
Zn6—Ce2—Zn7^xii	125.95 (10)	Ce3—Zn2—Mg3^xviii	119.3 (2)
Zn8^x—Ce2—Zn7^xii	79.03 (11)	Zn6^xvii—Zn2—Mg3^xviii	169.1 (5)
Zn8^xi—Ce2—Zn7^xii	112.51 (8)	Zn6^xxiv—Zn2—Mg3^xviii	103.4 (2)
Zn8—Ce2—Zn7^xii	154.90 (9)	Zn6—Zn2—Mg3^xviii	103.4 (2)
Zn7^ix—Ce2—Zn7^xii	45.42 (16)	Mg3—Zn2—Mg3^xviii	67.8 (5)
Zn6—Ce2—Zn7^viii	125.95 (10)	Zn4—Zn3—Zn4^xxvii	111.3 (2)
Zn8^x—Ce2—Zn7^viii	112.51 (8)	Zn4—Zn3—Zn4ⁱⁱ	111.3 (2)
Zn8^xi—Ce2—Zn7^viii	79.03 (11)	Zn4^xxvii—Zn3—Zn4ⁱⁱ	111.3 (2)
Zn8—Ce2—Zn7^viii	154.90 (9)	Zn4—Zn3—Mg3^xviii	61.9 (3)
Zn7^ix—Ce2—Zn7^viii	89.03 (14)	Zn4^xxvii—Zn3—Mg3^xviii	123.55 (18)
Zn7^xii—Ce2—Zn7^viii	50.08 (18)	Zn4ⁱⁱ—Zn3—Mg3^xviii	123.54 (18)
Zn6—Ce2—Zn7^xiii	125.95 (10)	Zn4—Zn3—Mg3	123.54 (18)
Zn8^x—Ce2—Zn7^xiii	154.90 (9)	Zn4^xxvii—Zn3—Mg3	61.9 (3)
Zn8^xi—Ce2—Zn7^xiii	79.03 (11)	Zn4ⁱⁱ—Zn3—Mg3	123.55 (18)
Zn8—Ce2—Zn7^xiii	112.51 (8)	Mg3^xviii—Zn3—Mg3	76.7 (5)
Zn7^ix—Ce2—Zn7^xiii	108.05 (19)	Zn4—Zn3—Mg3^xxvi	123.55 (18)
Zn7^xii—Ce2—Zn7^xiii	89.03 (14)	Zn4^xxvii—Zn3—Mg3^xxvi	123.54 (18)
Zn7^viii—Ce2—Zn7^xiii	45.42 (16)	Zn4ⁱⁱ—Zn3—Mg3^xxvi	61.9 (3)
Zn6—Ce2—Zn7^xiv	125.95 (10)	Mg3^xviii—Zn3—Mg3^xxvi	76.7 (5)
Zn8^x—Ce2—Zn7^xiv	112.51 (8)	Mg3—Zn3—Mg3^xxvi	76.7 (5)
Zn8^xi—Ce2—Zn7^xiv	154.90 (9)	Zn4—Zn3—Zn3ⁱⁱ	58.51 (19)
Zn8—Ce2—Zn7^xiv	79.03 (11)	Zn4^xxvii—Zn3—Zn3ⁱⁱ	107.6 (2)
Zn7^ix—Ce2—Zn7^xiv	50.08 (18)	Zn4ⁱⁱ—Zn3—Zn3ⁱⁱ	58.52 (19)
Zn7^xii—Ce2—Zn7^xiv	89.03 (14)	Mg3^xviii—Zn3—Zn3ⁱⁱ	111.3 (3)
Zn7^viii—Ce2—Zn7^xiv	108.05 (19)	Mg3—Zn3—Zn3ⁱⁱ	169.5 (3)
Zn7^xiii—Ce2—Zn7^xiv	89.03 (14)	Mg3^xxvi—Zn3—Zn3ⁱⁱ	111.3 (3)
Zn6—Ce2—Zn7^vii	125.95 (10)	Zn4—Zn3—Zn3^xxvii	58.51 (19)
Zn8^x—Ce2—Zn7^vii	154.90 (9)	Zn4^xxvii—Zn3—Zn3^xxvii	58.51 (19)
Zn8^xi—Ce2—Zn7^vii	112.51 (8)	Zn4ⁱⁱ—Zn3—Zn3^xxvii	107.6 (2)
Zn8—Ce2—Zn7^vii	79.03 (11)	Mg3^xviii—Zn3—Zn3^xxvii	111.3 (3)
Zn7^ix—Ce2—Zn7^vii	89.03 (14)	Mg3—Zn3—Zn3^xxvii	111.3 (3)
Zn7^xii—Ce2—Zn7^vii	108.05 (19)	Mg3^xxvi—Zn3—Zn3^xxvii	169.5 (3)
Zn7^viii—Ce2—Zn7^vii	89.03 (14)	Zn3ⁱⁱ—Zn3—Zn3^xxvii	60.0
Zn7^xiii—Ce2—Zn7^vii	50.08 (18)	Zn4—Zn3—Zn3^xxxiii	107.6 (2)
Zn7^xiv—Ce2—Zn7^vii	45.42 (16)	Zn4^xxvii—Zn3—Zn3^xxxiii	58.51 (19)
Zn6—Ce2—Zn10^xv	80.91 (8)	Zn4ⁱⁱ—Zn3—Zn3^xxxiii	58.52 (19)
Zn8^x—Ce2—Zn10^xv	78.00 (7)	Mg3^xviii—Zn3—Zn3^xxxiii	169.5 (3)
Zn8^xi—Ce2—Zn10^xv	45.12 (7)	Mg3—Zn3—Zn3^xxxiii	111.3 (3)
Zn8—Ce2—Zn10^xv	128.16 (14)	Mg3^xxvi—Zn3—Zn3^xxxiii	111.3 (3)
Zn7^ix—Ce2—Zn10^xv	111.75 (10)	Zn3ⁱⁱ—Zn3—Zn3^xxxiii	60.0
Zn7^xii—Ce2—Zn10^xv	67.41 (10)	Zn3^xxvii—Zn3—Zn3^xxxiii	60.0
Zn7^viii—Ce2—Zn10^xv	45.95 (9)	Zn3—Zn4—Zn3ⁱⁱ	63.0 (4)
Zn7^xiii—Ce2—Zn10^xv	77.04 (10)	Zn3—Zn4—Zn3^xxvii	63.0 (4)
Zn7^xiv—Ce2—Zn10^xv	152.48 (15)	Zn3ⁱⁱ—Zn4—Zn3^xxvii	63.0 (4)
Zn7^vii—Ce2—Zn10^xv	127.09 (12)	Zn3—Zn4—Zn9^xxxiv	178.1 (3)
Zn6—Ce2—Zn10^xvi	80.91 (8)	Zn3ⁱⁱ—Zn4—Zn9^xxxiv	118.58 (19)
Zn8^x—Ce2—Zn10^xvi	45.12 (7)	Zn3^xxvii—Zn4—Zn9^xxxiv	118.58 (19)
Zn8^xi—Ce2—Zn10^xvi	128.16 (14)	Zn3—Zn4—Zn9^xxxv	118.58 (19)
Zn8—Ce2—Zn10^xvi	78.00 (7)	Zn3ⁱⁱ—Zn4—Zn9^xxxv	178.1 (3)
Zn7^ix—Ce2—Zn10^xvi	45.95 (9)	Zn3^xxvii—Zn4—Zn9^xxxv	118.58 (19)
Zn7^xii—Ce2—Zn10^xvi	77.04 (10)	Zn9^xxxiv—Zn4—Zn9^xxxv	59.8 (2)
Zn7^viii—Ce2—Zn10^xvi	127.09 (12)	Zn3—Zn4—Zn9	118.58 (19)
Zn7^xiii—Ce2—Zn10^xvi	152.48 (15)	Zn3ⁱⁱ—Zn4—Zn9	118.58 (19)
Zn7^xiv—Ce2—Zn10^xvi	67.41 (10)	Zn3^xxvii—Zn4—Zn9	178.1 (3)
Zn7^vii—Ce2—Zn10^xvi	111.75 (10)	Zn9^xxxiv—Zn4—Zn9	59.8 (2)
Zn10^xv—Ce2—Zn10^xvi	117.55 (4)	Zn9^xxxv—Zn4—Zn9	59.8 (2)
Zn6^xvii—Ce3—Zn6	87.8 (3)	Zn3—Zn4—Mg3^xviii	60.3 (4)
Zn6^xvii—Ce3—Zn2^xvii	61.50 (14)	Zn3ⁱⁱ—Zn4—Mg3^xviii	113.7 (3)
Zn6—Ce3—Zn2^xvii	61.50 (14)	Zn3^xxvii—Zn4—Mg3^xviii	113.7 (3)
Zn6^xvii—Ce3—Zn2	61.50 (14)	Zn9^xxxiv—Zn4—Mg3^xviii	117.8 (4)
Zn6—Ce3—Zn2	61.50 (14)	Zn9^xxxv—Zn4—Mg3^xviii	67.0 (3)
Zn2^xvii—Ce3—Zn2	97.0 (5)	Zn9—Zn4—Mg3^xviii	67.0 (3)
Zn6^xvii—Ce3—Zn8^xi	110.94 (15)	Zn3—Zn4—Mg3^xxxvi	113.7 (3)
Zn6—Ce3—Zn8^xi	51.75 (11)	Zn3ⁱⁱ—Zn4—Mg3^xxxvi	60.3 (4)
Zn2^xvii—Ce3—Zn8^xi	50.59 (13)	Zn3^xxvii—Zn4—Mg3^xxxvi	113.7 (3)
Zn2—Ce3—Zn8^xi	113.21 (18)	Zn9^xxxiv—Zn4—Mg3^xxxvi	67.0 (3)
Zn6^xvii—Ce3—Zn8	110.94 (15)	Zn9^xxxv—Zn4—Mg3^xxxvi	117.8 (4)
Zn6—Ce3—Zn8	51.75 (11)	Zn9—Zn4—Mg3^xxxvi	67.0 (3)
Zn2^xvii—Ce3—Zn8	113.21 (18)	Mg3^xviii—Zn4—Mg3^xxxvi	118.39 (15)
Zn2—Ce3—Zn8	50.59 (13)	Zn3—Zn4—Mg3^xxvii	113.7 (3)
Zn8^xi—Ce3—Zn8	86.8 (2)	Zn3ⁱⁱ—Zn4—Mg3^xxvii	113.7 (3)
Zn6^xvii—Ce3—Zn8^xviii	51.75 (11)	Zn3^xxvii—Zn4—Mg3^xxvii	60.3 (4)
Zn6—Ce3—Zn8^xviii	110.94 (15)	Zn9^xxxiv—Zn4—Mg3^xxvii	67.0 (3)
Zn2^xvii—Ce3—Zn8^xviii	113.21 (18)	Zn9^xxxv—Zn4—Mg3^xxvii	67.0 (3)
Zn2—Ce3—Zn8^xviii	50.59 (13)	Zn9—Zn4—Mg3^xxvii	117.8 (4)
Zn8^xi—Ce3—Zn8^xviii	159.07 (17)	Mg3^xviii—Zn4—Mg3^xxvii	118.38 (15)
Zn8—Ce3—Zn8^xviii	89.5 (2)	Mg3^xxxvi—Zn4—Mg3^xxvii	118.39 (15)
Zn6^xvii—Ce3—Zn8^xvii	51.75 (11)	Zn5^xxxvii—Zn5—Zn5^xxxviii	60.0
Zn6—Ce3—Zn8^xvii	110.94 (15)	Zn5^xxxvii—Zn5—Zn5^xxiv	60.0
Zn2^xvii—Ce3—Zn8^xvii	50.59 (13)	Zn5^xxxviii—Zn5—Zn5^xxiv	60.0
Zn2—Ce3—Zn8^xvii	113.21 (18)	Zn5^xxxvii—Zn5—Zn9	120.10 (11)
Zn8^xi—Ce3—Zn8^xvii	89.5 (2)	Zn5^xxxviii—Zn5—Zn9	179.88 (13)
Zn8—Ce3—Zn8^xvii	159.07 (17)	Zn5^xxiv—Zn5—Zn9	120.10 (11)
Zn8^xviii—Ce3—Zn8^xvii	86.8 (2)	Zn5^xxxvii—Zn5—Zn9^xxxv	179.88 (12)
Zn6^xvii—Ce3—Zn10^x	155.47 (8)	Zn5^xxxviii—Zn5—Zn9^xxxv	120.10 (11)
Zn6—Ce3—Zn10^x	85.22 (15)	Zn5^xxiv—Zn5—Zn9^xxxv	120.10 (11)
Zn2^xvii—Ce3—Zn10^x	94.69 (16)	Zn9—Zn5—Zn9^xxxv	59.8 (2)
Zn2—Ce3—Zn10^x	132.72 (8)	Zn5^xxxvii—Zn5—Zn9^xxxiv	120.10 (11)
Zn8^xi—Ce3—Zn10^x	47.70 (9)	Zn5^xxxviii—Zn5—Zn9^xxxiv	120.10 (11)
Zn8—Ce3—Zn10^x	82.76 (11)	Zn5^xxiv—Zn5—Zn9^xxxiv	179.88 (13)
Zn8^xviii—Ce3—Zn10^x	151.82 (13)	Zn9—Zn5—Zn9^xxxiv	59.8 (2)
Zn8^xvii—Ce3—Zn10^x	109.54 (10)	Zn9^xxxv—Zn5—Zn9^xxxiv	59.8 (2)
Zn6^xvii—Ce3—Zn10^xix	155.47 (8)	Zn5^xxxvii—Zn5—Mg2^xxxix	113.41 (16)
Zn6—Ce3—Zn10^xix	85.22 (15)	Zn5^xxxviii—Zn5—Mg2^xxxix	62.6 (2)
Zn2^xvii—Ce3—Zn10^xix	132.72 (8)	Zn5^xxiv—Zn5—Mg2^xxxix	113.41 (16)
Zn2—Ce3—Zn10^xix	94.69 (16)	Zn9—Zn5—Mg2^xxxix	117.3 (3)
Zn8^xi—Ce3—Zn10^xix	82.76 (11)	Zn9^xxxv—Zn5—Mg2^xxxix	66.63 (16)
Zn8—Ce3—Zn10^xix	47.70 (9)	Zn9^xxxiv—Zn5—Mg2^xxxix	66.63 (16)
Zn8^xviii—Ce3—Zn10^xix	109.54 (10)	Zn5^xxxvii—Zn5—Mg2^x	113.41 (16)
Zn8^xvii—Ce3—Zn10^xix	151.82 (13)	Zn5^xxxviii—Zn5—Mg2^x	113.41 (16)
Zn10^x—Ce3—Zn10^xix	46.94 (11)	Zn5^xxiv—Zn5—Mg2^x	62.6 (2)
Zn6^xvii—Ce3—Zn10^xx	85.22 (15)	Zn9—Zn5—Mg2^x	66.63 (16)
Zn6—Ce3—Zn10^xx	155.47 (8)	Zn9^xxxv—Zn5—Mg2^x	66.63 (16)
Zn2^xvii—Ce3—Zn10^xx	132.72 (8)	Zn9^xxxiv—Zn5—Mg2^x	117.3 (3)
Zn2—Ce3—Zn10^xx	94.69 (16)	Mg2^xxxix—Zn5—Mg2^x	118.17 (9)
Zn8^xi—Ce3—Zn10^xx	151.82 (13)	Zn5^xxxvii—Zn5—Mg2ⁱⁱ	62.6 (2)
Zn8—Ce3—Zn10^xx	109.54 (10)	Zn5^xxxviii—Zn5—Mg2ⁱⁱ	113.41 (16)
Zn8^xviii—Ce3—Zn10^xx	47.70 (9)	Zn5^xxiv—Zn5—Mg2ⁱⁱ	113.41 (16)
Zn8^xvii—Ce3—Zn10^xx	82.76 (11)	Zn9—Zn5—Mg2ⁱⁱ	66.63 (16)
Zn10^x—Ce3—Zn10^xx	109.98 (14)	Zn9^xxxv—Zn5—Mg2ⁱⁱ	117.3 (3)
Zn10^xix—Ce3—Zn10^xx	91.41 (13)	Zn9^xxxiv—Zn5—Mg2ⁱⁱ	66.63 (16)
Zn6^xvii—Ce3—Zn10^xxi	85.22 (15)	Mg2^xxxix—Zn5—Mg2ⁱⁱ	118.17 (9)
Zn6—Ce3—Zn10^xxi	155.47 (8)	Mg2^x—Zn5—Mg2ⁱⁱ	118.17 (9)
Zn2^xvii—Ce3—Zn10^xxi	94.69 (16)	Zn5^xxxvii—Zn5—Ce1^xl	118.75 (12)
Zn2—Ce3—Zn10^xxi	132.72 (8)	Zn5^xxxviii—Zn5—Ce1^xl	67.70 (10)
Zn8^xi—Ce3—Zn10^xxi	109.54 (10)	Zn5^xxiv—Zn5—Ce1^xl	67.70 (10)
Zn8—Ce3—Zn10^xxi	151.82 (13)	Zn9—Zn5—Ce1^xl	112.26 (13)
Zn8^xviii—Ce3—Zn10^xxi	82.76 (11)	Zn9^xxxv—Zn5—Ce1^xl	61.37 (12)
Zn8^xvii—Ce3—Zn10^xxi	47.70 (9)	Zn9^xxxiv—Zn5—Ce1^xl	112.26 (13)
Zn10^x—Ce3—Zn10^xxi	91.41 (13)	Mg2^xxxix—Zn5—Ce1^xl	61.53 (3)
Zn10^xix—Ce3—Zn10^xxi	109.98 (14)	Mg2^x—Zn5—Ce1^xl	61.53 (3)
Zn10^xx—Ce3—Zn10^xxi	46.94 (11)	Mg2ⁱⁱ—Zn5—Ce1^xl	178.7 (3)
Zn10^xxii—Ce4—Zn10^xiv	85.73 (13)	Zn5^xxxvii—Zn5—Ce1^vii	67.70 (10)
Zn10^xxii—Ce4—Zn10	68.93 (12)	Zn5^xxxviii—Zn5—Ce1^vii	118.75 (12)
Zn10^xiv—Ce4—Zn10	124.47 (16)	Zn5^xxiv—Zn5—Ce1^vii	67.70 (10)
Zn10^xxii—Ce4—Zn10^xvi	124.47 (16)	Zn9—Zn5—Ce1^vii	61.37 (12)
Zn10^xiv—Ce4—Zn10^xvi	68.93 (12)	Zn9^xxxv—Zn5—Ce1^vii	112.26 (13)
Zn10—Ce4—Zn10^xvi	85.73 (13)	Zn9^xxxiv—Zn5—Ce1^vii	112.26 (13)
Zn10^xxii—Ce4—Zn8ⁱⁱⁱ	48.51 (8)	Mg2^xxxix—Zn5—Ce1^vii	178.7 (3)
Zn10^xiv—Ce4—Zn8ⁱⁱⁱ	48.51 (8)	Mg2^x—Zn5—Ce1^vii	61.53 (3)
Zn10—Ce4—Zn8ⁱⁱⁱ	115.79 (11)	Mg2ⁱⁱ—Zn5—Ce1^vii	61.53 (3)
Zn10^xvi—Ce4—Zn8ⁱⁱⁱ	115.79 (11)	Ce1^xl—Zn5—Ce1^vii	118.73 (5)
Zn10^xxii—Ce4—Zn8^x	115.79 (11)	Zn5^xxxvii—Zn5—Ce1^xli	67.70 (10)
Zn10^xiv—Ce4—Zn8^x	115.79 (11)	Zn5^xxxviii—Zn5—Ce1^xli	67.70 (10)
Zn10—Ce4—Zn8^x	48.51 (8)	Zn5^xxiv—Zn5—Ce1^xli	118.75 (12)
Zn10^xvi—Ce4—Zn8^x	48.51 (8)	Zn9—Zn5—Ce1^xli	112.26 (13)
Zn8ⁱⁱⁱ—Ce4—Zn8^x	151.8 (2)	Zn9^xxxv—Zn5—Ce1^xli	112.26 (13)
Zn10^xxii—Ce4—Zn9^x	49.74 (9)	Zn9^xxxiv—Zn5—Ce1^xli	61.37 (12)
Zn10^xiv—Ce4—Zn9^x	135.31 (10)	Mg2^xxxix—Zn5—Ce1^xli	61.53 (3)
Zn10—Ce4—Zn9^x	49.74 (9)	Mg2^x—Zn5—Ce1^xli	178.7 (3)
Zn10^xvi—Ce4—Zn9^x	135.31 (10)	Mg2ⁱⁱ—Zn5—Ce1^xli	61.53 (3)
Zn8ⁱⁱⁱ—Ce4—Zn9^x	90.97 (3)	Ce1^xl—Zn5—Ce1^xli	118.73 (5)
Zn8^x—Ce4—Zn9^x	90.97 (3)	Ce1^vii—Zn5—Ce1^xli	118.73 (5)
Zn10^xxii—Ce4—Zn9ⁱⁱⁱ	135.31 (10)	Zn1—Zn6—Zn8^x	112.28 (19)
Zn10^xiv—Ce4—Zn9ⁱⁱⁱ	49.74 (9)	Zn1—Zn6—Zn8^xi	112.28 (19)
Zn10—Ce4—Zn9ⁱⁱⁱ	135.31 (10)	Zn8^x—Zn6—Zn8^xi	106.5 (2)
Zn10^xvi—Ce4—Zn9ⁱⁱⁱ	49.74 (9)	Zn1—Zn6—Zn8	112.28 (19)
Zn8ⁱⁱⁱ—Ce4—Zn9ⁱⁱⁱ	90.97 (3)	Zn8^x—Zn6—Zn8	106.5 (2)
Zn8^x—Ce4—Zn9ⁱⁱⁱ	90.97 (3)	Zn8^xi—Zn6—Zn8	106.5 (2)
Zn9^x—Ce4—Zn9ⁱⁱⁱ	172.0 (2)	Zn1—Zn6—Ce2	180.00 (16)
Zn10^xxii—Ce4—Zn7^xii	47.05 (9)	Zn8^x—Zn6—Ce2	67.72 (19)
Zn10^xiv—Ce4—Zn7^xii	79.25 (11)	Zn8^xi—Zn6—Ce2	67.72 (19)
Zn10—Ce4—Zn7^xii	47.05 (9)	Zn8—Zn6—Ce2	67.72 (19)
Zn10^xvi—Ce4—Zn7^xii	79.25 (11)	Zn1—Zn6—Ce3^xi	81.34 (16)
Zn8ⁱⁱⁱ—Ce4—Zn7^xii	76.86 (11)	Zn8^x—Zn6—Ce3^xi	66.40 (12)
Zn8^x—Ce4—Zn7^xii	76.86 (11)	Zn8^xi—Zn6—Ce3^xi	66.40 (12)
Zn9^x—Ce4—Zn7^xii	72.65 (13)	Zn8—Zn6—Ce3^xi	166.4 (3)
Zn9ⁱⁱⁱ—Ce4—Zn7^xii	115.31 (15)	Ce2—Zn6—Ce3^xi	98.66 (16)
Zn10^xxii—Ce4—Zn7^ix	79.25 (11)	Zn1—Zn6—Ce3^x	81.34 (16)
Zn10^xiv—Ce4—Zn7^ix	47.05 (9)	Zn8^x—Zn6—Ce3^x	66.40 (12)
Zn10—Ce4—Zn7^ix	79.25 (11)	Zn8^xi—Zn6—Ce3^x	166.4 (3)
Zn10^xvi—Ce4—Zn7^ix	47.05 (9)	Zn8—Zn6—Ce3^x	66.40 (12)
Zn8ⁱⁱⁱ—Ce4—Zn7^ix	76.86 (11)	Ce2—Zn6—Ce3^x	98.66 (16)
Zn8^x—Ce4—Zn7^ix	76.86 (11)	Ce3^xi—Zn6—Ce3^x	117.78 (8)
Zn9^x—Ce4—Zn7^ix	115.31 (15)	Zn1—Zn6—Ce3	81.34 (16)
Zn9ⁱⁱⁱ—Ce4—Zn7^ix	72.65 (13)	Zn8^x—Zn6—Ce3	166.4 (3)
Zn7^xii—Ce4—Zn7^ix	42.66 (16)	Zn8^xi—Zn6—Ce3	66.40 (12)
Zn10^xxii—Ce4—Mg3^xxiii	55.2 (2)	Zn8—Zn6—Ce3	66.40 (12)
Zn10^xiv—Ce4—Mg3^xxiii	98.1 (2)	Ce2—Zn6—Ce3	98.66 (16)
Zn10—Ce4—Mg3^xxiii	105.1 (3)	Ce3^xi—Zn6—Ce3	117.77 (8)
Zn10^xvi—Ce4—Mg3^xxiii	166.6 (2)	Ce3^x—Zn6—Ce3	117.77 (8)
Zn8ⁱⁱⁱ—Ce4—Mg3^xxiii	52.6 (2)	Zn1—Zn6—Zn2^xxiv	58.5 (2)
Zn8^x—Ce4—Mg3^xxiii	144.9 (2)	Zn8^x—Zn6—Zn2^xxiv	53.8 (2)
Zn9^x—Ce4—Mg3^xxiii	56.5 (3)	Zn8^xi—Zn6—Zn2^xxiv	126.34 (7)
Zn9ⁱⁱⁱ—Ce4—Mg3^xxiii	119.5 (3)	Zn8—Zn6—Zn2^xxiv	126.34 (7)
Zn7^xii—Ce4—Mg3^xxiii	102.2 (2)	Ce2—Zn6—Zn2^xxiv	121.5 (2)
Zn7^ix—Ce4—Mg3^xxiii	126.3 (2)	Ce3^xi—Zn6—Zn2^xxiv	59.99 (14)
Zn10^xxii—Ce4—Mg3^xxiv	105.1 (3)	Ce3^x—Zn6—Zn2^xxiv	59.99 (14)
Zn10^xiv—Ce4—Mg3^xxiv	166.6 (2)	Ce3—Zn6—Zn2^xxiv	139.8 (4)
Zn10—Ce4—Mg3^xxiv	55.2 (2)	Zn1—Zn6—Zn2	58.5 (2)
Zn10^xvi—Ce4—Mg3^xxiv	98.1 (2)	Zn8^x—Zn6—Zn2	126.34 (7)
Zn8ⁱⁱⁱ—Ce4—Mg3^xxiv	144.9 (2)	Zn8^xi—Zn6—Zn2	126.34 (7)
Zn8^x—Ce4—Mg3^xxiv	52.6 (2)	Zn8—Zn6—Zn2	53.8 (2)
Zn9^x—Ce4—Mg3^xxiv	56.5 (3)	Ce2—Zn6—Zn2	121.5 (2)
Zn9ⁱⁱⁱ—Ce4—Mg3^xxiv	119.5 (3)	Ce3^xi—Zn6—Zn2	139.8 (4)
Zn7^xii—Ce4—Mg3^xxiv	102.2 (2)	Ce3^x—Zn6—Zn2	59.99 (14)
Zn7^ix—Ce4—Mg3^xxiv	126.3 (2)	Ce3—Zn6—Zn2	59.99 (14)
Mg3^xxiii—Ce4—Mg3^xxiv	94.7 (4)	Zn2^xxiv—Zn6—Zn2	95.1 (3)
Zn7ⁱⁱ—Mg1—Zn7^xii	94.70 (3)	Zn1—Zn6—Zn2^xvii	58.5 (2)
Zn7ⁱⁱ—Mg1—Zn7^ix	116.21 (6)	Zn8^x—Zn6—Zn2^xvii	126.35 (7)
Zn7^xii—Mg1—Zn7^ix	47.78 (18)	Zn8^xi—Zn6—Zn2^xvii	53.8 (2)
Zn7ⁱⁱ—Mg1—Zn7ⁱ	52.72 (15)	Zn8—Zn6—Zn2^xvii	126.34 (7)
Zn7^xii—Mg1—Zn7ⁱ	116.21 (6)	Ce2—Zn6—Zn2^xvii	121.5 (2)
Zn7^ix—Mg1—Zn7ⁱ	94.70 (3)	Ce3^xi—Zn6—Zn2^xvii	59.99 (14)
Zn7ⁱⁱ—Mg1—Zn7^viii	94.70 (3)	Ce3^x—Zn6—Zn2^xvii	139.8 (4)
Zn7^xii—Mg1—Zn7^viii	52.72 (15)	Ce3—Zn6—Zn2^xvii	59.99 (14)
Zn7^ix—Mg1—Zn7^viii	94.70 (3)	Zn2^xxiv—Zn6—Zn2^xvii	95.1 (3)
Zn7ⁱ—Mg1—Zn7^viii	146.72 (12)	Zn2—Zn6—Zn2^xvii	95.1 (3)
Zn7ⁱⁱ—Mg1—Zn7ⁱⁱⁱ	52.72 (15)	Zn7ⁱⁱ—Zn7—Zn10^viii	109.43 (12)
Zn7^xii—Mg1—Zn7ⁱⁱⁱ	146.72 (12)	Zn7ⁱⁱ—Zn7—Zn10^xlii	109.43 (12)
Zn7^ix—Mg1—Zn7ⁱⁱⁱ	146.72 (12)	Zn10^viii—Zn7—Zn10^xlii	84.35 (19)
Zn7ⁱ—Mg1—Zn7ⁱⁱⁱ	52.72 (15)	Zn7ⁱⁱ—Zn7—Zn7^xii	120.0
Zn7^viii—Mg1—Zn7ⁱⁱⁱ	116.21 (6)	Zn10^viii—Zn7—Zn7^xii	88.06 (12)
Zn7ⁱⁱ—Mg1—Zn7	47.78 (18)	Zn10^xlii—Zn7—Zn7^xii	129.61 (12)
Zn7^xii—Mg1—Zn7	52.72 (15)	Zn7ⁱⁱ—Zn7—Zn7^viii	120.000 (1)
Zn7^ix—Mg1—Zn7	94.70 (3)	Zn10^viii—Zn7—Zn7^viii	129.61 (12)
Zn7ⁱ—Mg1—Zn7	94.70 (3)	Zn10^xlii—Zn7—Zn7^viii	88.06 (12)
Zn7^viii—Mg1—Zn7	52.72 (15)	Zn7^xii—Zn7—Zn7^viii	60.0
Zn7ⁱⁱⁱ—Mg1—Zn7	94.70 (3)	Zn7ⁱⁱ—Zn7—Mg1	66.11 (9)
Zn7ⁱⁱ—Mg1—Zn7^xiii	116.21 (6)	Zn10^viii—Zn7—Mg1	137.75 (9)
Zn7^xii—Mg1—Zn7^xiii	94.70 (3)	Zn10^xlii—Zn7—Mg1	137.75 (9)
Zn7^ix—Mg1—Zn7^xiii	116.21 (6)	Zn7^xii—Zn7—Mg1	63.64 (8)
Zn7ⁱ—Mg1—Zn7^xiii	146.72 (12)	Zn7^viii—Zn7—Mg1	63.64 (8)
Zn7^viii—Mg1—Zn7^xiii	47.78 (18)	Zn7ⁱⁱ—Zn7—Ce1ⁱⁱ	174.63 (9)
Zn7ⁱⁱⁱ—Mg1—Zn7^xiii	94.70 (3)	Zn10^viii—Zn7—Ce1ⁱⁱ	66.85 (12)
Zn7—Mg1—Zn7^xiii	94.70 (3)	Zn10^xlii—Zn7—Ce1ⁱⁱ	66.85 (12)
Zn7ⁱⁱ—Mg1—Zn7^xi	94.70 (3)	Zn7^xii—Zn7—Ce1ⁱⁱ	64.43 (8)
Zn7^xii—Mg1—Zn7^xi	94.70 (3)	Zn7^viii—Zn7—Ce1ⁱⁱ	64.43 (8)
Zn7^ix—Mg1—Zn7^xi	52.72 (15)	Mg1—Zn7—Ce1ⁱⁱ	119.26 (16)
Zn7ⁱ—Mg1—Zn7^xi	47.78 (18)	Zn7ⁱⁱ—Zn7—Ce2^xiv	67.29 (8)
Zn7^viii—Mg1—Zn7^xi	146.72 (12)	Zn10^viii—Zn7—Ce2^xiv	72.01 (9)
Zn7ⁱⁱⁱ—Mg1—Zn7^xi	94.70 (3)	Zn10^xlii—Zn7—Ce2^xiv	152.42 (18)
Zn7—Mg1—Zn7^xi	116.21 (6)	Zn7^xii—Zn7—Ce2^xiv	64.96 (9)
Zn7^xiii—Mg1—Zn7^xi	146.72 (12)	Zn7^viii—Zn7—Ce2^xiv	117.83 (10)
Zn7ⁱⁱ—Mg1—Zn7^xiv	146.72 (12)	Mg1—Zn7—Ce2^xiv	67.81 (10)
Zn7^xii—Mg1—Zn7^xiv	94.70 (3)	Ce1ⁱⁱ—Zn7—Ce2^xiv	114.02 (9)
Zn7^ix—Mg1—Zn7^xiv	52.72 (15)	Zn7ⁱⁱ—Zn7—Ce2^vii	67.29 (8)
Zn7ⁱ—Mg1—Zn7^xiv	94.70 (3)	Zn10^viii—Zn7—Ce2^vii	152.42 (18)
Zn7^viii—Mg1—Zn7^xiv	116.21 (6)	Zn10^xlii—Zn7—Ce2^vii	72.01 (9)
Zn7ⁱⁱⁱ—Mg1—Zn7^xiv	116.21 (6)	Zn7^xii—Zn7—Ce2^vii	117.83 (10)
Zn7—Mg1—Zn7^xiv	146.72 (12)	Zn7^viii—Zn7—Ce2^vii	64.96 (9)
Zn7^xiii—Mg1—Zn7^xiv	94.70 (3)	Mg1—Zn7—Ce2^vii	67.81 (10)
Zn7^xi—Mg1—Zn7^xiv	52.72 (15)	Ce1ⁱⁱ—Zn7—Ce2^vii	114.02 (9)
Zn7ⁱⁱ—Mg1—Zn7^vii	146.72 (12)	Ce2^xiv—Zn7—Ce2^vii	125.78 (17)
Zn7^xii—Mg1—Zn7^vii	116.21 (6)	Zn7ⁱⁱ—Zn7—Ce4ⁱ	68.67 (8)
Zn7^ix—Mg1—Zn7^vii	94.70 (3)	Zn10^viii—Zn7—Ce4ⁱ	60.27 (11)
Zn7ⁱ—Mg1—Zn7^vii	116.21 (6)	Zn10^xlii—Zn7—Ce4ⁱ	60.27 (11)
Zn7^viii—Mg1—Zn7^vii	94.70 (3)	Zn7^xii—Zn7—Ce4ⁱ	147.20 (3)
Zn7ⁱⁱⁱ—Mg1—Zn7^vii	94.70 (3)	Zn7^viii—Zn7—Ce4ⁱ	147.20 (3)
Zn7—Mg1—Zn7^vii	146.72 (12)	Mg1—Zn7—Ce4ⁱ	134.78 (16)
Zn7^xiii—Mg1—Zn7^vii	52.72 (15)	Ce1ⁱⁱ—Zn7—Ce4ⁱ	105.96 (14)
Zn7^xi—Mg1—Zn7^vii	94.70 (3)	Ce2^xiv—Zn7—Ce4ⁱ	94.88 (11)
Zn7^xiv—Mg1—Zn7^vii	47.78 (18)	Ce2^vii—Zn7—Ce4ⁱ	94.88 (11)
Zn7ⁱⁱ—Mg1—Zn7^x	94.70 (3)	Zn10^xi—Zn8—Zn10^xix	110.7 (2)
Zn7^xii—Mg1—Zn7^x	146.72 (12)	Zn10^xi—Zn8—Zn2	123.90 (13)
Zn7^ix—Mg1—Zn7^x	146.72 (12)	Zn10^xix—Zn8—Zn2	123.90 (13)
Zn7ⁱ—Mg1—Zn7^x	94.70 (3)	Zn10^xi—Zn8—Zn6	106.38 (16)
Zn7^viii—Mg1—Zn7^x	94.70 (3)	Zn10^xix—Zn8—Zn6	106.39 (16)
Zn7ⁱⁱⁱ—Mg1—Zn7^x	47.78 (18)	Zn2—Zn8—Zn6	71.3 (3)
Zn7—Mg1—Zn7^x	116.21 (6)	Zn10^xi—Zn8—Mg3^xviii	66.9 (3)
Zn7^xiii—Mg1—Zn7^x	52.72 (15)	Zn10^xix—Zn8—Mg3^xviii	128.1 (3)
Zn7^xi—Mg1—Zn7^x	116.21 (6)	Zn2—Zn8—Mg3^xviii	70.1 (3)
Zn7^xiv—Mg1—Zn7^x	94.70 (3)	Zn6—Zn8—Mg3^xviii	124.4 (3)
Zn7^vii—Mg1—Zn7^x	52.72 (15)	Zn10^xi—Zn8—Mg3^xxvi	128.1 (3)
Zn5^xxv—Mg2—Zn5ⁱⁱ	54.8 (4)	Zn10^xix—Zn8—Mg3^xxvi	66.9 (3)
Zn5^xxv—Mg2—Zn10^x	103.70 (19)	Zn2—Zn8—Mg3^xxvi	70.1 (3)
Zn5ⁱⁱ—Mg2—Zn10^x	128.9 (3)	Zn6—Zn8—Mg3^xxvi	124.4 (3)
Zn5^xxv—Mg2—Zn10^xix	128.9 (3)	Mg3^xviii—Zn8—Mg3^xxvi	75.8 (6)
Zn5ⁱⁱ—Mg2—Zn10^xix	103.70 (19)	Zn10^xi—Zn8—Ce4^xi	64.98 (11)
Zn10^x—Mg2—Zn10^xix	50.25 (18)	Zn10^xix—Zn8—Ce4^xi	64.98 (11)
Zn5^xxv—Mg2—Zn10^xx	128.9 (3)	Zn2—Zn8—Ce4^xi	127.1 (3)
Zn5ⁱⁱ—Mg2—Zn10^xx	103.70 (19)	Zn6—Zn8—Ce4^xi	161.7 (3)
Zn10^x—Mg2—Zn10^xx	121.7 (5)	Mg3^xviii—Zn8—Ce4^xi	68.7 (2)
Zn10^xix—Mg2—Zn10^xx	99.5 (4)	Mg3^xxvi—Zn8—Ce4^xi	68.7 (2)
Zn5^xxv—Mg2—Zn10^xxi	103.70 (19)	Zn10^xi—Zn8—Ce3^x	67.06 (9)
Zn5ⁱⁱ—Mg2—Zn10^xxi	128.9 (3)	Zn10^xix—Zn8—Ce3^x	165.0 (2)
Zn10^x—Mg2—Zn10^xxi	99.5 (4)	Zn2—Zn8—Ce3^x	63.31 (13)
Zn10^xix—Mg2—Zn10^xxi	121.7 (5)	Zn6—Zn8—Ce3^x	61.85 (10)
Zn10^xx—Mg2—Zn10^xxi	50.25 (18)	Mg3^xviii—Zn8—Ce3^x	65.6 (2)
Zn5^xxv—Mg2—Zn9^xxv	55.1 (2)	Mg3^xxvi—Zn8—Ce3^x	126.8 (3)
Zn5ⁱⁱ—Mg2—Zn9^xxv	103.5 (4)	Ce4^xi—Zn8—Ce3^x	123.14 (9)
Zn10^x—Mg2—Zn9^xxv	93.51 (14)	Zn10^xi—Zn8—Ce3	165.0 (2)
Zn10^xix—Mg2—Zn9^xxv	143.5 (3)	Zn10^xix—Zn8—Ce3	67.06 (9)
Zn10^xx—Mg2—Zn9^xxv	97.13 (14)	Zn2—Zn8—Ce3	63.30 (13)
Zn10^xxi—Mg2—Zn9^xxv	51.77 (11)	Zn6—Zn8—Ce3	61.85 (10)
Zn5^xxv—Mg2—Zn9ⁱⁱ	103.5 (4)	Mg3^xviii—Zn8—Ce3	126.8 (3)
Zn5ⁱⁱ—Mg2—Zn9ⁱⁱ	55.1 (2)	Mg3^xxvi—Zn8—Ce3	65.6 (2)
Zn10^x—Mg2—Zn9ⁱⁱ	97.13 (14)	Ce4^xi—Zn8—Ce3	123.15 (9)
Zn10^xix—Mg2—Zn9ⁱⁱ	51.77 (11)	Ce3^x—Zn8—Ce3	110.92 (17)
Zn10^xx—Mg2—Zn9ⁱⁱ	93.51 (14)	Zn10^xi—Zn8—Ce2	72.94 (15)
Zn10^xxi—Mg2—Zn9ⁱⁱ	143.5 (3)	Zn10^xix—Zn8—Ce2	72.94 (15)
Zn9^xxv—Mg2—Zn9ⁱⁱ	158.1 (6)	Zn2—Zn8—Ce2	132.1 (3)
Zn5^xxv—Mg2—Zn9^xi	55.1 (2)	Zn6—Zn8—Ce2	60.85 (19)
Zn5ⁱⁱ—Mg2—Zn9^xi	103.5 (4)	Mg3^xviii—Zn8—Ce2	139.2 (3)
Zn10^x—Mg2—Zn9^xi	51.77 (11)	Mg3^xxvi—Zn8—Ce2	139.2 (3)
Zn10^xix—Mg2—Zn9^xi	97.13 (14)	Ce4^xi—Zn8—Ce2	100.81 (16)
Zn10^xx—Mg2—Zn9^xi	143.5 (3)	Ce3^x—Zn8—Ce2	92.56 (11)
Zn10^xxi—Mg2—Zn9^xi	93.51 (14)	Ce3—Zn8—Ce2	92.56 (11)
Zn9^xxv—Mg2—Zn9^xi	52.92 (19)	Zn10^xliii—Zn9—Zn10^xi	81.6 (2)
Zn9ⁱⁱ—Mg2—Zn9^xi	122.0 (3)	Zn10^xliii—Zn9—Zn9^xxxv	169.17 (10)
Zn5^xxv—Mg2—Zn9^xviii	103.5 (4)	Zn10^xi—Zn9—Zn9^xxxv	109.18 (10)
Zn5ⁱⁱ—Mg2—Zn9^xviii	55.1 (2)	Zn10^xliii—Zn9—Zn9^xxxiv	109.18 (10)
Zn10^x—Mg2—Zn9^xviii	143.5 (3)	Zn10^xi—Zn9—Zn9^xxxiv	169.17 (10)
Zn10^xix—Mg2—Zn9^xviii	93.51 (14)	Zn9^xxxv—Zn9—Zn9^xxxiv	60.0
Zn10^xx—Mg2—Zn9^xviii	51.77 (11)	Zn10^xliii—Zn9—Zn4	116.28 (18)
Zn10^xxi—Mg2—Zn9^xviii	97.13 (14)	Zn10^xi—Zn9—Zn4	116.28 (19)
Zn9^xxv—Mg2—Zn9^xviii	122.0 (3)	Zn9^xxxv—Zn9—Zn4	60.08 (12)
Zn9ⁱⁱ—Mg2—Zn9^xviii	52.92 (19)	Zn9^xxxiv—Zn9—Zn4	60.08 (12)
Zn9^xi—Mg2—Zn9^xviii	158.1 (6)	Zn10^xliii—Zn9—Zn5	115.39 (17)
Zn5^xxv—Mg2—Ce3	152.6 (2)	Zn10^xi—Zn9—Zn5	115.39 (17)
Zn5ⁱⁱ—Mg2—Ce3	152.6 (2)	Zn9^xxxv—Zn9—Zn5	60.10 (11)
Zn10^x—Mg2—Ce3	60.8 (3)	Zn9^xxxiv—Zn9—Zn5	60.10 (11)
Zn10^xix—Mg2—Ce3	60.8 (3)	Zn4—Zn9—Zn5	109.7 (2)
Zn10^xx—Mg2—Ce3	60.8 (3)	Zn10^xliii—Zn9—Mg2^x	123.8 (2)
Zn10^xxi—Mg2—Ce3	60.8 (3)	Zn10^xi—Zn9—Mg2^x	61.2 (2)
Zn9^xxv—Mg2—Ce3	101.0 (3)	Zn9^xxxv—Zn9—Mg2^x	63.54 (10)
Zn9ⁱⁱ—Mg2—Ce3	101.0 (3)	Zn9^xxxiv—Zn9—Mg2^x	110.4 (2)
Zn9^xi—Mg2—Ce3	101.0 (3)	Zn4—Zn9—Mg2^x	117.52 (17)
Zn9^xviii—Mg2—Ce3	101.0 (3)	Zn5—Zn9—Mg2^x	58.2 (3)
Zn5^xxv—Mg2—Ce1^xiv	68.4 (2)	Zn10^xliii—Zn9—Mg2ⁱⁱ	61.2 (2)
Zn5ⁱⁱ—Mg2—Ce1^xiv	68.4 (2)	Zn10^xi—Zn9—Mg2ⁱⁱ	123.8 (2)
Zn10^x—Mg2—Ce1^xiv	60.47 (9)	Zn9^xxxv—Zn9—Mg2ⁱⁱ	110.4 (2)
Zn10^xix—Mg2—Ce1^xiv	60.47 (9)	Zn9^xxxiv—Zn9—Mg2ⁱⁱ	63.54 (10)
Zn10^xx—Mg2—Ce1^xiv	153.68 (10)	Zn4—Zn9—Mg2ⁱⁱ	117.52 (17)
Zn10^xxi—Mg2—Ce1^xiv	153.68 (10)	Zn5—Zn9—Mg2ⁱⁱ	58.2 (3)
Zn9^xxv—Mg2—Ce1^xiv	109.1 (2)	Mg2^x—Zn9—Mg2ⁱⁱ	105.3 (5)
Zn9ⁱⁱ—Mg2—Ce1^xiv	61.03 (14)	Zn10^xliii—Zn9—Mg3^xviii	124.3 (2)
Zn9^xi—Mg2—Ce1^xiv	61.03 (14)	Zn10^xi—Zn9—Mg3^xviii	61.73 (19)
Zn9^xviii—Mg2—Ce1^xiv	109.1 (2)	Zn9^xxxv—Zn9—Mg3^xviii	63.75 (17)
Ce3—Mg2—Ce1^xiv	114.5 (2)	Zn9^xxxiv—Zn9—Mg3^xviii	110.56 (19)
Zn3—Mg3—Zn8^xxvi	102.6 (4)	Zn4—Zn9—Mg3^xviii	58.3 (2)
Zn3—Mg3—Zn8^xviii	102.6 (4)	Zn5—Zn9—Mg3^xviii	117.8 (2)
Zn8^xxvi—Mg3—Zn8^xviii	98.9 (4)	Mg2^x—Zn9—Mg3^xviii	74.5 (3)
Zn3—Mg3—Zn4^xxvii	57.9 (3)	Mg2ⁱⁱ—Zn9—Mg3^xviii	173.8 (3)
Zn8^xxvi—Mg3—Zn4^xxvii	129.4 (2)	Zn10^xliii—Zn9—Mg3^xxxvi	61.7 (2)
Zn8^xviii—Mg3—Zn4^xxvii	129.4 (2)	Zn10^xi—Zn9—Mg3^xxxvi	124.3 (2)
Zn3—Mg3—Zn10^xxiv	130.0 (2)	Zn9^xxxv—Zn9—Mg3^xxxvi	110.56 (19)
Zn8^xxvi—Mg3—Zn10^xxiv	51.01 (16)	Zn9^xxxiv—Zn9—Mg3^xxxvi	63.75 (17)
Zn8^xviii—Mg3—Zn10^xxiv	121.0 (4)	Zn4—Zn9—Mg3^xxxvi	58.3 (2)
Zn4^xxvii—Mg3—Zn10^xxiv	103.1 (4)	Zn5—Zn9—Mg3^xxxvi	117.7 (2)
Zn3—Mg3—Zn10^xxviii	130.0 (2)	Mg2^x—Zn9—Mg3^xxxvi	173.8 (3)
Zn8^xxvi—Mg3—Zn10^xxviii	121.0 (4)	Mg2ⁱⁱ—Zn9—Mg3^xxxvi	74.5 (3)
Zn8^xviii—Mg3—Zn10^xxviii	51.01 (16)	Mg3^xviii—Zn9—Mg3^xxxvi	105.0 (5)
Zn4^xxvii—Mg3—Zn10^xxviii	103.1 (4)	Zn10^xliii—Zn9—Ce4^xi	61.82 (14)
Zn10^xxiv—Mg3—Zn10^xxviii	97.7 (5)	Zn10^xi—Zn9—Ce4^xi	61.82 (14)
Zn3—Mg3—Zn9^xxix	105.9 (4)	Zn9^xxxv—Zn9—Ce4^xi	123.22 (9)
Zn8^xxvi—Mg3—Zn9^xxix	143.0 (5)	Zn9^xxxiv—Zn9—Ce4^xi	123.22 (9)
Zn8^xviii—Mg3—Zn9^xxix	97.3 (2)	Zn4—Zn9—Ce4^xi	74.41 (17)
Zn4^xxvii—Mg3—Zn9^xxix	54.7 (3)	Zn5—Zn9—Ce4^xi	175.9 (2)
Zn10^xxiv—Mg3—Zn9^xxix	92.3 (4)	Mg2^x—Zn9—Ce4^xi	120.2 (3)
Zn10^xxviii—Mg3—Zn9^xxix	51.2 (2)	Mg2ⁱⁱ—Zn9—Ce4^xi	120.2 (3)
Zn3—Mg3—Zn9^xxvi	105.9 (4)	Mg3^xviii—Zn9—Ce4^xi	64.13 (19)
Zn8^xxvi—Mg3—Zn9^xxvi	97.3 (2)	Mg3^xxxvi—Zn9—Ce4^xi	64.13 (19)
Zn8^xviii—Mg3—Zn9^xxvi	143.0 (5)	Zn10^xliii—Zn9—Ce1^vii	63.80 (13)
Zn4^xxvii—Mg3—Zn9^xxvi	54.7 (3)	Zn10^xi—Zn9—Ce1^vii	63.80 (13)
Zn10^xxiv—Mg3—Zn9^xxvi	51.2 (2)	Zn9^xxxv—Zn9—Ce1^vii	119.83 (9)
Zn10^xxviii—Mg3—Zn9^xxvi	92.3 (4)	Zn9^xxxiv—Zn9—Ce1^vii	119.83 (9)
Zn9^xxix—Mg3—Zn9^xxvi	52.5 (3)	Zn4—Zn9—Ce1^vii	179.9 (3)
Zn3—Mg3—Zn2	94.1 (5)	Zn5—Zn9—Ce1^vii	70.20 (16)
Zn8^xxvi—Mg3—Zn2	51.2 (2)	Mg2^x—Zn9—Ce1^vii	62.43 (15)
Zn8^xviii—Mg3—Zn2	51.2 (2)	Mg2ⁱⁱ—Zn9—Ce1^vii	62.43 (15)
Zn4^xxvii—Mg3—Zn2	152.0 (6)	Mg3^xviii—Zn9—Ce1^vii	121.8 (2)
Zn10^xxiv—Mg3—Zn2	95.2 (3)	Mg3^xxxvi—Zn9—Ce1^vii	121.8 (2)
Zn10^xxviii—Mg3—Zn2	95.2 (3)	Ce4^xi—Zn9—Ce1^vii	105.70 (17)
Zn9^xxix—Mg3—Zn2	146.3 (3)	Zn10^xv—Zn10—Zn8^x	110.32 (12)
Zn9^xxvi—Mg3—Zn2	146.3 (3)	Zn10^xv—Zn10—Zn7^xii	91.94 (12)
Zn3—Mg3—Ce3^xxx	150.6 (6)	Zn8^x—Zn10—Zn7^xii	103.84 (18)
Zn8^xxvi—Mg3—Ce3^xxx	60.6 (2)	Zn10^xv—Zn10—Zn9^x	123.52 (14)
Zn8^xviii—Mg3—Ce3^xxx	60.6 (2)	Zn8^x—Zn10—Zn9^x	121.2 (2)
Zn4^xxvii—Mg3—Ce3^xxx	151.5 (6)	Zn7^xii—Zn10—Zn9^x	96.70 (14)
Zn10^xxiv—Mg3—Ce3^xxx	60.5 (2)	Zn10^xv—Zn10—Mg2^xi	64.87 (9)
Zn10^xxviii—Mg3—Ce3^xxx	60.5 (2)	Zn8^x—Zn10—Mg2^xi	125.7 (3)
Zn9^xxix—Mg3—Ce3^xxx	100.4 (4)	Zn7^xii—Zn10—Mg2^xi	129.7 (3)
Zn9^xxvi—Mg3—Ce3^xxx	100.4 (4)	Zn9^x—Zn10—Mg2^xi	67.1 (2)
Zn2—Mg3—Ce3^xxx	56.5 (2)	Zn10^xv—Zn10—Mg3^xxiv	127.4 (2)
Zn3—Mg3—Ce4^xxxi	73.0 (2)	Zn8^x—Zn10—Mg3^xxiv	62.1 (3)
Zn8^xxvi—Mg3—Ce4^xxxi	58.73 (10)	Zn7^xii—Zn10—Mg3^xxiv	140.4 (3)
Zn8^xviii—Mg3—Ce4^xxxi	154.2 (5)	Zn9^x—Zn10—Mg3^xxiv	67.1 (3)
Zn4^xxvii—Mg3—Ce4^xxxi	70.7 (2)	Mg2^xi—Zn10—Mg3^xxiv	78.8 (3)
Zn10^xxiv—Mg3—Ce4^xxxi	57.05 (9)	Zn10^xv—Zn10—Ce4	162.27 (8)
Zn10^xxviii—Mg3—Ce4^xxxi	149.6 (5)	Zn8^x—Zn10—Ce4	66.51 (11)
Zn9^xxix—Mg3—Ce4^xxxi	108.4 (4)	Zn7^xii—Zn10—Ce4	72.68 (14)
Zn9^xxvi—Mg3—Ce4^xxxi	59.36 (17)	Zn9^x—Zn10—Ce4	68.44 (14)
Zn2—Mg3—Ce4^xxxi	103.1 (3)	Mg2^xi—Zn10—Ce4	131.91 (15)
Ce3^xxx—Mg3—Ce4^xxxi	110.8 (2)	Mg3^xxiv—Zn10—Ce4	67.8 (2)
Zn3—Mg3—Ce4^xx	73.0 (2)	Zn10^xv—Zn10—Ce3^xi	66.53 (6)
Zn8^xxvi—Mg3—Ce4^xx	154.1 (5)	Zn8^x—Zn10—Ce3^xi	65.23 (12)
Zn8^xviii—Mg3—Ce4^xx	58.73 (10)	Zn7^xii—Zn10—Ce3^xi	147.71 (14)
Zn4^xxvii—Mg3—Ce4^xx	70.7 (2)	Zn9^x—Zn10—Ce3^xi	115.11 (14)
Zn10^xxiv—Mg3—Ce4^xx	149.6 (5)	Mg2^xi—Zn10—Ce3^xi	64.2 (3)
Zn10^xxviii—Mg3—Ce4^xx	57.05 (9)	Mg3^xxiv—Zn10—Ce3^xi	63.8 (2)
Zn9^xxix—Mg3—Ce4^xx	59.36 (17)	Ce4—Zn10—Ce3^xi	122.89 (11)
Zn9^xxvi—Mg3—Ce4^xx	108.4 (4)	Zn10^xv—Zn10—Ce1ⁱⁱ	66.64 (6)
Zn2—Mg3—Ce4^xx	103.1 (3)	Zn8^x—Zn10—Ce1ⁱⁱ	167.29 (19)
Ce3^xxx—Mg3—Ce4^xx	110.8 (2)	Zn7^xii—Zn10—Ce1ⁱⁱ	64.59 (13)
Ce4^xxxi—Mg3—Ce4^xx	138.1 (4)	Zn9^x—Zn10—Ce1ⁱⁱ	67.49 (14)
Zn6—Zn1—Zn6^xxxii	109.5	Mg2^xi—Zn10—Ce1ⁱⁱ	65.2 (2)
Zn6—Zn1—Zn6^xxiv	109.5	Mg3^xxiv—Zn10—Ce1ⁱⁱ	130.0 (3)
Zn6^xxxii—Zn1—Zn6^xxiv	109.5	Ce4—Zn10—Ce1ⁱⁱ	112.32 (10)
Zn6—Zn1—Zn6^xvii	109.5	Ce3^xi—Zn10—Ce1ⁱⁱ	121.37 (11)
Zn6^xxxii—Zn1—Zn6^xvii	109.5	Zn10^xv—Zn10—Ce2	68.44 (5)
Zn6^xxiv—Zn1—Zn6^xvii	109.5	Zn8^x—Zn10—Ce2	61.94 (14)
Zn6—Zn1—Zn2^xxxii	180.00 (16)	Zn7^xii—Zn10—Ce2	62.04 (11)
Zn6^xxxii—Zn1—Zn2^xxxii	70.53 (16)	Zn9^x—Zn10—Ce2	157.32 (15)
Zn6^xxiv—Zn1—Zn2^xxxii	70.53 (16)	Mg2^xi—Zn10—Ce2	131.78 (17)
Zn6^xvii—Zn1—Zn2^xxxii	70.53 (16)	Mg3^xxiv—Zn10—Ce2	123.6 (3)
Zn6—Zn1—Zn2^xxiv	70.53 (16)	Ce4—Zn10—Ce2	95.95 (9)
Zn6^xxxii—Zn1—Zn2^xxiv	70.53 (16)	Ce3^xi—Zn10—Ce2	87.00 (10)
Zn6^xxiv—Zn1—Zn2^xxiv	70.53 (16)	Ce1ⁱⁱ—Zn10—Ce2	106.32 (11)

Symmetry codes: (i) −y+1/2, z, −x+1/2; (ii) −x+1/2, −y+1/2, z; (iii) z, −x+1/2, −y+1/2; (iv) z, −y+1/2, −x+1/2; (v) −x+1/2, z, −y+1/2; (vi) −y+1/2, −x+1/2, z; (vii) −x+1/2, y, −z+1/2; (viii) y, −z+1/2, −x+1/2; (ix) −z+1/2, −x+1/2, y; (x) z, x, y; (xi) y, z, x; (xii) −z+1/2, x, −y+1/2; (xiii) −y+1/2, −z+1/2, x; (xiv) x, −y+1/2, −z+1/2; (xv) y, x, z; (xvi) x, z, y; (xvii) x, −y, −z; (xviii) y, −z, −x; (xix) z, y, x; (xx) z, −x, −y; (xxi) z, −y, −x; (xxii) x, −z+1/2, −y+1/2; (xxiii) −y, z+1/2, −x+1/2; (xxiv) −x, y, −z; (xxv) −x+1/2, y−1/2, −z; (xxvi) −z, x, −y; (xxvii) x, −y+1/2, −z−1/2; (xxviii) y, −x, −z; (xxix) −y+1/2, −z, x−1/2; (xxx) −y, z, −x; (xxxi) −x, −y+1/2, z−1/2; (xxxii) −x, −y, z; (xxxiii) −x+1/2, y, −z−1/2; (xxxiv) −y+1/2, z+1/2, −x; (xxxv) −z, −x+1/2, y−1/2; (xxxvi) z+1/2, −x+1/2, −y; (xxxvii) x, −y+1, −z; (xxxviii) −x, −y+1, z; (xxxix) y, z+1/2, x−1/2; (xl) x−1/2, y, z−1/2; (xli) −x+1/2, −y+1, z−1/2; (xlii) −z+1/2, y, −x+1/2; (xliii) −z+1/2, −y+1/2, x.

Experimental details

Crystal data
Chemical formula	Ce₂₀Mg₁₉Zn₈₁
M_r	8559.26
Crystal system, space group	Cubic, F43m
Temperature (K)	295
a (Å)	21.1979 (8)
V (Å³)	9525.3 (6)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	29.39
Crystal size (mm)	0.11 × 0.09 × 0.07

Data collection
Diffractometer	Oxford Diffraction Xcalibur diffractometer
Absorption correction	Analytical (CrysAlis RED; Oxford Diffraction, 2005)
T_min, T_max	0.056, 0.122
No. of measured, independent and observed [I > 2σ(I)] reflections	1009, 544, 388
R_int	0.034
(sin θ/λ)_max (Å⁻¹)	0.624

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.044, 0.101, 1.01
No. of reflections	544
No. of parameters	73
Δρ_max, Δρ_min (e Å⁻³)	1.63, −1.89
Absolute structure	Flack (1983), with how many Friedel pairs?
Absolute structure parameter	0.3 (2)

Computer programs: CrysAlis CCD (Oxford Diffraction, 2004), CrysAlis RED (Oxford Diffraction, 2005), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 1999).

Selected bond lengths (Å) top

Ce2—Zn6	3.044 (9)	Mg3—Ce3ⁱⁱ	3.325 (13)
Mg2—Zn10ⁱ	3.024 (8)	Zn1—Zn6	2.598 (8)

Symmetry codes: (i) z, x, y; (ii) −y, z, −x.

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