La_4.27Mg_2.89Zn₃₀, a new structure type with strong positional disorder

Ternary tetra­lanthanum trimagnesium tricontazinc, La_4.27Mg_2.89Zn₃₀, crystallizes as a new structure type. It belongs to the structural family that may be derived from the hexa­gonal CaCu₅ and Th₂Ni₁₇ structure types by combination of inter­nal deformation and multiple substitution. The triangular 3₆ and hexa­gonal 6₃ nets are alternately stacked with Kagomé 3636 nets. The atoms with the largest radius (La) are enclosed in 18-vertex polyhedra (distorted pseudo-Frank-Kasper polyhedra). The coordination polyhedra of the two Mg atoms are bicapped and monocapped hexa­gonal anti­prisms, with coordination numbers of 14 and 13, respectively. For all the Zn atoms, the typical icosa­hedral coordination is observed. In the direction of the six- and threefold axes, strong positional disorder is observed as a result of partial substitutions of La atoms by pairs of Mg atoms.

S1. Comment

Recently, intermetallic compounds containing rare earths, transition metals and magnesium have been of particular interest to researchers because of their useful properties as modern lightweight alloys and hydrogen-storage materials. The crystal structures, physical properties and hydrogenation behaviour of these materials have been reviewed by Rodewald et al. (2007). The most heavily studied of these intermetallic compounds have been those with metals such as nickel and copper. Only two ternary compounds, i.e. La₂Mg₃Zn₃, cubic, a = 7.145 Å (Melnik et al., 1978) and La₃(Zn_0.874Mg_0.126)₁₁ (Pavlyuk et al., 2010), were investigated from the La–Mg–Zn ternary system. The result of our crystallographic studies of a new intermetallic compound, La_4.27Mg_2.89Zn₃₀, is presented here.

During the systematic study of the ternary alloys of La–Mg–Zn from the concentration region with a high content of zinc a new ternary phase was detected. The powder diffraction pattern of this compound is similar to the powder pattern of the RE₂Zn₁₇ (RE, rare earth metals) binary phase, but has some differences. It was decided to investigate this phase further, using single-crystal methods. The single-crystal data showed that the title compound crystallized in the hexagonal crystal class (space group P6₃/mmc). The projection of the unit cell and coordination polyhedra are shown in Fig. 1. The number of neighbouring atoms correlates well with the dimensions of the central atoms. The largest atoms La are enclosed in 18-vertex polyhedra that can be treated as distorted pseudo-Frank–Kasper polyhedra. The coordination polyhedra of Mg1 and Mg2 atoms are bicapped and monocapped hexagonal antiprisms, with coordination numbers (CN) of 14 and 13 respectively. All the zinc atoms are surrounded by 12 nearest neighbours in the form of icosahedra (CN = 12). The shortest interatomic distances in La_4.27Mg_2.89Zn₃₀ are in the ranges typical for intermetallic compounds containing La, Mg and Zn, and indicate metallic-type bonding.

A detailed crystal chemical analysis shows that the title structure is an intergrowth of fragments of CaCu₅ and Th₂Ni₁₇ types. It should be noted that the La–Zn binary system forms LaZn₅ (Pavlyuk et al., 1997) and La₂Zn₁₇ (Iandelli & Palenzona, 1967) with the CaCu₅ and Th₂Zn₁₇ structure types, respectively. In the Th₂Ni₁₇ structure (Florio et al., 1956), which also crystallizes in P6₃/mmc, the nickel atoms occupy the 12k, 12j, 6g and 4f positions, and the Th atoms are located in the 2b and 2c sites. In the La_4.27Mg_2.89Zn₃₀ structure the zinc atoms occupy 12k, 12j and 6g sites but the 4f site is partialy occupied by the Mg2 atom. The Mg1 atom partialy occupies the 4e site, which is not occupied in Th₂Ni₁₇. The La1 atom partialy occupies the 2b site and the 2c site is fully occupied by the La3 atom. The La2 atom partialy occupies the 2d site, which also is not occupied in Th₂Ni₁₇. In the structure of the title compound so-called split atoms are observable. Atoms are distributed over some sites, which are located close to each other. The split positions of La1—Mg1, Mg1—Mg1 and La2—Mg2 are observed in the direction of the sixfold and threefold axes, respectively (Fig. 2). Thus, in the La_4.27Mg_2.89Zn₃₀ structure sub-cells with compositions of La₆Zn₃₀ and La₂Mg_2.89Zn₃₀ (Fig. 2) can be selected. The La₆Zn₃₀ sub-cell corresponds to the sixfold unit cell of LaZn₅ which has the CaCu₅ structure type. CaCu₅ belongs to the family of structures with large coordination polyhedra (CN = 20 for Ca atom) and in which triangular 3₆ and hexagonal 6₃ nets are alternatively stacked with kagomè 3636 nets. The same type of net is observed in the title compound (Fig. 3). It should be noted that La1—Mg1, Mg1—Mg1 and La2—Mg2 split atoms are located in the channels of this nets.

Known derivatives of the CaCu₅ type can be formed by partial or complete substitution of larger (R) atoms by various proportions of smaller-sized atoms (M) or by the shift of layers perpendicular to the sixfold axis (Krypyakevich, 1977). In the first case, if one third of the R atoms are replaced by pairs of M atoms, structures of the R₂M₁₇ composition (structural types hexagonal Th₂Ni₁₇ and rhombohedral Th₂Zn₁₇) are obtained. The substitution of half the R atoms by pairs of M atoms results in teragonal [tetragonal?] cells of ThMn₁₂. In the case of shited layers, there is a change in symmetry from hexagonal to orthorhombic and the structures of the BaZn₅ and SrZn₅ (Baenziger & Conant, 1956) are realized. The title structure is an intergrowth of fragments of both CaCu₅ and Th₂Ni₁₇ types and belongs to the first group of derivatives. The scheme of the relationship CaCu₅–La_4.27Mg_2.89Zn₃₀–Th₂Ni₁₇ is shown in Fig. 4. The title compound is an example of a class whose representative members may be derived from the hexagonal CaCu₅ and Th₂Ni₁₇ structure types by combination of internal deformation and multiple substitution..

The formation of ternary intermetallic magnesium structures which are related to the structure of binary phases has been previously observed. Typically, these structures are formed by ordered or partial substitution of rare earth metal atoms by magnesium atoms. For example, REMg₂Cu₉ (Solokha et al., 2006) is an hexagonal ordered superstructure of the CeNi₃ type and REMg₂Ni₉ (Kadir et al., 1997) is a rhombohedral ordered superstructure of the PuNi₃ type. Such substitution is possible because obviously in these cases a decisive role belongs to steric factors. The atomic radius of magnesium is only 9–11% smaller than atoms of the rare earth metals. On the other hand, magnesium has a different electronic structure. This apparently is the reason why in the title compound magnesium atoms cannot substitute for lanthanum atoms. Thus they try to `push' lanthanum atoms out of the occupied sites very close to them and form split positions. In general, this mechanism is a multiple substitution, in which a pair of smaller atoms replaces one atom of larger size. In the title structure this substitution is not complete but only partial.

Related literature

For related literature, see: Baenziger & Conant (1956); Farrugia (1999); Florio et al. (1956); Iandelli & Palenzona (1967); Kadir et al. (1997); Krypyakevich (1977); Melnik et al. (1978); Pavlyuk et al. (1997, 2010); Rodewald et al. (2007); Solokha et al. (2006).

S2. Experimental

Lanthanum, magnesium and zinc, all with a nominal purity more than 99.9 wt%, were used as starting elements. First, the powders of the pure metals with a stoichiometry La₁₀Mg₁₀Zn₈₀ were pressed into pellets, 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 rate from room temperature to 670 K was 5 K min^-1. This temperature was maintained over 3 d and then the temperature was increased from 670 to 1070 K over 4 d. The alloy was annealed at this temperature for 3 h and slowly cooled to room temperature. After the melting and annealing procedures, the total weight loss was less than 2%. 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 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 for the title compound is 11.6–11.5% at. La, 8.8–7.8% at. Mg and 79.6–80.8% at. Zn). A tabular-shaped single crystal, exhibiting metallic lustre, was isolated by mechanical fragmentation from the reaction.

S3. Refinement

The systematic absences indicated five possible space groups, P31c (163), P31c (159), P6₃mc (186), P6₃/mmc (194), P62c (190). A statistical test of the distribution of the E values using the program E-STATS from the WinGX system (Farrugia, 1999) suggested that the structure is centrosymmetric. The analysis of systematic extinctions yielded the space group P6₃/mmc (No. 194) which was confirmed by the following structure refinement. The structure was solved by direct methods. The zinc atoms fully occupied the 12k, 12j and 6g sites. The 2c site was fully occupied by the La3 atom. During the refinement of the atomic parameters of other atoms, two features were found: first, the La1 and La2 atoms partialy occupy the 2b and 2c sites, respectively; second, two peaks of different heights on the Fourier map of the residual electron density with a very short distance to the La1 and La2 atoms. Therefore, this structure is positionally disordered. The refinement of the structure model with La1—Mg1, Mg1—Mg1 and La2—Mg2 split atoms leads to a sharp reduction in the residual factor from R = 0.052 to R = 0.013. The final refined chemical composition of the title compound is very well correlated with the data of electron probe microanalysis.

In the final refinement cycles all atoms were successfully refined with anisotropic thermal displacement parameters. The atomic coordinates were standardized using the STRUCTURE TIDY program (Gelato & Parthé, 1987).

Computing details

Data collection: CrysAlis CCD (Oxford Diffraction, 2008); cell refinement: CrysAlis CCD (Oxford Diffraction, 2008); data reduction: CrysAlis RED (Oxford Diffraction, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2006); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures

	Fig. 1. A clinographic projection of the La4.27Mg2.89Zn30 unit-cell contents and the coordination polyhedra of atoms.
	Fig. 2. The La4.27Mg2.89Zn30 structure as a combination of La6Zn30 and La2Mg2.89Zn30 sub-cells.
	Fig. 3. The triangular 36 and hexagonal 63 atomic nets in the (a) La4.27Mg2.89Zn30, (b) CaCu5 and (c) Th2Ni17 structure types.
	Fig. 4. A scheme showing the relationship between the CaCu5, La4.27Mg2.89Zn30 and Th2Ni17 structure types.

Ternary tetralanthanum trimagnesium tricontazinc

Crystal data

La4.27Mg2.89Zn30	Dx = 6.143 Mg m^−3
Mr = 2625.71	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P63/mmc	Cell parameters from 262 reflections
Hall symbol: -P 6c 2c	θ = 2.5–27.6°
a = 9.4415 (4) Å	µ = 31.10 mm^−1
c = 9.1937 (8) Å	T = 293 K
V = 709.75 (7) Å^3	Irregularly shaped, metallic dark grey
Z = 1	0.09 × 0.07 × 0.05 mm
F(000) = 1179.9

Data collection

Oxford Diffraction Xcalibur diffractometer	342 independent reflections
Radiation source: fine-focus sealed tube	299 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.049
Detector resolution: 0 pixels mm^-1	θmax = 27.5°, θmin = 2.5°
ω scans	h = −12→12
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2008)	k = −12→12
Tmin = 0.089, Tmax = 0.198	l = 0→11
3083 measured reflections

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.013	Secondary atom site location: difference Fourier map
wR(F^2) = 0.048	w = 1/[σ^2(Fo^2) + (0.0212P)^2 + 0.6192P] where P = (Fo^2 + 2Fc^2)/3
S = 1.12	(Δ/σ)max < 0.001
342 reflections	Δρmax = 0.58 e Å^−3
31 parameters	Δρmin = −0.33 e Å^−3

Special details

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	Occ. (<1)
La1	0.0000	0.0000	0.2500	0.0239 (3)	0.719 (2)
La2	0.3333	0.6667	0.7500	0.0245 (5)	0.418 (3)
La3	0.3333	0.6667	0.2500	0.02234 (17)
Zn1	0.5000	0.0000	0.0000	0.02805 (19)
Zn2	0.16613 (2)	0.33226 (4)	0.01078 (6)	0.03623 (19)
Zn3	0.35491 (6)	0.02724 (6)	0.2500	0.02964 (18)
Mg1	0.0000	0.0000	0.0937 (13)	0.014 (2)	0.1407 (11)
Mg2	0.3333	0.6667	0.5986 (9)	0.0688 (18)	0.582 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
La1	0.0195 (3)	0.0195 (3)	0.0325 (5)	0.00977 (14)	0.000	0.000
La2	0.0206 (5)	0.0206 (5)	0.0322 (8)	0.0103 (3)	0.000	0.000
La3	0.0197 (2)	0.0197 (2)	0.0277 (3)	0.00983 (10)	0.000	0.000
Zn1	0.0255 (3)	0.0261 (3)	0.0328 (4)	0.01303 (15)	−0.00008 (14)	−0.0002 (3)
Zn2	0.0238 (2)	0.0244 (3)	0.0607 (4)	0.01220 (13)	−0.00013 (12)	−0.0003 (2)
Zn3	0.0281 (2)	0.0275 (3)	0.0334 (3)	0.01400 (19)	0.000	0.000
Mg1	0.020 (3)	0.020 (3)	0.003 (5)	0.0099 (16)	0.000	0.000
Mg2	0.054 (2)	0.054 (2)	0.099 (5)	0.0269 (10)	0.000	0.000

Geometric parameters (Å, º)

La1—Mg1^i	1.437 (12)	Zn1—Mg2^xxxiii	2.872 (3)
La1—Mg1	1.437 (12)	Zn1—Mg2^xxxiv	2.872 (3)
La1—Mg1^ii	3.160 (12)	Zn1—La2^xii	3.5653 (2)
La1—Mg1^iii	3.160 (12)	Zn1—La2^xxxv	3.5653 (2)
La1—Zn3^iv	3.2300 (4)	Zn2—Zn2^xxxvi	2.7240 (4)
La1—Zn3^v	3.2300 (4)	Zn2—Zn2^xxvii	2.7240 (4)
La1—Zn3	3.2300 (4)	Zn2—Zn1^xxiii	2.7317 (2)
La1—Zn3^vi	3.2300 (4)	Zn2—Zn1^viii	2.7317 (2)
La1—Zn3^vii	3.2300 (4)	Zn2—Zn3^xxxvi	2.7918 (5)
La1—Zn3^viii	3.2300 (4)	Zn2—Zn3^xxxvii	2.7918 (5)
La1—Zn2^viii	3.4954 (5)	Zn2—Mg1	2.822 (3)
La1—Zn2^i	3.4954 (5)	Zn2—Zn3^iv	2.8448 (5)
La2—Mg2	1.392 (8)	Zn2—Zn3^viii	2.8448 (5)
La2—Mg2^ix	1.392 (8)	Zn2—Mg1^iii	2.882 (4)
La2—Zn3^x	2.9171 (5)	Zn2—Mg2^i	2.913 (3)
La2—Zn3^xi	2.9171 (5)	Zn3—Zn1^xxxviii	2.7528 (3)
La2—Zn3^xii	2.9171 (5)	Zn3—Zn2^xxxix	2.7918 (5)
La2—Zn3^xiii	2.9171 (5)	Zn3—Zn2^xxvii	2.7918 (5)
La2—Zn3^xiv	2.9171 (5)	Zn3—Zn3^iv	2.8364 (9)
La2—Zn3^xv	2.9171 (5)	Zn3—Zn2^v	2.8448 (5)
La2—Zn1^xvi	3.5653 (2)	Zn3—Zn2^xl	2.8448 (5)
La2—Zn1^xvii	3.5653 (2)	Zn3—La2^xii	2.9171 (5)
La2—Zn1^xviii	3.5653 (2)	Zn3—Zn3^xxxi	2.9970 (8)
La2—Zn1^xix	3.5653 (2)	Zn3—Mg2^xii	3.232 (4)
La3—Mg2^i	3.205 (8)	Zn3—Mg2^xxxiv	3.232 (4)
La3—Mg2	3.205 (8)	Mg1—Mg1^iii	1.72 (2)
La3—Zn3^xx	3.3072 (5)	Mg1—Zn2^viii	2.822 (3)
La3—Zn3^xxi	3.3072 (5)	Mg1—Zn2^v	2.822 (3)
La3—Zn3^xxii	3.3072 (5)	Mg1—Mg1^i	2.87 (2)
La3—Zn3^viii	3.3072 (5)	Mg1—Zn2^iii	2.882 (4)
La3—Zn3^iv	3.3072 (5)	Mg1—Zn2^xxvii	2.882 (4)
La3—Zn3^xxiii	3.3072 (5)	Mg1—Zn2^xxxvi	2.882 (4)
La3—Zn2^xxiv	3.5090 (5)	Mg1—La1^iii	3.160 (12)
La3—Zn2^xxv	3.5090 (5)	Mg2—Mg2^ix	2.783 (16)
La3—Zn2	3.5090 (5)	Mg2—Zn1^xvii	2.872 (3)
La3—Zn2^xxvi	3.5090 (5)	Mg2—Zn1^xix	2.872 (3)
Zn1—Zn2^xxvii	2.7317 (2)	Mg2—Zn1^xli	2.872 (3)
Zn1—Zn2^xxviii	2.7317 (2)	Mg2—Zn2^xxiv	2.913 (3)
Zn1—Zn2^xxix	2.7317 (2)	Mg2—Zn2^i	2.913 (3)
Zn1—Zn2^v	2.7317 (2)	Mg2—Zn2^xxvi	2.913 (3)
Zn1—Zn3^xxx	2.7528 (3)	Mg2—Zn3^x	3.232 (4)
Zn1—Zn3^xxxi	2.7528 (3)	Mg2—Zn3^xii	3.232 (4)
Zn1—Zn3^xxxii	2.7528 (3)	Mg2—Zn3^xi	3.232 (4)
Zn1—Zn3	2.7528 (3)
Mg1^i—La1—Mg1	180.000 (3)	Zn2^xxviii—Zn1—La2^xxxv	69.099 (10)
Mg1^i—La1—Mg1^ii	0.000 (2)	Zn2^xxix—Zn1—La2^xxxv	110.901 (10)
Mg1—La1—Mg1^ii	180.000 (2)	Zn2^v—Zn1—La2^xxxv	69.099 (10)
Mg1^i—La1—Mg1^iii	180.0	Zn3^xxx—Zn1—La2^xxxv	53.121 (11)
Mg1—La1—Mg1^iii	0.000 (1)	Zn3^xxxi—Zn1—La2^xxxv	126.879 (11)
Mg1^ii—La1—Mg1^iii	180.0	Zn3^xxxii—Zn1—La2^xxxv	53.121 (11)
Mg1^i—La1—Zn3^iv	90.000 (1)	Zn3—Zn1—La2^xxxv	126.879 (11)
Mg1—La1—Zn3^iv	90.000 (1)	Mg2^xxxiii—Zn1—La2^xxxv	21.74 (15)
Mg1^ii—La1—Zn3^iv	90.0	Mg2^xxxiv—Zn1—La2^xxxv	158.26 (15)
Mg1^iii—La1—Zn3^iv	90.0	La2^xii—Zn1—La2^xxxv	180.0
Mg1^i—La1—Zn3^v	90.000 (1)	Zn2^xxxvi—Zn2—Zn2^xxvii	119.476 (6)
Mg1—La1—Zn3^v	90.000 (1)	Zn2^xxxvi—Zn2—Zn1^xxiii	173.74 (4)
Mg1^ii—La1—Zn3^v	90.0	Zn2^xxvii—Zn2—Zn1^xxiii	60.093 (6)
Mg1^iii—La1—Zn3^v	90.0	Zn2^xxxvi—Zn2—Zn1^viii	60.093 (6)
Zn3^iv—La1—Zn3^v	172.091 (18)	Zn2^xxvii—Zn2—Zn1^viii	173.74 (4)
Mg1^i—La1—Zn3	90.0	Zn1^xxiii—Zn2—Zn1^viii	119.552 (13)
Mg1—La1—Zn3	90.0	Zn2^xxxvi—Zn2—Zn3^xxxvi	114.16 (3)
Mg1^ii—La1—Zn3	90.0	Zn2^xxvii—Zn2—Zn3^xxxvi	62.08 (2)
Mg1^iii—La1—Zn3	90.0	Zn1^xxiii—Zn2—Zn3^xxxvi	59.774 (10)
Zn3^iv—La1—Zn3	52.091 (18)	Zn1^viii—Zn2—Zn3^xxxvi	111.99 (2)
Zn3^v—La1—Zn3	120.0	Zn2^xxxvi—Zn2—Zn3^xxxvii	62.08 (2)
Mg1^i—La1—Zn3^vi	90.0	Zn2^xxvii—Zn2—Zn3^xxxvii	114.16 (3)
Mg1—La1—Zn3^vi	90.0	Zn1^xxiii—Zn2—Zn3^xxxvii	111.99 (2)
Mg1^ii—La1—Zn3^vi	90.0	Zn1^viii—Zn2—Zn3^xxxvii	59.774 (10)
Mg1^iii—La1—Zn3^vi	90.0	Zn3^xxxvi—Zn2—Zn3^xxxvii	61.06 (2)
Zn3^iv—La1—Zn3^vi	120.0	Zn2^xxxvi—Zn2—Mg1	62.58 (5)
Zn3^v—La1—Zn3^vi	67.909 (18)	Zn2^xxvii—Zn2—Mg1	62.58 (5)
Zn3—La1—Zn3^vi	172.091 (18)	Zn1^xxiii—Zn2—Mg1	119.55 (3)
Mg1^i—La1—Zn3^vii	90.0	Zn1^viii—Zn2—Mg1	119.55 (3)
Mg1—La1—Zn3^vii	90.0	Zn3^xxxvi—Zn2—Mg1	107.2 (2)
Mg1^ii—La1—Zn3^vii	90.0	Zn3^xxxvii—Zn2—Mg1	107.2 (2)
Mg1^iii—La1—Zn3^vii	90.0	Zn2^xxxvi—Zn2—Zn3^iv	126.69 (3)
Zn3^iv—La1—Zn3^vii	120.0	Zn2^xxvii—Zn2—Zn3^iv	60.128 (18)
Zn3^v—La1—Zn3^vii	52.091 (18)	Zn1^xxiii—Zn2—Zn3^iv	59.119 (9)
Zn3—La1—Zn3^vii	67.909 (18)	Zn1^viii—Zn2—Zn3^iv	125.64 (2)
Zn3^vi—La1—Zn3^vii	120.0	Zn3^xxxvi—Zn2—Zn3^iv	110.039 (9)
Mg1^i—La1—Zn3^viii	90.0	Zn3^xxxvii—Zn2—Zn3^iv	170.74 (2)
Mg1—La1—Zn3^viii	90.0	Mg1—Zn2—Zn3^iv	77.20 (18)
Mg1^ii—La1—Zn3^viii	90.0	Zn2^xxxvi—Zn2—Zn3^viii	60.128 (18)
Mg1^iii—La1—Zn3^viii	90.0	Zn2^xxvii—Zn2—Zn3^viii	126.69 (3)
Zn3^iv—La1—Zn3^viii	67.909 (18)	Zn1^xxiii—Zn2—Zn3^viii	125.64 (2)
Zn3^v—La1—Zn3^viii	120.0	Zn1^viii—Zn2—Zn3^viii	59.119 (9)
Zn3—La1—Zn3^viii	120.0	Zn3^xxxvi—Zn2—Zn3^viii	170.74 (2)
Zn3^vi—La1—Zn3^viii	52.091 (18)	Zn3^xxxvii—Zn2—Zn3^viii	110.039 (9)
Zn3^vii—La1—Zn3^viii	172.091 (18)	Mg1—Zn2—Zn3^viii	77.20 (17)
Mg1^i—La1—Zn2^viii	128.991 (9)	Zn3^iv—Zn2—Zn3^viii	78.72 (2)
Mg1—La1—Zn2^viii	51.009 (9)	Zn2^xxxvi—Zn2—Mg1^iii	60.37 (3)
Mg1^ii—La1—Zn2^viii	128.991 (9)	Zn2^xxvii—Zn2—Mg1^iii	60.37 (3)
Mg1^iii—La1—Zn2^viii	51.009 (8)	Zn1^xxiii—Zn2—Mg1^iii	117.47 (5)
Zn3^iv—La1—Zn2^viii	134.292 (8)	Zn1^viii—Zn2—Mg1^iii	117.47 (5)
Zn3^v—La1—Zn2^viii	49.856 (7)	Zn3^xxxvi—Zn2—Mg1^iii	77.07 (19)
Zn3—La1—Zn2^viii	134.292 (8)	Zn3^xxxvii—Zn2—Mg1^iii	77.07 (19)
Zn3^vi—La1—Zn2^viii	49.856 (7)	Mg1—Zn2—Mg1^iii	35.1 (5)
Zn3^vii—La1—Zn2^viii	86.927 (7)	Zn3^iv—Zn2—Mg1^iii	104.20 (17)
Zn3^viii—La1—Zn2^viii	86.927 (7)	Zn3^viii—Zn2—Mg1^iii	104.20 (17)
Mg1^i—La1—Zn2^i	51.009 (9)	Zn2^xxxvi—Zn2—Mg2^i	116.29 (4)
Mg1—La1—Zn2^i	128.991 (9)	Zn2^xxvii—Zn2—Mg2^i	116.29 (4)
Mg1^ii—La1—Zn2^i	51.009 (8)	Zn1^xxiii—Zn2—Mg2^i	61.07 (2)
Mg1^iii—La1—Zn2^i	128.991 (9)	Zn1^viii—Zn2—Mg2^i	61.07 (2)
Zn3^iv—La1—Zn2^i	49.856 (7)	Zn3^xxxvi—Zn2—Mg2^i	68.97 (13)
Zn3^v—La1—Zn2^i	134.292 (8)	Zn3^xxxvii—Zn2—Mg2^i	68.97 (13)
Zn3—La1—Zn2^i	86.927 (7)	Mg1—Zn2—Mg2^i	175.5 (2)
Zn3^vi—La1—Zn2^i	86.927 (7)	Zn3^iv—Zn2—Mg2^i	106.22 (11)
Zn3^vii—La1—Zn2^i	134.292 (8)	Zn3^viii—Zn2—Mg2^i	106.22 (11)
Zn3^viii—La1—Zn2^i	49.856 (7)	Mg1^iii—Zn2—Mg2^i	140.3 (3)
Zn2^viii—La1—Zn2^i	134.262 (6)	Zn2^xxxvi—Zn2—La1	70.014 (14)
Mg2—La2—Mg2^ix	180.000 (3)	Zn2^xxvii—Zn2—La1	70.014 (14)
Mg2—La2—Zn3^x	90.000 (1)	Zn1^xxiii—Zn2—La1	114.398 (11)
Mg2^ix—La2—Zn3^x	90.000 (1)	Zn1^viii—Zn2—La1	114.398 (11)
Mg2—La2—Zn3^xi	90.000 (2)	Zn3^xxxvi—Zn2—La1	126.293 (15)
Mg2^ix—La2—Zn3^xi	90.000 (2)	Zn3^xxxvii—Zn2—La1	126.293 (15)
Zn3^x—La2—Zn3^xi	58.179 (15)	Mg1—Zn2—La1	23.3 (2)
Mg2—La2—Zn3^xii	90.000 (3)	Zn3^iv—Zn2—La1	60.218 (12)
Mg2^ix—La2—Zn3^xii	90.000 (3)	Zn3^viii—Zn2—La1	60.218 (12)
Zn3^x—La2—Zn3^xii	61.821 (15)	Mg1^iii—Zn2—La1	58.5 (2)
Zn3^xi—La2—Zn3^xii	120.0	Mg2^i—Zn2—La1	161.21 (15)
Mg2—La2—Zn3^xiii	90.000 (3)	Zn1^xxxviii—Zn3—Zn1	113.220 (14)
Mg2^ix—La2—Zn3^xiii	90.000 (3)	Zn1^xxxviii—Zn3—Zn2^xxxix	59.029 (8)
Zn3^x—La2—Zn3^xiii	120.0	Zn1—Zn3—Zn2^xxxix	156.85 (2)
Zn3^xi—La2—Zn3^xiii	61.821 (15)	Zn1^xxxviii—Zn3—Zn2^xxvii	156.85 (2)
Zn3^xii—La2—Zn3^xiii	178.179 (15)	Zn1—Zn3—Zn2^xxvii	59.029 (8)
Mg2—La2—Zn3^xiv	90.000 (2)	Zn2^xxxix—Zn3—Zn2^xxvii	118.36 (2)
Mg2^ix—La2—Zn3^xiv	90.000 (2)	Zn1^xxxviii—Zn3—Zn3^iv	110.014 (9)
Zn3^x—La2—Zn3^xiv	120.0	Zn1—Zn3—Zn3^iv	110.014 (9)
Zn3^xi—La2—Zn3^xiv	178.179 (15)	Zn2^xxxix—Zn3—Zn3^iv	59.469 (11)
Zn3^xii—La2—Zn3^xiv	58.179 (15)	Zn2^xxvii—Zn3—Zn3^iv	59.469 (11)
Zn3^xiii—La2—Zn3^xiv	120.0	Zn1^xxxviii—Zn3—Zn2^v	140.07 (2)
Mg2—La2—Zn3^xv	90.000 (1)	Zn1—Zn3—Zn2^v	58.393 (9)
Mg2^ix—La2—Zn3^xv	90.000 (1)	Zn2^xxxix—Zn3—Zn2^v	142.64 (2)
Zn3^x—La2—Zn3^xv	178.179 (15)	Zn2^xxvii—Zn3—Zn2^v	57.790 (10)
Zn3^xi—La2—Zn3^xv	120.0	Zn3^iv—Zn3—Zn2^v	109.179 (11)
Zn3^xii—La2—Zn3^xv	120.0	Zn1^xxxviii—Zn3—Zn2^xl	58.393 (9)
Zn3^xiii—La2—Zn3^xv	58.179 (15)	Zn1—Zn3—Zn2^xl	140.07 (2)
Zn3^xiv—La2—Zn3^xv	61.821 (15)	Zn2^xxxix—Zn3—Zn2^xl	57.790 (10)
Mg2—La2—Zn1^xvi	130.141 (3)	Zn2^xxvii—Zn3—Zn2^xl	142.64 (2)
Mg2^ix—La2—Zn1^xvi	49.859 (3)	Zn3^iv—Zn3—Zn2^xl	109.179 (11)
Zn3^x—La2—Zn1^xvi	49.013 (4)	Zn2^v—Zn3—Zn2^xl	101.26 (2)
Zn3^xi—La2—Zn1^xvi	89.304 (6)	Zn1^xxxviii—Zn3—La2^xii	77.866 (11)
Zn3^xii—La2—Zn1^xvi	49.013 (4)	Zn1—Zn3—La2^xii	77.866 (11)
Zn3^xiii—La2—Zn1^xvi	131.915 (4)	Zn2^xxxix—Zn3—La2^xii	79.105 (14)
Zn3^xiv—La2—Zn1^xvi	89.304 (6)	Zn2^xxvii—Zn3—La2^xii	79.105 (14)
Zn3^xv—La2—Zn1^xvi	131.915 (4)	Zn3^iv—Zn3—La2^xii	60.910 (8)
Mg2—La2—Zn1^xvii	49.859 (4)	Zn2^v—Zn3—La2^xii	129.336 (12)
Mg2^ix—La2—Zn1^xvii	130.141 (4)	Zn2^xl—Zn3—La2^xii	129.336 (12)
Zn3^x—La2—Zn1^xvii	89.304 (6)	Zn1^xxxviii—Zn3—Zn3^xxxi	57.020 (7)
Zn3^xi—La2—Zn1^xvii	49.013 (4)	Zn1—Zn3—Zn3^xxxi	57.020 (7)
Zn3^xii—La2—Zn1^xvii	131.915 (4)	Zn2^xxxix—Zn3—Zn3^xxxi	108.146 (11)
Zn3^xiii—La2—Zn1^xvii	49.013 (4)	Zn2^xxvii—Zn3—Zn3^xxxi	108.146 (11)
Zn3^xiv—La2—Zn1^xvii	131.915 (4)	Zn3^iv—Zn3—Zn3^xxxi	120.0
Zn3^xv—La2—Zn1^xvii	89.304 (6)	Zn2^v—Zn3—Zn3^xxxi	107.796 (10)
Zn1^xvi—La2—Zn1^xvii	135.056 (2)	Zn2^xl—Zn3—Zn3^xxxi	107.796 (10)
Mg2—La2—Zn1^xviii	130.141 (4)	La2^xii—Zn3—Zn3^xxxi	59.090 (8)
Mg2^ix—La2—Zn1^xviii	49.859 (4)	Zn1^xxxviii—Zn3—La1	122.512 (8)
Zn3^x—La2—Zn1^xviii	89.304 (6)	Zn1—Zn3—La1	122.512 (8)
Zn3^xi—La2—Zn1^xviii	49.013 (4)	Zn2^xxxix—Zn3—La1	73.582 (11)
Zn3^xii—La2—Zn1^xviii	131.915 (4)	Zn2^xxvii—Zn3—La1	73.582 (11)
Zn3^xiii—La2—Zn1^xviii	49.013 (4)	Zn3^iv—Zn3—La1	63.955 (9)
Zn3^xiv—La2—Zn1^xviii	131.915 (4)	Zn2^v—Zn3—La1	69.926 (12)
Zn3^xv—La2—Zn1^xviii	89.304 (6)	Zn2^xl—Zn3—La1	69.926 (12)
Zn1^xvi—La2—Zn1^xviii	82.912 (4)	La2^xii—Zn3—La1	124.865 (15)
Zn1^xvii—La2—Zn1^xviii	80.282 (5)	Zn3^xxxi—Zn3—La1	176.045 (9)
Mg2—La2—Zn1^xix	49.859 (3)	Zn1^xxxviii—Zn3—Mg2^xii	56.69 (10)
Mg2^ix—La2—Zn1^xix	130.141 (3)	Zn1—Zn3—Mg2^xii	99.77 (11)
Zn3^x—La2—Zn1^xix	49.013 (4)	Zn2^xxxix—Zn3—Mg2^xii	57.29 (11)
Zn3^xi—La2—Zn1^xix	89.304 (6)	Zn2^xxvii—Zn3—Mg2^xii	101.49 (11)
Zn3^xii—La2—Zn1^xix	49.013 (4)	Zn3^iv—Zn3—Mg2^xii	63.97 (3)
Zn3^xiii—La2—Zn1^xix	131.915 (4)	Zn2^v—Zn3—Mg2^xii	154.82 (13)
Zn3^xiv—La2—Zn1^xix	89.304 (6)	Zn2^xl—Zn3—Mg2^xii	103.84 (13)
Zn3^xv—La2—Zn1^xix	131.915 (4)	La2^xii—Zn3—Mg2^xii	25.50 (13)
Zn1^xvi—La2—Zn1^xix	80.282 (5)	Zn3^xxxi—Zn3—Mg2^xii	62.38 (3)
Zn1^xvii—La2—Zn1^xix	82.912 (4)	La1—Zn3—Mg2^xii	121.06 (4)
Zn1^xviii—La2—Zn1^xix	135.056 (2)	Zn1^xxxviii—Zn3—Mg2^xxxiv	99.77 (11)
Mg2^i—La3—Mg2	180.000 (1)	Zn1—Zn3—Mg2^xxxiv	56.69 (10)
Mg2^i—La3—Zn3^xx	90.0	Zn2^xxxix—Zn3—Mg2^xxxiv	101.49 (11)
Mg2—La3—Zn3^xx	90.0	Zn2^xxvii—Zn3—Mg2^xxxiv	57.29 (11)
Mg2^i—La3—Zn3^xxi	90.000 (1)	Zn3^iv—Zn3—Mg2^xxxiv	63.97 (3)
Mg2—La3—Zn3^xxi	90.000 (1)	Zn2^v—Zn3—Mg2^xxxiv	103.84 (13)
Zn3^xx—La3—Zn3^xxi	66.116 (16)	Zn2^xl—Zn3—Mg2^xxxiv	154.82 (13)
Mg2^i—La3—Zn3^xxii	90.000 (1)	La2^xii—Zn3—Mg2^xxxiv	25.50 (13)
Mg2—La3—Zn3^xxii	90.000 (1)	Zn3^xxxi—Zn3—Mg2^xxxiv	62.38 (3)
Zn3^xx—La3—Zn3^xxii	53.884 (16)	La1—Zn3—Mg2^xxxiv	121.06 (4)
Zn3^xxi—La3—Zn3^xxii	120.0	Mg2^xii—Zn3—Mg2^xxxiv	51.0 (3)
Mg2^i—La3—Zn3^viii	90.000 (1)	La1—Mg1—Mg1^iii	180.000 (1)
Mg2—La3—Zn3^viii	90.000 (1)	La1—Mg1—Zn2^viii	105.7 (2)
Zn3^xx—La3—Zn3^viii	120.0	Mg1^iii—Mg1—Zn2^viii	74.3 (2)
Zn3^xxi—La3—Zn3^viii	53.884 (16)	La1—Mg1—Zn2	105.7 (2)
Zn3^xxii—La3—Zn3^viii	173.884 (16)	Mg1^iii—Mg1—Zn2	74.3 (2)
Mg2^i—La3—Zn3^iv	90.0	Zn2^viii—Mg1—Zn2	112.99 (19)
Mg2—La3—Zn3^iv	90.0	La1—Mg1—Zn2^v	105.7 (2)
Zn3^xx—La3—Zn3^iv	173.884 (16)	Mg1^iii—Mg1—Zn2^v	74.3 (2)
Zn3^xxi—La3—Zn3^iv	120.0	Zn2^viii—Mg1—Zn2^v	112.99 (19)
Zn3^xxii—La3—Zn3^iv	120.0	Zn2—Mg1—Zn2^v	112.99 (19)
Zn3^viii—La3—Zn3^iv	66.116 (16)	La1—Mg1—Mg1^i	0.0
Mg2^i—La3—Zn3^xxiii	90.0	Mg1^iii—Mg1—Mg1^i	180.000 (1)
Mg2—La3—Zn3^xxiii	90.0	Zn2^viii—Mg1—Mg1^i	105.7 (2)
Zn3^xx—La3—Zn3^xxiii	120.0	Zn2—Mg1—Mg1^i	105.7 (2)
Zn3^xxi—La3—Zn3^xxiii	173.884 (16)	Zn2^v—Mg1—Mg1^i	105.7 (2)
Zn3^xxii—La3—Zn3^xxiii	66.116 (16)	La1—Mg1—Zn2^iii	109.5 (2)
Zn3^viii—La3—Zn3^xxiii	120.0	Mg1^iii—Mg1—Zn2^iii	70.5 (2)
Zn3^iv—La3—Zn3^xxiii	53.884 (16)	Zn2^viii—Mg1—Zn2^iii	57.05 (8)
Mg2^i—La3—Zn2^xxiv	128.811 (9)	Zn2—Mg1—Zn2^iii	144.9 (5)
Mg2—La3—Zn2^xxiv	51.189 (9)	Zn2^v—Mg1—Zn2^iii	57.05 (8)
Zn3^xx—La3—Zn2^xxiv	49.226 (7)	Mg1^i—Mg1—Zn2^iii	109.5 (2)
Zn3^xxi—La3—Zn2^xxiv	49.226 (7)	La1—Mg1—Zn2^xxvii	109.5 (2)
Zn3^xxii—La3—Zn2^xxiv	87.618 (6)	Mg1^iii—Mg1—Zn2^xxvii	70.5 (2)
Zn3^viii—La3—Zn2^xxiv	87.618 (6)	Zn2^viii—Mg1—Zn2^xxvii	144.9 (5)
Zn3^iv—La3—Zn2^xxiv	133.999 (8)	Zn2—Mg1—Zn2^xxvii	57.05 (8)
Zn3^xxiii—La3—Zn2^xxiv	133.999 (8)	Zn2^v—Mg1—Zn2^xxvii	57.05 (8)
Mg2^i—La3—Zn2^xxv	51.189 (9)	Mg1^i—Mg1—Zn2^xxvii	109.5 (2)
Mg2—La3—Zn2^xxv	128.811 (9)	Zn2^iii—Mg1—Zn2^xxvii	109.5 (2)
Zn3^xx—La3—Zn2^xxv	49.226 (7)	La1—Mg1—Zn2^xxxvi	109.5 (2)
Zn3^xxi—La3—Zn2^xxv	49.226 (7)	Mg1^iii—Mg1—Zn2^xxxvi	70.5 (2)
Zn3^xxii—La3—Zn2^xxv	87.618 (6)	Zn2^viii—Mg1—Zn2^xxxvi	57.05 (8)
Zn3^viii—La3—Zn2^xxv	87.618 (6)	Zn2—Mg1—Zn2^xxxvi	57.05 (8)
Zn3^iv—La3—Zn2^xxv	133.999 (8)	Zn2^v—Mg1—Zn2^xxxvi	144.9 (5)
Zn3^xxiii—La3—Zn2^xxv	133.999 (8)	Mg1^i—Mg1—Zn2^xxxvi	109.5 (2)
Zn2^xxiv—La3—Zn2^xxv	77.622 (17)	Zn2^iii—Mg1—Zn2^xxxvi	109.5 (2)
Mg2^i—La3—Zn2	51.189 (9)	Zn2^xxvii—Mg1—Zn2^xxxvi	109.5 (2)
Mg2—La3—Zn2	128.811 (9)	La1—Mg1—La1^iii	180.0
Zn3^xx—La3—Zn2	133.999 (8)	Mg1^iii—Mg1—La1^iii	0.0
Zn3^xxi—La3—Zn2	87.618 (6)	Zn2^viii—Mg1—La1^iii	74.3 (2)
Zn3^xxii—La3—Zn2	133.999 (8)	Zn2—Mg1—La1^iii	74.3 (2)
Zn3^viii—La3—Zn2	49.226 (7)	Zn2^v—Mg1—La1^iii	74.3 (2)
Zn3^iv—La3—Zn2	49.226 (7)	Mg1^i—Mg1—La1^iii	180.000 (1)
Zn3^xxiii—La3—Zn2	87.618 (6)	Zn2^iii—Mg1—La1^iii	70.5 (2)
Zn2^xxiv—La3—Zn2	134.140 (6)	Zn2^xxvii—Mg1—La1^iii	70.5 (2)
Zn2^xxv—La3—Zn2	84.880 (13)	Zn2^xxxvi—Mg1—La1^iii	70.5 (2)
Mg2^i—La3—Zn2^xxvi	128.811 (9)	La2—Mg2—Mg2^ix	0.000 (1)
Mg2—La3—Zn2^xxvi	51.189 (9)	La2—Mg2—Zn1^xvii	108.40 (15)
Zn3^xx—La3—Zn2^xxvi	87.618 (6)	Mg2^ix—Mg2—Zn1^xvii	108.40 (15)
Zn3^xxi—La3—Zn2^xxvi	133.999 (8)	La2—Mg2—Zn1^xix	108.40 (15)
Zn3^xxii—La3—Zn2^xxvi	49.226 (7)	Mg2^ix—Mg2—Zn1^xix	108.40 (15)
Zn3^viii—La3—Zn2^xxvi	133.999 (8)	Zn1^xvii—Mg2—Zn1^xix	110.52 (15)
Zn3^iv—La3—Zn2^xxvi	87.618 (6)	La2—Mg2—Zn1^xli	108.40 (15)
Zn3^xxiii—La3—Zn2^xxvi	49.226 (7)	Mg2^ix—Mg2—Zn1^xli	108.40 (15)
Zn2^xxiv—La3—Zn2^xxvi	84.880 (13)	Zn1^xvii—Mg2—Zn1^xli	110.52 (15)
Zn2^xxv—La3—Zn2^xxvi	134.140 (6)	Zn1^xix—Mg2—Zn1^xli	110.52 (15)
Zn2—La3—Zn2^xxvi	134.140 (6)	La2—Mg2—Zn2^xxiv	110.20 (15)
Zn2^xxvii—Zn1—Zn2^xxviii	180.000 (8)	Mg2^ix—Mg2—Zn2^xxiv	110.20 (15)
Zn2^xxvii—Zn1—Zn2^xxix	120.187 (13)	Zn1^xvii—Mg2—Zn2^xxiv	56.34 (6)
Zn2^xxviii—Zn1—Zn2^xxix	59.813 (13)	Zn1^xix—Mg2—Zn2^xxiv	56.34 (6)
Zn2^xxvii—Zn1—Zn2^v	59.813 (13)	Zn1^xli—Mg2—Zn2^xxiv	141.4 (3)
Zn2^xxviii—Zn1—Zn2^v	120.187 (13)	La2—Mg2—Zn2^i	110.20 (15)
Zn2^xxix—Zn1—Zn2^v	180.000 (4)	Mg2^ix—Mg2—Zn2^i	110.20 (15)
Zn2^xxvii—Zn1—Zn3^xxx	62.489 (14)	Zn1^xvii—Mg2—Zn2^i	56.34 (6)
Zn2^xxviii—Zn1—Zn3^xxx	117.511 (14)	Zn1^xix—Mg2—Zn2^i	141.4 (3)
Zn2^xxix—Zn1—Zn3^xxx	118.803 (13)	Zn1^xli—Mg2—Zn2^i	56.34 (6)
Zn2^v—Zn1—Zn3^xxx	61.197 (13)	Zn2^xxiv—Mg2—Zn2^i	108.73 (15)
Zn2^xxvii—Zn1—Zn3^xxxi	117.511 (14)	La2—Mg2—Zn2^xxvi	110.20 (15)
Zn2^xxviii—Zn1—Zn3^xxxi	62.489 (14)	Mg2^ix—Mg2—Zn2^xxvi	110.20 (15)
Zn2^xxix—Zn1—Zn3^xxxi	61.197 (13)	Zn1^xvii—Mg2—Zn2^xxvi	141.4 (3)
Zn2^v—Zn1—Zn3^xxxi	118.803 (13)	Zn1^xix—Mg2—Zn2^xxvi	56.34 (6)
Zn3^xxx—Zn1—Zn3^xxxi	180.0	Zn1^xli—Mg2—Zn2^xxvi	56.34 (6)
Zn2^xxvii—Zn1—Zn3^xxxii	118.803 (13)	Zn2^xxiv—Mg2—Zn2^xxvi	108.73 (15)
Zn2^xxviii—Zn1—Zn3^xxxii	61.197 (13)	Zn2^i—Mg2—Zn2^xxvi	108.73 (15)
Zn2^xxix—Zn1—Zn3^xxxii	62.489 (14)	La2—Mg2—La3	180.0
Zn2^v—Zn1—Zn3^xxxii	117.511 (14)	Mg2^ix—Mg2—La3	180.000 (1)
Zn3^xxx—Zn1—Zn3^xxxii	65.961 (15)	Zn1^xvii—Mg2—La3	71.60 (15)
Zn3^xxxi—Zn1—Zn3^xxxii	114.039 (15)	Zn1^xix—Mg2—La3	71.60 (15)
Zn2^xxvii—Zn1—Zn3	61.197 (13)	Zn1^xli—Mg2—La3	71.60 (15)
Zn2^xxviii—Zn1—Zn3	118.803 (13)	Zn2^xxiv—Mg2—La3	69.80 (15)
Zn2^xxix—Zn1—Zn3	117.511 (14)	Zn2^i—Mg2—La3	69.80 (15)
Zn2^v—Zn1—Zn3	62.489 (14)	Zn2^xxvi—Mg2—La3	69.80 (15)
Zn3^xxx—Zn1—Zn3	114.039 (15)	La2—Mg2—Zn3^x	64.50 (13)
Zn3^xxxi—Zn1—Zn3	65.961 (15)	Mg2^ix—Mg2—Zn3^x	64.50 (13)
Zn3^xxxii—Zn1—Zn3	180.000 (19)	Zn1^xvii—Mg2—Zn3^x	97.03 (3)
Zn2^xxvii—Zn1—Mg2^xxxiii	117.41 (3)	Zn1^xix—Mg2—Zn3^x	53.21 (2)
Zn2^xxviii—Zn1—Mg2^xxxiii	62.59 (3)	Zn1^xli—Mg2—Zn3^x	152.17 (7)
Zn2^xxix—Zn1—Mg2^xxxiii	117.41 (3)	Zn2^xxiv—Mg2—Zn3^x	53.73 (2)
Zn2^v—Zn1—Mg2^xxxiii	62.59 (3)	Zn2^i—Mg2—Zn3^x	151.09 (5)
Zn3^xxx—Zn1—Mg2^xxxiii	70.10 (13)	Zn2^xxvi—Mg2—Zn3^x	99.33 (2)
Zn3^xxxi—Zn1—Mg2^xxxiii	109.90 (13)	La3—Mg2—Zn3^x	115.50 (13)
Zn3^xxxii—Zn1—Mg2^xxxiii	70.10 (13)	La2—Mg2—Zn3^xii	64.50 (13)
Zn3—Zn1—Mg2^xxxiii	109.90 (13)	Mg2^ix—Mg2—Zn3^xii	64.50 (13)
Zn2^xxvii—Zn1—Mg2^xxxiv	62.59 (3)	Zn1^xvii—Mg2—Zn3^xii	152.17 (7)
Zn2^xxviii—Zn1—Mg2^xxxiv	117.41 (3)	Zn1^xix—Mg2—Zn3^xii	53.21 (2)
Zn2^xxix—Zn1—Mg2^xxxiv	62.59 (3)	Zn1^xli—Mg2—Zn3^xii	97.03 (3)
Zn2^v—Zn1—Mg2^xxxiv	117.41 (3)	Zn2^xxiv—Mg2—Zn3^xii	99.33 (2)
Zn3^xxx—Zn1—Mg2^xxxiv	109.90 (13)	Zn2^i—Mg2—Zn3^xii	151.09 (5)
Zn3^xxxi—Zn1—Mg2^xxxiv	70.10 (13)	Zn2^xxvi—Mg2—Zn3^xii	53.73 (2)
Zn3^xxxii—Zn1—Mg2^xxxiv	109.90 (13)	La3—Mg2—Zn3^xii	115.50 (13)
Zn3—Zn1—Mg2^xxxiv	70.10 (13)	Zn3^x—Mg2—Zn3^xii	55.24 (7)
Mg2^xxxiii—Zn1—Mg2^xxxiv	180.0 (3)	La2—Mg2—Zn3^xi	64.50 (13)
Zn2^xxvii—Zn1—La2^xii	69.099 (10)	Mg2^ix—Mg2—Zn3^xi	64.50 (13)
Zn2^xxviii—Zn1—La2^xii	110.901 (10)	Zn1^xvii—Mg2—Zn3^xi	53.21 (2)
Zn2^xxix—Zn1—La2^xii	69.099 (10)	Zn1^xix—Mg2—Zn3^xi	97.03 (3)
Zn2^v—Zn1—La2^xii	110.901 (10)	Zn1^xli—Mg2—Zn3^xi	152.17 (7)
Zn3^xxx—Zn1—La2^xii	126.879 (11)	Zn2^xxiv—Mg2—Zn3^xi	53.73 (2)
Zn3^xxxi—Zn1—La2^xii	53.121 (11)	Zn2^i—Mg2—Zn3^xi	99.33 (2)
Zn3^xxxii—Zn1—La2^xii	126.879 (11)	Zn2^xxvi—Mg2—Zn3^xi	151.09 (5)
Zn3—Zn1—La2^xii	53.121 (11)	La3—Mg2—Zn3^xi	115.50 (13)
Mg2^xxxiii—Zn1—La2^xii	158.26 (15)	Zn3^x—Mg2—Zn3^xi	52.06 (6)
Mg2^xxxiv—Zn1—La2^xii	21.74 (15)	Zn3^xii—Mg2—Zn3^xi	102.82 (15)
Zn2^xxvii—Zn1—La2^xxxv	110.901 (10)

Symmetry codes: (i) x, y, −z+1/2; (ii) −x, −y, z+1/2; (iii) −x, −y, −z; (iv) x, x−y, z; (v) −x+y, −x, z; (vi) −x+y, y, z; (vii) −y, −x, z; (viii) −y, x−y, z; (ix) x, y, −z+3/2; (x) x−y, −y+1, −z+1; (xi) y, −x+y+1, −z+1; (xii) −x+1, −y+1, −z+1; (xiii) y, x, −z+1; (xiv) −x+1, −x+y+1, −z+1; (xv) x−y, x, −z+1; (xvi) x, y+1, z+1; (xvii) y, −x+y+1, z+1/2; (xviii) −y, x−y, z+1; (xix) −x+1, −y+1, z+1/2; (xx) x, y+1, z; (xxi) −y, −x+1, z; (xxii) −x+y+1, y+1, z; (xxiii) −x+y+1, −x+1, z; (xxiv) −x+y, −x+1, −z+1/2; (xxv) −x+y, −x+1, z; (xxvi) −y+1, x−y+1, −z+1/2; (xxvii) y, −x+y, −z; (xxviii) −y+1, x−y, z; (xxix) x−y+1, x, −z; (xxx) x−y, −y, −z; (xxxi) −x+y+1, y, z; (xxxii) −x+1, −y, −z; (xxxiii) x, y−1, −z+1/2; (xxxiv) −x+1, −y+1, z−1/2; (xxxv) x, y−1, z−1; (xxxvi) x−y, x, −z; (xxxvii) y, x, −z; (xxxviii) −x+1, −y, z+1/2; (xxxix) y, −x+y, z+1/2; (xl) −x+y, −x, −z+1/2; (xli) x−y, x, z+1/2.