Orthorhombic charge density wave on the tetragonal lattice of EuAl₄

EuAl₄ possesses the BaAl₄ crystal structure type with tetragonal symmetry I4/mmm. It undergoes a charge density wave (CDW) transition at T_CDW = 145 K and features four consecutive antiferromagnetic phase transitions below 16 K. Here we use single-crystal X-ray diffraction to determine the incommensurately modulated crystal structure of EuAl₄ in its CDW state. The CDW is shown to be incommensurate with modulation wave vector q = (0,0,0.1781 (3)) at 70 K. The symmetry of the incommensurately modulated crystal structure is orthorhombic with superspace group Fmmm(00σ)s00, where Fmmm is a subgroup of I4/mmm of index 2. Both the lattice and the atomic coordinates of the basic structure remain tetragonal. Symmetry breaking is entirely due to the modulation wave, where atoms Eu and Al1 have displacements exclusively along a, while the fourfold rotation would require equal displacement amplitudes along a and b. The calculated band structure of the basic structure and interatomic distances in the modulated crystal structure both indicate the Al atoms as the location of the CDW. The tem­per­ature dependence of the specific heat reveals an anomaly at T_CDW = 145 K of a magnitude similar to canonical CDW systems. The present discovery of orthorhombic symmetry for the CDW state of EuAl₄ leads to the suggestion of monoclinic instead of orthorhombic symmetry for the third AFM state.

1. Introduction

EuAl₄ has attracted attention because it develops a charge density wave (CDW) below T_CDW = 145.1 K and exhibits four successive magnetic transitions below 16 K (Nakamura et al., 2015; Shimomura et al., 2019). EuAl₄ adopts the BaAl₄ structure type that has symmetry according to the tetragonal space group I4/mmm (Parthé et al., 1983; Nakamura et al., 2015), as shown in Fig. 1. It belongs to a large family of isostructural compounds, including magnetic EuGa₄, fully ordered EuAl₂Ga₂ and nonmagnetic SrAl₄ and BaAl₄ (Nakamura et al., 2016; Stavinoha et al., 2018; Ōnuki et al., 2020). Recently, a symmetry-protected nontrivial topology of the electronic band structure was proposed for BaAl₄ (Wang et al., 2021). In the case of magnetic EuAl₄, a chiral spin structure, like skyrmions reported in some divalent Eu compounds, such as EuPtSi (Kaneko et al., 2019; Ōnuki et al., 2020), was proposed on the basis of the observation of the topological Hall resistivity and muon-spin rotation and relaxation (μSR) studies (Shang et al., 2021; Zhu et al., 2022). If such a nontrivial texture was confirmed, EuAl₄ would represent a rare case of a compound where one could observe the co-existence of exotic magnetic order and a CDW. Since these exotic electronic and spin structures depend on the symmetry, knowledge of the true symmetry of the crystal structure is thus of utmost importance for understanding non­trivial magnetic properties. Here we show that the CDW transition of EuAl₄ is accompanied by a lowering of the symmetry towards orthorhombic, and we present the incommensurately modulated CDW crystal structure.

Figure 1 The crystal structure of EuAl4 with the space group I4/mmm in the periodic phase at 250 K. Depicted is the I-centred unit cell with basis vectors aI, bI and cI. Brown spheres correspond to the Eu atoms, dark-blue spheres represent Al1 atoms and green spheres stand for Al2 atoms. The shortest interatomic distances are: d(Eu—Eu) = 4.3949 (2) Å, d(Al1—Al1) = 3.1077 (1) Å, d(Al2—Al1) = 2.664 (1) Å and d(Al2—Al2) = 2.568 (4) Å.

EuAl₄ is one of a few compounds (Schutte et al., 1993) where the lowering of the crystal symmetry at a phase transition is governed by the symmetry of the incommensurate modulation wave describing the CDW, while any lattice distortion could not be detected in the present high-resolution diffraction experiment with synchrotron radiation. This feature might explain why the lowering of symmetry has not been found in earlier studies on EuAl₄.

This behaviour is in contrast to other CDW materials, like Er₂Ir₃Si₅, Lu₂Ir₃Si₅ and BaFe₂Al₉, for which the CDW transitions are accompanied by large lattice distortions (Ramakrishnan et al., 2020, 2021; Meier et al., 2021).

The phenomenon of CDW was originally identified as a property of crystals with quasi-one-dimensional (1D) electron bands, such as NbSe₃ and K_0.3MoO₃ (Gruner, 1994; Monceau, 2012). A CDW is formed due to Fermi surface nesting (FSN), where the nesting vector of the periodic structure becomes the wave vector of the CDW of the metallic bands, as well as of the accompanying modulation of the atomic positions (periodic lattice distortion or PLD). The modulation wave vector can be commensurate or incommensurate with respect to the underlying periodic basic structure. More recent research has found that CDWs can develop in crystalline materials that lack the 1D property of their crystal structures and rather possess three-dimensionally (3D) structured electron bands. Alternate mechanisms have been proposed for the formation of CDWs in 3D compounds, including the mechanism of q-dependent electron–phonon coupling (EPC) (Zhu et al., 2015, 2017). Strongly correlated electron systems may also support the formation of CDWs (Chen et al., 2016). The latter are often found for rare-earth-containing intermetallic compounds, like the series of isostructural compounds R₅Ir₄Si₁₀ (R = rare earth) (Ramakrishnan & van Smaalen, 2017).

The interplay between CDWs and magnetism in rare-earth compounds continues to attract attention. A competition between these two symmetry-breaking phenomena can be expected, because both CDWs and magnetic order depend on the Fermi surface through FSN and the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between the localized magnetic moments of the 4f electrons, as it is found for EuAl₄ (Kobata et al., 2016). In the case of magnetoelastic coupling, the lattice distortion may couple to the PLD or the lattice distortion in the CDW state or to the EPC. Experimentally, the co-existence of a CDW and antiferromagnetic (AFM) order has been established for Er₅Ir₄Si₁₀ and Sm₂Ru₃Ge₅ (Galli et al., 2002; Kuo et al., 2020). The series of compounds RNiC₂ (R = Pr, Nd, Gd, Tb, Dy, Ho or Er) exhibit both CDW and AFM phase transitions (Roman et al., 2018; Shimomura et al., 2016; Kolincio et al., 2017; Maeda et al., 2019). SmNiC₂ is an exception in this series, since it develops ferromagnetic (FM) order below T_C = 17.7 K, at which transition the CDW is destroyed (Shimomura et al., 2009; Wölfel et al., 2010). Recently, co-existence of CDW and FM orders was found for the field-induced FM state of TmNiC₂ (Kolincio et al., 2020).

Magnetism of EuAl₄ is related to localized magnetic moments of the Eu atoms in their divalent state: the electronic configuration 4f⁷ implies J = S = 7/2 and L = 0, where J is the total angular momentum, S is the spin angular momentum and L is the orbital angular momentum (Wernick et al., 1967; Nakamura et al., 2015). This allows the study of the collective magnetism without single-ion anisotropy, as divalent Eu has zero orbital angular momentum. Magnetic interactions are governed by the RKKY interaction (Nakamura et al., 2015). Neutron diffraction has established that the AFM order involves an incommensurate modulation wave (Kaneko et al., 2021). Single-crystal X-ray diffraction (SXRD) has shown the co-existence of the incommensurate CDW modulation and AFM order (Shimomura et al., 2019). Furthermore, Shimomura et al. (2019) proposed a lowering of the lattice symmetry at the third magnetic transition towards Immm orthorhombic. This is essentially different from the present discovery of Fmmm orthorhombic symmetry below the CDW transition.

EuAl₄ possesses a 3D band structure with localized 4f electrons of Eu well below the Fermi surface (Kobata et al., 2016). The CDW mainly involves orbitals of the Al atoms (Kaneko et al., 2021). This is in agreement with the observation of a CDW with T_CDW = 243 K in isostructural SrAl₄, where nonmagnetic Sr replaces Eu (Nakamura et al., 2016; Niki et al., 2020). Here we present electronic band structure calculations for the tetragonal structure of EuAl₄. They confirm that the location of the CDW is on the Al atoms. They reveal a 3D band structure with a highly structured Fermi surface.

2. Experimental and computational details

Single crystals of EuAl₄ were synthesized by the Al self-flux method. The elements europium (Lieco, 99.9% purity) and aluminium (Alfa Aesar, 99.999%) were filled into an alumina crucible in the ratio 1:20. The crucible was sealed in an evacuated quartz glass ampoule. It was heated to a tem­per­ature of 1323 K and held at this tem­per­ature for 24 h. The crucible was then cooled to 1073 K over a period of 6 h and then cooled slowly at a rate of 2 K h⁻¹ to 923 K, at which point the crystals were separated from the molten metal by centrifugation. The 1:4 stoichiometry of the product was confirmed by energy-dispersive X-ray spectroscopy (EDX), as well as by structure refinement against SXRD data.

X-ray diffraction experiments were performed at Beamline P24 of PETRA III at DESY in Hamburg, employing radiation of wavelength 0.5000 Å. The tem­per­ature of the specimen was controlled by a CRYOCOOL open-flow helium gas cryostat. Complete data sets of the intensities of the Bragg reflections were measured at tem­per­atures of 250 K (tetragonal phase) and of 70 and 20 K (CDW phase). Each run of data collection comprises 3640 frames, corresponding to a rotation of the crystal over 364°, which was repeated 10 times. These data were binned to a data set of 364 frames of 1° of rotation and 10 s exposure time, using the SNBL toolbox (Dyadkin et al., 2016); see §S1 in the supporting information.

The EVAL15 software suite (Schreurs et al., 2010) was used for processing the SXRD data. At 250 K, a single run was collected at a crystal-to-detector distance of 110 mm and without a 2θ offset of the detector. At 70 and 20 K, a crystal-to-detector distance of 260 mm required two runs, with and without 2θ offset, respectively. The two binned runs for 70 K and those for 20 K were integrated separately, and subsequently merged in the module ANY of EVAL15. SADABS (Sheldrick, 2008) was used for scaling and absorption correction with Laue symmetry 4/mmm for the 250 K data and mmm for the 70 and 20 K data. The reflection file produced was imported into JANA2006 (Petricek et al., 2014, 2016). Table 1 gives the crystallographic information.

Table 1
Crystallographic data of crystal A of EuAl₄ at 250, 70 and 20 K

Refinement method used: least-squares on F. The superspace group (SSG; No.) is given according to Stokes et al. (2011).

Temperature (K)	250	70	20
Crystal system	Tetragonal	Orthorhombic	Orthorhombic
Space group; SSG	I4/mmm	Fmmm(00σ)s00	Fmmm(00σ)s00
No.	139	69.1.17.2	69.1.17.2
a (Å)	4.3949 (1)	6.1992 (4)	6.1991 (3)
b (Å)	4.3949	6.2001 (4)	6.1987 (4)
c (Å)	11.1607 (3)	11.1477 (3)	11.1488 (4)
Volume (Å^3)	215.57 (1)	428.47 (4)	428.41 (4)
Wavevector, qz	–	0.1781 (3)	0.1741 (2)
Z	2	4	4
Wavelength (Å)	0.50000	0.50000	0.50000
Detector distance (mm)	110	260	260
2θ-offset (°)	0	0, 25	0, 25
χ-offset (°)	−60	−60	−60
Rotation per image (°)	1	1	1
[sin(θ)/λ]max (Å^−1)	0.682610	0.748910	0.749031
Absorption, μ (mm^−1)	5.8373	5.9090	5.9100
Tmin, Tmax	0.3211, 0.3712	0.3209, 0.3732	0.3192, 0.3676
Criterion of observability	I > 3σ(I)	I > 3σ(I)	I > 3σ(I)
Number of main reflections
measured	1407	473	470
unique (obs/all)	109/109	174/174	176/176
Number of satellites
measured	–	929	928
unique (obs/all)	–	279/316	263/322
Rint main (obs/all)	0.0374/0.0374	0.0136/0.0136	0.0188/0.0188
Rint sat (obs/all)	–	0.0581/0.0588	0.0606/0.0616
No. of parameters	9	18	18
RF main (obs)	0.0147	0.0165	0.0213
RF sat (obs)	–	0.0369	0.0311
wRF main (all)	0.0214	0.0203	0.0230
wRF sat (all)	–	0.0395	0.0336
wRF all (all)	0.0214	0.0245	0.0250
GoF (obs/all)	1.53/1.53	1.13/1.09	0.93/0.88
Δρmin, Δρmax (e Å^−3)	−1.35, 1.15	−2.40, 3.58	−1.49, 1.58

The magnetic susceptibility χ(T) has been measured for tem­per­atures in the range 2.5–300 K, using a commercial SQUID magnetometer (MPMS5 by Quantum Design, USA). Measurements were made in fields of 0.1 and 0.5 T.

The specific heat, C_p(T), was measured from 220 to 8 K by the thermal relaxation method, using a physical property measuring system (PPMS, Quantum Design, USA).

Density functional theory (DFT)-based calculations were performed within the generalized gradient approximation (GGA) using the projector augmented (PAW) wave method, as implemented in the Vienna Ab-initio Simulation Package (VASP) (Kresse & Joubert, 1999; Kresse & Furthmüller, 1996). The Perdew–Burke–Ernzerhof (PBE) functional was used to consider the exchange–correlation effects (Perdew et al., 1996). An energy cut-off of 380 eV was used for the plane-wave basis set, and a Γ-centred 9 × 9 × 9 k mesh was employed for the bulk Brillouin zone sampling. Spin-orbit coupling effects were considered in all the calculations. We employed Eu²⁺ by considering the remaining 4f electrons as core electrons. A tight-binding Hamiltonian was generated to compute the Fermi surface on a finer k grid (Marzari & Vanderbilt, 1997). The FermiSurfer software package was used to visualize the Fermi surface (Kawamura, 2019).

3. Discussion

3.1. Analysis of the CDW structure

SXRD at 250 K confirmed the I4/mmm crystal structure of EuAl₄. The SXRD data at 70 K revealed satellite reflections at positions that can be described by the modulation wave vector q = (0,0,0.1781 (3)), in agreement with the results of Nakamura et al. (2015) and Shimomura et al. (2019). Visualization of the SXRD data was done with aid of CrysAlis PRO (Rigaku OD, 2019). Figs. 2(a) and 2(b) show a small part of the (0,k,l) plane of the reconstructed reciprocal lattice. Satellite reflections along c* are clearly visible at 70 K [Fig. 2(b)]. Upon further cooling to 20 K, there is a reduction by 0.004 in the σ₃ component of the modulation wave vector, in agreement with Shimomura et al. (2019). Higher-order satellite reflections have not been observed, probably because of the limited dynamic range in our experiment [compare to Shimomura et al. (2019)].

Figure 2 Excerpt of the reconstructed reciprocal layer (0,k,l) for SXRD data measured at (a) T = 250 K and (b) T = 70 K. Indices are given for several main reflections. Panel (b) is better resolved than panel (a) because of the longer crystal-to-detector distance at 70 K. Dark bands are due to insensitive pixels between the active modules of the PILATUS3 X CdTe 1M detector.

We note that the lattice parameters in the CDW phase do not give evidence for an orthorhombic lattice distortion. This could explain why earlier work has not found this symmetry lowering.

In order to determine the crystal structure of the CDW phase, we have tested different superspace groups for its symmetry (see Table S2 in the supporting information). It is noticed that the tetragonal lattice allows two fundamentally different orthorhombic lattices as subgroups: Immm preserves the mirror planes perpendicular to the a and b axes of I4/mmm, while Fmmm preserves the diagonal mirror planes. These properties also explain the different numbers of unique reflections with correspondingly different redundancies for averaging in the two symmetries, because coverage of reciprocal space is incomplete in the present experiment. Table 2 provides the crystallographic data for three of the refined crystal structures (compare Table S2 in the supporting information). The three models, i.e. A, B and C, are discussed below.

Table 2
Crystallographic data for the three models for the modulated crystal structure at 70 K, based on different superspace groups

Criterion of observability: I > 3σ(I).

Model	A	B	C
a (Å)	4.3834 (3)	4.3835 (3)	6.1992 (4)
b (Å)	4.3834	4.3841 (3)	6.2001 (4)
c (Å)	11.1488 (4)	11.1475 (3)	11.1477 (3)
V (Å^3)	214.21 (2)	214.23 (2)	428.47 (4)
q	0.1782 (3)c*	0.1781 (3)c*	0.1781 (3)c*
SSG	I4/mmm(00σ)0000	Immm(00σ)s00	Fmmm(00σ)s00
Rint main (obs/all)%	1.53/1.53	1.28/1.28	1.36/1.36
Rint sat (obs/all)%	7.43/7.49	6.75/6.85	5.81/5.88
RF main (obs/all)%	4.37/4.37	1.96/1.96	1.65/1.65
RF sat (obs/all)%	60.46/70.53	5.25/5.83	3.69/4.05
Unique main (obs/all)	130/130	225/225	174/174
Unique sat (obs/all)	215/254	365/425	279/316
No. of parameters	13	19	18

3.1.1. Model A

In the diffraction pattern, we did not observe any splitting of the main or satellite reflections, where split reflections would indicate a twinned crystal of lower symmetry. Also, we did not find a distortion in the lattice parameters, as it would occur for a single-domain crystal of lower symmetry. Furthermore, the preservation of tetragonal symmetry within the CDW phase was reported in the literature (Nakamura et al., 2015; Shimomura et al., 2019). Therefore, initial data processing was performed under the assumption of tetragonal symmetry, employing point group 4/mmm for scaling and absorption correction in SADABS (Sheldrick, 2008). Structure refinements of the incommensurately modulated structure were performed with a model with superspace group I4/mmm(00σ)0000. Table 2 shows that R_int, as well as R_F, for the main reflections are reasonably low, indicating that the average structure of the CDW phase is still tetragonal in good approximation. This conclusion is reinforced by the fact that refinement of the average structure against main reflections leads to an R_F value of 1.55%, an excellent fit. However, the R_F value is 60.46% for the satellite reflections. This high value indicates that the satellite reflections are not well fitted and that the CDW modulation does not have tetragonal symmetry.

This makes Model A an unsuitable candidate for the incommensurate CDW structure. Other tetragonal superspace groups were also tested, leading to similar failures in describing the modulation wave or with reflection conditions violated by the measured SXRD data (see Table S2 in the supporting information). As a result, we can rule out tetragonal symmetry for the modulated CDW crystal structure.

3.1.2. Model B

As a second model we considered a lowering of the symmetry from tetragonal I4/mmm to its orthorhombic subgroup Immm. This orthorhombic point symmetry was used for scaling and absorption correction of the SXRD data in SADABS (Sheldrick, 2008). The CDW phase transition allows for pseudomerohedral twinning of two differently oriented domains on the tetragonal lattice, that are related by the missing fourfold rotation (Parsons, 2003). Since split reflections or a lattice distortion could not be detected in the SXRD data, all Bragg reflections have contributions from both domains. The structure refinement of a model in superspace group Immm(00σ)s00 has lead to a twin volume ratio of 0.485:0.515, thus explaining the nearly tetragonal point symmetry of the SXRD data. R values indicate a good fit to the SXRD data for this model (Table 2). As a result, this model is a prime candidate for describing the incommensurately modulated crystal structure of the CDW phase.

3.1.3. Model C

As the last model we present model C with symmetry according to Fmmm, the other orthorhombic subgroup, which now preserves the diagonal mirror planes of I4/mmm. Scaling and absorption correction of the SXRD data was performed with SADABS according to the differently oriented point group mmm (Sheldrick, 2008). Again, two domains are possible that are related by the missing fourfold rotation. The structure refinement of a model in superspace group Fmmm(00σ)s00 has lead to a twin volume ratio of 0.454 (4):0.546, thus explaining the nearly tetragonal point symmetry of the SXRD data. R values indicate an excellent fit to the SXRD data for this model (Table 2), which is significantly better than that of model B. Furthermore, the refined parameters possess slightly smaller s.u. values in model C than in model B, while the number of parameters is one smaller in model C (Tables S4 and S5 in the supporting information). Therefore, the best fit to the SXRD data has been obtained for a modulated crystal structure with symmetry according to the superspace group Fmmm(00σ)s00. Fmmm(00σ)0s0 is an alternate setting of this superspace group, while all other symmetries lead to a worse fit to the SXRD data (Table S2 in the supporting information).

Recently, Kaneko et al. (2021) proposed that the CDW of EuAl₄ involves displacements of the Al atoms perpendicular to c, while Eu would not be involved in the PLD. The present crystal structure involves atomic modulations exclusively perpendicular to c, as it is enforced by the superspace symmetry (Table S5). However, the modulation amplitudes are of comparable magnitude for all three atoms, i.e. Eu, Al1 and Al2. Nevertheless, a non-zero modulation amplitude is not evidence by itself that the involved atom must contribute electronic states to the CDW. The atomic modulation may also be caused by the elastic coupling to other atoms that are carrying the CDW. In EuAl₄, the shortest interatomic distances are between Al2 atoms and Al1–Al2 (Fig. 3). They are hardly modulated and form a two-dimensional (2D) network of Al perpendicular to c (Fig. 1). The largest modulation is found for the next shorter Al—Al distance between Al1 atoms (Fig. 3). This strong modulation suggests that the CDW resides on the layers of Al atoms. Eu is elastically coupled to Al1 and Al2 (Fig. S2) and is not part of the CDW. The t plots of interatomic distances cannot elaborate on the precise location: the CDW resides either on the Al1 atoms or on a network of Al1 and Al2 atoms (Fig. 3).

Figure 3 t-Plot of the interatomic distances (Å) d(Al1—Al1), d(Al2—Al1) and d(Al2—Al2) at 70 K, where the first atom is the central atom. The number on each curve is the number of the symmetry operator that is applied to the second atom of the bond pair. Symmetry operators are listed in Table S6 in the supporting information.

3.2. Electronic structure and Fermi surface

Fig. 4(a) shows the calculated band structure along the high-symmetry directions in the primitive Brillouin zone of the periodic crystal structure of EuAl₄ with I4/mmm symmetry. Both the valence and conduction bands cross the Fermi level E_F, resolving its metallic ground state. Importantly, the bands along Γ–Z have a substantial energy dispersion. This indicates the 3D nature of the Fermi surface as discussed below. There is a Dirac nodal crossing above the Fermi level along the Γ–Z direction, which is protected by C_4z rotational symmetry. EuAl₄ thus realizes a Dirac semimetallic state. To resolve the electronic states near E_F, we present the atom-projected density of states (PDOS) in Fig. 4(b); Eu PDOS is in blue and Al PDOS is in red. The Al states are dominant at E_F, indicating that Al atoms are predominantly metallic and more likely undergo CDW modulations, in agreement with the analysis of PLD (§3.1) and the literature. PDOS of Eu is comprised of d states at the Fermi level, while 4f states are well below E_F, in agreement with the literature (Kobata et al., 2016).

Figure 4 (a) Bulk band structure and (b) density-of-states (DOS) of EuAl4. The dashed lines in parts (a) and (b) mark the Fermi level at energy (E) zero. The calculated (c) hole (blue) and (d) electron (yellow) Fermi pockets in the primitive bulk Brillouin zone. Three-dimensionally (3D) structured hole and electron Fermi pockets are resolved.

We present the calculated Fermi pockets associated with the valence (h⁺) and conduction states (e⁻) in Figs. 4(c) and 4(d). They reveal a hole pocket centred on Γ and an electron Fermi pocket centred on Z. Both Fermi pockets are highly structured. The e⁻ Fermi pocket suggests the possibility of nesting perpendicular to the c axes. For the h⁺ pocket, a possible FSN is not clearly resolved. It should however be noted that because of the 3D nature of the Fermi surface, the nesting may have a complicated structure. These results do not clearly indicate FSN as a mechanism for the formation of the CDW state in EuAl₄.

3.3. Magnetic susceptibility

The tem­per­ature dependence of the magnetic susceptibility, measured with magnetic fields of 0.1 and 0.5 T, is shown for 2.4–300 K in Fig. S1 of the supporting information. Any change of the susceptibility at the CDW transition (e.g. as a change of Pauli paramagnetism) is masked by the large value of the paramagnetic susceptibility. However, the low-tem­per­ature data reveal an AFM transition below 16 K, which agrees with the previously published value (Nakamura et al., 2015).

3.4. Specific heat

The tem­per­ature dependence of the specific heat (C_p) is shown for 8–210 K in Fig. 5. The high-tem­per­ature data clearly reveal a small broad jump of ΔC_p = 2.5 J mol⁻¹ K⁻¹ at 145 K, suggesting a thermodynamic phase transition (CDW) at 145 K. Such an anomaly in the tem­per­ature dependence of the specific heat is consistent with that observed in canonical CDW systems, like NbSe₃ (Tomić et al., 1981). The low-tem­per­ature data display multiple AFM transitions, which have also been observed in earlier studies (Nakamura et al., 2015).

Figure 5 Temperature dependence of the specific heat Cp from 8 to 210 K. The lower inset (a) provides an enlarged view around the anomaly at 145 K, where ΔC = 2.5 J mol^−1 K^−1. The upper inset (b) displays Cp versus T at low tem­per­atures in the range 8–25 K.

4. Conclusions

EuAl₄ possesses the BaAl₄ crystal structure type with tetragonal symmetry I4/mmm. It undergoes a CDW transition at T_CDW = 145 K. Here we have presented the incommensurately modulated crystal structure of EuAl₄ in its CDW state. Structure refinements according to the superspace approach have shown that: (i) the modulation is incommensurate with modulation wave vector q = (0,0,0.1781 (3)) at 70 K, in agreement with Shimomura et al. (2019); and (ii) the symmetry of the CDW crystal structure is orthorhombic with superspace group Fmmm(00σ)s00, where Fmmm is a subgroup of I4/mmm of index 2. Despite this group–subgroup relation, we did not find any lattice distortion in the SXRD data. In addition, the atomic positions of the basic structure of Fmmm(00σ)s00 still obey the I4/mmm symmetry (Table S4). Symmetry breaking is entirely in the modulation wave (CDW and PLD), where atoms Eu and Al1 have displacements exclusively along a of the F-centred unit cell (Table S5), while the fourfold rotation would require equal displacement amplitudes along a and b.

One interesting question is the location of the CDW. Analysis of the modulation of interatomic distances (§3.1), as well as features of the electronic band structure (§3.2), have indicated the Al atoms as supporting the CDW, in agreement with the literature (Kobata et al., 2016; Kaneko et al., 2021).

Compounds of rare earth (R) and transition metals, like R₅Ir₄Si₁₀ and R₂Ir₃Si₅, contain highly correlated electron systems, with accompanying influence on the mechanism of formation of CDWs. In EuAl₄, the majority element is the light p-block metal aluminium. Band structure calculations have shown that simple FSN is not a possible mechanism of CDW formation, in agreement with Kobata et al. (2016). Furthermore, the weak anomaly in C_p(T) near T_CDW is similar to anomalies of canonical CDW materials and it is much smaller than observed for the rare-earth–transition-metal base compounds; again this would support the FSN mechanism. An alternative possibility is that the CDW is related to the nesting of nontrivial bands that are present in the band structure (Shi et al., 2021; Chiu et al., 2022).

The present discovery of orthorhombic symmetry for the CDW state of EuAl₄ is important for modelling of the electronic properties of the CDW state, as well as for identifying the correct magnetic order and understanding the magnetic properties of the four AFM states below 16 K.

Recent work has used tetragonal symmetry for analysing the AFM states (Shang et al., 2021; Kaneko et al., 2021). Alternatively, Shimomura et al. (2019) have proposed orthorhombic Immm symmetry for the third AFM state. This orthorhombic subgroup incorporates the perpendicular mirror planes of I4/mmm, while presently found Fmmm is based on the diagonal mirror planes of I4/mmm. On the other hand, Shimomura et al. (2019) report peak splitting in neutron diffraction into `three maxima.' Together with the present observation of lowering of symmetry at the CDW transition, this suggests that the third AFM state could have monoclinic symmetry (c unique) instead of orthorhombic symmetry, since, apparently, both the diagonal and perpendicular mirror planes are lost. Establishing the lattice symmetries in the magnetically ordered phases would require full structural analysis at tem­per­atures below 15 K.

Supporting information

Computing details

(I)

Crystal data

Al4Eu	Dx = 4.004 Mg m^−3
Mr = 259.9	Synchrotron radiation, λ = 0.5 Å
Tetragonal, I4/mmm	Cell parameters from 1000 reflections
Hall symbol: -I 4;-2	θ = 1.5–20°
a = 4.3949 (1) Å	µ = 5.87 mm^−1
c = 11.1607 (3) Å	T = 250 K
V = 215.57 (1) Å^3	Irregular, black
Z = 2	0.1 × 0.06 × 0.02 mm
F(000) = 230

Data collection

Huber four-circle diffractometer	109 independent reflections
Radiation source: synchrotron	109 reflections with I > 3σ(I)
Si111 and Si311 monochromator	Rint = 0.037
area detector with phi scans	θmax = 20.0°, θmin = 2.6°
Absorption correction: empirical (using intensity measurements) SADABS, Program for Empirical Absorption Correction of Area Detector Data, G. M. Sheldrick, 1996	h = −6→6
Tmin = 0.321, Tmax = 0.371	k = −6→6
1407 measured reflections	l = −14→14

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.015	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
wR(F^2) = 0.021	(Δ/σ)max = 0.0001
S = 1.53	Δρmax = 1.15 e Å^−3
109 reflections	Δρmin = −1.35 e Å^−3
9 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 80 (70)

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

	x	y	z	Uiso*/Ueq
Eu1	0	0	0	0.0098 (2)
Al1	0	0.5	0.25	0.0107 (5)
Al2	0	0	0.3849 (2)	0.0102 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Eu1	0.0083 (3)	0.0083 (3)	0.0126 (4)	0	0	0
Al1	0.0112 (8)	0.0112 (8)	0.0098 (10)	0	0	0
Al2	0.0103 (8)	0.0103 (8)	0.0099 (10)	0	0	0

Geometric parameters (Å, º)

Eu1—Eu1^i	4.3949 (2)	Al1—Al1^iii	4.3949 (2)
Eu1—Eu1^ii	4.3949 (2)	Al1—Al1^iv	4.3949 (2)
Eu1—Eu1^iii	4.3949 (2)	Al1—Al1^vii	3.1077 (1)
Eu1—Eu1^iv	4.3949 (2)	Al1—Al1^xviii	3.1077 (1)
Eu1—Al1^ii	3.5516 (1)	Al1—Al1^viii	3.1077 (1)
Eu1—Al1	3.5516 (1)	Al1—Al1^xix	3.1077 (1)
Eu1—Al1^v	3.5516 (1)	Al1—Al2	2.6640 (14)
Eu1—Al1^vi	3.5516 (1)	Al1—Al2^iii	2.6640 (14)
Eu1—Al1^vii	3.5516 (1)	Al1—Al2^xi	4.629 (2)
Eu1—Al1^viii	3.5516 (1)	Al1—Al2^xii	4.629 (2)
Eu1—Al1^ix	3.5516 (1)	Al1—Al2^xx	4.629 (2)
Eu1—Al1^x	3.5516 (1)	Al1—Al2^xxi	4.629 (2)
Eu1—Al2	4.296 (3)	Al1—Al2^xv	2.6640 (14)
Eu1—Al2^v	3.3625 (10)	Al1—Al2^xvii	2.6640 (14)
Eu1—Al2^xi	3.3625 (10)	Al2—Al2^i	4.3949 (2)
Eu1—Al2^vi	3.3625 (10)	Al2—Al2^ii	4.3949 (2)
Eu1—Al2^xii	3.3625 (10)	Al2—Al2^iii	4.3949 (2)
Eu1—Al2^xiii	4.296 (3)	Al2—Al2^iv	4.3949 (2)
Eu1—Al2^xiv	3.3625 (10)	Al2—Al2^xx	2.568 (4)
Eu1—Al2^xv	3.3625 (10)	Al2—Al2^xiv	4.328 (2)
Eu1—Al2^xvi	3.3625 (10)	Al2—Al2^xv	4.328 (2)
Eu1—Al2^xvii	3.3625 (10)	Al2—Al2^xvi	4.328 (2)
Al1—Al1^i	4.3949 (2)	Al2—Al2^xvii	4.328 (2)
Al1—Al1^ii	4.3949 (2)
Eu1^i—Eu1—Eu1^ii	90	Al1^ii—Al1—Al2^xx	61.660 (15)
Eu1^i—Eu1—Eu1^iii	90	Al1^ii—Al1—Al2^xxi	118.340 (15)
Eu1^i—Eu1—Eu1^iv	180	Al1^ii—Al1—Al2^xv	90
Eu1^i—Eu1—Al1^ii	90	Al1^ii—Al1—Al2^xvii	90
Eu1^i—Eu1—Al1	90	Al1^iii—Al1—Al1^iv	90
Eu1^i—Eu1—Al1^v	51.7772 (10)	Al1^iii—Al1—Al1^vii	135.0000 (9)
Eu1^i—Eu1—Al1^vi	128.2228 (10)	Al1^iii—Al1—Al1^xviii	45.0000 (9)
Eu1^i—Eu1—Al1^vii	51.7772 (10)	Al1^iii—Al1—Al1^viii	135.0000 (9)
Eu1^i—Eu1—Al1^viii	128.2228 (10)	Al1^iii—Al1—Al1^xix	45.0000 (9)
Eu1^i—Eu1—Al1^ix	90	Al1^iii—Al1—Al2	145.57 (4)
Eu1^i—Eu1—Al1^x	90	Al1^iii—Al1—Al2^iii	34.43 (4)
Eu1^i—Eu1—Al2	90	Al1^iii—Al1—Al2^xi	90
Eu1^i—Eu1—Al2^v	49.193 (14)	Al1^iii—Al1—Al2^xii	90
Eu1^i—Eu1—Al2^xi	49.193 (14)	Al1^iii—Al1—Al2^xx	118.340 (15)
Eu1^i—Eu1—Al2^vi	130.807 (14)	Al1^iii—Al1—Al2^xxi	61.660 (15)
Eu1^i—Eu1—Al2^xii	130.807 (14)	Al1^iii—Al1—Al2^xv	90
Eu1^i—Eu1—Al2^xiii	90	Al1^iii—Al1—Al2^xvii	90
Eu1^i—Eu1—Al2^xiv	49.193 (14)	Al1^iv—Al1—Al1^vii	135.0000 (9)
Eu1^i—Eu1—Al2^xv	49.193 (14)	Al1^iv—Al1—Al1^xviii	135.0000 (9)
Eu1^i—Eu1—Al2^xvi	130.807 (14)	Al1^iv—Al1—Al1^viii	45.0000 (9)
Eu1^i—Eu1—Al2^xvii	130.807 (14)	Al1^iv—Al1—Al1^xix	45.0000 (9)
Eu1^ii—Eu1—Eu1^iii	180	Al1^iv—Al1—Al2	90
Eu1^ii—Eu1—Eu1^iv	90	Al1^iv—Al1—Al2^iii	90
Eu1^ii—Eu1—Al1^ii	51.7772 (10)	Al1^iv—Al1—Al2^xi	118.340 (15)
Eu1^ii—Eu1—Al1	128.2228 (10)	Al1^iv—Al1—Al2^xii	61.660 (15)
Eu1^ii—Eu1—Al1^v	90	Al1^iv—Al1—Al2^xx	90
Eu1^ii—Eu1—Al1^vi	90	Al1^iv—Al1—Al2^xxi	90
Eu1^ii—Eu1—Al1^vii	90	Al1^iv—Al1—Al2^xv	145.57 (4)
Eu1^ii—Eu1—Al1^viii	90	Al1^iv—Al1—Al2^xvii	34.43 (4)
Eu1^ii—Eu1—Al1^ix	51.7772 (10)	Al1^vii—Al1—Al1^xviii	90.0000 (18)
Eu1^ii—Eu1—Al1^x	128.2228 (10)	Al1^vii—Al1—Al1^viii	90.0000 (18)
Eu1^ii—Eu1—Al2	90	Al1^vii—Al1—Al1^xix	180
Eu1^ii—Eu1—Al2^v	49.193 (14)	Al1^vii—Al1—Al2	54.32 (2)
Eu1^ii—Eu1—Al2^xi	130.807 (14)	Al1^vii—Al1—Al2^iii	125.68 (2)
Eu1^ii—Eu1—Al2^vi	49.193 (14)	Al1^vii—Al1—Al2^xi	70.387 (10)
Eu1^ii—Eu1—Al2^xii	130.807 (14)	Al1^vii—Al1—Al2^xii	109.613 (10)
Eu1^ii—Eu1—Al2^xiii	90	Al1^vii—Al1—Al2^xx	70.387 (10)
Eu1^ii—Eu1—Al2^xiv	49.193 (14)	Al1^vii—Al1—Al2^xxi	109.613 (10)
Eu1^ii—Eu1—Al2^xv	130.807 (14)	Al1^vii—Al1—Al2^xv	54.32 (2)
Eu1^ii—Eu1—Al2^xvi	49.193 (14)	Al1^vii—Al1—Al2^xvii	125.68 (2)
Eu1^ii—Eu1—Al2^xvii	130.807 (14)	Al1^xviii—Al1—Al1^viii	180
Eu1^iii—Eu1—Eu1^iv	90	Al1^xviii—Al1—Al1^xix	90.0000 (18)
Eu1^iii—Eu1—Al1^ii	128.2228 (10)	Al1^xviii—Al1—Al2	125.68 (2)
Eu1^iii—Eu1—Al1	51.7772 (10)	Al1^xviii—Al1—Al2^iii	54.32 (2)
Eu1^iii—Eu1—Al1^v	90	Al1^xviii—Al1—Al2^xi	70.387 (10)
Eu1^iii—Eu1—Al1^vi	90	Al1^xviii—Al1—Al2^xii	109.613 (10)
Eu1^iii—Eu1—Al1^vii	90	Al1^xviii—Al1—Al2^xx	109.613 (10)
Eu1^iii—Eu1—Al1^viii	90	Al1^xviii—Al1—Al2^xxi	70.387 (10)
Eu1^iii—Eu1—Al1^ix	128.2228 (10)	Al1^xviii—Al1—Al2^xv	54.32 (2)
Eu1^iii—Eu1—Al1^x	51.7772 (10)	Al1^xviii—Al1—Al2^xvii	125.68 (2)
Eu1^iii—Eu1—Al2	90	Al1^viii—Al1—Al1^xix	90.0000 (18)
Eu1^iii—Eu1—Al2^v	130.807 (14)	Al1^viii—Al1—Al2	54.32 (2)
Eu1^iii—Eu1—Al2^xi	49.193 (14)	Al1^viii—Al1—Al2^iii	125.68 (2)
Eu1^iii—Eu1—Al2^vi	130.807 (14)	Al1^viii—Al1—Al2^xi	109.613 (10)
Eu1^iii—Eu1—Al2^xii	49.193 (14)	Al1^viii—Al1—Al2^xii	70.387 (10)
Eu1^iii—Eu1—Al2^xiii	90	Al1^viii—Al1—Al2^xx	70.387 (10)
Eu1^iii—Eu1—Al2^xiv	130.807 (14)	Al1^viii—Al1—Al2^xxi	109.613 (10)
Eu1^iii—Eu1—Al2^xv	49.193 (14)	Al1^viii—Al1—Al2^xv	125.68 (2)
Eu1^iii—Eu1—Al2^xvi	130.807 (14)	Al1^viii—Al1—Al2^xvii	54.32 (2)
Eu1^iii—Eu1—Al2^xvii	49.193 (14)	Al1^xix—Al1—Al2	125.68 (2)
Eu1^iv—Eu1—Al1^ii	90	Al1^xix—Al1—Al2^iii	54.32 (2)
Eu1^iv—Eu1—Al1	90	Al1^xix—Al1—Al2^xi	109.613 (10)
Eu1^iv—Eu1—Al1^v	128.2228 (10)	Al1^xix—Al1—Al2^xii	70.387 (10)
Eu1^iv—Eu1—Al1^vi	51.7772 (10)	Al1^xix—Al1—Al2^xx	109.613 (10)
Eu1^iv—Eu1—Al1^vii	128.2228 (10)	Al1^xix—Al1—Al2^xxi	70.387 (10)
Eu1^iv—Eu1—Al1^viii	51.7772 (10)	Al1^xix—Al1—Al2^xv	125.68 (2)
Eu1^iv—Eu1—Al1^ix	90	Al1^xix—Al1—Al2^xvii	54.32 (2)
Eu1^iv—Eu1—Al1^x	90	Al2—Al1—Al2^iii	111.15 (6)
Eu1^iv—Eu1—Al2	90	Al2—Al1—Al2^xi	119.84 (4)
Eu1^iv—Eu1—Al2^v	130.807 (14)	Al2—Al1—Al2^xii	119.84 (4)
Eu1^iv—Eu1—Al2^xi	130.807 (14)	Al2—Al1—Al2^xx	27.23 (5)
Eu1^iv—Eu1—Al2^vi	49.193 (14)	Al2—Al1—Al2^xxi	83.91 (5)
Eu1^iv—Eu1—Al2^xii	49.193 (14)	Al2—Al1—Al2^xv	108.64 (3)
Eu1^iv—Eu1—Al2^xiii	90	Al2—Al1—Al2^xvii	108.64 (3)
Eu1^iv—Eu1—Al2^xiv	130.807 (14)	Al2^iii—Al1—Al2^xi	119.84 (4)
Eu1^iv—Eu1—Al2^xv	130.807 (14)	Al2^iii—Al1—Al2^xii	119.84 (4)
Eu1^iv—Eu1—Al2^xvi	49.193 (14)	Al2^iii—Al1—Al2^xx	83.91 (5)
Eu1^iv—Eu1—Al2^xvii	49.193 (14)	Al2^iii—Al1—Al2^xxi	27.23 (5)
Al1^ii—Eu1—Al1	76.446 (2)	Al2^iii—Al1—Al2^xv	108.64 (3)
Al1^ii—Eu1—Al1^v	128.1108 (11)	Al2^iii—Al1—Al2^xvii	108.64 (3)
Al1^ii—Eu1—Al1^vi	128.1108 (11)	Al2^xi—Al1—Al2^xii	56.68 (2)
Al1^ii—Eu1—Al1^vii	51.8892 (11)	Al2^xi—Al1—Al2^xx	140.774 (14)
Al1^ii—Eu1—Al1^viii	51.8892 (11)	Al2^xi—Al1—Al2^xxi	140.774 (14)
Al1^ii—Eu1—Al1^ix	103.554 (2)	Al2^xi—Al1—Al2^xv	27.23 (5)
Al1^ii—Eu1—Al1^x	180	Al2^xi—Al1—Al2^xvii	83.91 (5)
Al1^ii—Eu1—Al2	38.2228 (10)	Al2^xii—Al1—Al2^xx	140.774 (14)
Al1^ii—Eu1—Al2^v	84.01 (4)	Al2^xii—Al1—Al2^xxi	140.774 (14)
Al1^ii—Eu1—Al2^xi	134.78 (3)	Al2^xii—Al1—Al2^xv	83.91 (5)
Al1^ii—Eu1—Al2^vi	84.01 (4)	Al2^xii—Al1—Al2^xvii	27.23 (5)
Al1^ii—Eu1—Al2^xii	134.78 (3)	Al2^xx—Al1—Al2^xxi	56.68 (2)
Al1^ii—Eu1—Al2^xiii	141.7772 (10)	Al2^xx—Al1—Al2^xv	119.84 (4)
Al1^ii—Eu1—Al2^xiv	45.22 (3)	Al2^xx—Al1—Al2^xvii	119.84 (4)
Al1^ii—Eu1—Al2^xv	95.99 (4)	Al2^xxi—Al1—Al2^xv	119.84 (4)
Al1^ii—Eu1—Al2^xvi	45.22 (3)	Al2^xxi—Al1—Al2^xvii	119.84 (4)
Al1^ii—Eu1—Al2^xvii	95.99 (4)	Al2^xv—Al1—Al2^xvii	111.15 (6)
Al1—Eu1—Al1^v	128.1108 (11)	Eu1—Al2—Eu1^xxiv	112.45 (4)
Al1—Eu1—Al1^vi	128.1108 (11)	Eu1—Al2—Eu1^xxii	112.45 (4)
Al1—Eu1—Al1^vii	51.8892 (11)	Eu1—Al2—Eu1^xxv	112.45 (4)
Al1—Eu1—Al1^viii	51.8892 (11)	Eu1—Al2—Eu1^xxiii	112.45 (4)
Al1—Eu1—Al1^ix	180	Eu1—Al2—Al1^ii	55.57 (4)
Al1—Eu1—Al1^x	103.554 (2)	Eu1—Al2—Al1	55.57 (4)
Al1—Eu1—Al2	38.2228 (10)	Eu1—Al2—Al1^xxiv	151.660 (15)
Al1—Eu1—Al2^v	134.78 (3)	Eu1—Al2—Al1^xxv	151.660 (15)
Al1—Eu1—Al2^xi	84.01 (4)	Eu1—Al2—Al1^vii	55.57 (4)
Al1—Eu1—Al2^vi	134.78 (3)	Eu1—Al2—Al1^viii	55.57 (4)
Al1—Eu1—Al2^xii	84.01 (4)	Eu1—Al2—Al1^xxvi	151.660 (15)
Al1—Eu1—Al2^xiii	141.7772 (10)	Eu1—Al2—Al1^xxvii	151.660 (15)
Al1—Eu1—Al2^xiv	95.99 (4)	Eu1—Al2—Al2^i	90.00 (5)
Al1—Eu1—Al2^xv	45.22 (3)	Eu1—Al2—Al2^ii	90.00 (5)
Al1—Eu1—Al2^xvi	95.99 (4)	Eu1—Al2—Al2^iii	90.00 (5)
Al1—Eu1—Al2^xvii	45.22 (3)	Eu1—Al2—Al2^iv	90.00 (5)
Al1^v—Eu1—Al1^vi	76.446 (2)	Eu1—Al2—Al2^xx	180
Al1^v—Eu1—Al1^vii	103.554 (2)	Eu1—Al2—Al2^xiv	45.89 (3)
Al1^v—Eu1—Al1^viii	180	Eu1—Al2—Al2^xv	45.89 (3)
Al1^v—Eu1—Al1^ix	51.8892 (11)	Eu1—Al2—Al2^xvi	45.89 (3)
Al1^v—Eu1—Al1^x	51.8892 (11)	Eu1—Al2—Al2^xvii	45.89 (3)
Al1^v—Eu1—Al2	141.7772 (10)	Eu1^xxiv—Al2—Eu1^xxii	81.61 (3)
Al1^v—Eu1—Al2^v	45.22 (3)	Eu1^xxiv—Al2—Eu1^xxv	81.61 (3)
Al1^v—Eu1—Al2^xi	45.22 (3)	Eu1^xxiv—Al2—Eu1^xxiii	135.10 (8)
Al1^v—Eu1—Al2^vi	95.99 (4)	Eu1^xxiv—Al2—Al1^ii	71.1457 (18)
Al1^v—Eu1—Al2^xii	95.99 (4)	Eu1^xxiv—Al2—Al1	139.02 (2)
Al1^v—Eu1—Al2^xiii	38.2228 (10)	Eu1^xxiv—Al2—Al1^xxiv	49.73 (3)
Al1^v—Eu1—Al2^xiv	84.01 (4)	Eu1^xxiv—Al2—Al1^xxv	88.52 (5)
Al1^v—Eu1—Al2^xv	84.01 (4)	Eu1^xxiv—Al2—Al1^vii	71.1457 (18)
Al1^v—Eu1—Al2^xvi	134.78 (3)	Eu1^xxiv—Al2—Al1^viii	139.02 (2)
Al1^v—Eu1—Al2^xvii	134.78 (3)	Eu1^xxiv—Al2—Al1^xxvi	49.73 (3)
Al1^vi—Eu1—Al1^vii	180	Eu1^xxiv—Al2—Al1^xxvii	88.52 (5)
Al1^vi—Eu1—Al1^viii	103.554 (2)	Eu1^xxiv—Al2—Al2^i	49.193 (17)
Al1^vi—Eu1—Al1^ix	51.8892 (11)	Eu1^xxiv—Al2—Al2^ii	49.193 (17)
Al1^vi—Eu1—Al1^x	51.8892 (11)	Eu1^xxiv—Al2—Al2^iii	130.81 (3)
Al1^vi—Eu1—Al2	141.7772 (10)	Eu1^xxiv—Al2—Al2^iv	130.81 (3)
Al1^vi—Eu1—Al2^v	95.99 (4)	Eu1^xxiv—Al2—Al2^xx	67.55 (4)
Al1^vi—Eu1—Al2^xi	95.99 (4)	Eu1^xxiv—Al2—Al2^xiv	66.56 (3)
Al1^vi—Eu1—Al2^vi	45.22 (3)	Eu1^xxiv—Al2—Al2^xv	105.41 (2)
Al1^vi—Eu1—Al2^xii	45.22 (3)	Eu1^xxiv—Al2—Al2^xvi	105.41 (2)
Al1^vi—Eu1—Al2^xiii	38.2228 (10)	Eu1^xxiv—Al2—Al2^xvii	158.35 (7)
Al1^vi—Eu1—Al2^xiv	134.78 (3)	Eu1^xxii—Al2—Eu1^xxv	135.10 (8)
Al1^vi—Eu1—Al2^xv	134.78 (3)	Eu1^xxii—Al2—Eu1^xxiii	81.61 (3)
Al1^vi—Eu1—Al2^xvi	84.01 (4)	Eu1^xxii—Al2—Al1^ii	139.02 (2)
Al1^vi—Eu1—Al2^xvii	84.01 (4)	Eu1^xxii—Al2—Al1	71.1457 (18)
Al1^vii—Eu1—Al1^viii	76.446 (2)	Eu1^xxii—Al2—Al1^xxiv	49.73 (3)
Al1^vii—Eu1—Al1^ix	128.1108 (11)	Eu1^xxii—Al2—Al1^xxv	88.52 (5)
Al1^vii—Eu1—Al1^x	128.1108 (11)	Eu1^xxii—Al2—Al1^vii	71.1457 (18)
Al1^vii—Eu1—Al2	38.2228 (10)	Eu1^xxii—Al2—Al1^viii	139.02 (2)
Al1^vii—Eu1—Al2^v	84.01 (4)	Eu1^xxii—Al2—Al1^xxvi	88.52 (5)
Al1^vii—Eu1—Al2^xi	84.01 (4)	Eu1^xxii—Al2—Al1^xxvii	49.73 (3)
Al1^vii—Eu1—Al2^vi	134.78 (3)	Eu1^xxii—Al2—Al2^i	49.193 (17)
Al1^vii—Eu1—Al2^xii	134.78 (3)	Eu1^xxii—Al2—Al2^ii	130.81 (3)
Al1^vii—Eu1—Al2^xiii	141.7772 (10)	Eu1^xxii—Al2—Al2^iii	49.193 (17)
Al1^vii—Eu1—Al2^xiv	45.22 (3)	Eu1^xxii—Al2—Al2^iv	130.81 (3)
Al1^vii—Eu1—Al2^xv	45.22 (3)	Eu1^xxii—Al2—Al2^xx	67.55 (4)
Al1^vii—Eu1—Al2^xvi	95.99 (4)	Eu1^xxii—Al2—Al2^xiv	105.41 (2)
Al1^vii—Eu1—Al2^xvii	95.99 (4)	Eu1^xxii—Al2—Al2^xv	66.56 (3)
Al1^viii—Eu1—Al1^ix	128.1108 (11)	Eu1^xxii—Al2—Al2^xvi	158.35 (7)
Al1^viii—Eu1—Al1^x	128.1108 (11)	Eu1^xxii—Al2—Al2^xvii	105.41 (2)
Al1^viii—Eu1—Al2	38.2228 (10)	Eu1^xxv—Al2—Eu1^xxiii	81.61 (3)
Al1^viii—Eu1—Al2^v	134.78 (3)	Eu1^xxv—Al2—Al1^ii	71.1457 (18)
Al1^viii—Eu1—Al2^xi	134.78 (3)	Eu1^xxv—Al2—Al1	139.02 (2)
Al1^viii—Eu1—Al2^vi	84.01 (4)	Eu1^xxv—Al2—Al1^xxiv	88.52 (5)
Al1^viii—Eu1—Al2^xii	84.01 (4)	Eu1^xxv—Al2—Al1^xxv	49.73 (3)
Al1^viii—Eu1—Al2^xiii	141.7772 (10)	Eu1^xxv—Al2—Al1^vii	139.02 (2)
Al1^viii—Eu1—Al2^xiv	95.99 (4)	Eu1^xxv—Al2—Al1^viii	71.1457 (18)
Al1^viii—Eu1—Al2^xv	95.99 (4)	Eu1^xxv—Al2—Al1^xxvi	49.73 (3)
Al1^viii—Eu1—Al2^xvi	45.22 (3)	Eu1^xxv—Al2—Al1^xxvii	88.52 (5)
Al1^viii—Eu1—Al2^xvii	45.22 (3)	Eu1^xxv—Al2—Al2^i	130.81 (3)
Al1^ix—Eu1—Al1^x	76.446 (2)	Eu1^xxv—Al2—Al2^ii	49.193 (17)
Al1^ix—Eu1—Al2	141.7772 (10)	Eu1^xxv—Al2—Al2^iii	130.81 (3)
Al1^ix—Eu1—Al2^v	45.22 (3)	Eu1^xxv—Al2—Al2^iv	49.193 (17)
Al1^ix—Eu1—Al2^xi	95.99 (4)	Eu1^xxv—Al2—Al2^xx	67.55 (4)
Al1^ix—Eu1—Al2^vi	45.22 (3)	Eu1^xxv—Al2—Al2^xiv	105.41 (2)
Al1^ix—Eu1—Al2^xii	95.99 (4)	Eu1^xxv—Al2—Al2^xv	158.35 (7)
Al1^ix—Eu1—Al2^xiii	38.2228 (10)	Eu1^xxv—Al2—Al2^xvi	66.56 (3)
Al1^ix—Eu1—Al2^xiv	84.01 (4)	Eu1^xxv—Al2—Al2^xvii	105.41 (2)
Al1^ix—Eu1—Al2^xv	134.78 (3)	Eu1^xxiii—Al2—Al1^ii	139.02 (2)
Al1^ix—Eu1—Al2^xvi	84.01 (4)	Eu1^xxiii—Al2—Al1	71.1457 (18)
Al1^ix—Eu1—Al2^xvii	134.78 (3)	Eu1^xxiii—Al2—Al1^xxiv	88.52 (5)
Al1^x—Eu1—Al2	141.7772 (10)	Eu1^xxiii—Al2—Al1^xxv	49.73 (3)
Al1^x—Eu1—Al2^v	95.99 (4)	Eu1^xxiii—Al2—Al1^vii	139.02 (2)
Al1^x—Eu1—Al2^xi	45.22 (3)	Eu1^xxiii—Al2—Al1^viii	71.1457 (18)
Al1^x—Eu1—Al2^vi	95.99 (4)	Eu1^xxiii—Al2—Al1^xxvi	88.52 (5)
Al1^x—Eu1—Al2^xii	45.22 (3)	Eu1^xxiii—Al2—Al1^xxvii	49.73 (3)
Al1^x—Eu1—Al2^xiii	38.2228 (10)	Eu1^xxiii—Al2—Al2^i	130.81 (3)
Al1^x—Eu1—Al2^xiv	134.78 (3)	Eu1^xxiii—Al2—Al2^ii	130.81 (3)
Al1^x—Eu1—Al2^xv	84.01 (4)	Eu1^xxiii—Al2—Al2^iii	49.193 (17)
Al1^x—Eu1—Al2^xvi	134.78 (3)	Eu1^xxiii—Al2—Al2^iv	49.193 (17)
Al1^x—Eu1—Al2^xvii	84.01 (4)	Eu1^xxiii—Al2—Al2^xx	67.55 (4)
Al2—Eu1—Al2^v	112.45 (4)	Eu1^xxiii—Al2—Al2^xiv	158.35 (7)
Al2—Eu1—Al2^xi	112.45 (4)	Eu1^xxiii—Al2—Al2^xv	105.41 (2)
Al2—Eu1—Al2^vi	112.45 (4)	Eu1^xxiii—Al2—Al2^xvi	105.41 (2)
Al2—Eu1—Al2^xii	112.45 (4)	Eu1^xxiii—Al2—Al2^xvii	66.56 (3)
Al2—Eu1—Al2^xiii	180	Al1^ii—Al2—Al1	111.15 (9)
Al2—Eu1—Al2^xiv	67.55 (4)	Al1^ii—Al2—Al1^xxiv	119.84 (3)
Al2—Eu1—Al2^xv	67.55 (4)	Al1^ii—Al2—Al1^xxv	119.84 (3)
Al2—Eu1—Al2^xvi	67.55 (4)	Al1^ii—Al2—Al1^vii	71.36 (4)
Al2—Eu1—Al2^xvii	67.55 (4)	Al1^ii—Al2—Al1^viii	71.36 (4)
Al2^v—Eu1—Al2^xi	81.61 (2)	Al1^ii—Al2—Al1^xxvi	96.09 (3)
Al2^v—Eu1—Al2^vi	81.61 (2)	Al1^ii—Al2—Al1^xxvii	152.77 (6)
Al2^v—Eu1—Al2^xii	135.10 (6)	Al1^ii—Al2—Al2^i	90.00 (3)
Al2^v—Eu1—Al2^xiii	67.55 (4)	Al1^ii—Al2—Al2^ii	34.43 (3)
Al2^v—Eu1—Al2^xiv	44.90 (6)	Al1^ii—Al2—Al2^iii	145.57 (8)
Al2^v—Eu1—Al2^xv	98.39 (2)	Al1^ii—Al2—Al2^iv	90.00 (3)
Al2^v—Eu1—Al2^xvi	98.39 (2)	Al1^ii—Al2—Al2^xx	124.43 (4)
Al2^v—Eu1—Al2^xvii	180	Al1^ii—Al2—Al2^xiv	35.68 (2)
Al2^xi—Eu1—Al2^vi	135.10 (6)	Al1^ii—Al2—Al2^xv	91.45 (6)
Al2^xi—Eu1—Al2^xii	81.61 (2)	Al1^ii—Al2—Al2^xvi	35.68 (2)
Al2^xi—Eu1—Al2^xiii	67.55 (4)	Al1^ii—Al2—Al2^xvii	91.45 (6)
Al2^xi—Eu1—Al2^xiv	98.39 (2)	Al1—Al2—Al1^xxiv	119.84 (3)
Al2^xi—Eu1—Al2^xv	44.90 (6)	Al1—Al2—Al1^xxv	119.84 (3)
Al2^xi—Eu1—Al2^xvi	180	Al1—Al2—Al1^vii	71.36 (4)
Al2^xi—Eu1—Al2^xvii	98.39 (2)	Al1—Al2—Al1^viii	71.36 (4)
Al2^vi—Eu1—Al2^xii	81.61 (2)	Al1—Al2—Al1^xxvi	152.77 (6)
Al2^vi—Eu1—Al2^xiii	67.55 (4)	Al1—Al2—Al1^xxvii	96.09 (3)
Al2^vi—Eu1—Al2^xiv	98.39 (2)	Al1—Al2—Al2^i	90.00 (3)
Al2^vi—Eu1—Al2^xv	180	Al1—Al2—Al2^ii	145.57 (8)
Al2^vi—Eu1—Al2^xvi	44.90 (6)	Al1—Al2—Al2^iii	34.43 (3)
Al2^vi—Eu1—Al2^xvii	98.39 (2)	Al1—Al2—Al2^iv	90.00 (3)
Al2^xii—Eu1—Al2^xiii	67.55 (4)	Al1—Al2—Al2^xx	124.43 (4)
Al2^xii—Eu1—Al2^xiv	180	Al1—Al2—Al2^xiv	91.45 (6)
Al2^xii—Eu1—Al2^xv	98.39 (2)	Al1—Al2—Al2^xv	35.68 (2)
Al2^xii—Eu1—Al2^xvi	98.39 (2)	Al1—Al2—Al2^xvi	91.45 (6)
Al2^xii—Eu1—Al2^xvii	44.90 (6)	Al1—Al2—Al2^xvii	35.68 (2)
Al2^xiii—Eu1—Al2^xiv	112.45 (4)	Al1^xxiv—Al2—Al1^xxv	56.68 (3)
Al2^xiii—Eu1—Al2^xv	112.45 (4)	Al1^xxiv—Al2—Al1^vii	96.09 (3)
Al2^xiii—Eu1—Al2^xvi	112.45 (4)	Al1^xxiv—Al2—Al1^viii	152.77 (6)
Al2^xiii—Eu1—Al2^xvii	112.45 (4)	Al1^xxiv—Al2—Al1^xxvi	39.23 (2)
Al2^xiv—Eu1—Al2^xv	81.61 (2)	Al1^xxiv—Al2—Al1^xxvii	39.23 (2)
Al2^xiv—Eu1—Al2^xvi	81.61 (2)	Al1^xxiv—Al2—Al2^i	61.66 (4)
Al2^xiv—Eu1—Al2^xvii	135.10 (6)	Al1^xxiv—Al2—Al2^ii	90.00 (4)
Al2^xv—Eu1—Al2^xvi	135.10 (6)	Al1^xxiv—Al2—Al2^iii	90.00 (4)
Al2^xv—Eu1—Al2^xvii	81.61 (2)	Al1^xxiv—Al2—Al2^iv	118.34 (6)
Al2^xvi—Eu1—Al2^xvii	81.61 (2)	Al1^xxiv—Al2—Al2^xx	28.340 (15)
Eu1—Al1—Eu1^iii	76.446 (2)	Al1^xxiv—Al2—Al2^xiv	111.81 (2)
Eu1—Al1—Eu1^xxii	128.1108 (11)	Al1^xxiv—Al2—Al2^xv	111.81 (2)
Eu1—Al1—Eu1^xxiii	128.1108 (11)	Al1^xxiv—Al2—Al2^xvi	148.60 (3)
Eu1—Al1—Al1^i	90	Al1^xxiv—Al2—Al2^xvii	148.60 (3)
Eu1—Al1—Al1^ii	51.7772 (10)	Al1^xxv—Al2—Al1^vii	152.77 (6)
Eu1—Al1—Al1^iii	128.2228 (10)	Al1^xxv—Al2—Al1^viii	96.09 (3)
Eu1—Al1—Al1^iv	90	Al1^xxv—Al2—Al1^xxvi	39.23 (2)
Eu1—Al1—Al1^vii	64.0554 (9)	Al1^xxv—Al2—Al1^xxvii	39.23 (2)
Eu1—Al1—Al1^xviii	115.9446 (9)	Al1^xxv—Al2—Al2^i	118.34 (6)
Eu1—Al1—Al1^viii	64.0554 (9)	Al1^xxv—Al2—Al2^ii	90.00 (4)
Eu1—Al1—Al1^xix	115.9446 (9)	Al1^xxv—Al2—Al2^iii	90.00 (4)
Eu1—Al1—Al2	86.20 (4)	Al1^xxv—Al2—Al2^iv	61.66 (4)
Eu1—Al1—Al2^iii	162.65 (4)	Al1^xxv—Al2—Al2^xx	28.340 (15)
Eu1—Al1—Al2^xi	46.255 (8)	Al1^xxv—Al2—Al2^xiv	148.60 (3)
Eu1—Al1—Al2^xii	46.255 (8)	Al1^xxv—Al2—Al2^xv	148.60 (3)
Eu1—Al1—Al2^xx	113.437 (15)	Al1^xxv—Al2—Al2^xvi	111.81 (2)
Eu1—Al1—Al2^xxi	170.117 (15)	Al1^xxv—Al2—Al2^xvii	111.81 (2)
Eu1—Al1—Al2^xv	63.63 (3)	Al1^vii—Al2—Al1^viii	111.15 (9)
Eu1—Al1—Al2^xvii	63.63 (3)	Al1^vii—Al2—Al1^xxvi	119.84 (3)
Eu1^iii—Al1—Eu1^xxii	128.1108 (11)	Al1^vii—Al2—Al1^xxvii	119.84 (3)
Eu1^iii—Al1—Eu1^xxiii	128.1108 (11)	Al1^vii—Al2—Al2^i	34.43 (3)
Eu1^iii—Al1—Al1^i	90	Al1^vii—Al2—Al2^ii	90.00 (3)
Eu1^iii—Al1—Al1^ii	128.2228 (10)	Al1^vii—Al2—Al2^iii	90.00 (3)
Eu1^iii—Al1—Al1^iii	51.7772 (10)	Al1^vii—Al2—Al2^iv	145.57 (8)
Eu1^iii—Al1—Al1^iv	90	Al1^vii—Al2—Al2^xx	124.43 (4)
Eu1^iii—Al1—Al1^vii	115.9446 (9)	Al1^vii—Al2—Al2^xiv	35.68 (2)
Eu1^iii—Al1—Al1^xviii	64.0554 (9)	Al1^vii—Al2—Al2^xv	35.68 (2)
Eu1^iii—Al1—Al1^viii	115.9446 (9)	Al1^vii—Al2—Al2^xvi	91.45 (6)
Eu1^iii—Al1—Al1^xix	64.0554 (9)	Al1^vii—Al2—Al2^xvii	91.45 (6)
Eu1^iii—Al1—Al2	162.65 (4)	Al1^viii—Al2—Al1^xxvi	119.84 (3)
Eu1^iii—Al1—Al2^iii	86.20 (4)	Al1^viii—Al2—Al1^xxvii	119.84 (3)
Eu1^iii—Al1—Al2^xi	46.255 (8)	Al1^viii—Al2—Al2^i	145.57 (8)
Eu1^iii—Al1—Al2^xii	46.255 (8)	Al1^viii—Al2—Al2^ii	90.00 (3)
Eu1^iii—Al1—Al2^xx	170.117 (15)	Al1^viii—Al2—Al2^iii	90.00 (3)
Eu1^iii—Al1—Al2^xxi	113.437 (15)	Al1^viii—Al2—Al2^iv	34.43 (3)
Eu1^iii—Al1—Al2^xv	63.63 (3)	Al1^viii—Al2—Al2^xx	124.43 (4)
Eu1^iii—Al1—Al2^xvii	63.63 (3)	Al1^viii—Al2—Al2^xiv	91.45 (6)
Eu1^xxii—Al1—Eu1^xxiii	76.446 (2)	Al1^viii—Al2—Al2^xv	91.45 (6)
Eu1^xxii—Al1—Al1^i	51.7772 (10)	Al1^viii—Al2—Al2^xvi	35.68 (2)
Eu1^xxii—Al1—Al1^ii	90	Al1^viii—Al2—Al2^xvii	35.68 (2)
Eu1^xxii—Al1—Al1^iii	90	Al1^xxvi—Al2—Al1^xxvii	56.68 (3)
Eu1^xxii—Al1—Al1^iv	128.2228 (10)	Al1^xxvi—Al2—Al2^i	90.00 (4)
Eu1^xxii—Al1—Al1^vii	64.0554 (9)	Al1^xxvi—Al2—Al2^ii	61.66 (4)
Eu1^xxii—Al1—Al1^xviii	64.0554 (9)	Al1^xxvi—Al2—Al2^iii	118.34 (6)
Eu1^xxii—Al1—Al1^viii	115.9446 (9)	Al1^xxvi—Al2—Al2^iv	90.00 (4)
Eu1^xxii—Al1—Al1^xix	115.9446 (9)	Al1^xxvi—Al2—Al2^xx	28.340 (15)
Eu1^xxii—Al1—Al2	63.63 (3)	Al1^xxvi—Al2—Al2^xiv	111.81 (2)
Eu1^xxii—Al1—Al2^iii	63.63 (3)	Al1^xxvi—Al2—Al2^xv	148.60 (3)
Eu1^xxii—Al1—Al2^xi	113.437 (15)	Al1^xxvi—Al2—Al2^xvi	111.81 (2)
Eu1^xxii—Al1—Al2^xii	170.117 (15)	Al1^xxvi—Al2—Al2^xvii	148.60 (3)
Eu1^xxii—Al1—Al2^xx	46.255 (8)	Al1^xxvii—Al2—Al2^i	90.00 (4)
Eu1^xxii—Al1—Al2^xxi	46.255 (8)	Al1^xxvii—Al2—Al2^ii	118.34 (6)
Eu1^xxii—Al1—Al2^xv	86.20 (4)	Al1^xxvii—Al2—Al2^iii	61.66 (4)
Eu1^xxii—Al1—Al2^xvii	162.65 (4)	Al1^xxvii—Al2—Al2^iv	90.00 (4)
Eu1^xxiii—Al1—Al1^i	128.2228 (10)	Al1^xxvii—Al2—Al2^xx	28.340 (15)
Eu1^xxiii—Al1—Al1^ii	90	Al1^xxvii—Al2—Al2^xiv	148.60 (3)
Eu1^xxiii—Al1—Al1^iii	90	Al1^xxvii—Al2—Al2^xv	111.81 (2)
Eu1^xxiii—Al1—Al1^iv	51.7772 (10)	Al1^xxvii—Al2—Al2^xvi	148.60 (3)
Eu1^xxiii—Al1—Al1^vii	115.9446 (9)	Al1^xxvii—Al2—Al2^xvii	111.81 (2)
Eu1^xxiii—Al1—Al1^xviii	115.9446 (9)	Al2^i—Al2—Al2^ii	90
Eu1^xxiii—Al1—Al1^viii	64.0554 (9)	Al2^i—Al2—Al2^iii	90
Eu1^xxiii—Al1—Al1^xix	64.0554 (9)	Al2^i—Al2—Al2^iv	180
Eu1^xxiii—Al1—Al2	63.63 (3)	Al2^i—Al2—Al2^xx	90.00 (5)
Eu1^xxiii—Al1—Al2^iii	63.63 (3)	Al2^i—Al2—Al2^xiv	59.49 (3)
Eu1^xxiii—Al1—Al2^xi	170.117 (15)	Al2^i—Al2—Al2^xv	59.49 (3)
Eu1^xxiii—Al1—Al2^xii	113.437 (15)	Al2^i—Al2—Al2^xvi	120.51 (5)
Eu1^xxiii—Al1—Al2^xx	46.255 (8)	Al2^i—Al2—Al2^xvii	120.51 (5)
Eu1^xxiii—Al1—Al2^xxi	46.255 (8)	Al2^ii—Al2—Al2^iii	180
Eu1^xxiii—Al1—Al2^xv	162.65 (4)	Al2^ii—Al2—Al2^iv	90
Eu1^xxiii—Al1—Al2^xvii	86.20 (4)	Al2^ii—Al2—Al2^xx	90.00 (5)
Al1^i—Al1—Al1^ii	90	Al2^ii—Al2—Al2^xiv	59.49 (3)
Al1^i—Al1—Al1^iii	90	Al2^ii—Al2—Al2^xv	120.51 (5)
Al1^i—Al1—Al1^iv	180	Al2^ii—Al2—Al2^xvi	59.49 (3)
Al1^i—Al1—Al1^vii	45.0000 (9)	Al2^ii—Al2—Al2^xvii	120.51 (5)
Al1^i—Al1—Al1^xviii	45.0000 (9)	Al2^iii—Al2—Al2^iv	90
Al1^i—Al1—Al1^viii	135.0000 (9)	Al2^iii—Al2—Al2^xx	90.00 (5)
Al1^i—Al1—Al1^xix	135.0000 (9)	Al2^iii—Al2—Al2^xiv	120.51 (5)
Al1^i—Al1—Al2	90	Al2^iii—Al2—Al2^xv	59.49 (3)
Al1^i—Al1—Al2^iii	90	Al2^iii—Al2—Al2^xvi	120.51 (5)
Al1^i—Al1—Al2^xi	61.660 (15)	Al2^iii—Al2—Al2^xvii	59.49 (3)
Al1^i—Al1—Al2^xii	118.340 (15)	Al2^iv—Al2—Al2^xx	90.00 (5)
Al1^i—Al1—Al2^xx	90	Al2^iv—Al2—Al2^xiv	120.51 (5)
Al1^i—Al1—Al2^xxi	90	Al2^iv—Al2—Al2^xv	120.51 (5)
Al1^i—Al1—Al2^xv	34.43 (4)	Al2^iv—Al2—Al2^xvi	59.49 (3)
Al1^i—Al1—Al2^xvii	145.57 (4)	Al2^iv—Al2—Al2^xvii	59.49 (3)
Al1^ii—Al1—Al1^iii	180	Al2^xx—Al2—Al2^xiv	134.11 (3)
Al1^ii—Al1—Al1^iv	90	Al2^xx—Al2—Al2^xv	134.11 (3)
Al1^ii—Al1—Al1^vii	45.0000 (9)	Al2^xx—Al2—Al2^xvi	134.11 (3)
Al1^ii—Al1—Al1^xviii	135.0000 (9)	Al2^xx—Al2—Al2^xvii	134.11 (3)
Al1^ii—Al1—Al1^viii	45.0000 (9)	Al2^xiv—Al2—Al2^xv	61.03 (3)
Al1^ii—Al1—Al1^xix	135.0000 (9)	Al2^xiv—Al2—Al2^xvi	61.03 (3)
Al1^ii—Al1—Al2	34.43 (4)	Al2^xiv—Al2—Al2^xvii	91.79 (6)
Al1^ii—Al1—Al2^iii	145.57 (4)	Al2^xv—Al2—Al2^xvi	91.79 (6)
Al1^ii—Al1—Al2^xi	90	Al2^xv—Al2—Al2^xvii	61.03 (3)
Al1^ii—Al1—Al2^xii	90	Al2^xvi—Al2—Al2^xvii	61.03 (3)

Symmetry codes: (i) x−1, y, z; (ii) x, y−1, z; (iii) x, y+1, z; (iv) x+1, y, z; (v) x−1/2, y−1/2, z−1/2; (vi) x+1/2, y−1/2, z−1/2; (vii) −y, x, z; (viii) −y+1, x, z; (ix) −y+1/2, x−1/2, z−1/2; (x) −y+1/2, x+1/2, z−1/2; (xi) x−1/2, y+1/2, z−1/2; (xii) x+1/2, y+1/2, z−1/2; (xiii) −x, y, −z; (xiv) −x−1/2, y−1/2, −z+1/2; (xv) −x−1/2, y+1/2, −z+1/2; (xvi) −x+1/2, y−1/2, −z+1/2; (xvii) −x+1/2, y+1/2, −z+1/2; (xviii) −y, x+1, z; (xix) −y+1, x+1, z; (xx) −x, y, −z+1; (xxi) −x, y+1, −z+1; (xxii) x−1/2, y+1/2, z+1/2; (xxiii) x+1/2, y+1/2, z+1/2; (xxiv) x−1/2, y−1/2, z+1/2; (xxv) x+1/2, y−1/2, z+1/2; (xxvi) −y+1/2, x−1/2, z+1/2; (xxvii) −y+1/2, x+1/2, z+1/2.

(II)

Crystal data

Al4Eu	F(000) = 460
Mr = 259.9	Dx = 4.029 Mg m^−3
Orthorhombic, Fmmm(00γ)s00†	Synchrotron radiation, λ = 0.5 Å
q = 0.174100c*	Cell parameters from 1000 reflections
a = 6.1991 (3) Å	θ = 1.5–22°
b = 6.1987 (4) Å	µ = 5.91 mm^−1
c = 11.1488 (4) Å	T = 20 K
V = 428.41 (4) Å^3	Irregular, black
Z = 4	0.1 × 0.06 × 0.02 mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, −x₂, x₃, x₄+1/2; (3) −x₁, x₂, −x₃, −x₄; (4) x₁, −x₂, −x₃, −x₄+1/2; (5) −x₁, −x₂, −x₃, −x₄; (6) x₁, x₂, −x₃, −x₄+1/2; (7) x₁, −x₂, x₃, x₄; (8) −x₁, x₂, x₃, x₄+1/2; (9) x₁, x₂+1/2, x₃+1/2, x₄; (10) −x₁, −x₂+1/2, x₃+1/2, x₄+1/2; (11) −x₁, x₂+1/2, −x₃+1/2, −x₄; (12) x₁, −x₂+1/2, −x₃+1/2, −x₄+1/2; (13) −x₁, −x₂+1/2, −x₃+1/2, −x₄; (14) x₁, x₂+1/2, −x₃+1/2, −x₄+1/2; (15) x₁, −x₂+1/2, x₃+1/2, x₄; (16) −x₁, x₂+1/2, x₃+1/2, x₄+1/2; (17) x₁+1/2, x₂, x₃+1/2, x₄; (18) −x₁+1/2, −x₂, x₃+1/2, x₄+1/2; (19) −x₁+1/2, x₂, −x₃+1/2, −x₄; (20) x₁+1/2, −x₂, −x₃+1/2, −x₄+1/2; (21) −x₁+1/2, −x₂, −x₃+1/2, −x₄; (22) x₁+1/2, x₂, −x₃+1/2, −x₄+1/2; (23) x₁+1/2, −x₂, x₃+1/2, x₄; (24) −x₁+1/2, x₂, x₃+1/2, x₄+1/2; (25) x₁+1/2, x₂+1/2, x₃, x₄; (26) −x₁+1/2, −x₂+1/2, x₃, x₄+1/2; (27) −x₁+1/2, x₂+1/2, −x₃, −x₄; (28) x₁+1/2, −x₂+1/2, −x₃, −x₄+1/2; (29) −x₁+1/2, −x₂+1/2, −x₃, −x₄; (30) x₁+1/2, x₂+1/2, −x₃, −x₄+1/2; (31) x₁+1/2, −x₂+1/2, x₃, x₄; (32) −x₁+1/2, x₂+1/2, x₃, x₄+1/2.

Data collection

Huber four-circle diffractometer	498 independent reflections
Radiation source: synchrotron	439 reflections with I > 3σ(I)
Si111 and Si311 monochromator	Rint = 0.023
area detector with phi scans	θmax = 22.0°, θmin = 2.6°
Absorption correction: empirical (using intensity measurements) SADABS, Program for Empirical Absorption Correction of Area Detector Data, G. M. Sheldrick, 1996	h = −9→6
Tmin = 0.319, Tmax = 0.368	k = −7→7
1398 measured reflections	l = −7→16

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.024	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
wR(F^2) = 0.025	(Δ/σ)max < 0.001
S = 0.88	Δρmax = 1.58 e Å^−3
498 reflections	Δρmin = −1.49 e Å^−3
18 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 130 (30)

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

	x	y	z	Uiso*/Ueq
Eu1	0	0	0	0.0061 (2)
Al1	0.25	0.25	0.25	0.0074 (10)
Al2	0	0	0.38495 (13)	0.0061 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Eu1	0.0000 (4)	0.0124 (5)	0.00587 (17)	0	0	0
Al1	0.0038 (17)	0.011 (2)	0.0074 (6)	0	0	0
Al2	0.0016 (15)	0.011 (2)	0.0058 (6)	0	0	0

Geometric parameters (Å, º)

	Average	Minimum	Maximum
Eu1—Eu1^i	4.3833 (7)	4.3833 (9)	4.3833 (9)
Eu1—Eu1^ii	4.3833 (7)	4.3833 (9)	4.3833 (9)
Eu1—Eu1^iii	4.3833 (7)	4.3833 (9)	4.3833 (9)
Eu1—Eu1^iv	4.3833 (7)	4.3833 (9)	4.3833 (9)
Eu1—Al1	3.5455 (11)	3.4971 (13)	3.5955 (13)
Eu1—Al1^v	3.5465 (11)	3.4971 (13)	3.5955 (13)
Eu1—Al1^vi	3.5455 (11)	3.4971 (13)	3.5955 (13)
Eu1—Al1^i	3.5465 (11)	3.4971 (13)	3.5955 (13)
Eu1—Al1^vii	3.5455 (11)	3.4971 (13)	3.5955 (13)
Eu1—Al1^viii	3.5465 (11)	3.4971 (13)	3.5955 (13)
Eu1—Al1^ix	3.5455 (11)	3.4971 (13)	3.5955 (13)
Eu1—Al1^x	3.5465 (11)	3.4971 (13)	3.5955 (13)
Eu1—Al2	4.2927 (15)	4.2918 (15)	4.2937 (15)
Eu1—Al2^v	3.3544 (6)	3.3543 (6)	3.3546 (6)
Eu1—Al2^xi	3.3544 (6)	3.3543 (6)	3.3546 (6)
Eu1—Al2^vi	3.355 (2)	3.309 (3)	3.400 (3)
Eu1—Al2^xii	3.354 (2)	3.309 (3)	3.400 (3)
Eu1—Al2^xiii	4.2927 (15)	4.2918 (15)	4.2937 (15)
Eu1—Al2^xiv	3.3544 (6)	3.3543 (6)	3.3546 (6)
Eu1—Al2^xv	3.3544 (6)	3.3543 (6)	3.3546 (6)
Eu1—Al2^xvi	3.354 (2)	3.309 (3)	3.400 (3)
Eu1—Al2^xvii	3.355 (2)	3.309 (3)	3.400 (3)
Al1—Al1^i	4.383 (2)	4.383 (3)	4.383 (3)
Al1—Al1^ii	4.383 (2)	4.383 (3)	4.383 (3)
Al1—Al1^iii	4.383 (2)	4.383 (3)	4.383 (3)
Al1—Al1^iv	4.383 (2)	4.383 (3)	4.383 (3)
Al1—Al1^viii	3.101 (2)	3.100 (4)	3.103 (4)
Al1—Al1^xviii	3.101 (2)	3.100 (4)	3.103 (4)
Al1—Al1^ix	3.098 (2)	2.953 (4)	3.246 (4)
Al1—Al1^xix	3.101 (2)	2.953 (4)	3.246 (4)
Al1—Al2	2.660 (2)	2.652 (2)	2.669 (2)
Al1—Al2^xi	4.6230 (17)	4.5960 (18)	4.6498 (18)
Al1—Al2^xii	4.6224 (17)	4.5960 (18)	4.6498 (18)
Al1—Al2^iv	2.660 (2)	2.652 (2)	2.669 (2)
Al1—Al2^xx	4.6225 (17)	4.5960 (18)	4.6498 (18)
Al1—Al2^xv	2.660 (2)	2.652 (2)	2.669 (2)
Al1—Al2^xvii	2.660 (2)	2.652 (2)	2.669 (2)
Al1—Al2^xxi	4.6229 (17)	4.5960 (18)	4.6498 (18)
Al2—Al2^i	4.383 (2)	4.383 (3)	4.383 (3)
Al2—Al2^ii	4.383 (2)	4.383 (3)	4.383 (3)
Al2—Al2^iii	4.383 (2)	4.383 (3)	4.383 (3)
Al2—Al2^iv	4.383 (2)	4.383 (3)	4.383 (3)
Al2—Al2^xx	2.566 (2)	2.565 (2)	2.567 (2)
Al2—Al2^xiv	4.3216 (15)	4.3198 (15)	4.3234 (15)
Al2—Al2^xv	4.3216 (15)	4.3198 (15)	4.3234 (15)
Al2—Al2^xvi	4.320 (3)	4.195 (3)	4.448 (3)
Al2—Al2^xvii	4.322 (3)	4.195 (3)	4.448 (3)
Eu1^i—Eu1—Eu1^ii	89.996 (11)	89.996 (8)	89.996 (8)
Eu1^i—Eu1—Eu1^iii	90.004 (8)	90.004 (8)	90.004 (8)
Eu1^i—Eu1—Eu1^iv	180	180	180
Eu1^i—Eu1—Al1	128.16 (2)	127.15 (2)	129.18 (2)
Eu1^i—Eu1—Al1^v	90.00 (3)	89.62 (3)	90.40 (3)
Eu1^i—Eu1—Al1^vi	89.99 (3)	89.60 (3)	90.38 (3)
Eu1^i—Eu1—Al1^i	51.82 (2)	50.82 (2)	52.85 (2)
Eu1^i—Eu1—Al1^vii	51.84 (2)	50.82 (2)	52.85 (2)
Eu1^i—Eu1—Al1^viii	90.00 (3)	89.60 (3)	90.38 (3)
Eu1^i—Eu1—Al1^ix	90.01 (3)	89.62 (3)	90.40 (3)
Eu1^i—Eu1—Al1^x	128.18 (2)	127.15 (2)	129.18 (2)
Eu1^i—Eu1—Al2	89.99 (2)	88.80 (2)	91.20 (2)
Eu1^i—Eu1—Al2^v	49.20 (4)	48.43 (4)	49.98 (4)
Eu1^i—Eu1—Al2^xi	130.79 (4)	130.02 (4)	131.57 (4)
Eu1^i—Eu1—Al2^vi	49.202 (12)	49.090 (10)	49.318 (11)
Eu1^i—Eu1—Al2^xii	130.796 (11)	130.682 (11)	130.910 (10)
Eu1^i—Eu1—Al2^xiii	90.01 (2)	88.80 (2)	91.20 (2)
Eu1^i—Eu1—Al2^xiv	49.21 (4)	48.43 (4)	49.98 (4)
Eu1^i—Eu1—Al2^xv	130.80 (4)	130.02 (4)	131.57 (4)
Eu1^i—Eu1—Al2^xvi	49.204 (12)	49.090 (10)	49.318 (11)
Eu1^i—Eu1—Al2^xvii	130.798 (11)	130.682 (11)	130.910 (10)
Eu1^ii—Eu1—Eu1^iii	180	180	180
Eu1^ii—Eu1—Eu1^iv	90.004 (8)	90.004 (8)	90.004 (8)
Eu1^ii—Eu1—Al1	90.01 (3)	89.62 (3)	90.40 (3)
Eu1^ii—Eu1—Al1^v	128.18 (2)	127.15 (2)	129.18 (2)
Eu1^ii—Eu1—Al1^vi	51.84 (2)	50.82 (2)	52.85 (2)
Eu1^ii—Eu1—Al1^i	90.00 (3)	89.60 (3)	90.38 (3)
Eu1^ii—Eu1—Al1^vii	89.99 (3)	89.60 (3)	90.38 (3)
Eu1^ii—Eu1—Al1^viii	51.82 (2)	50.82 (2)	52.85 (2)
Eu1^ii—Eu1—Al1^ix	128.16 (2)	127.15 (2)	129.18 (2)
Eu1^ii—Eu1—Al1^x	90.00 (3)	89.62 (3)	90.40 (3)
Eu1^ii—Eu1—Al2	89.99 (2)	88.80 (2)	91.20 (2)
Eu1^ii—Eu1—Al2^v	130.79 (4)	130.02 (4)	131.57 (4)
Eu1^ii—Eu1—Al2^xi	49.20 (4)	48.43 (4)	49.98 (4)
Eu1^ii—Eu1—Al2^vi	49.202 (12)	49.090 (10)	49.318 (11)
Eu1^ii—Eu1—Al2^xii	130.796 (11)	130.682 (11)	130.910 (10)
Eu1^ii—Eu1—Al2^xiii	90.01 (2)	88.80 (2)	91.20 (2)
Eu1^ii—Eu1—Al2^xiv	130.80 (4)	130.02 (4)	131.57 (4)
Eu1^ii—Eu1—Al2^xv	49.21 (4)	48.43 (4)	49.98 (4)
Eu1^ii—Eu1—Al2^xvi	49.204 (12)	49.090 (10)	49.318 (11)
Eu1^ii—Eu1—Al2^xvii	130.798 (11)	130.682 (11)	130.910 (10)
Eu1^iii—Eu1—Eu1^iv	89.996 (11)	89.996 (8)	89.996 (8)
Eu1^iii—Eu1—Al1	89.99 (3)	89.60 (3)	90.38 (3)
Eu1^iii—Eu1—Al1^v	51.82 (2)	50.82 (2)	52.85 (2)
Eu1^iii—Eu1—Al1^vi	128.16 (2)	127.15 (2)	129.18 (2)
Eu1^iii—Eu1—Al1^i	90.00 (3)	89.62 (3)	90.40 (3)
Eu1^iii—Eu1—Al1^vii	90.01 (3)	89.62 (3)	90.40 (3)
Eu1^iii—Eu1—Al1^viii	128.18 (2)	127.15 (2)	129.18 (2)
Eu1^iii—Eu1—Al1^ix	51.84 (2)	50.82 (2)	52.85 (2)
Eu1^iii—Eu1—Al1^x	90.00 (3)	89.60 (3)	90.38 (3)
Eu1^iii—Eu1—Al2	90.01 (2)	88.80 (2)	91.20 (2)
Eu1^iii—Eu1—Al2^v	49.21 (4)	48.43 (4)	49.98 (4)
Eu1^iii—Eu1—Al2^xi	130.80 (4)	130.02 (4)	131.57 (4)
Eu1^iii—Eu1—Al2^vi	130.798 (11)	130.682 (11)	130.910 (10)
Eu1^iii—Eu1—Al2^xii	49.204 (12)	49.090 (10)	49.318 (11)
Eu1^iii—Eu1—Al2^xiii	89.99 (2)	88.80 (2)	91.20 (2)
Eu1^iii—Eu1—Al2^xiv	49.20 (4)	48.43 (4)	49.98 (4)
Eu1^iii—Eu1—Al2^xv	130.79 (4)	130.02 (4)	131.57 (4)
Eu1^iii—Eu1—Al2^xvi	130.796 (11)	130.682 (11)	130.910 (10)
Eu1^iii—Eu1—Al2^xvii	49.202 (12)	49.090 (10)	49.318 (11)
Eu1^iv—Eu1—Al1	51.84 (2)	50.82 (2)	52.85 (2)
Eu1^iv—Eu1—Al1^v	90.00 (3)	89.60 (3)	90.38 (3)
Eu1^iv—Eu1—Al1^vi	90.01 (3)	89.62 (3)	90.40 (3)
Eu1^iv—Eu1—Al1^i	128.18 (2)	127.15 (2)	129.18 (2)
Eu1^iv—Eu1—Al1^vii	128.16 (2)	127.15 (2)	129.18 (2)
Eu1^iv—Eu1—Al1^viii	90.00 (3)	89.62 (3)	90.40 (3)
Eu1^iv—Eu1—Al1^ix	89.99 (3)	89.60 (3)	90.38 (3)
Eu1^iv—Eu1—Al1^x	51.82 (2)	50.82 (2)	52.85 (2)
Eu1^iv—Eu1—Al2	90.01 (2)	88.80 (2)	91.20 (2)
Eu1^iv—Eu1—Al2^v	130.80 (4)	130.02 (4)	131.57 (4)
Eu1^iv—Eu1—Al2^xi	49.21 (4)	48.43 (4)	49.98 (4)
Eu1^iv—Eu1—Al2^vi	130.798 (11)	130.682 (11)	130.910 (10)
Eu1^iv—Eu1—Al2^xii	49.204 (12)	49.090 (10)	49.318 (11)
Eu1^iv—Eu1—Al2^xiii	89.99 (2)	88.80 (2)	91.20 (2)
Eu1^iv—Eu1—Al2^xiv	130.79 (4)	130.02 (4)	131.57 (4)
Eu1^iv—Eu1—Al2^xv	49.20 (4)	48.43 (4)	49.98 (4)
Eu1^iv—Eu1—Al2^xvi	130.796 (11)	130.682 (11)	130.910 (10)
Eu1^iv—Eu1—Al2^xvii	49.202 (12)	49.090 (10)	49.318 (11)
Al1—Eu1—Al1^v	128.15 (5)	127.98 (6)	128.35 (6)
Al1—Eu1—Al1^vi	128.20 (3)	126.40 (4)	129.99 (4)
Al1—Eu1—Al1^i	76.34 (3)	76.33 (3)	76.36 (3)
Al1—Eu1—Al1^vii	179.63 (2)	179.410 (18)	180
Al1—Eu1—Al1^viii	51.85 (5)	51.84 (6)	51.87 (4)
Al1—Eu1—Al1^ix	51.80 (3)	49.94 (4)	53.67 (4)
Al1—Eu1—Al1^x	103.66 (3)	103.09 (3)	104.20 (4)
Al1—Eu1—Al2	38.19 (3)	38.00 (3)	38.39 (3)
Al1—Eu1—Al2^v	134.77 (4)	134.37 (4)	135.17 (4)
Al1—Eu1—Al2^xi	84.09 (4)	82.73 (5)	85.43 (5)
Al1—Eu1—Al2^vi	134.78 (3)	134.49 (3)	135.06 (3)
Al1—Eu1—Al2^xii	84.09 (3)	83.32 (3)	84.85 (3)
Al1—Eu1—Al2^xiii	141.81 (3)	141.17 (4)	142.46 (4)
Al1—Eu1—Al2^xiv	95.91 (4)	94.53 (5)	97.30 (5)
Al1—Eu1—Al2^xv	45.23 (4)	45.01 (5)	45.49 (5)
Al1—Eu1—Al2^xvi	95.91 (3)	95.12 (3)	96.71 (3)
Al1—Eu1—Al2^xvii	45.22 (3)	44.94 (3)	45.52 (3)
Al1^v—Eu1—Al1^vi	76.34 (3)	76.33 (3)	76.36 (3)
Al1^v—Eu1—Al1^i	128.16 (3)	126.40 (4)	129.99 (4)
Al1^v—Eu1—Al1^vii	51.85 (5)	51.84 (6)	51.87 (4)
Al1^v—Eu1—Al1^viii	179.63 (2)	179.410 (18)	180
Al1^v—Eu1—Al1^ix	103.66 (3)	103.09 (3)	104.20 (4)
Al1^v—Eu1—Al1^x	51.84 (3)	49.94 (4)	53.67 (4)
Al1^v—Eu1—Al2	141.82 (3)	141.17 (4)	142.46 (4)
Al1^v—Eu1—Al2^v	45.23 (4)	45.01 (5)	45.49 (5)
Al1^v—Eu1—Al2^xi	95.94 (4)	94.53 (5)	97.30 (5)
Al1^v—Eu1—Al2^vi	95.93 (3)	95.12 (3)	96.71 (3)
Al1^v—Eu1—Al2^xii	45.22 (3)	44.94 (3)	45.52 (3)
Al1^v—Eu1—Al2^xiii	38.19 (3)	38.00 (3)	38.39 (3)
Al1^v—Eu1—Al2^xiv	84.07 (4)	82.73 (5)	85.43 (5)
Al1^v—Eu1—Al2^xv	134.77 (4)	134.37 (4)	135.17 (4)
Al1^v—Eu1—Al2^xvi	134.78 (3)	134.49 (3)	135.06 (3)
Al1^v—Eu1—Al2^xvii	84.07 (3)	83.32 (3)	84.85 (3)
Al1^vi—Eu1—Al1^i	128.15 (5)	127.98 (6)	128.35 (6)
Al1^vi—Eu1—Al1^vii	51.80 (3)	49.94 (4)	53.67 (4)
Al1^vi—Eu1—Al1^viii	103.66 (3)	103.09 (3)	104.20 (4)
Al1^vi—Eu1—Al1^ix	179.63 (2)	179.410 (18)	180
Al1^vi—Eu1—Al1^x	51.85 (5)	51.84 (6)	51.87 (4)
Al1^vi—Eu1—Al2	141.81 (3)	141.17 (4)	142.46 (4)
Al1^vi—Eu1—Al2^v	95.91 (4)	94.53 (5)	97.30 (5)
Al1^vi—Eu1—Al2^xi	45.23 (4)	45.01 (5)	45.49 (5)
Al1^vi—Eu1—Al2^vi	45.22 (3)	44.94 (3)	45.52 (3)
Al1^vi—Eu1—Al2^xii	95.91 (3)	95.12 (3)	96.71 (3)
Al1^vi—Eu1—Al2^xiii	38.19 (3)	38.00 (3)	38.39 (3)
Al1^vi—Eu1—Al2^xiv	134.77 (4)	134.37 (4)	135.17 (4)
Al1^vi—Eu1—Al2^xv	84.09 (4)	82.73 (5)	85.43 (5)
Al1^vi—Eu1—Al2^xvi	84.09 (3)	83.32 (3)	84.85 (3)
Al1^vi—Eu1—Al2^xvii	134.78 (3)	134.49 (3)	135.06 (3)
Al1^i—Eu1—Al1^vii	103.66 (3)	103.09 (3)	104.20 (4)
Al1^i—Eu1—Al1^viii	51.84 (3)	49.94 (4)	53.67 (4)
Al1^i—Eu1—Al1^ix	51.85 (5)	51.84 (6)	51.87 (4)
Al1^i—Eu1—Al1^x	179.63 (2)	179.410 (18)	180
Al1^i—Eu1—Al2	38.19 (3)	38.00 (3)	38.39 (3)
Al1^i—Eu1—Al2^v	84.07 (4)	82.73 (5)	85.43 (5)
Al1^i—Eu1—Al2^xi	134.77 (4)	134.37 (4)	135.17 (4)
Al1^i—Eu1—Al2^vi	84.07 (3)	83.32 (3)	84.85 (3)
Al1^i—Eu1—Al2^xii	134.78 (3)	134.49 (3)	135.06 (3)
Al1^i—Eu1—Al2^xiii	141.82 (3)	141.17 (4)	142.46 (4)
Al1^i—Eu1—Al2^xiv	45.23 (4)	45.01 (5)	45.49 (5)
Al1^i—Eu1—Al2^xv	95.94 (4)	94.53 (5)	97.30 (5)
Al1^i—Eu1—Al2^xvi	45.22 (3)	44.94 (3)	45.52 (3)
Al1^i—Eu1—Al2^xvii	95.93 (3)	95.12 (3)	96.71 (3)
Al1^vii—Eu1—Al1^viii	128.15 (5)	127.98 (6)	128.35 (6)
Al1^vii—Eu1—Al1^ix	128.20 (3)	126.40 (4)	129.99 (4)
Al1^vii—Eu1—Al1^x	76.34 (3)	76.33 (4)	76.36 (3)
Al1^vii—Eu1—Al2	141.81 (3)	141.17 (4)	142.46 (4)
Al1^vii—Eu1—Al2^v	45.23 (4)	45.01 (5)	45.49 (5)
Al1^vii—Eu1—Al2^xi	95.91 (4)	94.53 (5)	97.30 (5)
Al1^vii—Eu1—Al2^vi	45.22 (3)	44.94 (3)	45.52 (3)
Al1^vii—Eu1—Al2^xii	95.91 (3)	95.12 (3)	96.71 (3)
Al1^vii—Eu1—Al2^xiii	38.19 (3)	38.00 (3)	38.39 (3)
Al1^vii—Eu1—Al2^xiv	84.09 (4)	82.73 (5)	85.43 (5)
Al1^vii—Eu1—Al2^xv	134.77 (4)	134.37 (4)	135.17 (4)
Al1^vii—Eu1—Al2^xvi	84.09 (3)	83.32 (3)	84.85 (3)
Al1^vii—Eu1—Al2^xvii	134.78 (3)	134.49 (3)	135.06 (3)
Al1^viii—Eu1—Al1^ix	76.34 (3)	76.33 (4)	76.36 (3)
Al1^viii—Eu1—Al1^x	128.16 (3)	126.40 (4)	129.99 (4)
Al1^viii—Eu1—Al2	38.19 (3)	38.00 (3)	38.39 (3)
Al1^viii—Eu1—Al2^v	134.77 (4)	134.37 (4)	135.17 (4)
Al1^viii—Eu1—Al2^xi	84.07 (4)	82.73 (5)	85.43 (5)
Al1^viii—Eu1—Al2^vi	84.07 (3)	83.32 (3)	84.85 (3)
Al1^viii—Eu1—Al2^xii	134.78 (3)	134.49 (3)	135.06 (3)
Al1^viii—Eu1—Al2^xiii	141.82 (3)	141.17 (4)	142.46 (4)
Al1^viii—Eu1—Al2^xiv	95.94 (4)	94.53 (5)	97.30 (5)
Al1^viii—Eu1—Al2^xv	45.23 (4)	45.01 (5)	45.49 (5)
Al1^viii—Eu1—Al2^xvi	45.22 (3)	44.94 (3)	45.52 (3)
Al1^viii—Eu1—Al2^xvii	95.93 (3)	95.12 (3)	96.71 (3)
Al1^ix—Eu1—Al1^x	128.15 (5)	127.98 (6)	128.35 (6)
Al1^ix—Eu1—Al2	38.19 (3)	38.00 (3)	38.39 (3)
Al1^ix—Eu1—Al2^v	84.09 (4)	82.73 (5)	85.43 (5)
Al1^ix—Eu1—Al2^xi	134.77 (4)	134.37 (4)	135.17 (4)
Al1^ix—Eu1—Al2^vi	134.78 (3)	134.49 (3)	135.06 (3)
Al1^ix—Eu1—Al2^xii	84.09 (3)	83.32 (3)	84.85 (3)
Al1^ix—Eu1—Al2^xiii	141.81 (3)	141.17 (4)	142.46 (4)
Al1^ix—Eu1—Al2^xiv	45.23 (4)	45.01 (5)	45.49 (5)
Al1^ix—Eu1—Al2^xv	95.91 (4)	94.53 (5)	97.30 (5)
Al1^ix—Eu1—Al2^xvi	95.91 (3)	95.12 (3)	96.71 (3)
Al1^ix—Eu1—Al2^xvii	45.22 (3)	44.94 (3)	45.52 (3)
Al1^x—Eu1—Al2	141.82 (3)	141.17 (4)	142.46 (4)
Al1^x—Eu1—Al2^v	95.94 (4)	94.53 (5)	97.30 (5)
Al1^x—Eu1—Al2^xi	45.23 (4)	45.01 (5)	45.49 (5)
Al1^x—Eu1—Al2^vi	95.93 (3)	95.12 (3)	96.71 (3)
Al1^x—Eu1—Al2^xii	45.22 (3)	44.94 (3)	45.52 (3)
Al1^x—Eu1—Al2^xiii	38.19 (3)	38.00 (3)	38.39 (3)
Al1^x—Eu1—Al2^xiv	134.77 (4)	134.37 (4)	135.17 (4)
Al1^x—Eu1—Al2^xv	84.07 (4)	82.73 (5)	85.43 (5)
Al1^x—Eu1—Al2^xvi	134.78 (3)	134.49 (3)	135.06 (3)
Al1^x—Eu1—Al2^xvii	84.07 (3)	83.32 (3)	84.85 (3)
Al2—Eu1—Al2^v	112.46 (2)	112.44 (2)	112.48 (2)
Al2—Eu1—Al2^xi	112.46 (2)	112.44 (2)	112.48 (2)
Al2—Eu1—Al2^vi	112.46 (4)	110.50 (4)	114.47 (4)
Al2—Eu1—Al2^xii	112.50 (4)	110.50 (4)	114.47 (4)
Al2—Eu1—Al2^xiii	179.40 (4)	179.04 (5)	180
Al2—Eu1—Al2^xiv	67.54 (2)	67.52 (2)	67.56 (2)
Al2—Eu1—Al2^xv	67.54 (2)	67.52 (2)	67.56 (2)
Al2—Eu1—Al2^xvi	67.50 (4)	65.50 (4)	69.53 (4)
Al2—Eu1—Al2^xvii	67.54 (4)	65.50 (4)	69.53 (4)
Al2^v—Eu1—Al2^xi	135.02 (3)	135.01 (3)	135.04 (3)
Al2^v—Eu1—Al2^vi	81.58 (4)	80.92 (4)	82.25 (4)
Al2^v—Eu1—Al2^xii	81.60 (4)	80.92 (4)	82.25 (4)
Al2^v—Eu1—Al2^xiii	67.54 (2)	67.52 (2)	67.56 (2)
Al2^v—Eu1—Al2^xiv	44.98 (3)	44.96 (3)	44.99 (3)
Al2^v—Eu1—Al2^xv	179.76 (5)	179.60 (6)	180
Al2^v—Eu1—Al2^xvi	98.40 (4)	97.73 (4)	99.09 (4)
Al2^v—Eu1—Al2^xvii	98.42 (4)	97.73 (4)	99.09 (4)
Al2^xi—Eu1—Al2^vi	81.58 (4)	80.92 (4)	82.25 (4)
Al2^xi—Eu1—Al2^xii	81.60 (4)	80.92 (4)	82.25 (4)
Al2^xi—Eu1—Al2^xiii	67.54 (2)	67.52 (2)	67.56 (2)
Al2^xi—Eu1—Al2^xiv	179.76 (5)	179.60 (6)	180
Al2^xi—Eu1—Al2^xv	44.98 (3)	44.96 (3)	44.99 (3)
Al2^xi—Eu1—Al2^xvi	98.40 (4)	97.73 (4)	99.09 (4)
Al2^xi—Eu1—Al2^xvii	98.42 (4)	97.73 (4)	99.09 (4)
Al2^vi—Eu1—Al2^xii	135.04 (4)	135.03 (4)	135.04 (4)
Al2^vi—Eu1—Al2^xiii	67.54 (4)	65.50 (4)	69.53 (4)
Al2^vi—Eu1—Al2^xiv	98.42 (4)	97.73 (4)	99.09 (4)
Al2^vi—Eu1—Al2^xv	98.42 (4)	97.73 (4)	99.09 (4)
Al2^vi—Eu1—Al2^xvi	44.96 (4)	44.81 (4)	45.11 (4)
Al2^vi—Eu1—Al2^xvii	179.92 (3)	179.85 (4)	180
Al2^xii—Eu1—Al2^xiii	67.50 (4)	65.50 (4)	69.53 (4)
Al2^xii—Eu1—Al2^xiv	98.40 (4)	97.73 (4)	99.09 (4)
Al2^xii—Eu1—Al2^xv	98.40 (4)	97.73 (4)	99.09 (4)
Al2^xii—Eu1—Al2^xvi	179.92 (3)	179.85 (4)	180
Al2^xii—Eu1—Al2^xvii	44.96 (4)	44.81 (4)	45.11 (4)
Al2^xiii—Eu1—Al2^xiv	112.46 (2)	112.44 (2)	112.48 (2)
Al2^xiii—Eu1—Al2^xv	112.46 (2)	112.44 (2)	112.48 (2)
Al2^xiii—Eu1—Al2^xvi	112.50 (4)	110.50 (4)	114.47 (4)
Al2^xiii—Eu1—Al2^xvii	112.46 (4)	110.50 (4)	114.47 (4)
Al2^xiv—Eu1—Al2^xv	135.02 (3)	135.01 (3)	135.04 (3)
Al2^xiv—Eu1—Al2^xvi	81.60 (4)	80.92 (4)	82.25 (4)
Al2^xiv—Eu1—Al2^xvii	81.58 (4)	80.92 (4)	82.25 (4)
Al2^xv—Eu1—Al2^xvi	81.60 (4)	80.92 (4)	82.25 (4)
Al2^xv—Eu1—Al2^xvii	81.58 (4)	80.92 (4)	82.25 (4)
Al2^xvi—Eu1—Al2^xvii	135.04 (4)	135.03 (4)	135.04 (4)
Eu1—Al1—Eu1^xxii	128.15 (4)	128.132 (11)	128.18 (8)
Eu1—Al1—Eu1^xxiii	128.20 (4)	126.33 (8)	130.06 (8)
Eu1—Al1—Eu1^iv	76.342 (7)	76.327 (7)	76.358 (8)
Eu1—Al1—Al1^i	51.84 (2)	50.82 (2)	52.85 (3)
Eu1—Al1—Al1^ii	89.99 (3)	89.60 (2)	90.38 (2)
Eu1—Al1—Al1^iii	90.01 (3)	89.62 (5)	90.40 (5)
Eu1—Al1—Al1^iv	128.16 (2)	127.15 (3)	129.18 (2)
Eu1—Al1—Al1^viii	64.09 (2)	62.433 (17)	65.701 (14)
Eu1—Al1—Al1^xviii	115.89 (3)	114.84 (4)	116.83 (3)
Eu1—Al1—Al1^ix	64.10 (4)	63.17 (5)	65.03 (5)
Eu1—Al1—Al1^xix	115.90 (4)	114.97 (5)	116.83 (5)
Eu1—Al1—Al2	86.30 (5)	85.41 (6)	87.18 (6)
Eu1—Al1—Al2^xi	46.192 (13)	45.983 (13)	46.396 (12)
Eu1—Al1—Al2^xii	46.19 (3)	45.80 (3)	46.59 (3)
Eu1—Al1—Al2^iv	162.52 (5)	161.53 (7)	163.28 (5)
Eu1—Al1—Al2^xx	113.54 (5)	111.92 (5)	115.14 (5)
Eu1—Al1—Al2^xv	63.58 (3)	62.71 (2)	64.42 (2)
Eu1—Al1—Al2^xvii	63.59 (5)	61.81 (6)	65.31 (6)
Eu1—Al1—Al2^xxi	170.12 (4)	168.48 (5)	171.69 (5)
Eu1^xxii—Al1—Eu1^xxiii	76.342 (7)	76.327 (7)	76.358 (8)
Eu1^xxii—Al1—Eu1^iv	128.16 (4)	126.33 (8)	130.06 (8)
Eu1^xxii—Al1—Al1^i	90.00 (3)	89.60 (2)	90.38 (2)
Eu1^xxii—Al1—Al1^ii	51.82 (2)	50.82 (2)	52.85 (3)
Eu1^xxii—Al1—Al1^iii	128.18 (2)	127.15 (3)	129.18 (2)
Eu1^xxii—Al1—Al1^iv	90.00 (3)	89.62 (5)	90.40 (5)
Eu1^xxii—Al1—Al1^viii	64.06 (2)	62.432 (17)	65.702 (14)
Eu1^xxii—Al1—Al1^xviii	115.87 (3)	114.84 (4)	116.83 (3)
Eu1^xxii—Al1—Al1^ix	115.92 (4)	114.97 (5)	116.83 (5)
Eu1^xxii—Al1—Al1^xix	64.08 (4)	63.17 (5)	65.03 (5)
Eu1^xxii—Al1—Al2	63.56 (3)	62.71 (2)	64.42 (2)
Eu1^xxii—Al1—Al2^xi	113.51 (5)	111.92 (5)	115.14 (5)
Eu1^xxii—Al1—Al2^xii	170.09 (5)	168.48 (5)	171.69 (5)
Eu1^xxii—Al1—Al2^iv	63.56 (5)	61.81 (6)	65.31 (6)
Eu1^xxii—Al1—Al2^xx	46.195 (13)	45.983 (13)	46.396 (12)
Eu1^xxii—Al1—Al2^xv	86.28 (5)	85.41 (6)	87.17 (6)
Eu1^xxii—Al1—Al2^xvii	162.54 (5)	161.53 (7)	163.28 (5)
Eu1^xxii—Al1—Al2^xxi	46.20 (3)	45.80 (3)	46.59 (3)
Eu1^xxiii—Al1—Eu1^iv	128.15 (4)	128.132 (12)	128.18 (8)
Eu1^xxiii—Al1—Al1^i	90.01 (3)	89.62 (5)	90.40 (5)
Eu1^xxiii—Al1—Al1^ii	128.16 (2)	127.15 (3)	129.18 (2)
Eu1^xxiii—Al1—Al1^iii	51.84 (2)	50.82 (2)	52.85 (3)
Eu1^xxiii—Al1—Al1^iv	89.99 (3)	89.60 (2)	90.38 (2)
Eu1^xxiii—Al1—Al1^viii	115.89 (3)	114.84 (4)	116.83 (3)
Eu1^xxiii—Al1—Al1^xviii	64.09 (2)	62.432 (17)	65.702 (14)
Eu1^xxiii—Al1—Al1^ix	64.10 (4)	63.17 (5)	65.03 (5)
Eu1^xxiii—Al1—Al1^xix	115.90 (4)	114.97 (5)	116.83 (5)
Eu1^xxiii—Al1—Al2	63.59 (5)	61.81 (6)	65.31 (6)
Eu1^xxiii—Al1—Al2^xi	170.12 (4)	168.48 (5)	171.69 (5)
Eu1^xxiii—Al1—Al2^xii	113.54 (5)	111.92 (5)	115.14 (5)
Eu1^xxiii—Al1—Al2^iv	63.58 (3)	62.71 (2)	64.42 (2)
Eu1^xxiii—Al1—Al2^xx	46.20 (3)	45.80 (3)	46.59 (3)
Eu1^xxiii—Al1—Al2^xv	162.52 (5)	161.53 (7)	163.28 (5)
Eu1^xxiii—Al1—Al2^xvii	86.30 (5)	85.41 (6)	87.17 (6)
Eu1^xxiii—Al1—Al2^xxi	46.192 (13)	45.983 (13)	46.396 (12)
Eu1^iv—Al1—Al1^i	128.18 (2)	127.15 (3)	129.18 (2)
Eu1^iv—Al1—Al1^ii	90.00 (3)	89.62 (5)	90.40 (5)
Eu1^iv—Al1—Al1^iii	90.00 (3)	89.60 (2)	90.38 (2)
Eu1^iv—Al1—Al1^iv	51.82 (2)	50.82 (2)	52.85 (3)
Eu1^iv—Al1—Al1^viii	115.87 (3)	114.84 (4)	116.83 (3)
Eu1^iv—Al1—Al1^xviii	64.06 (2)	62.433 (17)	65.701 (14)
Eu1^iv—Al1—Al1^ix	115.92 (4)	114.97 (5)	116.83 (5)
Eu1^iv—Al1—Al1^xix	64.08 (4)	63.17 (5)	65.03 (5)
Eu1^iv—Al1—Al2	162.54 (5)	161.53 (7)	163.28 (5)
Eu1^iv—Al1—Al2^xi	46.20 (3)	45.80 (3)	46.59 (3)
Eu1^iv—Al1—Al2^xii	46.196 (13)	45.983 (13)	46.396 (12)
Eu1^iv—Al1—Al2^iv	86.28 (5)	85.41 (6)	87.18 (6)
Eu1^iv—Al1—Al2^xx	170.09 (5)	168.48 (5)	171.69 (5)
Eu1^iv—Al1—Al2^xv	63.56 (5)	61.81 (6)	65.31 (6)
Eu1^iv—Al1—Al2^xvii	63.56 (3)	62.71 (2)	64.42 (2)
Eu1^iv—Al1—Al2^xxi	113.51 (5)	111.92 (5)	115.14 (5)
Al1^i—Al1—Al1^ii	90.00 (4)	90.00 (4)	90.00 (4)
Al1^i—Al1—Al1^iii	90.00 (5)	90.00 (6)	90.00 (6)
Al1^i—Al1—Al1^iv	180	180	180
Al1^i—Al1—Al1^viii	45.02 (3)	42.29 (4)	47.71 (4)
Al1^i—Al1—Al1^xviii	135.03 (5)	132.29 (8)	137.71 (8)
Al1^i—Al1—Al1^ix	45.00 (6)	45.00 (6)	45.00 (6)
Al1^i—Al1—Al1^xix	135.00 (7)	135.00 (6)	135.00 (6)
Al1^i—Al1—Al2	34.51 (4)	34.41 (4)	34.68 (4)
Al1^i—Al1—Al2^xi	90.00 (3)	89.34 (3)	90.65 (3)
Al1^i—Al1—Al2^xii	90.01 (3)	89.35 (4)	90.66 (4)
Al1^i—Al1—Al2^iv	145.49 (4)	145.32 (4)	145.59 (4)
Al1^i—Al1—Al2^xx	61.71 (3)	61.08 (3)	62.32 (3)
Al1^i—Al1—Al2^xv	90.02 (6)	87.55 (5)	92.46 (5)
Al1^i—Al1—Al2^xvii	90.02 (6)	87.54 (8)	92.45 (8)
Al1^i—Al1—Al2^xxi	118.31 (3)	117.68 (3)	118.92 (3)
Al1^ii—Al1—Al1^iii	180	180	180
Al1^ii—Al1—Al1^iv	90.00 (5)	90.00 (6)	90.00 (6)
Al1^ii—Al1—Al1^viii	44.97 (3)	42.29 (4)	47.71 (4)
Al1^ii—Al1—Al1^xviii	134.98 (5)	132.29 (8)	137.71 (8)
Al1^ii—Al1—Al1^ix	135.00 (7)	135.00 (6)	135.00 (6)
Al1^ii—Al1—Al1^xix	45.00 (6)	45.00 (6)	45.00 (5)
Al1^ii—Al1—Al2	89.98 (6)	87.55 (5)	92.46 (5)
Al1^ii—Al1—Al2^xi	61.69 (3)	61.08 (3)	62.32 (3)
Al1^ii—Al1—Al2^xii	118.29 (3)	117.68 (3)	118.92 (3)
Al1^ii—Al1—Al2^iv	89.98 (6)	87.54 (8)	92.45 (8)
Al1^ii—Al1—Al2^xx	89.99 (3)	89.34 (3)	90.65 (3)
Al1^ii—Al1—Al2^xv	34.51 (4)	34.41 (4)	34.68 (4)
Al1^ii—Al1—Al2^xvii	145.49 (4)	145.32 (4)	145.59 (4)
Al1^ii—Al1—Al2^xxi	90.00 (3)	89.35 (4)	90.66 (4)
Al1^iii—Al1—Al1^iv	90.00 (4)	90.00 (4)	90.00 (4)
Al1^iii—Al1—Al1^viii	135.03 (5)	132.29 (8)	137.71 (8)
Al1^iii—Al1—Al1^xviii	45.02 (3)	42.29 (4)	47.71 (4)
Al1^iii—Al1—Al1^ix	45.00 (6)	45.00 (6)	45.00 (6)
Al1^iii—Al1—Al1^xix	135.00 (7)	135.00 (6)	135.00 (6)
Al1^iii—Al1—Al2	90.02 (6)	87.54 (8)	92.45 (8)
Al1^iii—Al1—Al2^xi	118.31 (3)	117.68 (3)	118.92 (3)
Al1^iii—Al1—Al2^xii	61.71 (3)	61.08 (3)	62.32 (3)
Al1^iii—Al1—Al2^iv	90.02 (6)	87.55 (5)	92.46 (5)
Al1^iii—Al1—Al2^xx	90.01 (3)	89.35 (4)	90.66 (4)
Al1^iii—Al1—Al2^xv	145.49 (4)	145.32 (4)	145.59 (4)
Al1^iii—Al1—Al2^xvii	34.51 (4)	34.41 (4)	34.68 (4)
Al1^iii—Al1—Al2^xxi	90.00 (3)	89.34 (3)	90.65 (3)
Al1^iv—Al1—Al1^viii	134.98 (5)	132.29 (8)	137.71 (8)
Al1^iv—Al1—Al1^xviii	44.97 (3)	42.29 (4)	47.71 (4)
Al1^iv—Al1—Al1^ix	135.00 (7)	135.00 (6)	135.00 (6)
Al1^iv—Al1—Al1^xix	45.00 (6)	45.00 (6)	45.00 (5)
Al1^iv—Al1—Al2	145.49 (4)	145.32 (4)	145.59 (4)
Al1^iv—Al1—Al2^xi	90.00 (3)	89.35 (4)	90.66 (4)
Al1^iv—Al1—Al2^xii	89.99 (3)	89.34 (3)	90.65 (3)
Al1^iv—Al1—Al2^iv	34.51 (4)	34.41 (4)	34.68 (4)
Al1^iv—Al1—Al2^xx	118.29 (3)	117.68 (3)	118.92 (3)
Al1^iv—Al1—Al2^xv	89.98 (6)	87.54 (8)	92.45 (8)
Al1^iv—Al1—Al2^xvii	89.98 (6)	87.55 (5)	92.46 (5)
Al1^iv—Al1—Al2^xxi	61.69 (3)	61.08 (3)	62.32 (3)
Al1^viii—Al1—Al1^xviii	176.53 (6)	174.59 (12)	179.88
Al1^viii—Al1—Al1^ix	90.03 (7)	87.29 (9)	92.71 (9)
Al1^viii—Al1—Al1^xix	89.97 (7)	87.29 (9)	92.71 (9)
Al1^viii—Al1—Al2	54.33 (6)	54.07 (6)	54.59 (6)
Al1^viii—Al1—Al2^xi	70.39 (4)	69.46 (4)	71.33 (4)
Al1^viii—Al1—Al2^xii	109.57 (4)	108.46 (4)	110.61 (4)
Al1^viii—Al1—Al2^iv	125.58 (7)	121.44 (9)	129.72 (8)
Al1^viii—Al1—Al2^xx	70.41 (4)	69.46 (4)	71.33 (4)
Al1^viii—Al1—Al2^xv	54.34 (6)	54.07 (6)	54.59 (6)
Al1^viii—Al1—Al2^xvii	125.66 (7)	121.44 (9)	129.72 (8)
Al1^viii—Al1—Al2^xxi	109.55 (4)	108.46 (4)	110.61 (4)
Al1^xviii—Al1—Al1^ix	90.03 (7)	87.29 (9)	92.71 (9)
Al1^xviii—Al1—Al1^xix	89.97 (7)	87.29 (9)	92.71 (9)
Al1^xviii—Al1—Al2	125.66 (7)	121.44 (9)	129.72 (8)
Al1^xviii—Al1—Al2^xi	109.55 (4)	108.46 (4)	110.61 (4)
Al1^xviii—Al1—Al2^xii	70.41 (4)	69.46 (4)	71.33 (4)
Al1^xviii—Al1—Al2^iv	54.34 (6)	54.07 (6)	54.59 (6)
Al1^xviii—Al1—Al2^xx	109.57 (4)	108.46 (4)	110.61 (4)
Al1^xviii—Al1—Al2^xv	125.58 (7)	121.44 (9)	129.72 (8)
Al1^xviii—Al1—Al2^xvii	54.33 (6)	54.07 (6)	54.59 (6)
Al1^xviii—Al1—Al2^xxi	70.39 (4)	69.46 (4)	71.33 (4)
Al1^ix—Al1—Al1^xix	180	180	180
Al1^ix—Al1—Al2	54.36 (5)	52.27 (6)	56.42 (6)
Al1^ix—Al1—Al2^xi	109.59 (3)	108.73 (3)	110.44 (3)
Al1^ix—Al1—Al2^xii	70.42 (3)	69.56 (3)	71.27 (3)
Al1^ix—Al1—Al2^iv	125.68 (6)	123.58 (6)	127.73 (6)
Al1^ix—Al1—Al2^xx	70.42 (3)	69.56 (3)	71.27 (3)
Al1^ix—Al1—Al2^xv	125.68 (6)	123.58 (6)	127.73 (6)
Al1^ix—Al1—Al2^xvii	54.36 (5)	52.27 (6)	56.42 (6)
Al1^ix—Al1—Al2^xxi	109.59 (3)	108.73 (3)	110.44 (3)
Al1^xix—Al1—Al2	125.64 (6)	123.58 (6)	127.73 (6)
Al1^xix—Al1—Al2^xi	70.41 (3)	69.56 (3)	71.27 (3)
Al1^xix—Al1—Al2^xii	109.58 (3)	108.73 (3)	110.44 (3)
Al1^xix—Al1—Al2^iv	54.32 (5)	52.27 (6)	56.42 (6)
Al1^xix—Al1—Al2^xx	109.58 (3)	108.73 (3)	110.44 (3)
Al1^xix—Al1—Al2^xv	54.32 (5)	52.27 (6)	56.42 (6)
Al1^xix—Al1—Al2^xvii	125.64 (6)	123.58 (6)	127.73 (6)
Al1^xix—Al1—Al2^xxi	70.41 (3)	69.56 (3)	71.27 (3)
Al2—Al1—Al2^xi	119.85 (7)	118.76 (5)	120.92 (5)
Al2—Al1—Al2^xii	119.89 (5)	117.84 (8)	121.86 (8)
Al2—Al1—Al2^iv	110.98 (5)	110.91 (5)	111.06 (5)
Al2—Al1—Al2^xx	27.26 (4)	26.54 (4)	28.02 (4)
Al2—Al1—Al2^xv	108.67 (8)	108.64 (11)	108.72 (11)
Al2—Al1—Al2^xvii	108.73 (7)	104.54 (10)	112.85 (11)
Al2—Al1—Al2^xxi	83.83 (4)	83.07 (4)	84.56 (4)
Al2^xi—Al1—Al2^xii	56.60 (3)	56.60 (3)	56.60 (3)
Al2^xi—Al1—Al2^iv	119.85 (5)	117.84 (8)	121.86 (8)
Al2^xi—Al1—Al2^xx	140.80 (5)	140.25 (8)	141.40 (8)
Al2^xi—Al1—Al2^xv	27.25 (4)	26.54 (4)	28.02 (4)
Al2^xi—Al1—Al2^xvii	83.83 (4)	83.07 (4)	84.56 (4)
Al2^xi—Al1—Al2^xxi	140.81 (4)	139.13 (7)	142.54 (7)
Al2^xii—Al1—Al2^iv	119.87 (7)	118.76 (5)	120.92 (5)
Al2^xii—Al1—Al2^xx	140.84 (4)	139.13 (7)	142.54 (7)
Al2^xii—Al1—Al2^xv	83.81 (4)	83.07 (4)	84.56 (4)
Al2^xii—Al1—Al2^xvii	27.26 (4)	26.54 (4)	28.02 (4)
Al2^xii—Al1—Al2^xxi	140.81 (5)	140.25 (8)	141.40 (8)
Al2^iv—Al1—Al2^xx	83.81 (4)	83.07 (4)	84.56 (4)
Al2^iv—Al1—Al2^xv	108.65 (7)	104.54 (10)	112.85 (11)
Al2^iv—Al1—Al2^xvii	108.67 (8)	108.64 (11)	108.72 (11)
Al2^iv—Al1—Al2^xxi	27.25 (4)	26.54 (4)	28.02 (4)
Al2^xx—Al1—Al2^xv	119.87 (7)	118.76 (5)	120.92 (5)
Al2^xx—Al1—Al2^xvii	119.89 (5)	117.84 (8)	121.86 (8)
Al2^xx—Al1—Al2^xxi	56.60 (3)	56.60 (3)	56.60 (3)
Al2^xv—Al1—Al2^xvii	110.98 (5)	110.91 (5)	111.06 (5)
Al2^xv—Al1—Al2^xxi	119.85 (5)	117.84 (8)	121.86 (8)
Al2^xvii—Al1—Al2^xxi	119.85 (7)	118.76 (5)	120.92 (5)
Eu1—Al2—Eu1^xxiv	112.46 (2)	112.44 (2)	112.48 (2)
Eu1—Al2—Eu1^xxii	112.46 (2)	112.44 (2)	112.48 (2)
Eu1—Al2—Eu1^xxv	112.50 (5)	110.47 (5)	114.50 (5)
Eu1—Al2—Eu1^xxiii	112.46 (5)	110.47 (5)	114.50 (5)
Eu1—Al2—Al1	55.51 (4)	54.44 (4)	56.59 (4)
Eu1—Al2—Al1^xxiv	151.68 (5)	149.88 (4)	153.51 (4)
Eu1—Al2—Al1^xxv	151.71 (5)	149.88 (4)	153.51 (4)
Eu1—Al2—Al1^i	55.53 (4)	54.44 (4)	56.59 (4)
Eu1—Al2—Al1^xxvi	151.71 (5)	149.88 (4)	153.51 (4)
Eu1—Al2—Al1^viii	55.53 (4)	54.44 (4)	56.59 (4)
Eu1—Al2—Al1^ix	55.51 (4)	54.44 (4)	56.59 (4)
Eu1—Al2—Al1^xxvii	151.68 (5)	149.88 (4)	153.51 (4)
Eu1—Al2—Al2^i	90.01 (4)	88.80 (3)	91.20 (3)
Eu1—Al2—Al2^ii	90.01 (4)	88.80 (3)	91.20 (3)
Eu1—Al2—Al2^iii	89.99 (4)	88.80 (3)	91.20 (3)
Eu1—Al2—Al2^iv	89.99 (4)	88.80 (3)	91.20 (3)
Eu1—Al2—Al2^xx	177.58 (10)	176.21 (10)	180
Eu1—Al2—Al2^xiv	45.83 (2)	45.82 (2)	45.85 (2)
Eu1—Al2—Al2^xv	45.83 (2)	45.82 (2)	45.85 (2)
Eu1—Al2—Al2^xvi	45.82 (3)	45.73 (3)	45.89 (3)
Eu1—Al2—Al2^xvii	45.82 (3)	45.73 (3)	45.89 (3)
Eu1^xxiv—Al2—Eu1^xxii	135.02 (5)	135.01 (5)	135.04 (5)
Eu1^xxiv—Al2—Eu1^xxv	81.60 (4)	80.92 (3)	82.25 (3)
Eu1^xxiv—Al2—Eu1^xxiii	81.58 (4)	80.92 (3)	82.25 (3)
Eu1^xxiv—Al2—Al1	139.00 (8)	135.85 (8)	142.21 (8)
Eu1^xxiv—Al2—Al1^xxiv	49.72 (2)	48.58 (2)	50.88 (2)
Eu1^xxiv—Al2—Al1^xxv	88.45 (3)	87.84 (3)	89.08 (3)
Eu1^xxiv—Al2—Al1^i	71.184 (19)	70.096 (18)	72.278 (19)
Eu1^xxiv—Al2—Al1^xxvi	49.74 (2)	48.58 (2)	50.88 (2)
Eu1^xxiv—Al2—Al1^viii	139.06 (8)	135.85 (8)	142.21 (8)
Eu1^xxiv—Al2—Al1^ix	71.205 (19)	70.096 (18)	72.278 (19)
Eu1^xxiv—Al2—Al1^xxvii	88.46 (3)	87.84 (3)	89.08 (3)
Eu1^xxiv—Al2—Al2^i	49.21 (3)	48.43 (3)	49.98 (3)
Eu1^xxiv—Al2—Al2^ii	130.80 (6)	130.02 (6)	131.57 (6)
Eu1^xxiv—Al2—Al2^iii	49.20 (3)	48.43 (3)	49.98 (3)
Eu1^xxiv—Al2—Al2^iv	130.79 (6)	130.02 (6)	131.57 (6)
Eu1^xxiv—Al2—Al2^xx	67.51 (2)	67.50 (2)	67.52 (2)
Eu1^xxiv—Al2—Al2^xiv	66.629 (17)	66.622 (17)	66.636 (17)
Eu1^xxiv—Al2—Al2^xv	158.21 (4)	158.10 (4)	158.33 (4)
Eu1^xxiv—Al2—Al2^xvi	105.45 (4)	104.36 (4)	106.52 (4)
Eu1^xxiv—Al2—Al2^xvii	105.43 (4)	104.36 (4)	106.52 (4)
Eu1^xxii—Al2—Eu1^xxv	81.60 (4)	80.92 (3)	82.25 (3)
Eu1^xxii—Al2—Eu1^xxiii	81.58 (4)	80.92 (3)	82.25 (3)
Eu1^xxii—Al2—Al1	71.205 (19)	70.096 (18)	72.278 (19)
Eu1^xxii—Al2—Al1^xxiv	88.46 (3)	87.84 (3)	89.08 (3)
Eu1^xxii—Al2—Al1^xxv	49.74 (2)	48.58 (2)	50.88 (2)
Eu1^xxii—Al2—Al1^i	139.06 (8)	135.85 (8)	142.21 (8)
Eu1^xxii—Al2—Al1^xxvi	88.45 (3)	87.84 (3)	89.08 (3)
Eu1^xxii—Al2—Al1^viii	71.184 (19)	70.096 (18)	72.278 (19)
Eu1^xxii—Al2—Al1^ix	139.00 (8)	135.85 (8)	142.21 (8)
Eu1^xxii—Al2—Al1^xxvii	49.72 (2)	48.58 (2)	50.88 (2)
Eu1^xxii—Al2—Al2^i	130.80 (6)	130.02 (6)	131.57 (6)
Eu1^xxii—Al2—Al2^ii	49.21 (3)	48.43 (3)	49.98 (3)
Eu1^xxii—Al2—Al2^iii	130.79 (6)	130.02 (6)	131.57 (6)
Eu1^xxii—Al2—Al2^iv	49.20 (3)	48.43 (3)	49.98 (3)
Eu1^xxii—Al2—Al2^xx	67.51 (2)	67.50 (2)	67.52 (2)
Eu1^xxii—Al2—Al2^xiv	158.21 (4)	158.10 (4)	158.33 (4)
Eu1^xxii—Al2—Al2^xv	66.629 (17)	66.622 (17)	66.636 (17)
Eu1^xxii—Al2—Al2^xvi	105.45 (4)	104.36 (4)	106.52 (4)
Eu1^xxii—Al2—Al2^xvii	105.43 (4)	104.36 (4)	106.52 (4)
Eu1^xxv—Al2—Eu1^xxiii	135.04 (5)	135.03 (5)	135.04 (5)
Eu1^xxv—Al2—Al1	139.05 (6)	136.42 (6)	141.63 (6)
Eu1^xxv—Al2—Al1^xxiv	88.46 (4)	88.21 (4)	88.72 (4)
Eu1^xxv—Al2—Al1^xxv	49.72 (4)	49.23 (4)	50.22 (4)
Eu1^xxv—Al2—Al1^i	71.23 (7)	69.17 (6)	73.25 (7)
Eu1^xxv—Al2—Al1^xxvi	49.72 (4)	49.23 (4)	50.22 (4)
Eu1^xxv—Al2—Al1^viii	71.23 (7)	69.17 (6)	73.25 (7)
Eu1^xxv—Al2—Al1^ix	139.05 (6)	136.42 (6)	141.63 (6)
Eu1^xxv—Al2—Al1^xxvii	88.46 (4)	88.21 (4)	88.72 (4)
Eu1^xxv—Al2—Al2^i	49.20 (3)	49.09 (3)	49.32 (3)
Eu1^xxv—Al2—Al2^ii	49.20 (3)	49.09 (3)	49.32 (3)
Eu1^xxv—Al2—Al2^iii	130.80 (3)	130.68 (3)	130.91 (3)
Eu1^xxv—Al2—Al2^iv	130.80 (3)	130.68 (3)	130.91 (3)
Eu1^xxv—Al2—Al2^xx	67.53 (7)	65.71 (7)	69.32 (7)
Eu1^xxv—Al2—Al2^xiv	105.47 (5)	102.99 (5)	107.90 (5)
Eu1^xxv—Al2—Al2^xv	105.47 (5)	102.99 (5)	107.90 (5)
Eu1^xxv—Al2—Al2^xvi	66.68 (5)	64.74 (4)	68.63 (5)
Eu1^xxv—Al2—Al2^xvii	158.32 (6)	156.34 (6)	160.23 (6)
Eu1^xxiii—Al2—Al1	71.19 (7)	69.17 (6)	73.25 (7)
Eu1^xxiii—Al2—Al1^xxiv	49.73 (4)	49.23 (4)	50.22 (4)
Eu1^xxiii—Al2—Al1^xxv	88.46 (4)	88.21 (4)	88.72 (4)
Eu1^xxiii—Al2—Al1^i	139.00 (6)	136.42 (6)	141.63 (6)
Eu1^xxiii—Al2—Al1^xxvi	88.46 (4)	88.21 (4)	88.72 (4)
Eu1^xxiii—Al2—Al1^viii	139.00 (6)	136.42 (6)	141.63 (6)
Eu1^xxiii—Al2—Al1^ix	71.19 (7)	69.17 (6)	73.25 (7)
Eu1^xxiii—Al2—Al1^xxvii	49.73 (4)	49.23 (4)	50.22 (4)
Eu1^xxiii—Al2—Al2^i	130.80 (3)	130.68 (3)	130.91 (3)
Eu1^xxiii—Al2—Al2^ii	130.80 (3)	130.68 (3)	130.91 (3)
Eu1^xxiii—Al2—Al2^iii	49.20 (3)	49.09 (3)	49.32 (3)
Eu1^xxiii—Al2—Al2^iv	49.20 (3)	49.09 (3)	49.32 (3)
Eu1^xxiii—Al2—Al2^xx	67.50 (7)	65.71 (7)	69.32 (7)
Eu1^xxiii—Al2—Al2^xiv	105.42 (5)	102.99 (5)	107.90 (5)
Eu1^xxiii—Al2—Al2^xv	105.42 (5)	102.99 (5)	107.90 (5)
Eu1^xxiii—Al2—Al2^xvi	158.29 (6)	156.34 (6)	160.23 (6)
Eu1^xxiii—Al2—Al2^xvii	66.64 (5)	64.74 (4)	68.63 (5)
Al1—Al2—Al1^xxiv	119.85 (8)	118.54 (7)	121.16 (7)
Al1—Al2—Al1^xxv	119.88 (4)	117.96 (5)	121.74 (5)
Al1—Al2—Al1^i	110.98 (6)	110.91 (6)	111.06 (6)
Al1—Al2—Al1^xxvi	152.73 (6)	151.97 (6)	153.46 (6)
Al1—Al2—Al1^viii	71.33 (6)	71.32 (7)	71.34 (6)
Al1—Al2—Al1^ix	71.27 (6)	67.16 (7)	75.46 (7)
Al1—Al2—Al1^xxvii	96.17 (5)	95.44 (5)	96.93 (5)
Al1—Al2—Al2^i	145.49 (6)	145.32 (6)	145.59 (6)
Al1—Al2—Al2^ii	90.02 (5)	87.54 (5)	92.45 (5)
Al1—Al2—Al2^iii	89.98 (7)	87.55 (7)	92.46 (7)
Al1—Al2—Al2^iv	34.51 (4)	34.41 (3)	34.68 (4)
Al1—Al2—Al2^xx	124.39 (8)	122.73 (8)	125.97 (7)
Al1—Al2—Al2^xiv	91.32 (5)	88.81 (6)	93.80 (6)
Al1—Al2—Al2^xv	35.66 (5)	35.53 (5)	35.80 (4)
Al1—Al2—Al2^xvi	91.34 (5)	91.26 (4)	91.40 (6)
Al1—Al2—Al2^xvii	35.64 (4)	33.58 (6)	37.73 (5)
Al1^xxiv—Al2—Al1^xxv	56.60 (3)	56.60 (4)	56.60 (3)
Al1^xxiv—Al2—Al1^i	119.85 (3)	117.96 (4)	121.74 (4)
Al1^xxiv—Al2—Al1^xxvi	39.20 (4)	39.18 (5)	39.21 (3)
Al1^xxiv—Al2—Al1^viii	152.74 (6)	151.97 (6)	153.46 (6)
Al1^xxiv—Al2—Al1^ix	96.17 (5)	95.44 (5)	96.93 (5)
Al1^xxiv—Al2—Al1^xxvii	39.18 (2)	37.46 (4)	40.87 (4)
Al1^xxiv—Al2—Al2^i	90.00 (4)	89.35 (4)	90.66 (4)
Al1^xxiv—Al2—Al2^ii	118.31 (4)	117.68 (4)	118.92 (4)
Al1^xxiv—Al2—Al2^iii	61.69 (3)	61.08 (3)	62.32 (3)
Al1^xxiv—Al2—Al2^iv	90.00 (5)	89.34 (5)	90.65 (5)
Al1^xxiv—Al2—Al2^xx	28.33 (5)	27.49 (5)	29.25 (5)
Al1^xxiv—Al2—Al2^xiv	111.87 (3)	110.26 (4)	113.50 (4)
Al1^xxiv—Al2—Al2^xv	148.58 (5)	147.47 (5)	149.67 (4)
Al1^xxiv—Al2—Al2^xvi	148.64 (5)	147.55 (5)	149.71 (5)
Al1^xxiv—Al2—Al2^xvii	111.89 (6)	110.13 (5)	113.74 (5)
Al1^xxv—Al2—Al1^i	119.88 (8)	118.54 (8)	121.16 (8)
Al1^xxv—Al2—Al1^xxvi	39.16 (2)	37.46 (4)	40.87 (4)
Al1^xxv—Al2—Al1^viii	96.18 (5)	95.44 (5)	96.93 (5)
Al1^xxv—Al2—Al1^ix	152.73 (6)	151.97 (6)	153.46 (6)
Al1^xxv—Al2—Al1^xxvii	39.20 (4)	39.18 (5)	39.21 (3)
Al1^xxv—Al2—Al2^i	89.99 (5)	89.34 (5)	90.65 (5)
Al1^xxv—Al2—Al2^ii	61.71 (3)	61.08 (3)	62.32 (3)
Al1^xxv—Al2—Al2^iii	118.29 (4)	117.68 (4)	118.92 (4)
Al1^xxv—Al2—Al2^iv	90.01 (4)	89.35 (4)	90.66 (4)
Al1^xxv—Al2—Al2^xx	28.34 (5)	27.49 (5)	29.25 (5)
Al1^xxv—Al2—Al2^xiv	148.60 (5)	147.47 (5)	149.67 (4)
Al1^xxv—Al2—Al2^xv	111.90 (3)	110.26 (4)	113.50 (4)
Al1^xxv—Al2—Al2^xvi	111.93 (6)	110.13 (5)	113.74 (5)
Al1^xxv—Al2—Al2^xvii	148.62 (5)	147.55 (5)	149.71 (5)
Al1^i—Al2—Al1^xxvi	96.18 (5)	95.44 (5)	96.93 (5)
Al1^i—Al2—Al1^viii	71.35 (6)	67.16 (7)	75.46 (7)
Al1^i—Al2—Al1^ix	71.33 (6)	71.32 (7)	71.34 (6)
Al1^i—Al2—Al1^xxvii	152.74 (6)	151.97 (6)	153.46 (6)
Al1^i—Al2—Al2^i	34.51 (4)	34.41 (3)	34.68 (4)
Al1^i—Al2—Al2^ii	90.02 (7)	87.55 (7)	92.46 (7)
Al1^i—Al2—Al2^iii	89.98 (5)	87.54 (5)	92.45 (5)
Al1^i—Al2—Al2^iv	145.49 (6)	145.32 (6)	145.59 (6)
Al1^i—Al2—Al2^xx	124.42 (8)	122.73 (8)	125.97 (7)
Al1^i—Al2—Al2^xiv	35.67 (5)	35.53 (5)	35.80 (4)
Al1^i—Al2—Al2^xv	91.36 (5)	88.81 (6)	93.80 (6)
Al1^i—Al2—Al2^xvi	35.68 (4)	33.58 (6)	37.73 (5)
Al1^i—Al2—Al2^xvii	91.34 (5)	91.26 (4)	91.40 (6)
Al1^xxvi—Al2—Al1^viii	119.88 (8)	118.54 (8)	121.16 (8)
Al1^xxvi—Al2—Al1^ix	119.88 (3)	117.96 (4)	121.74 (4)
Al1^xxvi—Al2—Al1^xxvii	56.60 (3)	56.60 (3)	56.60 (3)
Al1^xxvi—Al2—Al2^i	61.71 (3)	61.08 (3)	62.32 (3)
Al1^xxvi—Al2—Al2^ii	89.99 (5)	89.34 (5)	90.65 (5)
Al1^xxvi—Al2—Al2^iii	90.01 (4)	89.35 (4)	90.66 (4)
Al1^xxvi—Al2—Al2^iv	118.29 (4)	117.68 (4)	118.92 (4)
Al1^xxvi—Al2—Al2^xx	28.34 (5)	27.49 (5)	29.25 (5)
Al1^xxvi—Al2—Al2^xiv	111.90 (3)	110.26 (4)	113.50 (4)
Al1^xxvi—Al2—Al2^xv	148.60 (5)	147.47 (5)	149.67 (4)
Al1^xxvi—Al2—Al2^xvi	111.93 (6)	110.13 (5)	113.74 (5)
Al1^xxvi—Al2—Al2^xvii	148.62 (5)	147.55 (5)	149.71 (5)
Al1^viii—Al2—Al1^ix	110.98 (6)	110.91 (6)	111.06 (6)
Al1^viii—Al2—Al1^xxvii	119.85 (4)	117.96 (5)	121.74 (5)
Al1^viii—Al2—Al2^i	90.02 (7)	87.55 (7)	92.46 (7)
Al1^viii—Al2—Al2^ii	34.51 (4)	34.41 (3)	34.68 (4)
Al1^viii—Al2—Al2^iii	145.49 (6)	145.32 (6)	145.59 (6)
Al1^viii—Al2—Al2^iv	89.98 (5)	87.54 (5)	92.45 (5)
Al1^viii—Al2—Al2^xx	124.42 (8)	122.73 (8)	125.97 (7)
Al1^viii—Al2—Al2^xiv	91.36 (5)	88.81 (6)	93.80 (6)
Al1^viii—Al2—Al2^xv	35.67 (5)	35.53 (5)	35.80 (4)
Al1^viii—Al2—Al2^xvi	35.68 (4)	33.58 (6)	37.73 (5)
Al1^viii—Al2—Al2^xvii	91.34 (5)	91.26 (4)	91.40 (6)
Al1^ix—Al2—Al1^xxvii	119.85 (8)	118.54 (7)	121.16 (7)
Al1^ix—Al2—Al2^i	90.02 (5)	87.54 (5)	92.45 (5)
Al1^ix—Al2—Al2^ii	145.49 (6)	145.32 (6)	145.59 (6)
Al1^ix—Al2—Al2^iii	34.51 (4)	34.41 (3)	34.68 (4)
Al1^ix—Al2—Al2^iv	89.98 (7)	87.55 (7)	92.46 (7)
Al1^ix—Al2—Al2^xx	124.39 (8)	122.73 (8)	125.97 (7)
Al1^ix—Al2—Al2^xiv	35.66 (5)	35.53 (5)	35.80 (4)
Al1^ix—Al2—Al2^xv	91.32 (5)	88.81 (6)	93.80 (6)
Al1^ix—Al2—Al2^xvi	91.34 (5)	91.26 (4)	91.40 (6)
Al1^ix—Al2—Al2^xvii	35.64 (4)	33.58 (6)	37.73 (5)
Al1^xxvii—Al2—Al2^i	118.31 (4)	117.68 (4)	118.92 (4)
Al1^xxvii—Al2—Al2^ii	90.00 (4)	89.35 (4)	90.66 (4)
Al1^xxvii—Al2—Al2^iii	90.00 (5)	89.34 (5)	90.65 (5)
Al1^xxvii—Al2—Al2^iv	61.69 (3)	61.08 (3)	62.32 (3)
Al1^xxvii—Al2—Al2^xx	28.33 (5)	27.49 (5)	29.25 (5)
Al1^xxvii—Al2—Al2^xiv	148.58 (5)	147.47 (5)	149.67 (4)
Al1^xxvii—Al2—Al2^xv	111.87 (3)	110.26 (4)	113.50 (4)
Al1^xxvii—Al2—Al2^xvi	148.64 (5)	147.55 (5)	149.71 (5)
Al1^xxvii—Al2—Al2^xvii	111.89 (6)	110.13 (5)	113.74 (5)
Al2^i—Al2—Al2^ii	90.00 (5)	90.00 (5)	90.00 (5)
Al2^i—Al2—Al2^iii	90.00 (3)	90.00 (3)	90.00 (3)
Al2^i—Al2—Al2^iv	180	180	180
Al2^i—Al2—Al2^xx	90.01 (6)	88.50 (6)	91.50 (6)
Al2^i—Al2—Al2^xiv	59.54 (4)	57.61 (4)	61.44 (4)
Al2^i—Al2—Al2^xv	120.50 (6)	118.56 (6)	122.39 (6)
Al2^i—Al2—Al2^xvi	59.54 (4)	58.62 (3)	60.48 (4)
Al2^i—Al2—Al2^xvii	120.48 (4)	119.52 (4)	121.38 (3)
Al2^ii—Al2—Al2^iii	180	180	180
Al2^ii—Al2—Al2^iv	90.00 (3)	90.00 (3)	90.00 (3)
Al2^ii—Al2—Al2^xx	90.01 (6)	88.50 (6)	91.50 (6)
Al2^ii—Al2—Al2^xiv	120.50 (6)	118.56 (6)	122.39 (6)
Al2^ii—Al2—Al2^xv	59.54 (4)	57.61 (4)	61.44 (4)
Al2^ii—Al2—Al2^xvi	59.54 (4)	58.62 (3)	60.48 (4)
Al2^ii—Al2—Al2^xvii	120.48 (4)	119.52 (4)	121.38 (3)
Al2^iii—Al2—Al2^iv	90.00 (5)	90.00 (5)	90.00 (5)
Al2^iii—Al2—Al2^xx	89.99 (6)	88.50 (6)	91.50 (6)
Al2^iii—Al2—Al2^xiv	59.50 (4)	57.61 (4)	61.44 (4)
Al2^iii—Al2—Al2^xv	120.46 (6)	118.56 (6)	122.39 (6)
Al2^iii—Al2—Al2^xvi	120.46 (4)	119.52 (4)	121.38 (3)
Al2^iii—Al2—Al2^xvii	59.52 (4)	58.62 (3)	60.48 (4)
Al2^iv—Al2—Al2^xx	89.99 (6)	88.50 (6)	91.50 (6)
Al2^iv—Al2—Al2^xiv	120.46 (6)	118.56 (6)	122.39 (6)
Al2^iv—Al2—Al2^xv	59.50 (4)	57.61 (4)	61.44 (4)
Al2^iv—Al2—Al2^xvi	120.46 (4)	119.52 (4)	121.38 (3)
Al2^iv—Al2—Al2^xvii	59.52 (4)	58.62 (3)	60.48 (4)
Al2^xx—Al2—Al2^xiv	134.05 (2)	133.95 (2)	134.15 (2)
Al2^xx—Al2—Al2^xv	134.05 (2)	133.95 (2)	134.15 (2)
Al2^xx—Al2—Al2^xvi	134.21 (10)	130.49 (9)	137.91 (9)
Al2^xx—Al2—Al2^xvii	134.14 (10)	130.49 (9)	137.91 (9)
Al2^xiv—Al2—Al2^xv	91.64 (4)	91.59 (4)	91.69 (4)
Al2^xiv—Al2—Al2^xvi	60.96 (4)	59.94 (4)	61.91 (4)
Al2^xiv—Al2—Al2^xvii	60.94 (4)	59.94 (4)	61.91 (4)
Al2^xv—Al2—Al2^xvi	60.96 (4)	59.94 (4)	61.91 (4)
Al2^xv—Al2—Al2^xvii	60.94 (4)	59.94 (4)	61.91 (4)
Al2^xvi—Al2—Al2^xvii	91.65 (5)	91.60 (5)	91.70 (5)

Symmetry codes: (i) x₁−1/2, x₂−1/2, x₃, x₄; (ii) x₁−1/2, x₂+1/2, x₃, x₄; (iii) x₁+1/2, x₂−1/2, x₃, x₄; (iv) x₁+1/2, x₂+1/2, x₃, x₄; (v) x₁, x₂−1/2, x₃−1/2, x₄; (vi) x₁−1/2, x₂, x₃−1/2, x₄; (vii) −x₁, −x₂, −x₃, −x₄; (viii) −x₁, −x₂+1/2, −x₃+1/2, −x₄; (ix) −x₁+1/2, −x₂, −x₃+1/2, −x₄; (x) −x₁+1/2, −x₂+1/2, −x₃, −x₄; (xi) x₁, x₂+1/2, x₃−1/2, x₄; (xii) x₁+1/2, x₂, x₃−1/2, x₄; (xiii) −x₁, x₂, −x₃, −x₄; (xiv) −x₁, x₂−1/2, −x₃+1/2, −x₄; (xv) −x₁, x₂+1/2, −x₃+1/2, −x₄; (xvi) −x₁−1/2, x₂, −x₃+1/2, −x₄; (xvii) −x₁+1/2, x₂, −x₃+1/2, −x₄; (xviii) −x₁+1, −x₂+1/2, −x₃+1/2, −x₄; (xix) −x₁+1/2, −x₂+1, −x₃+1/2, −x₄; (xx) −x₁, x₂, −x₃+1, −x₄; (xxi) −x₁+1/2, x₂+1/2, −x₃+1, −x₄; (xxii) x₁, x₂+1/2, x₃+1/2, x₄; (xxiii) x₁+1/2, x₂, x₃+1/2, x₄; (xxiv) x₁, x₂−1/2, x₃+1/2, x₄; (xxv) x₁−1/2, x₂, x₃+1/2, x₄; (xxvi) −x₁, −x₂, −x₃+1, −x₄; (xxvii) −x₁+1/2, −x₂+1/2, −x₃+1, −x₄.

(III)

Crystal data

Al4Eu	F(000) = 920
Mr = 259.9	Dx = 4.029 Mg m^−3
Orthorhombic, Fmmm(00γ)s00†	Synchrotron radiation, λ = 0.5 Å
q = 0.178100c*	Cell parameters from 1000 reflections
a = 6.1992 (4) Å	θ = 1.5–22°
b = 6.2001 (4) Å	µ = 5.91 mm^−1
c = 11.1477 (3) Å	T = 70 K
V = 428.47 (4) Å^3	Irregular, black
Z = 4	0.1 × 0.06 × 0.02 mm

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, −x₂, x₃, x₄+1/2; (3) −x₁, x₂, −x₃, −x₄; (4) x₁, −x₂, −x₃, −x₄+1/2; (5) −x₁, −x₂, −x₃, −x₄; (6) x₁, x₂, −x₃, −x₄+1/2; (7) x₁, −x₂, x₃, x₄; (8) −x₁, x₂, x₃, x₄+1/2; (9) x₁, x₂+1/2, x₃+1/2, x₄; (10) −x₁, −x₂+1/2, x₃+1/2, x₄+1/2; (11) −x₁, x₂+1/2, −x₃+1/2, −x₄; (12) x₁, −x₂+1/2, −x₃+1/2, −x₄+1/2; (13) −x₁, −x₂+1/2, −x₃+1/2, −x₄; (14) x₁, x₂+1/2, −x₃+1/2, −x₄+1/2; (15) x₁, −x₂+1/2, x₃+1/2, x₄; (16) −x₁, x₂+1/2, x₃+1/2, x₄+1/2; (17) x₁+1/2, x₂, x₃+1/2, x₄; (18) −x₁+1/2, −x₂, x₃+1/2, x₄+1/2; (19) −x₁+1/2, x₂, −x₃+1/2, −x₄; (20) x₁+1/2, −x₂, −x₃+1/2, −x₄+1/2; (21) −x₁+1/2, −x₂, −x₃+1/2, −x₄; (22) x₁+1/2, x₂, −x₃+1/2, −x₄+1/2; (23) x₁+1/2, −x₂, x₃+1/2, x₄; (24) −x₁+1/2, x₂, x₃+1/2, x₄+1/2; (25) x₁+1/2, x₂+1/2, x₃, x₄; (26) −x₁+1/2, −x₂+1/2, x₃, x₄+1/2; (27) −x₁+1/2, x₂+1/2, −x₃, −x₄; (28) x₁+1/2, −x₂+1/2, −x₃, −x₄+1/2; (29) −x₁+1/2, −x₂+1/2, −x₃, −x₄; (30) x₁+1/2, x₂+1/2, −x₃, −x₄+1/2; (31) x₁+1/2, −x₂+1/2, x₃, x₄; (32) −x₁+1/2, x₂+1/2, x₃, x₄+1/2.

Data collection

Huber four-circle diffractometer	490 independent reflections
Radiation source: synchrotron	453 reflections with I > 3σ(I)
Si111 and Si311 monochromator	Rint = 0.017
area detector with phi scans	θmax = 22.0°, θmin = 2.6°
Absorption correction: empirical (using intensity measurements) SADABS, Program for Empirical Absorption Correction of Area Detector Data, G. M. Sheldrick, 1996	h = −8→7
Tmin = 0.321, Tmax = 0.373	k = −9→4
1402 measured reflections	l = −7→16

Refinement

Refinement on F	0 constraints
R[F^2 > 2σ(F^2)] = 0.022	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
wR(F^2) = 0.025	(Δ/σ)max = 0.0001
S = 1.09	Δρmax = 3.58 e Å^−3
490 reflections	Δρmin = −2.40 e Å^−3
18 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 55 (10)

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

	x	y	z	Uiso*/Ueq
Eu1	0	0	0	0.0083 (2)
Al1	0.25	0.25	0.25	0.0080 (9)
Al2	0	0	0.38491 (12)	0.0077 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Eu1	0.0011 (3)	0.0157 (5)	0.00813 (16)	0	0	0
Al1	0.0080 (16)	0.008 (2)	0.0079 (5)	0	0	0
Al2	0.0034 (14)	0.0127 (19)	0.0069 (6)	0	0	0

Geometric parameters (Å, º)

	Average	Minimum	Maximum
Eu1—Eu1^i	4.3838 (6)	4.3838 (8)	4.3838 (8)
Eu1—Eu1^ii	4.3838 (6)	4.3838 (8)	4.3838 (8)
Eu1—Eu1^iii	4.3838 (6)	4.3838 (8)	4.3838 (8)
Eu1—Eu1^iv	4.3838 (6)	4.3838 (8)	4.3838 (8)
Eu1—Al1	3.5454 (9)	3.5041 (11)	3.5881 (11)
Eu1—Al1^v	3.5463 (9)	3.5041 (11)	3.5881 (11)
Eu1—Al1^vi	3.5454 (9)	3.5041 (11)	3.5881 (11)
Eu1—Al1^i	3.5463 (9)	3.5041 (11)	3.5881 (11)
Eu1—Al1^vii	3.5454 (9)	3.5041 (11)	3.5881 (11)
Eu1—Al1^viii	3.5463 (9)	3.5041 (11)	3.5881 (11)
Eu1—Al1^ix	3.5454 (9)	3.5041 (11)	3.5881 (11)
Eu1—Al1^x	3.5463 (9)	3.5041 (11)	3.5881 (11)
Eu1—Al2	4.2916 (14)	4.2909 (14)	4.2923 (14)
Eu1—Al2^v	3.3552 (5)	3.3551 (5)	3.3553 (5)
Eu1—Al2^xi	3.3552 (5)	3.3551 (5)	3.3553 (5)
Eu1—Al2^vi	3.355 (2)	3.316 (2)	3.394 (2)
Eu1—Al2^xii	3.354 (2)	3.316 (2)	3.394 (2)
Eu1—Al2^xiii	4.2916 (14)	4.2909 (14)	4.2923 (14)
Eu1—Al2^xiv	3.3552 (5)	3.3551 (5)	3.3553 (5)
Eu1—Al2^xv	3.3552 (5)	3.3551 (5)	3.3553 (5)
Eu1—Al2^xvi	3.354 (2)	3.316 (2)	3.394 (2)
Eu1—Al2^xvii	3.355 (2)	3.316 (2)	3.394 (2)
Al1—Al1^i	4.384 (2)	4.384 (2)	4.384 (2)
Al1—Al1^ii	4.384 (2)	4.384 (2)	4.384 (2)
Al1—Al1^iii	4.384 (2)	4.384 (2)	4.384 (2)
Al1—Al1^iv	4.384 (2)	4.384 (2)	4.384 (2)
Al1—Al1^viii	3.1009 (19)	3.100 (3)	3.102 (3)
Al1—Al1^xviii	3.1009 (19)	3.100 (3)	3.102 (3)
Al1—Al1^ix	3.0989 (17)	2.976 (3)	3.224 (3)
Al1—Al1^xix	3.1012 (17)	2.976 (3)	3.224 (3)
Al1—Al2	2.6592 (18)	2.6508 (19)	2.6687 (19)
Al1—Al2^iv	2.6591 (18)	2.6508 (19)	2.6687 (19)
Al1—Al2^xv	2.6591 (18)	2.6508 (19)	2.6687 (19)
Al1—Al2^xvii	2.6592 (18)	2.6508 (19)	2.6687 (19)
Al2—Al2^i	4.384 (2)	4.384 (2)	4.384 (2)
Al2—Al2^ii	4.384 (2)	4.384 (2)	4.384 (2)
Al2—Al2^iii	4.384 (2)	4.384 (2)	4.384 (2)
Al2—Al2^iv	4.384 (2)	4.384 (2)	4.384 (2)
Al2—Al2^xx	2.5666 (19)	2.5660 (19)	2.5673 (19)
Al2—Al2^xiv	4.3208 (13)	4.3194 (13)	4.3221 (13)
Al2—Al2^xv	4.3208 (13)	4.3194 (13)	4.3221 (13)
Al2—Al2^xvi	4.319 (2)	4.211 (3)	4.429 (3)
Al2—Al2^xvii	4.321 (2)	4.211 (3)	4.429 (3)
Eu1^i—Eu1—Eu1^ii	90.008 (9)	90.008 (7)	90.008 (7)
Eu1^i—Eu1—Eu1^iii	89.992 (8)	89.992 (7)	89.992 (7)
Eu1^i—Eu1—Eu1^iv	180	180	180
Eu1^i—Eu1—Al1	128.17 (2)	127.31 (2)	129.04 (2)
Eu1^i—Eu1—Al1^v	89.99 (3)	89.67 (3)	90.33 (3)
Eu1^i—Eu1—Al1^vi	90.00 (3)	89.67 (3)	90.33 (3)
Eu1^i—Eu1—Al1^i	51.81 (2)	50.96 (2)	52.69 (2)
Eu1^i—Eu1—Al1^vii	51.83 (2)	50.96 (2)	52.69 (2)
Eu1^i—Eu1—Al1^viii	90.01 (3)	89.67 (3)	90.33 (3)
Eu1^i—Eu1—Al1^ix	90.00 (3)	89.67 (3)	90.33 (3)
Eu1^i—Eu1—Al1^x	128.19 (2)	127.31 (2)	129.04 (2)
Eu1^i—Eu1—Al2	89.990 (19)	88.963 (19)	91.037 (19)
Eu1^i—Eu1—Al2^v	49.19 (3)	48.53 (3)	49.87 (3)
Eu1^i—Eu1—Al2^xi	130.79 (3)	130.13 (3)	131.47 (3)
Eu1^i—Eu1—Al2^vi	49.209 (10)	49.112 (9)	49.309 (10)
Eu1^i—Eu1—Al2^xii	130.789 (10)	130.691 (10)	130.888 (9)
Eu1^i—Eu1—Al2^xiii	90.010 (19)	88.963 (19)	91.037 (19)
Eu1^i—Eu1—Al2^xiv	49.21 (3)	48.53 (3)	49.87 (3)
Eu1^i—Eu1—Al2^xv	130.81 (3)	130.13 (3)	131.47 (3)
Eu1^i—Eu1—Al2^xvi	49.211 (10)	49.112 (9)	49.309 (10)
Eu1^i—Eu1—Al2^xvii	130.791 (10)	130.691 (10)	130.888 (9)
Eu1^ii—Eu1—Eu1^iii	180	180	180
Eu1^ii—Eu1—Eu1^iv	89.992 (8)	89.992 (7)	89.992 (7)
Eu1^ii—Eu1—Al1	90.00 (3)	89.67 (3)	90.33 (3)
Eu1^ii—Eu1—Al1^v	128.19 (2)	127.31 (2)	129.04 (2)
Eu1^ii—Eu1—Al1^vi	51.83 (2)	50.96 (2)	52.69 (2)
Eu1^ii—Eu1—Al1^i	90.01 (3)	89.67 (3)	90.33 (3)
Eu1^ii—Eu1—Al1^vii	90.00 (3)	89.67 (3)	90.33 (3)
Eu1^ii—Eu1—Al1^viii	51.81 (2)	50.96 (2)	52.69 (2)
Eu1^ii—Eu1—Al1^ix	128.17 (2)	127.31 (2)	129.04 (2)
Eu1^ii—Eu1—Al1^x	89.99 (3)	89.67 (3)	90.33 (3)
Eu1^ii—Eu1—Al2	89.990 (19)	88.963 (19)	91.037 (19)
Eu1^ii—Eu1—Al2^v	130.79 (3)	130.13 (3)	131.47 (3)
Eu1^ii—Eu1—Al2^xi	49.19 (3)	48.53 (3)	49.87 (3)
Eu1^ii—Eu1—Al2^vi	49.209 (10)	49.112 (9)	49.309 (10)
Eu1^ii—Eu1—Al2^xii	130.789 (10)	130.691 (10)	130.888 (9)
Eu1^ii—Eu1—Al2^xiii	90.010 (19)	88.963 (19)	91.037 (19)
Eu1^ii—Eu1—Al2^xiv	130.81 (3)	130.13 (3)	131.47 (3)
Eu1^ii—Eu1—Al2^xv	49.21 (3)	48.53 (3)	49.87 (3)
Eu1^ii—Eu1—Al2^xvi	49.211 (10)	49.112 (9)	49.309 (10)
Eu1^ii—Eu1—Al2^xvii	130.791 (10)	130.691 (10)	130.888 (9)
Eu1^iii—Eu1—Eu1^iv	90.008 (9)	90.008 (7)	90.008 (7)
Eu1^iii—Eu1—Al1	90.00 (3)	89.67 (3)	90.33 (3)
Eu1^iii—Eu1—Al1^v	51.81 (2)	50.96 (2)	52.69 (2)
Eu1^iii—Eu1—Al1^vi	128.17 (2)	127.31 (2)	129.04 (2)
Eu1^iii—Eu1—Al1^i	89.99 (3)	89.67 (3)	90.33 (3)
Eu1^iii—Eu1—Al1^vii	90.00 (3)	89.67 (3)	90.33 (3)
Eu1^iii—Eu1—Al1^viii	128.19 (2)	127.31 (2)	129.04 (2)
Eu1^iii—Eu1—Al1^ix	51.83 (2)	50.96 (2)	52.69 (2)
Eu1^iii—Eu1—Al1^x	90.01 (3)	89.67 (3)	90.33 (3)
Eu1^iii—Eu1—Al2	90.010 (19)	88.963 (19)	91.037 (19)
Eu1^iii—Eu1—Al2^v	49.21 (3)	48.53 (3)	49.87 (3)
Eu1^iii—Eu1—Al2^xi	130.81 (3)	130.13 (3)	131.47 (3)
Eu1^iii—Eu1—Al2^vi	130.791 (10)	130.691 (10)	130.888 (9)
Eu1^iii—Eu1—Al2^xii	49.211 (10)	49.112 (9)	49.309 (10)
Eu1^iii—Eu1—Al2^xiii	89.990 (19)	88.963 (19)	91.037 (19)
Eu1^iii—Eu1—Al2^xiv	49.19 (3)	48.53 (3)	49.87 (3)
Eu1^iii—Eu1—Al2^xv	130.79 (3)	130.13 (3)	131.47 (3)
Eu1^iii—Eu1—Al2^xvi	130.789 (10)	130.691 (10)	130.888 (9)
Eu1^iii—Eu1—Al2^xvii	49.209 (10)	49.112 (9)	49.309 (10)
Eu1^iv—Eu1—Al1	51.83 (2)	50.96 (2)	52.69 (2)
Eu1^iv—Eu1—Al1^v	90.01 (3)	89.67 (3)	90.33 (3)
Eu1^iv—Eu1—Al1^vi	90.00 (3)	89.67 (3)	90.33 (3)
Eu1^iv—Eu1—Al1^i	128.19 (2)	127.31 (2)	129.04 (2)
Eu1^iv—Eu1—Al1^vii	128.17 (2)	127.31 (2)	129.04 (2)
Eu1^iv—Eu1—Al1^viii	89.99 (3)	89.67 (3)	90.33 (3)
Eu1^iv—Eu1—Al1^ix	90.00 (3)	89.67 (3)	90.33 (3)
Eu1^iv—Eu1—Al1^x	51.81 (2)	50.96 (2)	52.69 (2)
Eu1^iv—Eu1—Al2	90.010 (19)	88.963 (19)	91.037 (19)
Eu1^iv—Eu1—Al2^v	130.81 (3)	130.13 (3)	131.47 (3)
Eu1^iv—Eu1—Al2^xi	49.21 (3)	48.53 (3)	49.87 (3)
Eu1^iv—Eu1—Al2^vi	130.791 (10)	130.691 (10)	130.888 (9)
Eu1^iv—Eu1—Al2^xii	49.211 (10)	49.112 (9)	49.309 (10)
Eu1^iv—Eu1—Al2^xiii	89.990 (19)	88.963 (19)	91.037 (19)
Eu1^iv—Eu1—Al2^xiv	130.79 (3)	130.13 (3)	131.47 (3)
Eu1^iv—Eu1—Al2^xv	49.19 (3)	48.53 (3)	49.87 (3)
Eu1^iv—Eu1—Al2^xvi	130.789 (10)	130.691 (10)	130.888 (9)
Eu1^iv—Eu1—Al2^xvii	49.209 (10)	49.112 (9)	49.309 (10)
Al1—Eu1—Al1^v	128.15 (4)	128.14 (3)	128.17 (5)
Al1—Eu1—Al1^vi	128.18 (2)	126.67 (3)	129.67 (3)
Al1—Eu1—Al1^i	76.36 (3)	76.35 (3)	76.37 (3)
Al1—Eu1—Al1^vii	179.698 (13)	179.515 (3)	180
Al1—Eu1—Al1^viii	51.85 (4)	51.84 (5)	51.86 (3)
Al1—Eu1—Al1^ix	51.82 (2)	50.25 (4)	53.40 (3)
Al1—Eu1—Al1^x	103.64 (3)	103.26 (3)	104.01 (3)
Al1—Eu1—Al2	38.19 (3)	38.01 (3)	38.38 (3)
Al1—Eu1—Al2^v	134.78 (4)	134.41 (3)	135.16 (3)
Al1—Eu1—Al2^xi	84.08 (3)	82.93 (4)	85.22 (4)
Al1—Eu1—Al2^vi	134.78 (3)	134.49 (3)	135.08 (3)
Al1—Eu1—Al2^xii	84.09 (3)	83.40 (2)	84.77 (2)
Al1—Eu1—Al2^xiii	141.81 (3)	141.31 (3)	142.31 (3)
Al1—Eu1—Al2^xiv	95.92 (3)	94.75 (4)	97.10 (4)
Al1—Eu1—Al2^xv	45.22 (3)	45.04 (4)	45.43 (4)
Al1—Eu1—Al2^xvi	95.91 (3)	95.23 (2)	96.61 (2)
Al1—Eu1—Al2^xvii	45.22 (3)	44.95 (2)	45.49 (2)
Al1^v—Eu1—Al1^vi	76.36 (3)	76.35 (3)	76.37 (3)
Al1^v—Eu1—Al1^i	128.15 (2)	126.67 (3)	129.67 (3)
Al1^v—Eu1—Al1^vii	51.85 (4)	51.84 (5)	51.86 (3)
Al1^v—Eu1—Al1^viii	179.698 (13)	179.515 (3)	180
Al1^v—Eu1—Al1^ix	103.64 (3)	103.26 (3)	104.01 (3)
Al1^v—Eu1—Al1^x	51.85 (2)	50.25 (4)	53.40 (3)
Al1^v—Eu1—Al2	141.81 (3)	141.31 (3)	142.31 (3)
Al1^v—Eu1—Al2^v	45.22 (3)	45.04 (4)	45.43 (4)
Al1^v—Eu1—Al2^xi	95.94 (3)	94.75 (4)	97.10 (4)
Al1^v—Eu1—Al2^vi	95.93 (3)	95.23 (2)	96.61 (2)
Al1^v—Eu1—Al2^xii	45.21 (3)	44.95 (2)	45.49 (2)
Al1^v—Eu1—Al2^xiii	38.19 (3)	38.01 (3)	38.38 (3)
Al1^v—Eu1—Al2^xiv	84.06 (3)	82.93 (4)	85.22 (4)
Al1^v—Eu1—Al2^xv	134.78 (4)	134.41 (3)	135.16 (3)
Al1^v—Eu1—Al2^xvi	134.79 (3)	134.49 (3)	135.08 (3)
Al1^v—Eu1—Al2^xvii	84.07 (3)	83.40 (2)	84.77 (2)
Al1^vi—Eu1—Al1^i	128.15 (4)	128.14 (3)	128.17 (5)
Al1^vi—Eu1—Al1^vii	51.82 (2)	50.25 (4)	53.40 (3)
Al1^vi—Eu1—Al1^viii	103.64 (3)	103.26 (3)	104.01 (3)
Al1^vi—Eu1—Al1^ix	179.698 (13)	179.515 (3)	180
Al1^vi—Eu1—Al1^x	51.85 (4)	51.84 (5)	51.86 (3)
Al1^vi—Eu1—Al2	141.81 (3)	141.31 (3)	142.31 (3)
Al1^vi—Eu1—Al2^v	95.92 (3)	94.75 (4)	97.10 (4)
Al1^vi—Eu1—Al2^xi	45.22 (3)	45.04 (4)	45.43 (4)
Al1^vi—Eu1—Al2^vi	45.22 (3)	44.95 (2)	45.49 (2)
Al1^vi—Eu1—Al2^xii	95.91 (3)	95.23 (2)	96.61 (2)
Al1^vi—Eu1—Al2^xiii	38.19 (3)	38.01 (3)	38.38 (3)
Al1^vi—Eu1—Al2^xiv	134.78 (4)	134.41 (3)	135.16 (3)
Al1^vi—Eu1—Al2^xv	84.08 (3)	82.93 (4)	85.22 (4)
Al1^vi—Eu1—Al2^xvi	84.09 (3)	83.40 (2)	84.77 (2)
Al1^vi—Eu1—Al2^xvii	134.78 (3)	134.49 (3)	135.08 (3)
Al1^i—Eu1—Al1^vii	103.64 (3)	103.26 (3)	104.01 (3)
Al1^i—Eu1—Al1^viii	51.85 (2)	50.25 (4)	53.40 (3)
Al1^i—Eu1—Al1^ix	51.85 (4)	51.84 (5)	51.86 (3)
Al1^i—Eu1—Al1^x	179.698 (13)	179.515 (3)	180
Al1^i—Eu1—Al2	38.19 (3)	38.01 (3)	38.38 (3)
Al1^i—Eu1—Al2^v	84.06 (3)	82.93 (4)	85.22 (4)
Al1^i—Eu1—Al2^xi	134.78 (4)	134.41 (3)	135.16 (3)
Al1^i—Eu1—Al2^vi	84.07 (3)	83.40 (2)	84.77 (2)
Al1^i—Eu1—Al2^xii	134.79 (3)	134.49 (3)	135.08 (3)
Al1^i—Eu1—Al2^xiii	141.81 (3)	141.31 (3)	142.31 (3)
Al1^i—Eu1—Al2^xiv	45.22 (3)	45.04 (4)	45.43 (4)
Al1^i—Eu1—Al2^xv	95.94 (3)	94.75 (4)	97.10 (4)
Al1^i—Eu1—Al2^xvi	45.21 (3)	44.95 (2)	45.49 (2)
Al1^i—Eu1—Al2^xvii	95.93 (3)	95.23 (2)	96.61 (2)
Al1^vii—Eu1—Al1^viii	128.15 (4)	128.14 (3)	128.17 (5)
Al1^vii—Eu1—Al1^ix	128.18 (2)	126.67 (3)	129.67 (3)
Al1^vii—Eu1—Al1^x	76.36 (3)	76.35 (3)	76.37 (3)
Al1^vii—Eu1—Al2	141.81 (3)	141.31 (3)	142.31 (3)
Al1^vii—Eu1—Al2^v	45.22 (3)	45.04 (4)	45.43 (4)
Al1^vii—Eu1—Al2^xi	95.92 (3)	94.75 (4)	97.10 (4)
Al1^vii—Eu1—Al2^vi	45.22 (3)	44.95 (2)	45.49 (2)
Al1^vii—Eu1—Al2^xii	95.91 (3)	95.23 (2)	96.61 (2)
Al1^vii—Eu1—Al2^xiii	38.19 (3)	38.01 (3)	38.38 (3)
Al1^vii—Eu1—Al2^xiv	84.08 (3)	82.93 (4)	85.22 (4)
Al1^vii—Eu1—Al2^xv	134.78 (4)	134.41 (3)	135.16 (3)
Al1^vii—Eu1—Al2^xvi	84.09 (3)	83.40 (2)	84.77 (2)
Al1^vii—Eu1—Al2^xvii	134.78 (3)	134.49 (3)	135.08 (3)
Al1^viii—Eu1—Al1^ix	76.36 (3)	76.35 (3)	76.37 (3)
Al1^viii—Eu1—Al1^x	128.15 (2)	126.67 (3)	129.67 (3)
Al1^viii—Eu1—Al2	38.19 (3)	38.01 (3)	38.38 (3)
Al1^viii—Eu1—Al2^v	134.78 (4)	134.41 (3)	135.16 (3)
Al1^viii—Eu1—Al2^xi	84.06 (3)	82.93 (4)	85.22 (4)
Al1^viii—Eu1—Al2^vi	84.07 (3)	83.40 (2)	84.77 (2)
Al1^viii—Eu1—Al2^xii	134.79 (3)	134.49 (3)	135.08 (3)
Al1^viii—Eu1—Al2^xiii	141.81 (3)	141.31 (3)	142.31 (3)
Al1^viii—Eu1—Al2^xiv	95.94 (3)	94.75 (4)	97.10 (4)
Al1^viii—Eu1—Al2^xv	45.22 (3)	45.04 (4)	45.43 (4)
Al1^viii—Eu1—Al2^xvi	45.21 (3)	44.95 (2)	45.49 (2)
Al1^viii—Eu1—Al2^xvii	95.93 (3)	95.23 (2)	96.61 (2)
Al1^ix—Eu1—Al1^x	128.15 (4)	128.14 (3)	128.17 (5)
Al1^ix—Eu1—Al2	38.19 (3)	38.01 (3)	38.38 (3)
Al1^ix—Eu1—Al2^v	84.08 (3)	82.93 (4)	85.22 (4)
Al1^ix—Eu1—Al2^xi	134.78 (4)	134.41 (3)	135.16 (3)
Al1^ix—Eu1—Al2^vi	134.78 (3)	134.49 (3)	135.08 (3)
Al1^ix—Eu1—Al2^xii	84.09 (3)	83.40 (2)	84.77 (2)
Al1^ix—Eu1—Al2^xiii	141.81 (3)	141.31 (3)	142.31 (3)
Al1^ix—Eu1—Al2^xiv	45.22 (3)	45.04 (4)	45.43 (4)
Al1^ix—Eu1—Al2^xv	95.92 (3)	94.75 (4)	97.10 (4)
Al1^ix—Eu1—Al2^xvi	95.91 (3)	95.23 (2)	96.61 (2)
Al1^ix—Eu1—Al2^xvii	45.22 (3)	44.95 (2)	45.49 (2)
Al1^x—Eu1—Al2	141.81 (3)	141.31 (3)	142.31 (3)
Al1^x—Eu1—Al2^v	95.94 (3)	94.75 (4)	97.10 (4)
Al1^x—Eu1—Al2^xi	45.22 (3)	45.04 (4)	45.43 (4)
Al1^x—Eu1—Al2^vi	95.93 (3)	95.23 (2)	96.61 (2)
Al1^x—Eu1—Al2^xii	45.21 (3)	44.95 (2)	45.49 (2)
Al1^x—Eu1—Al2^xiii	38.19 (3)	38.01 (3)	38.38 (3)
Al1^x—Eu1—Al2^xiv	134.78 (4)	134.41 (3)	135.16 (3)
Al1^x—Eu1—Al2^xv	84.06 (3)	82.93 (4)	85.22 (4)
Al1^x—Eu1—Al2^xvi	134.79 (3)	134.49 (3)	135.08 (3)
Al1^x—Eu1—Al2^xvii	84.07 (3)	83.40 (2)	84.77 (2)
Al2—Eu1—Al2^v	112.47 (2)	112.46 (2)	112.48 (2)
Al2—Eu1—Al2^xi	112.47 (2)	112.46 (2)	112.48 (2)
Al2—Eu1—Al2^vi	112.47 (4)	110.78 (3)	114.20 (4)
Al2—Eu1—Al2^xii	112.50 (4)	110.78 (3)	114.20 (4)
Al2—Eu1—Al2^xiii	179.49 (4)	179.18 (4)	180
Al2—Eu1—Al2^xiv	67.53 (2)	67.52 (2)	67.55 (2)
Al2—Eu1—Al2^xv	67.53 (2)	67.52 (2)	67.55 (2)
Al2—Eu1—Al2^xvi	67.50 (4)	65.77 (4)	69.25 (3)
Al2—Eu1—Al2^xvii	67.53 (4)	65.77 (4)	69.25 (3)
Al2^v—Eu1—Al2^xi	135.02 (3)	135.01 (3)	135.03 (3)
Al2^v—Eu1—Al2^vi	81.58 (3)	81.01 (3)	82.16 (3)
Al2^v—Eu1—Al2^xii	81.59 (3)	81.01 (3)	82.16 (3)
Al2^v—Eu1—Al2^xiii	67.53 (2)	67.52 (2)	67.55 (2)
Al2^v—Eu1—Al2^xiv	44.98 (3)	44.97 (3)	44.99 (3)
Al2^v—Eu1—Al2^xv	179.76 (4)	179.61 (5)	180
Al2^v—Eu1—Al2^xvi	98.41 (3)	97.82 (3)	99.00 (3)
Al2^v—Eu1—Al2^xvii	98.42 (3)	97.82 (3)	99.00 (3)
Al2^xi—Eu1—Al2^vi	81.58 (3)	81.01 (3)	82.16 (3)
Al2^xi—Eu1—Al2^xii	81.59 (3)	81.01 (3)	82.16 (3)
Al2^xi—Eu1—Al2^xiii	67.53 (2)	67.52 (2)	67.55 (2)
Al2^xi—Eu1—Al2^xiv	179.76 (4)	179.61 (5)	180
Al2^xi—Eu1—Al2^xv	44.98 (3)	44.97 (3)	44.99 (3)
Al2^xi—Eu1—Al2^xvi	98.41 (3)	97.82 (3)	99.00 (3)
Al2^xi—Eu1—Al2^xvii	98.42 (3)	97.82 (3)	99.00 (3)
Al2^vi—Eu1—Al2^xii	135.03 (4)	135.02 (4)	135.03 (4)
Al2^vi—Eu1—Al2^xiii	67.53 (4)	65.77 (4)	69.25 (4)
Al2^vi—Eu1—Al2^xiv	98.42 (3)	97.82 (3)	99.00 (3)
Al2^vi—Eu1—Al2^xv	98.42 (3)	97.82 (3)	99.00 (3)
Al2^vi—Eu1—Al2^xvi	44.97 (4)	44.82 (4)	45.12 (4)
Al2^vi—Eu1—Al2^xvii	179.92 (2)	179.85 (4)	180
Al2^xii—Eu1—Al2^xiii	67.50 (4)	65.77 (4)	69.25 (4)
Al2^xii—Eu1—Al2^xiv	98.41 (3)	97.82 (3)	99.00 (3)
Al2^xii—Eu1—Al2^xv	98.41 (3)	97.82 (3)	99.00 (3)
Al2^xii—Eu1—Al2^xvi	179.92 (2)	179.85 (4)	180
Al2^xii—Eu1—Al2^xvii	44.97 (4)	44.82 (4)	45.12 (4)
Al2^xiii—Eu1—Al2^xiv	112.47 (2)	112.46 (2)	112.48 (2)
Al2^xiii—Eu1—Al2^xv	112.47 (2)	112.46 (2)	112.48 (2)
Al2^xiii—Eu1—Al2^xvi	112.50 (4)	110.78 (3)	114.20 (4)
Al2^xiii—Eu1—Al2^xvii	112.47 (4)	110.78 (3)	114.20 (4)
Al2^xiv—Eu1—Al2^xv	135.02 (3)	135.01 (3)	135.03 (3)
Al2^xiv—Eu1—Al2^xvi	81.59 (3)	81.01 (3)	82.16 (3)
Al2^xiv—Eu1—Al2^xvii	81.58 (3)	81.01 (3)	82.16 (3)
Al2^xv—Eu1—Al2^xvi	81.59 (3)	81.01 (3)	82.16 (3)
Al2^xv—Eu1—Al2^xvii	81.58 (3)	81.01 (3)	82.16 (3)
Al2^xvi—Eu1—Al2^xvii	135.03 (4)	135.02 (4)	135.03 (4)
Eu1—Al1—Eu1^xxi	128.15 (3)	127.99 (7)	128.33 (7)
Eu1—Al1—Eu1^xxii	128.18 (3)	126.60 (7)	129.75 (7)
Eu1—Al1—Eu1^iv	76.359 (6)	76.348 (6)	76.370 (7)
Eu1—Al1—Al1^i	51.829 (18)	50.96 (2)	52.69 (2)
Eu1—Al1—Al1^ii	90.00 (3)	89.671 (19)	90.331 (18)
Eu1—Al1—Al1^iii	90.00 (3)	89.67 (4)	90.33 (4)
Eu1—Al1—Al1^iv	128.171 (18)	127.31 (2)	129.04 (2)
Eu1—Al1—Al1^viii	64.09 (2)	62.675 (14)	65.466 (12)
Eu1—Al1—Al1^xviii	115.90 (3)	115.02 (3)	116.70 (3)
Eu1—Al1—Al1^ix	64.09 (3)	63.30 (4)	64.87 (4)
Eu1—Al1—Al1^xix	115.91 (3)	115.13 (4)	116.70 (4)
Eu1—Al1—Al2	86.28 (5)	85.52 (5)	87.02 (5)
Eu1—Al1—Al2^iv	162.54 (5)	161.72 (6)	163.22 (4)
Eu1—Al1—Al2^xv	63.60 (3)	62.85 (2)	64.32 (2)
Eu1—Al1—Al2^xvii	63.60 (4)	62.07 (5)	65.07 (5)
Eu1^xxi—Al1—Eu1^xxii	76.359 (6)	76.348 (6)	76.370 (7)
Eu1^xxi—Al1—Eu1^iv	128.15 (3)	126.60 (7)	129.75 (7)
Eu1^xxi—Al1—Al1^i	90.01 (3)	89.671 (19)	90.331 (18)
Eu1^xxi—Al1—Al1^ii	51.813 (18)	50.96 (2)	52.69 (2)
Eu1^xxi—Al1—Al1^iii	128.187 (18)	127.31 (2)	129.04 (2)
Eu1^xxi—Al1—Al1^iv	89.99 (3)	89.67 (4)	90.33 (4)
Eu1^xxi—Al1—Al1^viii	64.06 (2)	62.675 (14)	65.466 (12)
Eu1^xxi—Al1—Al1^xviii	115.88 (3)	115.02 (3)	116.70 (3)
Eu1^xxi—Al1—Al1^ix	115.93 (3)	115.13 (4)	116.70 (4)
Eu1^xxi—Al1—Al1^xix	64.07 (3)	63.30 (4)	64.87 (4)
Eu1^xxi—Al1—Al2	63.59 (3)	62.85 (2)	64.32 (2)
Eu1^xxi—Al1—Al2^iv	63.57 (4)	62.07 (5)	65.07 (5)
Eu1^xxi—Al1—Al2^xv	86.26 (5)	85.52 (5)	87.02 (5)
Eu1^xxi—Al1—Al2^xvii	162.56 (5)	161.73 (6)	163.22 (4)
Eu1^xxii—Al1—Eu1^iv	128.15 (3)	127.99 (7)	128.33 (7)
Eu1^xxii—Al1—Al1^i	90.00 (3)	89.67 (4)	90.33 (4)
Eu1^xxii—Al1—Al1^ii	128.171 (18)	127.31 (2)	129.04 (2)
Eu1^xxii—Al1—Al1^iii	51.829 (18)	50.96 (2)	52.69 (2)
Eu1^xxii—Al1—Al1^iv	90.00 (3)	89.671 (19)	90.331 (18)
Eu1^xxii—Al1—Al1^viii	115.90 (3)	115.02 (3)	116.70 (3)
Eu1^xxii—Al1—Al1^xviii	64.09 (2)	62.675 (14)	65.466 (12)
Eu1^xxii—Al1—Al1^ix	64.09 (3)	63.30 (4)	64.87 (4)
Eu1^xxii—Al1—Al1^xix	115.91 (3)	115.13 (4)	116.70 (4)
Eu1^xxii—Al1—Al2	63.60 (4)	62.07 (5)	65.07 (5)
Eu1^xxii—Al1—Al2^iv	63.60 (3)	62.85 (2)	64.32 (2)
Eu1^xxii—Al1—Al2^xv	162.54 (5)	161.73 (6)	163.22 (4)
Eu1^xxii—Al1—Al2^xvii	86.28 (5)	85.52 (5)	87.02 (5)
Eu1^iv—Al1—Al1^i	128.188 (18)	127.31 (2)	129.04 (2)
Eu1^iv—Al1—Al1^ii	89.99 (3)	89.67 (4)	90.33 (4)
Eu1^iv—Al1—Al1^iii	90.01 (3)	89.671 (19)	90.331 (18)
Eu1^iv—Al1—Al1^iv	51.812 (18)	50.96 (2)	52.69 (2)
Eu1^iv—Al1—Al1^viii	115.88 (3)	115.02 (3)	116.70 (3)
Eu1^iv—Al1—Al1^xviii	64.06 (2)	62.675 (14)	65.466 (12)
Eu1^iv—Al1—Al1^ix	115.93 (3)	115.13 (4)	116.70 (4)
Eu1^iv—Al1—Al1^xix	64.07 (3)	63.30 (4)	64.87 (4)
Eu1^iv—Al1—Al2	162.56 (5)	161.72 (6)	163.22 (4)
Eu1^iv—Al1—Al2^iv	86.26 (5)	85.52 (5)	87.02 (5)
Eu1^iv—Al1—Al2^xv	63.57 (4)	62.07 (5)	65.07 (5)
Eu1^iv—Al1—Al2^xvii	63.59 (3)	62.85 (2)	64.32 (2)
Al1^i—Al1—Al1^ii	90.01 (4)	90.01 (3)	90.01 (3)
Al1^i—Al1—Al1^iii	89.99 (4)	89.99 (5)	89.99 (5)
Al1^i—Al1—Al1^iv	180	180	180
Al1^i—Al1—Al1^viii	45.03 (3)	42.71 (3)	47.30 (3)
Al1^i—Al1—Al1^xviii	135.02 (4)	132.70 (7)	137.29 (7)
Al1^i—Al1—Al1^ix	45.00 (5)	45.00 (5)	45.00 (5)
Al1^i—Al1—Al1^xix	135.00 (6)	135.00 (5)	135.00 (5)
Al1^i—Al1—Al2	34.48 (3)	34.36 (3)	34.64 (4)
Al1^i—Al1—Al2^iv	145.52 (3)	145.36 (3)	145.64 (3)
Al1^i—Al1—Al2^xv	90.03 (5)	87.91 (4)	92.12 (4)
Al1^i—Al1—Al2^xvii	90.01 (5)	87.88 (6)	92.09 (6)
Al1^ii—Al1—Al1^iii	180	180	180
Al1^ii—Al1—Al1^iv	89.99 (4)	89.99 (5)	89.99 (5)
Al1^ii—Al1—Al1^viii	44.98 (3)	42.71 (3)	47.30 (3)
Al1^ii—Al1—Al1^xviii	134.97 (4)	132.70 (7)	137.29 (7)
Al1^ii—Al1—Al1^ix	135.00 (6)	135.00 (5)	135.00 (5)
Al1^ii—Al1—Al1^xix	45.00 (5)	45.00 (5)	45.00 (5)
Al1^ii—Al1—Al2	89.99 (5)	87.91 (4)	92.12 (4)
Al1^ii—Al1—Al2^iv	89.97 (5)	87.88 (6)	92.09 (6)
Al1^ii—Al1—Al2^xv	34.49 (3)	34.36 (3)	34.64 (4)
Al1^ii—Al1—Al2^xvii	145.52 (3)	145.36 (3)	145.64 (3)
Al1^iii—Al1—Al1^iv	90.01 (4)	90.01 (3)	90.01 (3)
Al1^iii—Al1—Al1^viii	135.02 (4)	132.70 (7)	137.29 (7)
Al1^iii—Al1—Al1^xviii	45.03 (3)	42.71 (3)	47.30 (3)
Al1^iii—Al1—Al1^ix	45.00 (5)	45.00 (5)	45.00 (5)
Al1^iii—Al1—Al1^xix	135.00 (6)	135.00 (5)	135.00 (5)
Al1^iii—Al1—Al2	90.01 (5)	87.88 (6)	92.09 (6)
Al1^iii—Al1—Al2^iv	90.03 (5)	87.91 (4)	92.12 (4)
Al1^iii—Al1—Al2^xv	145.51 (3)	145.36 (3)	145.64 (3)
Al1^iii—Al1—Al2^xvii	34.48 (3)	34.36 (3)	34.64 (4)
Al1^iv—Al1—Al1^viii	134.97 (4)	132.70 (7)	137.29 (7)
Al1^iv—Al1—Al1^xviii	44.98 (3)	42.71 (3)	47.30 (3)
Al1^iv—Al1—Al1^ix	135.00 (6)	135.00 (5)	135.00 (5)
Al1^iv—Al1—Al1^xix	45.00 (5)	45.00 (5)	45.00 (5)
Al1^iv—Al1—Al2	145.52 (3)	145.36 (3)	145.64 (3)
Al1^iv—Al1—Al2^iv	34.48 (3)	34.36 (3)	34.64 (4)
Al1^iv—Al1—Al2^xv	89.97 (5)	87.88 (6)	92.09 (6)
Al1^iv—Al1—Al2^xvii	89.99 (5)	87.91 (4)	92.12 (4)
Al1^viii—Al1—Al1^xviii	177.06 (5)	175.41 (10)	179.87029 (10)
Al1^viii—Al1—Al1^ix	90.02 (6)	87.71 (7)	92.29 (7)
Al1^viii—Al1—Al1^xix	89.98 (6)	87.71 (7)	92.29 (7)
Al1^viii—Al1—Al2	54.33 (5)	54.07 (5)	54.60 (5)
Al1^viii—Al1—Al2^iv	125.60 (6)	122.07 (7)	129.14 (7)
Al1^viii—Al1—Al2^xv	54.34 (5)	54.07 (5)	54.60 (5)
Al1^viii—Al1—Al2^xvii	125.67 (6)	122.07 (7)	129.14 (7)
Al1^xviii—Al1—Al1^ix	90.02 (6)	87.71 (7)	92.29 (7)
Al1^xviii—Al1—Al1^xix	89.98 (6)	87.71 (7)	92.29 (7)
Al1^xviii—Al1—Al2	125.67 (6)	122.07 (7)	129.14 (7)
Al1^xviii—Al1—Al2^iv	54.34 (5)	54.07 (5)	54.60 (5)
Al1^xviii—Al1—Al2^xv	125.60 (6)	122.07 (7)	129.14 (7)
Al1^xviii—Al1—Al2^xvii	54.33 (5)	54.07 (5)	54.60 (5)
Al1^ix—Al1—Al1^xix	180	180	180
Al1^ix—Al1—Al2	54.35 (4)	52.56 (5)	56.11 (5)
Al1^ix—Al1—Al2^iv	125.68 (5)	123.89 (5)	127.44 (5)
Al1^ix—Al1—Al2^xv	125.68 (5)	123.89 (5)	127.44 (5)
Al1^ix—Al1—Al2^xvii	54.35 (4)	52.56 (5)	56.11 (5)
Al1^xix—Al1—Al2	125.65 (5)	123.89 (5)	127.44 (5)
Al1^xix—Al1—Al2^iv	54.32 (4)	52.56 (5)	56.11 (5)
Al1^xix—Al1—Al2^xv	54.32 (4)	52.56 (5)	56.11 (5)
Al1^xix—Al1—Al2^xvii	125.65 (5)	123.89 (5)	127.44 (5)
Al2—Al1—Al2^iv	111.03 (4)	110.98 (4)	111.09 (4)
Al2—Al1—Al2^xv	108.67 (7)	108.46 (9)	108.89 (9)
Al2—Al1—Al2^xvii	108.70 (6)	105.12 (9)	112.21 (9)
Al2^iv—Al1—Al2^xv	108.63 (5)	105.12 (9)	112.21 (9)
Al2^iv—Al1—Al2^xvii	108.67 (7)	108.46 (9)	108.89 (9)
Al2^xv—Al1—Al2^xvii	111.03 (4)	110.98 (4)	111.09 (4)
Eu1—Al2—Eu1^xxiii	112.47 (2)	112.45 (2)	112.48 (2)
Eu1—Al2—Eu1^xxi	112.47 (2)	112.45 (2)	112.48 (2)
Eu1—Al2—Eu1^xxiv	112.50 (4)	110.75 (4)	114.23 (4)
Eu1—Al2—Eu1^xxii	112.47 (4)	110.75 (4)	114.23 (4)
Eu1—Al2—Al1	55.53 (3)	54.61 (3)	56.45 (3)
Eu1—Al2—Al1^i	55.55 (3)	54.61 (3)	56.45 (3)
Eu1—Al2—Al1^viii	55.55 (3)	54.61 (3)	56.45 (3)
Eu1—Al2—Al1^ix	55.53 (3)	54.61 (3)	56.45 (3)
Eu1—Al2—Al2^i	90.01 (3)	88.96 (3)	91.04 (3)
Eu1—Al2—Al2^ii	90.01 (3)	88.96 (3)	91.04 (3)
Eu1—Al2—Al2^iii	89.99 (3)	88.96 (3)	91.04 (3)
Eu1—Al2—Al2^iv	89.99 (3)	88.96 (3)	91.04 (3)
Eu1—Al2—Al2^xx	177.92 (8)	176.75 (8)	180
Eu1—Al2—Al2^xiv	45.855 (18)	45.846 (18)	45.865 (18)
Eu1—Al2—Al2^xv	45.855 (18)	45.846 (18)	45.865 (18)
Eu1—Al2—Al2^xvi	45.84 (3)	45.76 (3)	45.89 (3)
Eu1—Al2—Al2^xvii	45.84 (3)	45.76 (3)	45.89 (3)
Eu1^xxiii—Al2—Eu1^xxi	135.02 (4)	135.01 (4)	135.03 (4)
Eu1^xxiii—Al2—Eu1^xxiv	81.59 (3)	81.01 (3)	82.16 (3)
Eu1^xxiii—Al2—Eu1^xxii	81.58 (3)	81.01 (3)	82.16 (3)
Eu1^xxiii—Al2—Al1	139.01 (7)	136.31 (6)	141.77 (6)
Eu1^xxiii—Al2—Al1^i	71.175 (16)	70.255 (15)	72.100 (16)
Eu1^xxiii—Al2—Al1^viii	139.06 (7)	136.31 (6)	141.77 (6)
Eu1^xxiii—Al2—Al1^ix	71.192 (16)	70.255 (15)	72.100 (16)
Eu1^xxiii—Al2—Al2^i	49.21 (2)	48.53 (2)	49.87 (2)
Eu1^xxiii—Al2—Al2^ii	130.81 (5)	130.13 (5)	131.47 (5)
Eu1^xxiii—Al2—Al2^iii	49.19 (2)	48.53 (2)	49.87 (2)
Eu1^xxiii—Al2—Al2^iv	130.79 (5)	130.13 (5)	131.47 (5)
Eu1^xxiii—Al2—Al2^xx	67.51 (2)	67.51 (2)	67.52 (2)
Eu1^xxiii—Al2—Al2^xiv	66.613 (16)	66.608 (16)	66.618 (16)
Eu1^xxiii—Al2—Al2^xv	158.26 (4)	158.18 (4)	158.35 (4)
Eu1^xxiii—Al2—Al2^xvi	105.45 (3)	104.50 (3)	106.37 (3)
Eu1^xxiii—Al2—Al2^xvii	105.43 (3)	104.50 (3)	106.37 (3)
Eu1^xxi—Al2—Eu1^xxiv	81.59 (3)	81.01 (3)	82.16 (3)
Eu1^xxi—Al2—Eu1^xxii	81.58 (3)	81.01 (3)	82.16 (3)
Eu1^xxi—Al2—Al1	71.192 (16)	70.255 (15)	72.100 (16)
Eu1^xxi—Al2—Al1^i	139.06 (7)	136.31 (6)	141.77 (6)
Eu1^xxi—Al2—Al1^viii	71.175 (16)	70.255 (15)	72.100 (16)
Eu1^xxi—Al2—Al1^ix	139.01 (7)	136.31 (6)	141.77 (6)
Eu1^xxi—Al2—Al2^i	130.81 (5)	130.13 (5)	131.47 (5)
Eu1^xxi—Al2—Al2^ii	49.21 (2)	48.53 (2)	49.87 (2)
Eu1^xxi—Al2—Al2^iii	130.79 (5)	130.13 (5)	131.47 (5)
Eu1^xxi—Al2—Al2^iv	49.19 (2)	48.53 (2)	49.87 (2)
Eu1^xxi—Al2—Al2^xx	67.51 (2)	67.51 (2)	67.52 (2)
Eu1^xxi—Al2—Al2^xiv	158.26 (4)	158.18 (4)	158.35 (4)
Eu1^xxi—Al2—Al2^xv	66.613 (16)	66.608 (16)	66.618 (16)
Eu1^xxi—Al2—Al2^xvi	105.45 (3)	104.50 (3)	106.37 (3)
Eu1^xxi—Al2—Al2^xvii	105.43 (3)	104.50 (3)	106.37 (3)
Eu1^xxiv—Al2—Eu1^xxii	135.03 (4)	135.02 (4)	135.03 (4)
Eu1^xxiv—Al2—Al1	139.05 (5)	136.79 (5)	141.26 (5)
Eu1^xxiv—Al2—Al1^i	71.22 (6)	69.45 (5)	72.97 (6)
Eu1^xxiv—Al2—Al1^viii	71.22 (6)	69.45 (5)	72.97 (6)
Eu1^xxiv—Al2—Al1^ix	139.05 (5)	136.79 (5)	141.26 (5)
Eu1^xxiv—Al2—Al2^i	49.21 (3)	49.11 (3)	49.31 (3)
Eu1^xxiv—Al2—Al2^ii	49.21 (3)	49.11 (3)	49.31 (3)
Eu1^xxiv—Al2—Al2^iii	130.79 (3)	130.69 (3)	130.89 (3)
Eu1^xxiv—Al2—Al2^iv	130.79 (3)	130.69 (3)	130.89 (3)
Eu1^xxiv—Al2—Al2^xx	67.53 (6)	65.96 (6)	69.06 (6)
Eu1^xxiv—Al2—Al2^xiv	105.47 (4)	103.33 (4)	107.56 (4)
Eu1^xxiv—Al2—Al2^xv	105.47 (4)	103.33 (4)	107.56 (4)
Eu1^xxiv—Al2—Al2^xvi	66.66 (4)	64.98 (4)	68.34 (4)
Eu1^xxiv—Al2—Al2^xvii	158.35 (5)	156.63 (5)	159.99 (5)
Eu1^xxii—Al2—Al1	71.19 (6)	69.45 (5)	72.97 (6)
Eu1^xxii—Al2—Al1^i	139.01 (5)	136.79 (5)	141.26 (5)
Eu1^xxii—Al2—Al1^viii	139.01 (5)	136.79 (5)	141.26 (5)
Eu1^xxii—Al2—Al1^ix	71.19 (6)	69.45 (5)	72.97 (6)
Eu1^xxii—Al2—Al2^i	130.79 (3)	130.69 (3)	130.89 (3)
Eu1^xxii—Al2—Al2^ii	130.79 (3)	130.69 (3)	130.89 (3)
Eu1^xxii—Al2—Al2^iii	49.21 (3)	49.11 (3)	49.31 (3)
Eu1^xxii—Al2—Al2^iv	49.21 (3)	49.11 (3)	49.31 (3)
Eu1^xxii—Al2—Al2^xx	67.50 (6)	65.96 (6)	69.06 (6)
Eu1^xxii—Al2—Al2^xiv	105.43 (4)	103.33 (4)	107.56 (4)
Eu1^xxii—Al2—Al2^xv	105.43 (4)	103.33 (4)	107.56 (4)
Eu1^xxii—Al2—Al2^xvi	158.31 (5)	156.63 (5)	159.99 (5)
Eu1^xxii—Al2—Al2^xvii	66.63 (4)	64.98 (4)	68.34 (4)
Al1—Al2—Al1^i	111.03 (5)	110.98 (5)	111.09 (6)
Al1—Al2—Al1^viii	71.33 (5)	71.32 (6)	71.34 (5)
Al1—Al2—Al1^ix	71.30 (5)	67.79 (6)	74.88 (6)
Al1—Al2—Al2^i	145.52 (5)	145.36 (5)	145.64 (5)
Al1—Al2—Al2^ii	90.01 (4)	87.88 (4)	92.09 (4)
Al1—Al2—Al2^iii	89.99 (6)	87.91 (6)	92.12 (6)
Al1—Al2—Al2^iv	34.48 (3)	34.36 (3)	34.64 (3)
Al1—Al2—Al2^xx	124.40 (6)	122.95 (6)	125.78 (6)
Al1—Al2—Al2^xiv	91.36 (5)	89.21 (5)	93.49 (5)
Al1—Al2—Al2^xv	35.66 (4)	35.50 (4)	35.83 (4)
Al1—Al2—Al2^xvi	91.37 (4)	91.28 (4)	91.49 (5)
Al1—Al2—Al2^xvii	35.65 (3)	33.89 (5)	37.44 (5)
Al1^i—Al2—Al1^viii	71.37 (5)	67.79 (6)	74.88 (6)
Al1^i—Al2—Al1^ix	71.33 (5)	71.32 (6)	71.34 (5)
Al1^i—Al2—Al2^i	34.48 (3)	34.36 (3)	34.64 (3)
Al1^i—Al2—Al2^ii	90.03 (6)	87.91 (6)	92.12 (6)
Al1^i—Al2—Al2^iii	89.97 (4)	87.88 (4)	92.09 (4)
Al1^i—Al2—Al2^iv	145.52 (5)	145.36 (5)	145.64 (5)
Al1^i—Al2—Al2^xx	124.42 (6)	122.95 (6)	125.78 (6)
Al1^i—Al2—Al2^xiv	35.67 (4)	35.50 (4)	35.83 (4)
Al1^i—Al2—Al2^xv	91.40 (5)	89.21 (5)	93.49 (5)
Al1^i—Al2—Al2^xvi	35.68 (3)	33.89 (5)	37.44 (5)
Al1^i—Al2—Al2^xvii	91.37 (4)	91.28 (4)	91.49 (5)
Al1^viii—Al2—Al1^ix	111.03 (5)	110.98 (6)	111.09 (6)
Al1^viii—Al2—Al2^i	90.03 (6)	87.91 (6)	92.12 (6)
Al1^viii—Al2—Al2^ii	34.48 (3)	34.36 (3)	34.64 (3)
Al1^viii—Al2—Al2^iii	145.52 (5)	145.36 (5)	145.64 (5)
Al1^viii—Al2—Al2^iv	89.97 (4)	87.88 (4)	92.09 (4)
Al1^viii—Al2—Al2^xx	124.42 (6)	122.95 (6)	125.78 (6)
Al1^viii—Al2—Al2^xiv	91.40 (5)	89.21 (5)	93.49 (5)
Al1^viii—Al2—Al2^xv	35.67 (4)	35.50 (4)	35.83 (4)
Al1^viii—Al2—Al2^xvi	35.68 (3)	33.89 (5)	37.44 (5)
Al1^viii—Al2—Al2^xvii	91.37 (4)	91.28 (4)	91.49 (5)
Al1^ix—Al2—Al2^i	90.01 (4)	87.88 (4)	92.09 (4)
Al1^ix—Al2—Al2^ii	145.52 (5)	145.36 (5)	145.64 (5)
Al1^ix—Al2—Al2^iii	34.48 (3)	34.36 (3)	34.64 (3)
Al1^ix—Al2—Al2^iv	89.99 (6)	87.91 (6)	92.12 (6)
Al1^ix—Al2—Al2^xx	124.40 (6)	122.95 (6)	125.78 (6)
Al1^ix—Al2—Al2^xiv	35.66 (4)	35.50 (4)	35.83 (4)
Al1^ix—Al2—Al2^xv	91.36 (5)	89.21 (5)	93.49 (5)
Al1^ix—Al2—Al2^xvi	91.37 (4)	91.28 (4)	91.49 (5)
Al1^ix—Al2—Al2^xvii	35.65 (3)	33.89 (5)	37.44 (5)
Al2^i—Al2—Al2^ii	90.01 (4)	90.01 (4)	90.01 (4)
Al2^i—Al2—Al2^iii	89.99 (3)	89.99 (3)	89.99 (3)
Al2^i—Al2—Al2^iv	180	180	180
Al2^i—Al2—Al2^xx	90.01 (5)	88.72 (5)	91.28 (5)
Al2^i—Al2—Al2^xiv	59.52 (3)	57.85 (3)	61.16 (3)
Al2^i—Al2—Al2^xv	120.51 (5)	118.84 (5)	122.15 (5)
Al2^i—Al2—Al2^xvi	59.53 (3)	58.73 (3)	60.34 (3)
Al2^i—Al2—Al2^xvii	120.49 (3)	119.66 (3)	121.27 (3)
Al2^ii—Al2—Al2^iii	180	180	180
Al2^ii—Al2—Al2^iv	89.99 (3)	89.99 (3)	89.99 (3)
Al2^ii—Al2—Al2^xx	90.01 (5)	88.72 (5)	91.28 (5)
Al2^ii—Al2—Al2^xiv	120.51 (5)	118.84 (5)	122.15 (5)
Al2^ii—Al2—Al2^xv	59.52 (3)	57.85 (3)	61.16 (3)
Al2^ii—Al2—Al2^xvi	59.53 (3)	58.73 (3)	60.34 (3)
Al2^ii—Al2—Al2^xvii	120.49 (3)	119.66 (3)	121.27 (3)
Al2^iii—Al2—Al2^iv	90.01 (4)	90.01 (4)	90.01 (4)
Al2^iii—Al2—Al2^xx	89.99 (5)	88.72 (5)	91.28 (5)
Al2^iii—Al2—Al2^xiv	59.49 (3)	57.85 (3)	61.16 (3)
Al2^iii—Al2—Al2^xv	120.48 (5)	118.84 (5)	122.15 (5)
Al2^iii—Al2—Al2^xvi	120.47 (3)	119.66 (3)	121.27 (3)
Al2^iii—Al2—Al2^xvii	59.51 (3)	58.73 (3)	60.34 (3)
Al2^iv—Al2—Al2^xx	89.99 (5)	88.72 (5)	91.28 (5)
Al2^iv—Al2—Al2^xiv	120.48 (5)	118.84 (5)	122.15 (5)
Al2^iv—Al2—Al2^xv	59.49 (3)	57.85 (3)	61.16 (3)
Al2^iv—Al2—Al2^xvi	120.47 (3)	119.66 (3)	121.27 (3)
Al2^iv—Al2—Al2^xvii	59.51 (3)	58.73 (3)	60.34 (3)
Al2^xx—Al2—Al2^xiv	134.061 (19)	133.987 (19)	134.136 (18)
Al2^xx—Al2—Al2^xv	134.061 (19)	133.987 (19)	134.136 (18)
Al2^xx—Al2—Al2^xvi	134.19 (8)	130.98 (7)	137.36 (8)
Al2^xx—Al2—Al2^xvii	134.13 (8)	130.98 (7)	137.36 (8)
Al2^xiv—Al2—Al2^xv	91.69 (3)	91.66 (3)	91.73 (3)
Al2^xiv—Al2—Al2^xvi	60.98 (3)	60.11 (3)	61.81 (3)
Al2^xiv—Al2—Al2^xvii	60.97 (3)	60.11 (3)	61.81 (3)
Al2^xv—Al2—Al2^xvi	60.98 (3)	60.11 (3)	61.81 (3)
Al2^xv—Al2—Al2^xvii	60.97 (3)	60.11 (3)	61.81 (3)
Al2^xvi—Al2—Al2^xvii	91.69 (4)	91.65 (4)	91.72 (4)

Symmetry codes: (i) x₁−1/2, x₂−1/2, x₃, x₄; (ii) x₁−1/2, x₂+1/2, x₃, x₄; (iii) x₁+1/2, x₂−1/2, x₃, x₄; (iv) x₁+1/2, x₂+1/2, x₃, x₄; (v) x₁, x₂−1/2, x₃−1/2, x₄; (vi) x₁−1/2, x₂, x₃−1/2, x₄; (vii) −x₁, −x₂, −x₃, −x₄; (viii) −x₁, −x₂+1/2, −x₃+1/2, −x₄; (ix) −x₁+1/2, −x₂, −x₃+1/2, −x₄; (x) −x₁+1/2, −x₂+1/2, −x₃, −x₄; (xi) x₁, x₂+1/2, x₃−1/2, x₄; (xii) x₁+1/2, x₂, x₃−1/2, x₄; (xiii) −x₁, x₂, −x₃, −x₄; (xiv) −x₁, x₂−1/2, −x₃+1/2, −x₄; (xv) −x₁, x₂+1/2, −x₃+1/2, −x₄; (xvi) −x₁−1/2, x₂, −x₃+1/2, −x₄; (xvii) −x₁+1/2, x₂, −x₃+1/2, −x₄; (xviii) −x₁+1, −x₂+1/2, −x₃+1/2, −x₄; (xix) −x₁+1/2, −x₂+1, −x₃+1/2, −x₄; (xx) −x₁, x₂, −x₃+1, −x₄; (xxi) x₁, x₂+1/2, x₃+1/2, x₄; (xxii) x₁+1/2, x₂, x₃+1/2, x₄; (xxiii) x₁, x₂−1/2, x₃+1/2, x₄; (xxiv) x₁−1/2, x₂, x₃+1/2, x₄.