Structure solution of the Al69.2Cu20Cr10.8 ϕ phase

Samuha, S.; Tamari, R.; Grushko, B.; Meshi, L.

doi:10.1107/S1600576721011961

research papers

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 55| Part 1| February 2022| Pages 74-79

https://doi.org/10.1107/S1600576721011961

Structure solution of the Al_69.2Cu₂₀Cr_10.8 ϕ phase

Shmuel Samuha,^a,^b Rimon Tamari,^b Benjamin Grushko ^c and Louisa Meshi ^b ^*

^aNRCN, PO Box 9001, Beer-Sheva 84190, Israel, ^bDepartment of Materials Engineering, Ben Gurion University of the Negev, Beer Sheva 84105, Israel, and ^cPeter Grünberg Institut, Forschungszentrum Jülich, 52425 Jülich, Germany
^*Correspondence e-mail: louisa@bgu.ac.il

Edited by T. J. Sato, Tohoku University, Japan (Received 7 July 2021; accepted 10 November 2021)

The stable ϕ phase that forms below ∼923 K around the Al_69.2Cu_20.0Cr_10.8 composition was found to be hexagonal [P6₃, a = 11.045 (2), c = 12.688 (2) Å] and isostructural to the earlier reported Al_6.2Cu₂Re X phase [Samuha, Grushko & Meshi (2016). J. Alloys Compd. 670, 18–24]. Using the structural model of the latter, a successful Rietveld refinement of the XRD data for Al_69.5Cu_20.0Cr_10.5 was performed. Both ϕ and X were found to be structurally related to the Al_72.6Cu_11.0Cr_16.4 ζ phase [P6₃/m, a = 17.714, c = 12.591 Å; Sugiyama, Saito & Hiraga (2002). J. Alloys Compd. 342, 148–152], with a close lattice parameter c and a τ-times-larger lattice parameter a (τ is the golden mean). The structural relationship between ζ and ϕ was established on the basis of the similarity of their layered structures and common features. Additionally, the strong-reflections approach was successfully applied for the modeling of the ϕ phase based on the structural model of the ζ phase. The latter and the experimental structural model (retrieved following Rietveld refinement) were found to be essentially identical.

Keywords: intermetallics; Rietveld refinement; strong-reflections approach; electron crystallography; structure prediction.

CCDC reference: 2121302

1. Introduction

Investigation of the Al–Cu–Cr alloy system revealed several stable intermetallics, the structures of which had only been partially characterized [Grushko (2017 ) and references therein]. In the temperature range 843–1073 K and compositional range above 40 at.% Al, apart from the binaries, eight additional ternary compounds designated ζ, κ, ψ, S, ϕ, σ, β and Λ were revealed. The structures of the ζ phase of Al_72.6Cu_11.0Cr_16.4 and the κ phases of Al_67.4Cu_14.3Cr_18.3 were determined by single-crystal X-ray diffraction (XRD) [the latter is designated β by Sugiyama et al. (2002 )].

In the present work we report the structure solution of the ϕ phase and its structural relationship to the ζ phase. The ϕ phase was found to form at 923 K in a small compositional region around ∼Al₇₀Cu₁₉Cr₁₁, while at 973 K the same composition has been associated with the S phase, whose compositional region was found to extend towards ∼Al₇₉Cu₁₀Cr₁₁.

The structure solution of the ϕ phase was performed by Rietveld refinement of the XRD data based on the structural model of the isostructural Al_6.2Cu₂Re X phase (Samuha et al., 2016 ). Additionally, a structural model of the ϕ phase was deduced from the known structure of the ζ phase using the strong-reflections approach. The two models were proved to be essentially identical. For clarity, the scheme shown in Fig. 1 presents the different phases used in the current research as well as our aim.

Figure 1
Scheme of the present research to illustrate the relationship between the phases studied.

2. Experimental

An Al_69.5Cu_20.0Cr_10.5 alloy was produced from its constituent elements by levitation induction melting in a water-cooled copper crucible under an Ar atmosphere. The purity of Al was 99.999%, of Cu 99.95% and of Cr 99.99%. The sample was annealed under vacuum for 424 h at 923 K.

The alloy was studied by scanning electron microscopy (SEM), powder XRD and transmission electron microscopy (TEM). The compositions were analyzed by energy-dispersive X-ray analysis (EDX) with SEM. For the XRD examinations, the material was powdered in an agate mortar. The XRD pattern was recorded on a Rigaku D/MAX-2000 diffractometer equipped with a graphite monochromator with Cu Kα radiation. The measurements were performed within the 2θ range from 5 to 100° with a step size of 0.02° and a counting rate of 10 s per step. The FULLPROF software (Rodrigues-Carvajal, 1998 ) was used to analyze the XRD data.

For the TEM examinations, the powdered material was dispersed on a grid with a carbon film. The TEM study was carried out on a FASTEM JEOL-2010 electron microscope equipped with a Nanomegas `Spinning Star' precession unit. Diffraction patterns with a 120 mm camera length were recorded on a top-mounted Gatan Model 780 Dual Vision 300 camera with 1030 × 1300 pixels. The simulations of the precession electron diffraction (PED) patterns were performed using the program eMAP (Oleynikov, 2011 ). This program also allowed us to obtain the theoretical structure factors, calculating the 3D electron-density maps (EDMs) and extracting atomic positions from the EDMs.

3. Results and discussion

3.1. Refinement of the ϕ phase structure

The SEM examinations of the Al_69.5Cu_20.0Cr_10.5 alloy annealed at 923 K revealed a two-phase structure: the major phase with a composition close to that of the alloy and a minor phase of ∼Al_45.4Cu_53.7Cr_0.9. Since the corresponding complex powder XRD pattern could not be indexed using only known phases in this ternary system, the material was examined by electron diffraction with TEM. The corresponding PED patterns of the major ϕ phase indicated a hexagonal structure with the lattice parameters a = 11.0, c = 12.75 Å.

The crystal system, unit-cell parameters and intensity distribution in the PED patterns of the ϕ phase were found to resemble those of the Al–Cu–Re X phase [P6₃, a = 11.029, c = 12.746 Å (Meshi et al., 2009 )]. For example, the PED patterns along [100] of the ϕ and X phases are compared in Figs. 2(a) and 2(b), respectively. The crystal structure of the Al–Cu–Re X phase was deduced by Samuha et al. (2016) through the application of direct methods on the PED tomography data and refined against the powder XRD data by the Rietveld method.

Figure 2
Experimental PED patterns along the [100] orientation of the (a) ϕ phase and (b) X phase, and (c) the corresponding PED pattern of the ϕ phase simulated using the eMAP software (Oleynikov, 2011

). For the simulations the structural model of the ϕ phase was adopted from that of the X phase where Re was replaced by Cr.

These results allowed successful indexing of the major phase in the above-mentioned powder XRD pattern. The additional reflections of the minor phase were associated with those of the Al–Cu orthorhombic phase ζ_1Cu [Al₃Cu₄, Fmm2, a ≃ 8.14, b ≃ 14.3, c ≃ 10.0 Å (Gulay & Harbrecht, 2004 )].¹

The ϕ and X phases are formed around quite close equivalent compositions Al_69.5Cu_20.0Cr_10.5 and Al₆₅Cu₂₅Re₁₀ in the Al–Cu–Cr and Al–Cu–Re phase diagrams, respectively, whereas the Al_6.2Cu₂Re (Al_67.4Cu_21.7Cr_10.9) composition [which can be determined from the model proposed by Samuha et al. (2016)] is in between these two compositions. The deviation of the model composition from the measurements was ignored by Samuha et al. (2016). Considering the close atomic percentage of Cr and Re in these phases, the corresponding atoms could occupy the same sites, while some Cu in the X phase could be replaced by Al in the ϕ phase.

The correctness of this assumption was confirmed by the comparison of the experimental and simulated PED patterns of the ϕ phase in Figs. 2(a) and 2(c), respectively. The latter was calculated from the structural model of the Al–Cu–Re X phase, where Re was replaced by Cr, while Al and Cu were still fixed at their original positions. Figs. 2(a) and 2(c) illustrate the similar positions of the reflections (i.e. prove the correctness of the geometry of the unit cell), and the fact that the strongest reflections in both patterns are distributed in a similar manner and hierarchy further supports the correctness of the proposed atomic model.

Therefore, the model of the X phase was used as a starting point for the deduction of the structural model of the ϕ phase. It was refined by the Rietveld method on the powder XRD pattern using the FULLPROF software (Rodrigues-Carvajal, 1998). For convenience, the major ϕ phase was refined in Rietveld mode, while the minor ζ_1Cu phase was refined by applying the profile matching mode (i.e. refining only the geometry, without taking atom positions into account). The following parameters were refined: zero shift, lattice parameters, profile parameters, asymmetry parameters, atomic coordinates, displacement parameters and occupancy. Importantly, the last two parameter types were not refined simultaneously. First, displacement parameters were refined. After convergence, these factors were kept constant and the occupancy was refined until the program reached convergence. In the current work, an atom-type constraint was applied to the displacement parameters (e.g. all Al atoms were constrained to have the same displacement parameter etc.).

In order to adjust the composition, which was measured by EDS as Al_69.5Cu_20.0Cr_10.5, one could suggest that a twofold Cu site and a twofold Al site in the model published by Samuha et al. (2016) would be occupied by either both Cu or both Al [the composition of the phase studied by Samuha et al. (2016) was Al_65.2Cu_23.9Re_10.9 – richer in Cu and poorer in Al]. This idea was not confirmed by the refinement of the ϕ phase, which exhibited better results suggesting partial occupancy. Thus, two out of four Cu sixfold sites were suggested to be partially occupied by Al due to their position in the Cr coordination icosahedron. The details of the Rietveld refinement are summarized in Table 1; the atomic positions and displacement parameters are presented in Table 2.

Table 1
Details of the Rietveld refinement performed on the powder XRD data taken from the studied alloy

Parameter	Data
Structure refined	ϕ-Al_69.2Cu_20.0Cr_10.8
Space group	P6₃
Unit-cell parameters (nm)	a = 1.0999 (5) c = 1.2697 (9)
Additional phases generating diffraction peaks	ζ_1Cu-Al₃Cu₄. Treated in profile matching mode. Only the scale factors and lattice parameters were refined.
X-ray data range (2θ)	5.000–100.000
Zero shift	0.00157
Peak profile	Pseudo-Voigt (η = 0.87452)
Half-width parameters	U = 0.011425, V = −0.005877, W = 0.016688
Asymmetry parameters	P₁ = 0.03012, P₂ = 0.04394
Total number of reflections (of ϕ phase)	524
Reliability factors	R_p = 2.66, R_wp = 3.49, R_exp = 1.60, χ² = 4.77

Table 2
Atomic coordinates and displacement parameters for the ϕ phase structure after Rietveld refinement

Name	Wyckoff site	x	y	z	B_iso (Å²)	Occupancy
Cr1	6c	0.5682 (2)	0.9391 (3)	0.2718 (0)	0.941	1
Cr2	2b	0.3333 (3)	0.6666 (7)	0.5875 (1)	0.941	1
Cr3	2b	0.3333 (3)	0.6666 (7)	0.9357 (7)	0.941	1
Cu1	6c	0.9547 (5)	0.1964 (6)	0.0564 (8)	2.214	0.87
Al13	6c	0.9547 (5)	0.1964 (6)	0.0564 (8)	0.159	0.13
Cu2	2a	0.0000 (0)	0.0000 (0)	0.2822 (4)	2.214	1
Cu3	6c	0.9003 (4)	0.1612 (6)	0.2543 (0)	2.214	0.86
Al12	6c	0.9003 (4)	0.1612 (6)	0.2543 (0)	0.159	0.14
Cu4	6c	0.1943 (4)	0.2396 (1)	0.9618 (2)	2.152	1
Al1	6c	0.6811 (3)	0.0831 (7)	0.0745 (5)	0.159	1
Al2	6c	0.3815 (1)	0.4581 (5)	0.8754 (0)	0.159	1
Al3	6c	0.7048 (0)	0.2258 (7)	0.2746 (8)	0.159	1
Al4	6c	0.7675 (9)	0.9291 (7)	0.3640 (3)	0.159	1
Al5	6c	0.3061 (6)	0.8023 (4)	0.2356 (7)	0.159	1
Al6	6c	0.3578 (3)	0.5249 (3)	0.0700 (1)	0.159	1
Al7	6c	0.4466 (9)	0.0598 (2)	0.1542 (2)	0.159	1
Al8	6c	0.4838 (8)	0.8468 (6)	0.4356 (7)	0.159	1
Al9	6c	0.1218 (4)	0.4223 (3)	0.9457 (6)	0.159	1
Al10	6c	0.1448 (8)	0.2390 (5)	0.1566 (1)	0.159	1
Al11	2a	0.0000 (0)	0.0000 (0)	0.9981 (4)	0.159	1

The agreement factors for the refinement were R_p = 2.66%, R_wp = 3.49%, R_Bragg = 6.66% (of the ϕ phase) and R_Bragg = 0.788% (of Al₃Cu₄). The calculated and observed XRD profiles and the difference between them, as obtained following the refinement, are shown in Fig. 3. The interatomic distances are listed in Table 3. The occupancy refinement process led to the realistic stoichiometry of Al_69.2Cu_20.0Cr_10.8 and exhibited convergence.

Table 3
Interatomic distances for the ϕ phase (in Å)

CN is the coordination number. For simplicity, the coordination polyhedra of only heavy atoms are shown.

Cu4, CN = 12		Cu3\|Al12, CN = 13		Cu2, CN = 13
Al4	2.4377	Cu2	2.5333	Al4	2.4952
Al1	2.4569	Cu1\|Al13	2.5663	Al4	2.4959
Al11	2.4689	Al3	2.5942	Al4	2.4961
Al2	2.5040	Al4	2.6195	Cu3\|Al12	2.5333
Al9	2.5138	Al7	2.6222	Cu3\|Al12	2.5337
Al10	2.5324	Al10	2.684	Al11	2.7420
Cu3\|Al12	2.6863	Cu4	2.6863	Al10	2.7941
Cu1\|Al13	2.7137	Al10	2.7339	Al10	2.7944
Cu1\|Al13	2.7206	Al2	2.7729	Cu4	3.3287
Al4	2.8776	Al4	2.9259	Cu4	3.3288
Al6	3.0539	Al1	3.1128	Cu4	3.3290
Cu2	3.3288	Al9	3.1655
		Cr1	3.2308

Cu1\|Al13, CN = 11		Cr3, CN = 12		Cr2, CN = 12		Cr1, CN = 12
Al10	2.2874	Al6	2.4139	Al8	2.6658	Al8	2.2977
Al4	2.4678	Al6	2.4141	Al8	2.666	Al5	2.4454
Al7	2.5074	Al6	2.4145	Al3	2.7774	Al4	2.5363
Al11	2.5577	Al3	2.5007	Al3	2.7777	Al5	2.5387
Cu3\|Al12	2.5663	Al3	2.5011	Al3	2.7778	Al2	2.705
Al1	2.6289	Al3	2.5012	Al1	2.8391	Al3	2.7328
Al9	2.6382	Al9	2.5297	Al1	2.8393	Al10	2.7467
Cu4	2.7139	Al9	2.5298	Al7	2.8882	Al7	2.7475
Cu4	2.7205	Al2	2.7096	Al7	2.8885	Al6	2.7897
Al8	3.0476	Al2	2.7099	Al7	2.8886	Al9	2.8462
Al10	3.0931	Al2	2.7105			Al1	2.8914
						Cu3\|Al12	3.2311

Figure 3
Plot of the Rietveld refinement of the powder XRD pattern of the Al_69.5Cu_20.0Cr_10.5 alloy showing the observed XRD profile (red filled circles), calculated profile (black solid line) and difference between them (blue solid line). The vertical bars refer to the calculated peak positions of the ϕ phase (upper blue bars) and Al₃Cu₄ (bottom red bars).

The difference in the equivalent compositions of the ϕ and X phases illustrates the importance of the electron concentration for the stability of these phases. To compensate the increase of the absorption of 10 electrons by ∼10 Re atoms replaced by Cr, ∼5 atoms of Cu (each contributing only 1 electron) should be replaced by Al (each contributing 3 electrons). Therefore, to keep the same atomic structure the ϕ phase in the Al–Cu–Cr system had to form with a different (compared with the X phase) stoichiometry. These effects in the resulting stable atomic structures of allumindes were thoroughly discussed by Uziel et al. (2015 ) and Yaniv et al. (2018 , 2020 ). At the composition equivalent to that of the Al–Cu–Re X phase, the ψ phase is formed in Al–Cu–Cr, which has a different atomic structure (Grushko, 2017).

An analysis of the simulated PED patterns of ϕ and ζ revealed similar intensity distributions of the corresponding reflections (see Fig. 4). For convenience, the positions of the exceptionally strong reflections in these patterns are emphasized using blue, green and red circles, which are the same for both phases in a particular orientation. As can be seen, the strong reflections are distributed in a similar manner along these circles in both patterns. These structures are characterized by the related space groups P6₃ and P6₃/m, respectively, and have essentially the same c lattice parameters, while their a lattice parameters (11.0 and 17.6 Å) are approximately related by τ [where τ = (1 + 5^1/2)/2 ≃ 1.618 is the golden mean]. Their structural relation is quantitatively verified below using the strong-reflections approach (Christensen, 2004 , Christensen et al., 2004 ). This approach is strictly a reciprocal space method, based on the extraction of atomic positions of the unknown structure of an approximant of a quasicrystal (approximants are defined as periodic structures having the same coordination clusters as related quasicrystals) from a 3D EDM (Shechtman et al., 1984 ; Balanetskyy et al., 2004 ). The EDM is built using an adopted structure factor amplitude and phases of the strong reflections (which largely determine the atomic positions in a structure) from a known structure of a τ-related approximant. Use of the strongest reflections is based on the analysis of the relationship of the structure factor amplitudes and phases of reflections from a series of related quasicrystal approximants. Zhang et al. (2005 ) found that the strong reflections that are close to each other in reciprocal space have similar structure factor amplitudes and phases for all the approximants in the series. Therefore, the structure factor amplitudes and phases of strong reflections for an unknown approximant can be estimated from those of a known related approximant. To relate the different structures, it is essential to find the orientation matrix and to re-index the reflections. The strong-reflections approach was successfully applied for structure prediction, study of the structure relationship and solution of many complex approximants (e.g. He et al., 2007 ; Zhang et al., 2006 , 2008 ).

Figure 4
Simulated PED patterns along the [001] orientation and pseudo-tenfold [250] orientation of the (a), (c) ϕ phase and (b), (d) ζ phase.

3.2. Modeling of ϕ from the structure of ζ using the strong-reflections approach

Modeling is based on the extraction of the atomic positions of a `target' structure from a 3D EDM calculated by the inverse Fourier transform of the structure factor amplitudes and adopted phases of the strong reflections of a `related source' structure.

For the deduction of the structure of ϕ, the reflections of ζ were `hand-picked' according to the compatibility of the distribution of the strong reflections (with highest intensity in both patterns) present in the PED patterns of the two structures (see Table 4). As mentioned above, the only geometrical difference between ζ and ϕ is the length of their a lattice parameters, meaning that, for structure comparison only, a change of unit-cell dimensions is needed. Thus, the orientation matrix (A) was constructed for the re-indexing of the strongest reflections following equation (1):

$[(hkl)_{\phi} = \left({\matrix{ {{1 \mathord{\left/ {\vphantom {1 \tau }} \right. } \tau }} & 0 & 0 \cr 0 & {{1 \mathord{\left/ {\vphantom {1 \tau }} \right. } \tau }} & 0 \cr 0 & 0 & 1 \cr } } \right) (hkl)_{\zeta} . \eqno (1)]$

Using equation (1), a new set of h, k indexes of ϕ was obtained simply by re-indexing the h, k indexes of ζ (a_ϕ/a_ζ ≃ 1.1/1.7714 ≃ 1/τ). Note that this procedure was only carried out for the strongest reflections of ζ which were found to be compatible (comparing the net and ideal symmetry) with those of ϕ. After re-indexing, the strongest reflections in the PED patterns of ϕ exhibited one-to-one correspondence to those of ζ (see Fig. 4). For example the strongest reflections were

$[(710)\zeta\buildrel {(1)} \over \longrightarrow (410) \phi \quad {\rm and} \quad (063) \zeta \buildrel {(1)} \over \longrightarrow (043) \phi.]$

Next, the structure factor phases, which mainly determine the atomic positions in a structure, were modified according to their symmetry. For structurally related compounds, the relations of the structure factor phases of the strongest reflections are close (Christensen, 2004, Christensen et al., 2004), which is the case for ζ and ϕ. Owing to the difference in the existence of or lack of a center of symmetry, the structure factor phases of the strongest reflections of ζ should be modified by a shift of the origin, compatible with the space group of ϕ, which is non-centrosymmetric. For this case, from comparing common clusters (presented in the next section), the shift of the origin was found to be (−0.34, 0.40, −0.02). The new structure factor phases were calculated using equation (2):

$[\phi '(hkl) = \phi '(hkl) + 360^{\circ} \left(-0.34h + 0.4k + -0.02l \right). \eqno (2)]$

Following the shift of the origin, the phases of the symmetrically related reflections were close to those required by the symmetry of ϕ. Using eMAP (Oleynikov, 2011), 3D EDMs were calculated by the inverse Fourier transform of the structure factors. The calculation was based on the re-indexed strongest reflections of ζ incorporating the corresponding structure factor amplitudes and modified phases. The resulting 3D EDM viewed along the [001] orientation is shown in Fig. 5(a). Following the `peak hunting' procedure in eMAP (Oleynikov, 2011), the full theoretical model of ϕ was obtained. Thus, using a limited number of strong reflections, a successful deduction of the structure model of ϕ, based on that of ζ, was achieved. Comparison of the experimental structure of ϕ [Fig. 5(b)] with that deduced from ζ shows a close similarity. Using the Compstru software (Tasci et al., 2012 ) for a quantitative comparison of the atomic models (i.e. the model listed in Table 2 determined using the Rietveld refinement) with those derived applying the strong-reflections approach, the measure of similarity (Bergerhoff et al., 1999 ) was found to be Δ = 0.04 with the largest interatomic distance d = 0.56 Å, meaning essential identity.

Table 4
List of structure factor amplitudes and phases of the 15 strongest reflections used for the application of the strong-reflections approach

Crystallographic information was extracted from data obtained from the work by Sugiyama et al. (2002).

ζ-phase strong reflections
h	k	l	Amplitude	Phase
0	0	6	273.2	180
7	1	0	271.5	0
2	3	5	232.6	0
3	5	2	226.6	180
0	0	10	224.3	180
0	6	3	186.1	0
11	2	0	182.0	0
3	5	8	178.7	0
5	8	3	161.6	180
3	5	0	130.7	0
1	2	5	107.1	180
11	2	6	105.5	180
0	10	5	102.6	180
7	1	10	91.4	180
8	3	5	91.0	180

Figure 5
Deduced 3D EDM of (a) ϕ and (b) the structural model of ϕ determined experimentally, viewed along the [001] orientation. The Al, Cu and Cr atoms are marked in red, blue and green, respectively. The map consists of the spherical maxima that represent the atom positions in the unit cell, and their magnitude can be related to the atom types.

3.3. Family of τ-related hexagonal structures in Al-based alloy systems

Although the ϕ-type structure was only revealed in the Al–Cu–Cr (or Re) alloy systems, the ζ-type structure is also known in Al–Cr–Ni (Grushko et al., 2008 ), Al–Cr–Pd (Kowalski et al., 2010 ) and Al–Mn–Co (or Ni, or Fe) (Grushko et al., 2016 ). In addition to this family, there is a hexagonal λ-Al₄Mn structure [P6₃/m, a = 28.382, c = 12.4 Å (Kreiner & Franzen, 1997 )] with the lattice parameter c close to those of ϕ and ζ and the lattice parameter a about τ times larger than that of ζ. All this points to a large family of related phases.

Both ϕ and ζ can be represented as a six-layered structure perpendicular to the c axis (see Fig. 6). The common description of their layers includes type and packing: there are two approximately flat layers (designated F and f) and four puckered thick layers (designated P, P′, p, p′). The layers are organized in the PFP′pfp′ sequence, where the PFP′ layers are related by a 2₁ screw axis to the pfp′ layers. In the ϕ structure, the puckered layers consist of atoms that are arranged as if a pseudo-mirror exists in each of the flat layers. The only difference between the ϕ and the ζ structures, in this respect, is that the latter can be regarded as a mirror rather than a pseudo-mirror, as a result of the higher symmetry of ζ (P6₃/m versus P6₃).

Figure 6
Structures of ϕ (left) and ζ (right) projected along the [010] orientation.

The atoms in ϕ have similar icosahedral coordination. The I3 cluster (Kreiner & Franzen, 1997; Mo & Kuo, 2000 ) is of particular interest. It is constructed from three icosahedra built around the Cr atoms positioned in the flat layers. Since this cluster is not only present but also distributed in a similar manner in both structures, it can be regarded as the fundamental structural unit. The position of this cluster (presented in Fig. 7) in both structures is identical if a shift of the origin to (−0.34, 0.40, −0.02) is introduced. These facts provide proof from real space for the correctness of the atomic model and structural relationship, as there are many structural similarities between the structures of ϕ and ζ, mainly in their fundamental building blocks and layers.

Figure 7
I3 cluster in the structures of ϕ (left panel) and ζ (right panel) projected along the [010] orientation.

4. Conclusions

Rietveld refinement of the powder XRD data for the Al_69.5Cu_20.0Cr_10.5 ϕ phase [P6₃, a = 11.045 (2), c = 12.688 (2) Å] was successfully performed on the basis of the structural model of the isostructural Al_6.2Cu₂Re X phase. Using the strong-reflections approach, these phases were found to be structurally related to the Al_72.6Cu_11.0Cr_16.4 ζ phase (P6₃/m, a = 17.714, c = 12.591 Å) with a close lattice parameter c and a τ-times-larger lattice parameter a (τ is the golden mean). Structural similarities between the ζ and ϕ phases support their affiliation to the same family of τ-related phases.

Supporting information

CCDC reference: 2121302

Crystal structure: contains datablocks global, I. DOI: https://doi.org/10.1107/S1600576721011961/tu5013sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S1600576721011961/tu5013sup2.hkl

Computing details top

Program(s) used to refine structure: FULLPROF.

(I) top

Crystal data top

Al_63.64Cr₁₀Cu_18.38	V = 1330.5 (3) Å³
M_r = 3405.19	Z = 1
Hexagonal, P6₃	D_x = 4.250 Mg m⁻³
Hall symbol: P 6c	X-ray Cu Kα radiation, λ = 1.540560 Å
a = 10.9995 (10) Å	T = 298 K
c = 12.698 (1) Å	Specimen preparation: Prepared at 298 K

Data collection top

Rigaku diffractometer	Scan method: step
Radiation source: X-ray tube	2θ_min = 4.998°, 2θ_max = 99.998°, 2θ_step = 0.020°
C monochromator

Refinement top

R_p = 2.614	4751 data points
R_wp = 3.455	74 parameters
R_exp = 1.598	0 restraints
R_Bragg = 6.626

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Cr1	0.56822	0.93913	0.27180	0.017 (2)*
Cr2	0.33333	0.66667	0.58751	0.017 (2)*
Cr3	0.33333	0.66667	0.93577	0.017 (2)*
Cu1	0.95475	0.19646	0.05648	0.0255 (13)*	0.87199
Al13	0.95475	0.19646	0.05648	0.0040 (11)*	0.12800
Cu2	0.00000	0.00000	0.28224	0.0255 (13)*
Cu3	0.90034	0.16126	0.25430	0.0255 (13)*	0.85812
Al12	0.90034	0.16126	0.25430	0.0040 (11)*	0.14589
Cu4	0.19434	0.23961	0.96182	0.0255 (13)*
Al1	0.68113	0.08317	0.07455	0.0040 (11)*
Al2	0.38151	0.45815	0.87540	0.0040 (11)*
Al3	0.70480	0.22587	0.27468	0.0040 (11)*
Al4	0.76759	0.92917	0.36403	0.0040 (11)*
Al5	0.30616	0.80234	0.23567	0.0040 (11)*
Al6	0.35783	0.52493	0.07001	0.0040 (11)*
Al7	0.44669	0.05982	0.15422	0.0040 (11)*
Al8	0.48388	0.84686	0.43567	0.0040 (11)*
Al9	0.12184	0.42233	0.94576	0.0040 (11)*
Al10	0.14488	0.23905	0.15661	0.0040 (11)*
Al11	0.00000	0.00000	0.99814	0.0040 (11)*

Geometric parameters (Å, º) top

Cr1—Al8	2.2976	Al1—Al10^xiv	2.7155
Cr1—Al5ⁱ	2.4454	Al1—Cr2^xxiv	2.8393
Cr1—Al4	2.5363	Al1—Cr1^xxiii	2.8910
Cr1—Al5	2.5389	Al1—Al8^xxvii	2.8971
Cr1—Al2ⁱⁱ	2.7046	Al1—Al3	2.9293
Cr1—Al3ⁱⁱⁱ	2.7327	Al2—Al3^vii	2.4961
Cr1—Al10^iv	2.7467	Al2—Al9^iv	2.6026
Cr1—Al7ⁱⁱⁱ	2.7483	Al2—Al6^xi	2.6278
Cr1—Al6^iv	2.7899	Al2—Al3^viii	2.6902
Cr1—Al9^v	2.8464	Al2—Cr1^xxviii	2.7047
Cr1—Al1ⁱⁱⁱ	2.8911	Al2—Al12^vii	2.7721
Cr2—Al8	2.6657	Al2—Cu3^vii	2.7721
Cr2—Al8^iv	2.6657	Al2—Al8^xxviii	2.7874
Cr2—Al8ⁱ	2.6657	Al2—Al7^viii	2.8133
Cr2—Al3^vi	2.7781	Al2—Al9	2.8260
Cr2—Al3^vii	2.7781	Al3—Al9^xxiv	2.4424
Cr2—Al3^viii	2.7780	Al3—Al3^xviii	2.4913
Cr2—Al1^vi	2.8394	Al3—Al3^xiv	2.4913
Cr2—Al1^vii	2.8394	Al3—Al2^xxiv	2.4961
Cr2—Al1^viii	2.8394	Al3—Cr3^xxiv	2.5006
Cr2—Al7^vii	2.8885	Al3—Al2^xiii	2.6902
Cr2—Al7^vi	2.8885	Al3—Cr1^xxiii	2.7327
Cr2—Al7^viii	2.8885	Al3—Al7^xiv	2.7557
Cr3—Al6^ix	2.4143	Al3—Cr2^xxiv	2.7781
Cr3—Al6^x	2.4143	Al3—Al7	2.9241
Cr3—Al6^xi	2.4143	Al4—Cu4^xxvii	2.4374
Cr3—Al3^vi	2.5006	Al4—Al13^viii	2.4678
Cr3—Al3^vii	2.5006	Al4—Cu1^viii	2.4678
Cr3—Al3^viii	2.5006	Al4—Cu2^xxix	2.4958
Cr3—Al9ⁱ	2.5296	Al4—Al12ⁱⁱⁱ	2.6197
Cr3—Al9	2.5296	Al4—Cu3ⁱⁱⁱ	2.6197
Cr3—Al9^iv	2.5296	Al4—Al10^iv	2.6438
Cr3—Al2ⁱ	2.7101	Al4—Al9^v	2.7778
Cr3—Al2^iv	2.7101	Al4—Al11^v	2.8373
Cr3—Al2	2.7101	Al4—Cu4^v	2.8780
Cu1—Al10^xii	2.2869	Al4—Al8	2.9258
Cu1—Al4^xiii	2.4678	Al5—Cr1^iv	2.4454
Cu1—Al7^xiv	2.5077	Al5—Al7ⁱⁱⁱ	2.6650
Cu1—Al11^xv	2.5577	Al5—Al6ⁱ	2.6784
Cu1—Cu3	2.5663	Al5—Al6^iv	2.7139
Cu1—Al12	2.5663	Al5—Al10ⁱ	2.8523
Cu1—Al1	2.6293	Al5—Al5ⁱ	2.8788
Cu1—Al9^xv	2.6383	Al5—Al5^iv	2.8788
Cu1—Cu4^xv	2.7138	Al6—Cr3^xxx	2.4143
Cu1—Cu4^xvi	2.7204	Al6—Al1^xviii	2.5454
Al13—Al10^xii	2.2869	Al6—Al2^xxx	2.6278
Al13—Al4^xiii	2.4678	Al6—Al5^iv	2.6784
Al13—Al7^xiv	2.5077	Al6—Al5ⁱ	2.7139
Al13—Al11^xv	2.5577	Al6—Al9^xxxi	2.7167
Al13—Cu3	2.5663	Al6—Al9^xxx	2.7516
Al13—Al12	2.5663	Al6—Cr1ⁱ	2.7899
Al13—Al1	2.6293	Al6—Al7^xviii	2.8723
Al13—Al9^xv	2.6383	Al6—Al6ⁱ	2.9614
Al13—Cu4^xv	2.7138	Al6—Al6^iv	2.9614
Al13—Cu4^xvi	2.7204	Al7—Al13^xviii	2.5077
Cu2—Al4^xvii	2.4958	Al7—Cu1^xviii	2.5077
Cu2—Al4ⁱ	2.4958	Al7—Al12^xviii	2.6226
Cu2—Al4^xiv	2.4958	Al7—Cu3^xviii	2.6226
Cu2—Al12^xviii	2.5334	Al7—Al5^xxiii	2.6650
Cu2—Cu3^xviii	2.5334	Al7—Cr1^xxiii	2.7482
Cu2—Cu3^xix	2.5334	Al7—Al3^xviii	2.7557
Cu2—Al12^xix	2.5334	Al7—Al2^xiii	2.8133
Cu2—Cu3^xx	2.5335	Al7—Al6^xiv	2.8723
Cu2—Al12^xx	2.5335	Al7—Cr2^xxiv	2.8885
Cu2—Al11^xxi	2.7415	Al8—Al9^v	2.7598
Cu2—Al10	2.7943	Al8—Al2ⁱⁱ	2.7873
Cu2—Al10^xxii	2.7943	Al8—Al1^vi	2.8971
Cu3—Cu2^xii	2.5334	Al8—Al7^vi	2.9248
Cu3—Al3	2.5936	Al9—Al3^vii	2.4424
Cu3—Al4^xxiii	2.6197	Al9—Al2ⁱ	2.6027
Cu3—Al7^xiv	2.6226	Al9—Al13^xxvi	2.6384
Cu3—Al10^xii	2.6841	Al9—Cu1^xxvi	2.6384
Cu3—Cu4^xxiv	2.6863	Al9—Al6^ix	2.7167
Cu3—Al10^xiv	2.7342	Al9—Al6^xi	2.7516
Cu3—Al2^xxiv	2.7720	Al9—Al8^xxxii	2.7598
Cu3—Al4^xviii	2.9261	Al9—Al4^xxxii	2.7778
Al12—Cu2^xii	2.5334	Al9—Cr1^xxxii	2.8463
Al12—Al3	2.5936	Al10—Al13^xx	2.2869
Al12—Al4^xxiii	2.6197	Al10—Cu1^xx	2.2869
Al12—Al7^xiv	2.6226	Al10—Cu4^xxx	2.5319
Al12—Al10^xii	2.6841	Al10—Al4ⁱ	2.6438
Al12—Cu4^xxiv	2.6863	Al10—Al12^xx	2.6842
Al12—Al10^xiv	2.7342	Al10—Cu3^xx	2.6842
Al12—Al2^xxiv	2.7720	Al10—Al1^xviii	2.7156
Al12—Al4^xviii	2.9261	Al10—Cu3^xviii	2.7341
Cu4—Al4^vi	2.4374	Al10—Al12^xviii	2.7341
Cu4—Al1^xxv	2.4569	Al10—Cr1ⁱ	2.7467
Cu4—Al11	2.4687	Al10—Al5^iv	2.8524
Cu4—Al2	2.5044	Al11—Cu4^xxii	2.4687
Cu4—Al9	2.5139	Al11—Cu4^xxxiii	2.4688
Cu4—Al10^xi	2.5319	Al11—Al13^xxv	2.5577
Cu4—Al12^vii	2.6863	Al11—Cu1^xxv	2.5577
Cu4—Cu3^vii	2.6863	Al11—Cu1^xxxiv	2.5577
Cu4—Al13^xxvi	2.7137	Al11—Al13^xxxiv	2.5577
Cu4—Cu1^xxvi	2.7137	Al11—Al13^xxvi	2.5577
Cu4—Al13^xxv	2.7204	Al11—Cu1^xxvi	2.5577
Cu4—Cu1^xxv	2.7204	Al11—Cu2^viii	2.7415
Al1—Cu4^xvi	2.4570	Al11—Al4^vi	2.8373
Al1—Al6^xiv	2.5454	Al11—Al4^xxxv	2.8373
Al1—Al7	2.6602

Al8—Cr1—Al5ⁱ	81.1	Al3^vii—Al2—Al9^iv	103.1
Al8—Cr1—Al4	74.3	Cu4—Al2—Al9^iv	133.9
Al5ⁱ—Cr1—Al4	81.3	Al3^vii—Al2—Al6^xi	103.1
Al8—Cr1—Al5	79.3	Cu4—Al2—Al6^xi	73.0
Al5ⁱ—Cr1—Al5	70.5	Al9^iv—Al2—Al6^xi	62.6
Al4—Cr1—Al5	143.9	Al3^vii—Al2—Al3^viii	57.3
Al8—Cr1—Al2ⁱⁱ	67.2	Cu4—Al2—Al3^viii	153.9
Al5ⁱ—Cr1—Al2ⁱⁱ	136.0	Al9^iv—Al2—Al3^viii	54.9
Al4—Cr1—Al2ⁱⁱ	116.0	Al6^xi—Al2—Al3^viii	102.1
Al5—Cr1—Al2ⁱⁱ	74.1	Al3^vii—Al2—Cr1^xxviii	107.7
Al8—Cr1—Al3ⁱⁱⁱ	111.4	Cu4—Al2—Cr1^xxviii	143.4
Al5ⁱ—Cr1—Al3ⁱⁱⁱ	164.5	Al9^iv—Al2—Cr1^xxviii	64.8
Al4—Cr1—Al3ⁱⁱⁱ	93.2	Al6^xi—Al2—Cr1^xxviii	123.4
Al5—Cr1—Al3ⁱⁱⁱ	119.5	Al3^viii—Al2—Cr1^xxviii	60.9
Al2ⁱⁱ—Cr1—Al3ⁱⁱⁱ	59.3	Al3^vii—Al2—Cr3	57.2
Al8—Cr1—Al10^iv	126.3	Cu4—Al2—Cr3	105.9
Al5ⁱ—Cr1—Al10^iv	66.4	Al9^iv—Al2—Cr3	56.8
Al4—Cr1—Al10^iv	59.9	Al6^xi—Al2—Cr3	53.8
Al5—Cr1—Al10^iv	123.2	Al3^viii—Al2—Cr3	55.2
Al2ⁱⁱ—Cr1—Al10^iv	157.6	Cr1^xxviii—Al2—Cr3	109.7
Al3ⁱⁱⁱ—Cr1—Al10^iv	98.4	Al3^vii—Al2—Al12^vii	58.7
Al8—Cr1—Al7ⁱⁱⁱ	121.3	Cu4—Al2—Al12^vii	61.0
Al5ⁱ—Cr1—Al7ⁱⁱⁱ	117.6	Al9^iv—Al2—Al12^vii	160.6
Al4—Cr1—Al7ⁱⁱⁱ	155.7	Al6^xi—Al2—Al12^vii	124.8
Al5—Cr1—Al7ⁱⁱⁱ	60.4	Al3^viii—Al2—Al12^vii	106.1
Al2ⁱⁱ—Cr1—Al7ⁱⁱⁱ	62.1	Cr1^xxviii—Al2—Al12^vii	111.8
Al3ⁱⁱⁱ—Cr1—Al7ⁱⁱⁱ	64.5	Cr3—Al2—Al12^vii	110.8
Al10^iv—Cr1—Al7ⁱⁱⁱ	111.7	Al3^vii—Al2—Cu3^vii	58.7
Al8—Cr1—Al6^iv	131.6	Cu4—Al2—Cu3^vii	61.0
Al5ⁱ—Cr1—Al6^iv	61.1	Al9^iv—Al2—Cu3^vii	160.6
Al4—Cr1—Al6^iv	123.4	Al6^xi—Al2—Cu3^vii	124.8
Al5—Cr1—Al6^iv	61.0	Al3^viii—Al2—Cu3^vii	106.1
Al2ⁱⁱ—Cr1—Al6^iv	120.5	Cr1^xxviii—Al2—Cu3^vii	111.8
Al3ⁱⁱⁱ—Cr1—Al6^iv	111.7	Cr3—Al2—Cu3^vii	110.8
Al10^iv—Cr1—Al6^iv	66.5	Al12^vii—Al2—Cu3^vii	0.0
Al7ⁱⁱⁱ—Cr1—Al6^iv	62.5	Al3^vii—Al2—Al8^xxviii	155.4
Al8—Cr1—Al9^v	63.9	Cu4—Al2—Al8^xxviii	106.3
Al5ⁱ—Cr1—Al9^v	134.0	Al9^iv—Al2—Al8^xxviii	61.5
Al4—Cr1—Al9^v	61.8	Al6^xi—Al2—Al8^xxviii	87.1
Al5—Cr1—Al9^v	125.7	Al3^viii—Al2—Al8^xxviii	98.9
Al2ⁱⁱ—Cr1—Al9^v	55.8	Cr1^xxviii—Al2—Al8^xxviii	49.4
Al3ⁱⁱⁱ—Cr1—Al9^v	51.9	Cr3—Al2—Al8^xxviii	116.8
Al10^iv—Cr1—Al9^v	110.8	Al12^vii—Al2—Al8^xxviii	132.4
Al7ⁱⁱⁱ—Cr1—Al9^v	106.1	Cu3^vii—Al2—Al8^xxviii	132.4
Al6^iv—Cr1—Al9^v	163.5	Al3^vii—Al2—Al7^viii	62.2
Al8—Cr1—Al1ⁱⁱⁱ	174.1	Cu4—Al2—Al7^viii	114.8
Al5ⁱ—Cr1—Al1ⁱⁱⁱ	104.8	Al9^iv—Al2—Al7^viii	111.3
Al4—Cr1—Al1ⁱⁱⁱ	106.3	Al6^xi—Al2—Al7^viii	163.4
Al5—Cr1—Al1ⁱⁱⁱ	102.6	Al3^viii—Al2—Al7^viii	64.1
Al2ⁱⁱ—Cr1—Al1ⁱⁱⁱ	107.7	Cr1^xxviii—Al2—Al7^viii	59.7
Al3ⁱⁱⁱ—Cr1—Al1ⁱⁱⁱ	62.7	Cr3—Al2—Al7^viii	109.7
Al10^iv—Cr1—Al1ⁱⁱⁱ	57.5	Al12^vii—Al2—Al7^viii	56.0
Al7ⁱⁱⁱ—Cr1—Al1ⁱⁱⁱ	56.2	Cu3^vii—Al2—Al7^viii	56.0
Al6^iv—Cr1—Al1ⁱⁱⁱ	53.2	Al8^xxviii—Al2—Al7^viii	103.6
Al9^v—Cr1—Al1ⁱⁱⁱ	111.0	Al3^vii—Al2—Al9	54.2
Al8—Cr2—Al8^iv	73.5	Cu4—Al2—Al9	55.9
Al8—Cr2—Al8ⁱ	73.5	Al9^iv—Al2—Al9	107.4
Al8^iv—Cr2—Al8ⁱ	73.5	Al6^xi—Al2—Al9	60.5
Al8—Cr2—Al3^vi	118.2	Al3^viii—Al2—Al9	99.0
Al8^iv—Cr2—Al3^vi	114.2	Cr1^xxviii—Al2—Al9	159.6
Al8ⁱ—Cr2—Al3^vi	167.0	Cr3—Al2—Al9	54.3
Al8—Cr2—Al3^vii	167.0	Al12^vii—Al2—Al9	68.9
Al8^iv—Cr2—Al3^vii	118.2	Cu3^vii—Al2—Al9	68.9
Al8ⁱ—Cr2—Al3^vii	114.2	Al8^xxviii—Al2—Al9	145.6
Al3^vi—Cr2—Al3^vii	53.3	Al7^viii—Al2—Al9	110.6
Al8—Cr2—Al3^viii	114.2	Al9^xxiv—Al3—Al3^xviii	108.1
Al8^iv—Cr2—Al3^viii	167.0	Al9^xxiv—Al3—Al3^xiv	116.5
Al8ⁱ—Cr2—Al3^viii	118.2	Al3^xviii—Al3—Al3^xiv	60.0
Al3^vi—Cr2—Al3^viii	53.3	Al9^xxiv—Al3—Al2^xxiv	69.8
Al3^vii—Cr2—Al3^viii	53.3	Al3^xviii—Al3—Al2^xxiv	116.1
Al8—Cr2—Al1^vi	63.4	Al3^xiv—Al3—Al2^xxiv	65.3
Al8^iv—Cr2—Al1^vi	71.2	Al9^xxiv—Al3—Cr3^xxiv	61.5
Al8ⁱ—Cr2—Al1^vi	130.1	Al3^xviii—Al3—Cr3^xxiv	60.1
Al3^vi—Cr2—Al1^vi	62.9	Al3^xiv—Al3—Cr3^xxiv	60.1
Al3^vii—Cr2—Al1^vi	113.2	Al2^xxiv—Al3—Cr3^xxiv	65.7
Al3^viii—Cr2—Al1^vi	102.2	Al9^xxiv—Al3—Cu3	77.8
Al8—Cr2—Al1^vii	130.1	Al3^xviii—Al3—Cu3	174.1
Al8^iv—Cr2—Al1^vii	63.4	Al3^xiv—Al3—Cu3	118.3
Al8ⁱ—Cr2—Al1^vii	71.2	Al2^xxiv—Al3—Cu3	66.0
Al3^vi—Cr2—Al1^vii	102.2	Cr3^xxiv—Al3—Cu3	124.7
Al3^vii—Cr2—Al1^vii	62.9	Al9^xxiv—Al3—Al12	77.8
Al3^viii—Cr2—Al1^vii	113.2	Al3^xviii—Al3—Al12	174.1
Al1^vi—Cr2—Al1^vii	119.7	Al3^xiv—Al3—Al12	118.3
Al8—Cr2—Al1^viii	71.2	Al2^xxiv—Al3—Al12	66.0
Al8^iv—Cr2—Al1^viii	130.1	Cr3^xxiv—Al3—Al12	124.7
Al8ⁱ—Cr2—Al1^viii	63.4	Cu3—Al3—Al12	0.0
Al3^vi—Cr2—Al1^viii	113.2	Al9^xxiv—Al3—Al2^xiii	60.7
Al3^vii—Cr2—Al1^viii	102.2	Al3^xviii—Al3—Al2^xiii	57.4
Al3^viii—Cr2—Al1^viii	62.9	Al3^xiv—Al3—Al2^xiii	109.5
Al1^vi—Cr2—Al1^viii	119.7	Al2^xxiv—Al3—Al2^xiii	120.4
Al1^vii—Cr2—Al1^viii	119.7	Cr3^xxiv—Al3—Al2^xiii	62.8
Al8—Cr2—Al7^vii	124.1	Cu3—Al3—Al2^xiii	127.0
Al8^iv—Cr2—Al7^vii	63.4	Al12—Al3—Al2^xiii	127.0
Al8ⁱ—Cr2—Al7^vii	121.6	Al9^xxiv—Al3—Cr1^xxiii	66.5
Al3^vi—Cr2—Al7^vii	58.2	Al3^xviii—Al3—Cr1^xxiii	106.9
Al3^vii—Cr2—Al7^vii	62.1	Al3^xiv—Al3—Cr1^xxiii	166.9
Al3^viii—Cr2—Al7^vii	104.1	Al2^xxiv—Al3—Cr1^xxiii	125.7
Al1^vi—Cr2—Al7^vii	70.0	Cr3^xxiv—Al3—Cr1^xxiii	115.5
Al1^vii—Cr2—Al7^vii	55.3	Cu3—Al3—Cr1^xxiii	74.6
Al1^viii—Cr2—Al7^vii	164.3	Al12—Al3—Cr1^xxiii	74.6
Al8—Cr2—Al7^vi	63.4	Al2^xiii—Al3—Cr1^xxiii	59.8
Al8^iv—Cr2—Al7^vi	121.6	Al9^xxiv—Al3—Al7^xiv	126.1
Al8ⁱ—Cr2—Al7^vi	124.1	Al3^xviii—Al3—Al7^xiv	116.7
Al3^vi—Cr2—Al7^vi	62.1	Al3^xiv—Al3—Al7^xiv	67.5
Al3^vii—Cr2—Al7^vi	104.1	Al2^xxiv—Al3—Al7^xiv	64.6
Al3^viii—Cr2—Al7^vi	58.2	Cr3^xxiv—Al3—Al7^xiv	118.4
Al1^vi—Cr2—Al7^vi	55.3	Cu3—Al3—Al7^xiv	58.6
Al1^vii—Cr2—Al7^vi	164.3	Al12—Al3—Al7^xiv	58.6
Al1^viii—Cr2—Al7^vi	70.0	Al2^xiii—Al3—Al7^xiv	173.1
Al7^vii—Cr2—Al7^vi	111.8	Cr1^xxiii—Al3—Al7^xiv	122.1
Al8—Cr2—Al7^viii	121.6	Al9^xxiv—Al3—Cr2^xxiv	170.7
Al8^iv—Cr2—Al7^viii	124.1	Al3^xviii—Al3—Cr2^xxiv	63.4
Al8ⁱ—Cr2—Al7^viii	63.4	Al3^xiv—Al3—Cr2^xxiv	63.4
Al3^vi—Cr2—Al7^viii	104.1	Al2^xxiv—Al3—Cr2^xxiv	116.4
Al3^vii—Cr2—Al7^viii	58.2	Cr3^xxiv—Al3—Cr2^xxiv	113.7
Al3^viii—Cr2—Al7^viii	62.1	Cu3—Al3—Cr2^xxiv	110.7
Al1^vi—Cr2—Al7^viii	164.3	Al12—Al3—Cr2^xxiv	110.7
Al1^vii—Cr2—Al7^viii	70.0	Al2^xiii—Al3—Cr2^xxiv	110.2
Al1^viii—Cr2—Al7^viii	55.3	Cr1^xxiii—Al3—Cr2^xxiv	111.5
Al7^vii—Cr2—Al7^viii	111.8	Al7^xiv—Al3—Cr2^xxiv	62.9
Al7^vi—Cr2—Al7^viii	111.8	Al9^xxiv—Al3—Al7	112.6
Al6^ix—Cr3—Al6^x	75.7	Al3^xviii—Al3—Al7	60.6
Al6^ix—Cr3—Al6^xi	75.7	Al3^xiv—Al3—Al7	110.9
Al6^x—Cr3—Al6^xi	75.7	Al2^xxiv—Al3—Al7	176.2
Al6^ix—Cr3—Al3^vi	109.5	Cr3^xxiv—Al3—Al7	112.5
Al6^x—Cr3—Al3^vi	114.6	Cu3—Al3—Al7	117.1
Al6^xi—Cr3—Al3^vi	169.1	Al12—Al3—Al7	117.1
Al6^ix—Cr3—Al3^vii	114.6	Al2^xiii—Al3—Al7	60.0
Al6^x—Cr3—Al3^vii	169.1	Cr1^xxiii—Al3—Al7	58.0
Al6^xi—Cr3—Al3^vii	109.5	Al7^xiv—Al3—Al7	114.7
Al3^vi—Cr3—Al3^vii	59.8	Cr2^xxiv—Al3—Al7	60.8
Al6^ix—Cr3—Al3^viii	169.1	Cu4^xxvii—Al4—Al13^viii	67.4
Al6^x—Cr3—Al3^viii	109.5	Cu4^xxvii—Al4—Cu1^viii	67.4
Al6^xi—Cr3—Al3^viii	114.6	Al13^viii—Al4—Cu1^viii	0.0
Al3^vi—Cr3—Al3^viii	59.8	Cu4^xxvii—Al4—Cu2^xxix	84.9
Al3^vii—Cr3—Al3^viii	59.8	Al13^viii—Al4—Cu2^xxix	118.1
Al6^ix—Cr3—Al9ⁱ	67.6	Cu1^viii—Al4—Cu2^xxix	118.1
Al6^x—Cr3—Al9ⁱ	66.6	Cu4^xxvii—Al4—Cr1	138.6
Al6^xi—Cr3—Al9ⁱ	132.2	Al13^viii—Al4—Cr1	111.5
Al3^vi—Cr3—Al9ⁱ	58.1	Cu1^viii—Al4—Cr1	111.5
Al3^vii—Cr3—Al9ⁱ	113.0	Cu2^xxix—Al4—Cr1	124.6
Al3^viii—Cr3—Al9ⁱ	105.1	Cu4^xxvii—Al4—Al12ⁱⁱⁱ	142.1
Al6^ix—Cr3—Al9	66.6	Al13^viii—Al4—Al12ⁱⁱⁱ	116.8
Al6^x—Cr3—Al9	132.2	Cu1^viii—Al4—Al12ⁱⁱⁱ	116.8
Al6^xi—Cr3—Al9	67.6	Cu2^xxix—Al4—Al12ⁱⁱⁱ	59.3
Al3^vi—Cr3—Al9	105.1	Cr1—Al4—Al12ⁱⁱⁱ	77.6
Al3^vii—Cr3—Al9	58.1	Cu4^xxvii—Al4—Cu3ⁱⁱⁱ	142.1
Al3^viii—Cr3—Al9	113.0	Al13^viii—Al4—Cu3ⁱⁱⁱ	116.8
Al9ⁱ—Cr3—Al9	119.8	Cu1^viii—Al4—Cu3ⁱⁱⁱ	116.8
Al6^ix—Cr3—Al9^iv	132.2	Cu2^xxix—Al4—Cu3ⁱⁱⁱ	59.3
Al6^x—Cr3—Al9^iv	67.6	Cr1—Al4—Cu3ⁱⁱⁱ	77.6
Al6^xi—Cr3—Al9^iv	66.6	Al12ⁱⁱⁱ—Al4—Cu3ⁱⁱⁱ	0.0
Al3^vi—Cr3—Al9^iv	113.0	Cu4^xxvii—Al4—Al10^iv	116.1
Al3^vii—Cr3—Al9^iv	105.1	Al13^viii—Al4—Al10^iv	175.5
Al3^viii—Cr3—Al9^iv	58.1	Cu1^viii—Al4—Al10^iv	175.5
Al9ⁱ—Cr3—Al9^iv	119.8	Cu2^xxix—Al4—Al10^iv	65.8
Al9—Cr3—Al9^iv	119.8	Cr1—Al4—Al10^iv	64.0
Al6^ix—Cr3—Al2ⁱ	61.4	Al12ⁱⁱⁱ—Al4—Al10^iv	62.6
Al6^x—Cr3—Al2ⁱ	124.3	Cu3ⁱⁱⁱ—Al4—Al10^iv	62.6
Al6^xi—Cr3—Al2ⁱ	121.0	Cu4^xxvii—Al4—Al9^v	127.2
Al3^vi—Cr3—Al2ⁱ	57.1	Al13^viii—Al4—Al9^v	60.0
Al3^vii—Cr3—Al2ⁱ	62.0	Cu1^viii—Al4—Al9^v	60.0
Al3^viii—Cr3—Al2ⁱ	108.6	Cu2^xxix—Al4—Al9^v	122.8
Al9ⁱ—Cr3—Al2ⁱ	65.2	Cr1—Al4—Al9^v	64.6
Al9—Cr3—Al2ⁱ	59.4	Al12ⁱⁱⁱ—Al4—Al9^v	71.7
Al9^iv—Cr3—Al2ⁱ	166.1	Cu3ⁱⁱⁱ—Al4—Al9^v	71.7
Al6^ix—Cr3—Al2^iv	121.0	Al10^iv—Al4—Al9^v	116.2
Al6^x—Cr3—Al2^iv	61.4	Cu4^xxvii—Al4—Al11^v	55.2
Al6^xi—Cr3—Al2^iv	124.3	Al13^viii—Al4—Al11^v	57.1
Al3^vi—Cr3—Al2^iv	62.0	Cu1^viii—Al4—Al11^v	57.1
Al3^vii—Cr3—Al2^iv	108.6	Cu2^xxix—Al4—Al11^v	61.5
Al3^viii—Cr3—Al2^iv	57.1	Cr1—Al4—Al11^v	160.9
Al9ⁱ—Cr3—Al2^iv	59.4	Al12ⁱⁱⁱ—Al4—Al11^v	93.7
Al9—Cr3—Al2^iv	166.1	Cu3ⁱⁱⁱ—Al4—Al11^v	93.7
Al9^iv—Cr3—Al2^iv	65.2	Al10^iv—Al4—Al11^v	127.0
Al2ⁱ—Cr3—Al2^iv	112.3	Al9^v—Al4—Al11^v	96.7
Al6^ix—Cr3—Al2	124.3	Cu4^xxvii—Al4—Cu4^v	104.1
Al6^x—Cr3—Al2	121.0	Al13^viii—Al4—Cu4^v	60.4
Al6^xi—Cr3—Al2	61.4	Cu1^viii—Al4—Cu4^v	60.4
Al3^vi—Cr3—Al2	108.6	Cu2^xxix—Al4—Cu4^v	76.2
Al3^vii—Cr3—Al2	57.1	Cr1—Al4—Cu4^v	110.6
Al3^viii—Cr3—Al2	62.0	Al12ⁱⁱⁱ—Al4—Cu4^v	58.3
Al9ⁱ—Cr3—Al2	166.1	Cu3ⁱⁱⁱ—Al4—Cu4^v	58.3
Al9—Cr3—Al2	65.2	Al10^iv—Al4—Cu4^v	120.0
Al9^iv—Cr3—Al2	59.4	Al9^v—Al4—Cu4^v	52.7
Al2ⁱ—Cr3—Al2	112.3	Al11^v—Al4—Cu4^v	51.2
Al2^iv—Cr3—Al2	112.3	Cu4^xxvii—Al4—Al8	99.7
Al10^xii—Cu1—Al4^xiii	127.1	Al13^viii—Al4—Al8	68.2
Al10^xii—Cu1—Al7^xiv	89.3	Cu1^viii—Al4—Al8	68.2
Al4^xiii—Cu1—Al7^xiv	124.7	Cu2^xxix—Al4—Al8	173.5
Al10^xii—Cu1—Al11^xv	77.9	Cr1—Al4—Al8	49.1
Al4^xiii—Cu1—Al11^xv	68.7	Al12ⁱⁱⁱ—Al4—Al8	117.1
Al7^xiv—Cu1—Al11^xv	165.9	Cu3ⁱⁱⁱ—Al4—Al8	117.1
Al10^xii—Cu1—Cu3	66.9	Al10^iv—Al4—Al8	107.8
Al4^xiii—Cu1—Cu3	161.1	Al9^v—Al4—Al8	57.8
Al7^xiv—Cu1—Cu3	62.2	Al11^v—Al4—Al8	125.0
Al11^xv—Cu1—Cu3	106.6	Cu4^v—Al4—Al8	106.9
Al10^xii—Cu1—Al12	66.9	Cr1^iv—Al5—Cr1	155.7
Al4^xiii—Cu1—Al12	161.1	Cr1^iv—Al5—Al7ⁱⁱⁱ	136.8
Al7^xiv—Cu1—Al12	62.2	Cr1—Al5—Al7ⁱⁱⁱ	63.7
Al11^xv—Cu1—Al12	106.6	Cr1^iv—Al5—Al6ⁱ	65.8
Cu3—Cu1—Al12	0.0	Cr1—Al5—Al6ⁱ	129.6
Al10^xii—Cu1—Al1	139.6	Al7ⁱⁱⁱ—Al5—Al6ⁱ	103.4
Al4^xiii—Cu1—Al1	89.9	Cr1^iv—Al5—Al6^iv	131.5
Al7^xiv—Cu1—Al1	79.4	Cr1—Al5—Al6^iv	64.1
Al11^xv—Cu1—Al1	106.6	Al7ⁱⁱⁱ—Al5—Al6^iv	64.5
Cu3—Cu1—Al1	73.6	Al6ⁱ—Al5—Al6^iv	66.6
Al12—Cu1—Al1	73.6	Cr1^iv—Al5—Al10ⁱ	61.9
Al10^xii—Cu1—Al9^xv	88.2	Cr1—Al5—Al10ⁱ	138.1
Al4^xiii—Cu1—Al9^xv	65.8	Al7ⁱⁱⁱ—Al5—Al10ⁱ	75.3
Al7^xiv—Cu1—Al9^xv	77.4	Al6ⁱ—Al5—Al10ⁱ	66.5
Al11^xv—Cu1—Al9^xv	107.6	Al6^iv—Al5—Al10ⁱ	106.3
Cu3—Cu1—Al9^xv	131.6	Cr1^iv—Al5—Al5ⁱ	115.1
Al12—Cu1—Al9^xv	131.6	Cr1—Al5—Al5ⁱ	53.2
Al1—Cu1—Al9^xv	125.9	Al7ⁱⁱⁱ—Al5—Al5ⁱ	106.6
Al10^xii—Cu1—Cu4^xv	60.1	Al6ⁱ—Al5—Al5ⁱ	91.2
Al4^xiii—Cu1—Cu4^xv	67.3	Al6^iv—Al5—Al5ⁱ	57.1
Al7^xiv—Cu1—Cu4^xv	122.4	Al10ⁱ—Al5—Al5ⁱ	157.1
Al11^xv—Cu1—Cu4^xv	55.8	Cr1^iv—Al5—Al5^iv	56.3
Cu3—Cu1—Cu4^xv	126.4	Cr1—Al5—Al5^iv	112.1
Al12—Cu1—Cu4^xv	126.4	Al7ⁱⁱⁱ—Al5—Al5^iv	154.4
Al1—Cu1—Cu4^xv	154.5	Al6ⁱ—Al5—Al5^iv	58.3
Al9^xv—Cu1—Cu4^xv	56.0	Al6^iv—Al5—Al5^iv	90.5
Al10^xii—Cu1—Cu4^xvi	129.6	Al10ⁱ—Al5—Al5^iv	108.5
Al4^xiii—Cu1—Cu4^xvi	55.8	Al5ⁱ—Al5—Al5^iv	60.0
Al7^xiv—Cu1—Cu4^xvi	133.5	Cr3^xxx—Al6—Al1^xviii	136.4
Al11^xv—Cu1—Cu4^xvi	55.7	Cr3^xxx—Al6—Al2^xxx	64.9
Cu3—Cu1—Cu4^xvi	106.0	Al1^xviii—Al6—Al2^xxx	71.5
Al12—Cu1—Cu4^xvi	106.0	Cr3^xxx—Al6—Al5^iv	109.2
Al1—Cu1—Cu4^xvi	54.6	Al1^xviii—Al6—Al5^iv	108.4
Al9^xv—Cu1—Cu4^xvi	121.5	Al2^xxx—Al6—Al5^iv	150.1
Cu4^xv—Cu1—Cu4^xvi	101.3	Cr3^xxx—Al6—Al5ⁱ	108.1
Al10^xii—Al13—Al4^xiii	127.1	Al1^xviii—Al6—Al5ⁱ	107.5
Al10^xii—Al13—Al7^xiv	89.3	Al2^xxx—Al6—Al5ⁱ	145.1
Al4^xiii—Al13—Al7^xiv	124.7	Al5^iv—Al6—Al5ⁱ	64.5
Al10^xii—Al13—Al11^xv	77.9	Cr3^xxx—Al6—Al9^xxxi	58.7
Al4^xiii—Al13—Al11^xv	68.7	Al1^xviii—Al6—Al9^xxxi	98.3
Al7^xiv—Al13—Al11^xv	165.9	Al2^xxx—Al6—Al9^xxxi	58.3
Al10^xii—Al13—Cu3	66.9	Al5^iv—Al6—Al9^xxxi	146.3
Al4^xiii—Al13—Cu3	161.1	Al5ⁱ—Al6—Al9^xxxi	88.3
Al7^xiv—Al13—Cu3	62.2	Cr3^xxx—Al6—Al9^xxx	58.2
Al11^xv—Al13—Cu3	106.6	Al1^xviii—Al6—Al9^xxx	102.1
Al10^xii—Al13—Al12	66.9	Al2^xxx—Al6—Al9^xxx	63.3
Al4^xiii—Al13—Al12	161.1	Al5^iv—Al6—Al9^xxx	88.3
Al7^xiv—Al13—Al12	62.2	Al5ⁱ—Al6—Al9^xxx	144.7
Al11^xv—Al13—Al12	106.6	Al9^xxxi—Al6—Al9^xxx	106.3
Cu3—Al13—Al12	0.0	Cr3^xxx—Al6—Cr1ⁱ	158.2
Al10^xii—Al13—Al1	139.6	Al1^xviii—Al6—Cr1ⁱ	65.4
Al4^xiii—Al13—Al1	89.9	Al2^xxx—Al6—Cr1ⁱ	136.9
Al7^xiv—Al13—Al1	79.4	Al5^iv—Al6—Cr1ⁱ	53.1
Al11^xv—Al13—Al1	106.6	Al5ⁱ—Al6—Cr1ⁱ	54.9
Cu3—Al13—Al1	73.6	Al9^xxxi—Al6—Cr1ⁱ	127.0
Al12—Al13—Al1	73.6	Al9^xxx—Al6—Cr1ⁱ	126.0
Al10^xii—Al13—Al9^xv	88.2	Cr3^xxx—Al6—Al7^xviii	127.7
Al4^xiii—Al13—Al9^xv	65.8	Al1^xviii—Al6—Al7^xviii	58.4
Al7^xiv—Al13—Al9^xv	77.4	Al2^xxx—Al6—Al7^xviii	98.8
Al11^xv—Al13—Al9^xv	107.6	Al5^iv—Al6—Al7^xviii	106.4
Cu3—Al13—Al9^xv	131.6	Al5ⁱ—Al6—Al7^xviii	56.9
Al12—Al13—Al9^xv	131.6	Al9^xxxi—Al6—Al7^xviii	70.3
Al1—Al13—Al9^xv	125.9	Al9^xxx—Al6—Al7^xviii	158.2
Al10^xii—Al13—Cu4^xv	60.1	Cr1ⁱ—Al6—Al7^xviii	58.1
Al4^xiii—Al13—Cu4^xv	67.3	Cr3^xxx—Al6—Al6ⁱ	52.2
Al7^xiv—Al13—Cu4^xv	122.4	Al1^xviii—Al6—Al6ⁱ	151.7
Al11^xv—Al13—Cu4^xv	55.8	Al2^xxx—Al6—Al6ⁱ	108.2
Cu3—Al13—Cu4^xv	126.4	Al5^iv—Al6—Al6ⁱ	57.3
Al12—Al13—Cu4^xv	126.4	Al5ⁱ—Al6—Al6ⁱ	88.8
Al1—Al13—Cu4^xv	154.5	Al9^xxxi—Al6—Al6ⁱ	105.4
Al9^xv—Al13—Cu4^xv	56.0	Al9^xxx—Al6—Al6ⁱ	56.6
Al10^xii—Al13—Cu4^xvi	129.6	Cr1ⁱ—Al6—Al6ⁱ	109.7
Al4^xiii—Al13—Cu4^xvi	55.8	Al7^xviii—Al6—Al6ⁱ	145.1
Al7^xiv—Al13—Cu4^xvi	133.5	Cr3^xxx—Al6—Al6^iv	52.2
Al11^xv—Al13—Cu4^xvi	55.7	Al1^xviii—Al6—Al6^iv	148.3
Cu3—Al13—Cu4^xvi	106.0	Al2^xxx—Al6—Al6^iv	105.8
Al12—Al13—Cu4^xvi	106.0	Al5^iv—Al6—Al6^iv	89.5
Al1—Al13—Cu4^xvi	54.6	Al5ⁱ—Al6—Al6^iv	56.1
Al9^xv—Al13—Cu4^xvi	121.5	Al9^xxxi—Al6—Al6^iv	57.8
Cu4^xv—Al13—Cu4^xvi	101.3	Al9^xxx—Al6—Al6^iv	104.5
Al4^xvii—Cu2—Al4ⁱ	103.9	Cr1ⁱ—Al6—Al6^iv	110.3
Al4^xvii—Cu2—Al4^xiv	103.9	Al7^xviii—Al6—Al6^iv	91.9
Al4ⁱ—Cu2—Al4^xiv	103.9	Al6ⁱ—Al6—Al6^iv	60.0
Al4^xvii—Cu2—Al12^xviii	162.8	Al13^xviii—Al7—Cu1^xviii	0.0
Al4ⁱ—Cu2—Al12^xviii	62.8	Al13^xviii—Al7—Al12^xviii	60.0
Al4^xiv—Cu2—Al12^xviii	71.2	Cu1^xviii—Al7—Al12^xviii	60.0
Al4^xvii—Cu2—Cu3^xviii	162.8	Al13^xviii—Al7—Cu3^xviii	60.0
Al4ⁱ—Cu2—Cu3^xviii	62.8	Cu1^xviii—Al7—Cu3^xviii	60.0
Al4^xiv—Cu2—Cu3^xviii	71.2	Al12^xviii—Al7—Cu3^xviii	0.0
Al12^xviii—Cu2—Cu3^xviii	0.0	Al13^xviii—Al7—Al1	128.0
Al4^xvii—Cu2—Cu3^xix	71.2	Cu1^xviii—Al7—Al1	128.0
Al4ⁱ—Cu2—Cu3^xix	162.8	Al12^xviii—Al7—Al1	165.2
Al4^xiv—Cu2—Cu3^xix	62.8	Cu3^xviii—Al7—Al1	165.2
Al12^xviii—Cu2—Cu3^xix	118.1	Al13^xviii—Al7—Al5^xxiii	95.7
Cu3^xviii—Cu2—Cu3^xix	118.1	Cu1^xviii—Al7—Al5^xxiii	95.7
Al4^xvii—Cu2—Al12^xix	71.2	Al12^xviii—Al7—Al5^xxiii	84.4
Al4ⁱ—Cu2—Al12^xix	162.8	Cu3^xviii—Al7—Al5^xxiii	84.4
Al4^xiv—Cu2—Al12^xix	62.8	Al1—Al7—Al5^xxiii	105.6
Al12^xviii—Cu2—Al12^xix	118.1	Al13^xviii—Al7—Cr1^xxiii	151.3
Cu3^xviii—Cu2—Al12^xix	118.1	Cu1^xviii—Al7—Cr1^xxiii	151.3
Cu3^xix—Cu2—Al12^xix	0.0	Al12^xviii—Al7—Cr1^xxiii	115.2
Al4^xvii—Cu2—Cu3^xx	62.8	Cu3^xviii—Al7—Cr1^xxiii	115.2
Al4ⁱ—Cu2—Cu3^xx	71.2	Al1—Al7—Cr1^xxiii	64.6
Al4^xiv—Cu2—Cu3^xx	162.8	Al5^xxiii—Al7—Cr1^xxiii	55.9
Al12^xviii—Cu2—Cu3^xx	118.1	Al13^xviii—Al7—Al3^xviii	99.8
Cu3^xviii—Cu2—Cu3^xx	118.1	Cu1^xviii—Al7—Al3^xviii	99.8
Cu3^xix—Cu2—Cu3^xx	118.1	Al12^xviii—Al7—Al3^xviii	57.6
Al12^xix—Cu2—Cu3^xx	118.1	Cu3^xviii—Al7—Al3^xviii	57.6
Al4^xvii—Cu2—Al12^xx	62.8	Al1—Al7—Al3^xviii	107.6
Al4ⁱ—Cu2—Al12^xx	71.2	Al5^xxiii—Al7—Al3^xviii	121.7
Al4^xiv—Cu2—Al12^xx	162.8	Cr1^xxiii—Al7—Al3^xviii	99.5
Al12^xviii—Cu2—Al12^xx	118.1	Al13^xviii—Al7—Al2^xiii	120.5
Cu3^xviii—Cu2—Al12^xx	118.1	Cu1^xviii—Al7—Al2^xiii	120.5
Cu3^xix—Cu2—Al12^xx	118.1	Al12^xviii—Al7—Al2^xiii	61.2
Al12^xix—Cu2—Al12^xx	118.1	Cu3^xviii—Al7—Al2^xiii	61.2
Cu3^xx—Cu2—Al12^xx	0.0	Al1—Al7—Al2^xiii	111.3
Al4^xvii—Cu2—Al11^xxi	65.4	Al5^xxiii—Al7—Al2^xiii	70.5
Al4ⁱ—Cu2—Al11^xxi	65.4	Cr1^xxiii—Al7—Al2^xiii	58.2
Al4^xiv—Cu2—Al11^xxi	65.4	Al3^xviii—Al7—Al2^xiii	53.2
Al12^xviii—Cu2—Al11^xxi	98.0	Al13^xviii—Al7—Al6^xiv	104.2
Cu3^xviii—Cu2—Al11^xxi	98.0	Cu1^xviii—Al7—Al6^xiv	104.2
Cu3^xix—Cu2—Al11^xxi	98.0	Al12^xviii—Al7—Al6^xiv	139.3
Al12^xix—Cu2—Al11^xxi	98.0	Cu3^xviii—Al7—Al6^xiv	139.3
Cu3^xx—Cu2—Al11^xxi	98.0	Al1—Al7—Al6^xiv	54.6
Al12^xx—Cu2—Al11^xxi	98.0	Al5^xxiii—Al7—Al6^xiv	58.6
Al4^xvii—Cu2—Al10	123.0	Cr1^xxiii—Al7—Al6^xiv	59.5
Al4ⁱ—Cu2—Al10	59.7	Al3^xviii—Al7—Al6^xiv	155.9
Al4^xiv—Cu2—Al10	132.3	Al2^xiii—Al7—Al6^xiv	114.1
Al12^xviii—Cu2—Al10	61.5	Al13^xviii—Al7—Cr2^xxiv	100.3
Cu3^xviii—Cu2—Al10	61.5	Cu1^xviii—Al7—Cr2^xxiv	100.3
Cu3^xix—Cu2—Al10	137.1	Al12^xviii—Al7—Cr2^xxiv	106.6
Al12^xix—Cu2—Al10	137.1	Cu3^xviii—Al7—Cr2^xxiv	106.6
Cu3^xx—Cu2—Al10	60.3	Al1—Al7—Cr2^xxiv	61.4
Al12^xx—Cu2—Al10	60.3	Al5^xxiii—Al7—Cr2^xxiv	163.6
Al11^xxi—Cu2—Al10	124.8	Cr1^xxiii—Al7—Cr2^xxiv	107.8
Al4^xvii—Cu2—Al10^xxii	59.7	Al3^xviii—Al7—Cr2^xxiv	58.9
Al4ⁱ—Cu2—Al10^xxii	132.3	Al2^xiii—Al7—Cr2^xxiv	103.7
Al4^xiv—Cu2—Al10^xxii	123.0	Al6^xiv—Al7—Cr2^xxiv	113.4
Al12^xviii—Cu2—Al10^xxii	137.1	Al13^xviii—Al7—Al3	149.3
Cu3^xviii—Cu2—Al10^xxii	137.1	Cu1^xviii—Al7—Al3	149.3
Cu3^xix—Cu2—Al10^xxii	60.3	Al12^xviii—Al7—Al3	103.7
Al12^xix—Cu2—Al10^xxii	60.3	Cu3^xviii—Al7—Al3	103.7
Cu3^xx—Cu2—Al10^xxii	61.5	Al1—Al7—Al3	63.1
Al12^xx—Cu2—Al10^xxii	61.5	Al5^xxiii—Al7—Al3	109.1
Al11^xxi—Cu2—Al10^xxii	124.8	Cr1^xxiii—Al7—Al3	57.5
Al10—Cu2—Al10^xxii	90.6	Al3^xviii—Al7—Al3	51.9
Cu2^xii—Cu3—Cu1	95.3	Al2^xiii—Al7—Al3	55.9
Cu2^xii—Cu3—Al13	95.3	Al6^xiv—Al7—Al3	104.1
Cu1—Cu3—Al13	0.0	Cr2^xxiv—Al7—Al3	57.1
Cu2^xii—Cu3—Al3	152.4	Cr1—Al8—Cr2	161.3
Cu1—Cu3—Al3	102.7	Cr1—Al8—Al9^v	67.8
Al13—Cu3—Al3	102.7	Cr2—Al8—Al9^v	130.9
Cu2^xii—Cu3—Al4^xxiii	57.9	Cr1—Al8—Al2ⁱⁱ	63.4
Cu1—Cu3—Al4^xxiii	129.9	Cr2—Al8—Al2ⁱⁱ	124.5
Al13—Cu3—Al4^xxiii	129.9	Al9^v—Al8—Al2ⁱⁱ	56.0
Al3—Cu3—Al4^xxiii	94.6	Cr1—Al8—Al1^vi	127.0
Cu2^xii—Cu3—Al7^xiv	143.5	Cr2—Al8—Al1^vi	61.2
Cu1—Cu3—Al7^xiv	57.8	Al9^v—Al8—Al1^vi	89.4
Al13—Cu3—Al7^xiv	57.8	Al2ⁱⁱ—Al8—Al1^vi	64.2
Al3—Cu3—Al7^xiv	63.8	Cr1—Al8—Al7^vi	136.7
Al4^xxiii—Cu3—Al7^xiv	158.1	Cr2—Al8—Al7^vi	62.0
Cu2^xii—Cu3—Al10^xii	64.7	Al9^v—Al8—Al7^vi	68.9
Cu1—Cu3—Al10^xii	51.6	Al2ⁱⁱ—Al8—Al7^vi	94.0
Al13—Cu3—Al10^xii	51.6	Al1^vi—Al8—Al7^vi	54.4
Al3—Cu3—Al10^xii	142.6	Cr1—Al8—Al4	56.6
Al4^xxiii—Cu3—Al10^xii	122.5	Cr2—Al8—Al4	128.7
Al7^xiv—Cu3—Al10^xii	78.9	Al9^v—Al8—Al4	58.4
Cu2^xii—Cu3—Cu4^xxiv	79.2	Al2ⁱⁱ—Al8—Al4	102.1
Cu1—Cu3—Cu4^xxiv	157.0	Al1^vi—Al8—Al4	145.1
Al13—Cu3—Cu4^xxiv	157.0	Al7^vi—Al8—Al4	97.8
Al3—Cu3—Cu4^xxiv	91.4	Al3^vii—Al9—Cu4	99.3
Al4^xxiii—Cu3—Cu4^xxiv	65.7	Al3^vii—Al9—Cr3	60.4
Al7^xiv—Cu3—Cu4^xxiv	115.3	Cu4—Al9—Cr3	111.3
Al10^xii—Cu3—Cu4^xxiv	106.9	Al3^vii—Al9—Al2ⁱ	64.4
Cu2^xii—Cu3—Al10^xiv	63.9	Cu4—Al9—Al2ⁱ	163.6
Cu1—Cu3—Al10^xiv	71.3	Cr3—Al9—Al2ⁱ	63.7
Al13—Cu3—Al10^xiv	71.3	Al3^vii—Al9—Al13^xxvi	147.5
Al3—Cu3—Al10^xiv	102.2	Cu4—Al9—Al13^xxvi	63.5
Al4^xxiii—Cu3—Al10^xiv	59.1	Cr3—Al9—Al13^xxvi	149.9
Al7^xiv—Cu3—Al10^xiv	119.7	Al2ⁱ—Al9—Al13^xxvi	129.2
Al10^xii—Cu3—Al10^xiv	94.3	Al3^vii—Al9—Cu1^xxvi	147.5
Cu4^xxiv—Cu3—Al10^xiv	123.8	Cu4—Al9—Cu1^xxvi	63.5
Cu2^xii—Cu3—Al2^xxiv	130.7	Cr3—Al9—Cu1^xxvi	149.9
Cu1—Cu3—Al2^xxiv	119.9	Al2ⁱ—Al9—Cu1^xxvi	129.2
Al13—Cu3—Al2^xxiv	119.9	Al13^xxvi—Al9—Cu1^xxvi	0.0
Al3—Cu3—Al2^xxiv	55.3	Al3^vii—Al9—Al6^ix	106.5
Al4^xxiii—Cu3—Al2^xxiv	108.6	Cu4—Al9—Al6^ix	132.4
Al7^xiv—Cu3—Al2^xxiv	62.8	Cr3—Al9—Al6^ix	54.7
Al10^xii—Cu3—Al2^xxiv	109.8	Al2ⁱ—Al9—Al6^ix	59.2
Cu4^xxiv—Cu3—Al2^xxiv	54.6	Al13^xxvi—Al9—Al6^ix	105.1
Al10^xiv—Cu3—Al2^xxiv	155.4	Cu1^xxvi—Al9—Al6^ix	105.1
Cu2^xii—Cu3—Al4^xviii	53.8	Al3^vii—Al9—Al6^xi	101.0
Cu1—Cu3—Al4^xviii	107.6	Cu4—Al9—Al6^xi	70.7
Al13—Cu3—Al4^xviii	107.6	Cr3—Al9—Al6^xi	54.2
Al3—Cu3—Al4^xviii	135.8	Al2ⁱ—Al9—Al6^xi	112.9
Al4^xxiii—Cu3—Al4^xviii	90.1	Al13^xxvi—Al9—Al6^xi	98.7
Al7^xiv—Cu3—Al4^xviii	107.5	Cu1^xxvi—Al9—Al6^xi	98.7
Al10^xii—Cu3—Al4^xviii	56.0	Al6^ix—Al9—Al6^xi	65.6
Cu4^xxiv—Cu3—Al4^xviii	51.3	Al3^vii—Al9—Al8^xxxii	106.2
Al10^xiv—Cu3—Al4^xviii	117.5	Cu4—Al9—Al8^xxxii	124.3
Al2^xxiv—Cu3—Al4^xviii	81.6	Cr3—Al9—Al8^xxxii	124.5
Cu2^xii—Al12—Cu1	95.3	Al2ⁱ—Al9—Al8^xxxii	62.6
Cu2^xii—Al12—Al13	95.3	Al13^xxvi—Al9—Al8^xxxii	68.7
Cu1—Al12—Al13	0.0	Cu1^xxvi—Al9—Al8^xxxii	68.7
Cu2^xii—Al12—Al3	152.4	Al6^ix—Al9—Al8^xxxii	85.9
Cu1—Al12—Al3	102.7	Al6^xi—Al9—Al8^xxxii	145.2
Al13—Al12—Al3	102.7	Al3^vii—Al9—Al4^xxxii	94.2
Cu2^xii—Al12—Al4^xxiii	57.9	Cu4—Al9—Al4^xxxii	65.7
Cu1—Al12—Al4^xxiii	129.9	Cr3—Al9—Al4^xxxii	154.1
Al13—Al12—Al4^xxiii	129.9	Al2ⁱ—Al9—Al4^xxxii	111.4
Al3—Al12—Al4^xxiii	94.6	Al13^xxvi—Al9—Al4^xxxii	54.1
Cu2^xii—Al12—Al7^xiv	143.5	Cu1^xxvi—Al9—Al4^xxxii	54.1
Cu1—Al12—Al7^xiv	57.8	Al6^ix—Al9—Al4^xxxii	147.3
Al13—Al12—Al7^xiv	57.8	Al6^xi—Al9—Al4^xxxii	135.6
Al3—Al12—Al7^xiv	63.8	Al8^xxxii—Al9—Al4^xxxii	63.8
Al4^xxiii—Al12—Al7^xiv	158.1	Al3^vii—Al9—Al2	56.0
Cu2^xii—Al12—Al10^xii	64.7	Cu4—Al9—Al2	55.6
Cu1—Al12—Al10^xii	51.6	Cr3—Al9—Al2	60.5
Al13—Al12—Al10^xii	51.6	Al2ⁱ—Al9—Al2	112.0
Al3—Al12—Al10^xii	142.6	Al13^xxvi—Al9—Al2	118.6
Al4^xxiii—Al12—Al10^xii	122.5	Cu1^xxvi—Al9—Al2	118.6
Al7^xiv—Al12—Al10^xii	78.9	Al6^ix—Al9—Al2	109.7
Cu2^xii—Al12—Cu4^xxiv	79.2	Al6^xi—Al9—Al2	56.2
Cu1—Al12—Cu4^xxiv	157.0	Al8^xxxii—Al9—Al2	158.4
Al13—Al12—Cu4^xxiv	157.0	Al4^xxxii—Al9—Al2	102.8
Al3—Al12—Cu4^xxiv	91.4	Al3^vii—Al9—Cr1^xxxii	61.7
Al4^xxiii—Al12—Cu4^xxiv	65.7	Cu4—Al9—Cr1^xxxii	112.3
Al7^xiv—Al12—Cu4^xxiv	115.3	Cr3—Al9—Cr1^xxxii	110.8
Al10^xii—Al12—Cu4^xxiv	106.9	Al2ⁱ—Al9—Cr1^xxxii	59.3
Cu2^xii—Al12—Al10^xiv	63.9	Al13^xxvi—Al9—Cr1^xxxii	97.8
Cu1—Al12—Al10^xiv	71.3	Cu1^xxvi—Al9—Cr1^xxxii	97.8
Al13—Al12—Al10^xiv	71.3	Al6^ix—Al9—Cr1^xxxii	115.1
Al3—Al12—Al10^xiv	102.2	Al6^xi—Al9—Cr1^xxxii	162.6
Al4^xxiii—Al12—Al10^xiv	59.1	Al8^xxxii—Al9—Cr1^xxxii	48.4
Al7^xiv—Al12—Al10^xiv	119.7	Al4^xxxii—Al9—Cr1^xxxii	53.6
Al10^xii—Al12—Al10^xiv	94.3	Al2—Al9—Cr1^xxxii	110.3
Cu4^xxiv—Al12—Al10^xiv	123.8	Al13^xx—Al10—Cu1^xx	0.0
Cu2^xii—Al12—Al2^xxiv	130.7	Al13^xx—Al10—Cu4^xxx	68.3
Cu1—Al12—Al2^xxiv	119.9	Cu1^xx—Al10—Cu4^xxx	68.3
Al13—Al12—Al2^xxiv	119.9	Al13^xx—Al10—Al4ⁱ	128.1
Al3—Al12—Al2^xxiv	55.3	Cu1^xx—Al10—Al4ⁱ	128.1
Al4^xxiii—Al12—Al2^xxiv	108.6	Cu4^xxx—Al10—Al4ⁱ	162.8
Al7^xiv—Al12—Al2^xxiv	62.8	Al13^xx—Al10—Al12^xx	61.6
Al10^xii—Al12—Al2^xxiv	109.8	Cu1^xx—Al10—Al12^xx	61.6
Cu4^xxiv—Al12—Al2^xxiv	54.6	Cu4^xxx—Al10—Al12^xx	129.2
Al10^xiv—Al12—Al2^xxiv	155.4	Al4ⁱ—Al10—Al12^xx	66.6
Cu2^xii—Al12—Al4^xviii	53.8	Al13^xx—Al10—Cu3^xx	61.6
Cu1—Al12—Al4^xviii	107.6	Cu1^xx—Al10—Cu3^xx	61.6
Al13—Al12—Al4^xviii	107.6	Cu4^xxx—Al10—Cu3^xx	129.2
Al3—Al12—Al4^xviii	135.8	Al4ⁱ—Al10—Cu3^xx	66.6
Al4^xxiii—Al12—Al4^xviii	90.1	Al12^xx—Al10—Cu3^xx	0.0
Al7^xiv—Al12—Al4^xviii	107.5	Al13^xx—Al10—Al1^xviii	123.4
Al10^xii—Al12—Al4^xviii	56.0	Cu1^xx—Al10—Al1^xviii	123.4
Cu4^xxiv—Al12—Al4^xviii	51.3	Cu4^xxx—Al10—Al1^xviii	55.7
Al10^xiv—Al12—Al4^xviii	117.5	Al4ⁱ—Al10—Al1^xviii	108.4
Al2^xxiv—Al12—Al4^xviii	81.6	Al12^xx—Al10—Al1^xviii	175.0
Al4^vi—Cu4—Al1^xxv	94.8	Cu3^xx—Al10—Al1^xviii	175.0
Al4^vi—Cu4—Al11	70.7	Al13^xx—Al10—Cu3^xviii	140.6
Al1^xxv—Cu4—Al11	115.2	Cu1^xx—Al10—Cu3^xviii	140.6
Al4^vi—Cu4—Al2	97.8	Cu4^xxx—Al10—Cu3^xviii	106.5
Al1^xxv—Cu4—Al2	75.1	Al4ⁱ—Al10—Cu3^xviii	58.3
Al11—Cu4—Al2	164.6	Al12^xx—Al10—Cu3^xviii	106.6
Al4^vi—Cu4—Al9	144.2	Cu3^xx—Al10—Cu3^xviii	106.6
Al1^xxv—Cu4—Al9	112.0	Al1^xviii—Al10—Cu3^xviii	69.7
Al11—Cu4—Al9	114.7	Al13^xx—Al10—Al12^xviii	140.6
Al2—Cu4—Al9	68.5	Cu1^xx—Al10—Al12^xviii	140.6
Al4^vi—Cu4—Al10^xi	127.9	Cu4^xxx—Al10—Al12^xviii	106.5
Al1^xxv—Cu4—Al10^xi	65.9	Al4ⁱ—Al10—Al12^xviii	58.3
Al11—Cu4—Al10^xi	75.2	Al12^xx—Al10—Al12^xviii	106.6
Al2—Cu4—Al10^xi	120.2	Cu3^xx—Al10—Al12^xviii	106.6
Al9—Cu4—Al10^xi	85.8	Al1^xviii—Al10—Al12^xviii	69.7
Al4^vi—Cu4—Al12^vii	69.5	Cu3^xviii—Al10—Al12^xviii	0.0
Al1^xxv—Cu4—Al12^vii	133.1	Al13^xx—Al10—Cr1ⁱ	146.8
Al11—Cu4—Al12^vii	101.2	Cu1^xx—Al10—Cr1ⁱ	146.8
Al2—Cu4—Al12^vii	64.4	Cu4^xxx—Al10—Cr1ⁱ	114.1
Al9—Cu4—Al12^vii	74.9	Al4ⁱ—Al10—Cr1ⁱ	56.1
Al10^xi—Cu4—Al12^vii	157.0	Al12^xx—Al10—Cr1ⁱ	112.1
Al4^vi—Cu4—Cu3^vii	69.5	Cu3^xx—Al10—Cr1ⁱ	112.1
Al1^xxv—Cu4—Cu3^vii	133.1	Al1^xviii—Al10—Cr1ⁱ	63.9
Al11—Cu4—Cu3^vii	101.2	Cu3^xviii—Al10—Cr1ⁱ	72.2
Al2—Cu4—Cu3^vii	64.4	Al12^xviii—Al10—Cr1ⁱ	72.2
Al9—Cu4—Cu3^vii	74.9	Al13^xx—Al10—Cu2	95.3
Al10^xi—Cu4—Cu3^vii	157.0	Cu1^xx—Al10—Cu2	95.3
Al12^vii—Cu4—Cu3^vii	0.0	Cu4^xxx—Al10—Cu2	125.5
Al4^vi—Cu4—Al13^xxvi	127.9	Al4ⁱ—Al10—Cu2	54.6
Al1^xxv—Cu4—Al13^xxvi	117.0	Al12^xx—Al10—Cu2	55.0
Al11—Cu4—Al13^xxvi	58.9	Cu3^xx—Al10—Cu2	55.0
Al2—Cu4—Al13^xxvi	128.5	Al1^xviii—Al10—Cu2	122.3
Al9—Cu4—Al13^xxvi	60.5	Cu3^xviii—Al10—Cu2	54.5
Al10^xi—Cu4—Al13^xxvi	51.6	Al12^xviii—Al10—Cu2	54.5
Al12^vii—Cu4—Al13^xxvi	106.7	Cr1ⁱ—Al10—Cu2	107.0
Cu3^vii—Cu4—Al13^xxvi	106.7	Al13^xx—Al10—Al5^iv	95.9
Al4^vi—Cu4—Cu1^xxvi	127.9	Cu1^xx—Al10—Al5^iv	95.9
Al1^xxv—Cu4—Cu1^xxvi	117.0	Cu4^xxx—Al10—Al5^iv	114.1
Al11—Cu4—Cu1^xxvi	58.9	Al4ⁱ—Al10—Al5^iv	72.3
Al2—Cu4—Cu1^xxvi	128.5	Al12^xx—Al10—Al5^iv	79.8
Al9—Cu4—Cu1^xxvi	60.5	Cu3^xx—Al10—Al5^iv	79.8
Al10^xi—Cu4—Cu1^xxvi	51.6	Al1^xviii—Al10—Al5^iv	99.1
Al12^vii—Cu4—Cu1^xxvi	106.7	Cu3^xviii—Al10—Al5^iv	119.9
Cu3^vii—Cu4—Cu1^xxvi	106.7	Al12^xviii—Al10—Al5^iv	119.9
Al13^xxvi—Cu4—Cu1^xxvi	0.0	Cr1ⁱ—Al10—Al5^iv	51.8
Al4^vi—Cu4—Al13^xxv	56.9	Cu2—Al10—Al5^iv	119.3
Al1^xxv—Cu4—Al13^xxv	60.8	Cu4^xxii—Al11—Cu4	116.6
Al11—Cu4—Al13^xxv	58.8	Cu4^xxii—Al11—Cu4^xxxiii	116.6
Al2—Cu4—Al13^xxv	124.0	Cu4—Al11—Cu4^xxxiii	116.6
Al9—Cu4—Al13^xxv	157.8	Cu4^xxii—Al11—Al13^xxv	173.9
Al10^xi—Cu4—Al13^xxv	72.0	Cu4—Al11—Al13^xxv	65.5
Al12^vii—Cu4—Al13^xxv	126.1	Cu4^xxxiii—Al11—Al13^xxv	65.3
Cu3^vii—Cu4—Al13^xxv	126.1	Cu4^xxii—Al11—Cu1^xxv	173.9
Al13^xxvi—Cu4—Al13^xxv	102.6	Cu4—Al11—Cu1^xxv	65.5
Cu1^xxvi—Cu4—Al13^xxv	102.6	Cu4^xxxiii—Al11—Cu1^xxv	65.3
Al4^vi—Cu4—Cu1^xxv	56.9	Al13^xxv—Al11—Cu1^xxv	0.0
Al1^xxv—Cu4—Cu1^xxv	60.8	Cu4^xxii—Al11—Cu1^xxxiv	65.3
Al11—Cu4—Cu1^xxv	58.8	Cu4—Al11—Cu1^xxxiv	173.9
Al2—Cu4—Cu1^xxv	124.0	Cu4^xxxiii—Al11—Cu1^xxxiv	65.5
Al9—Cu4—Cu1^xxv	157.8	Al13^xxv—Al11—Cu1^xxxiv	112.0
Al10^xi—Cu4—Cu1^xxv	72.0	Cu1^xxv—Al11—Cu1^xxxiv	112.0
Al12^vii—Cu4—Cu1^xxv	126.1	Cu4^xxii—Al11—Al13^xxxiv	65.3
Cu3^vii—Cu4—Cu1^xxv	126.1	Cu4—Al11—Al13^xxxiv	173.9
Al13^xxvi—Cu4—Cu1^xxv	102.6	Cu4^xxxiii—Al11—Al13^xxxiv	65.5
Cu1^xxvi—Cu4—Cu1^xxv	102.6	Al13^xxv—Al11—Al13^xxxiv	112.0
Al13^xxv—Cu4—Cu1^xxv	0.0	Cu1^xxv—Al11—Al13^xxxiv	112.0
Cu4^xvi—Al1—Al6^xiv	75.2	Cu1^xxxiv—Al11—Al13^xxxiv	0.0
Cu4^xvi—Al1—Al13	64.6	Cu4^xxii—Al11—Al13^xxvi	65.5
Al6^xiv—Al1—Al13	134.4	Cu4—Al11—Al13^xxvi	65.3
Cu4^xvi—Al1—Cu1	64.6	Cu4^xxxiii—Al11—Al13^xxvi	173.9
Al6^xiv—Al1—Cu1	134.4	Al13^xxv—Al11—Al13^xxvi	112.0
Al13—Al1—Cu1	0.0	Cu1^xxv—Al11—Al13^xxvi	112.0
Cu4^xvi—Al1—Al7	140.5	Cu1^xxxiv—Al11—Al13^xxvi	112.0
Al6^xiv—Al1—Al7	66.9	Al13^xxxiv—Al11—Al13^xxvi	112.0
Al13—Al1—Al7	154.6	Cu4^xxii—Al11—Cu1^xxvi	65.5
Cu1—Al1—Al7	154.6	Cu4—Al11—Cu1^xxvi	65.3
Cu4^xvi—Al1—Al10^xiv	58.4	Cu4^xxxiii—Al11—Cu1^xxvi	173.9
Al6^xiv—Al1—Al10^xiv	70.4	Al13^xxv—Al11—Cu1^xxvi	112.0
Al13—Al1—Al10^xiv	70.7	Cu1^xxv—Al11—Cu1^xxvi	112.0
Cu1—Al1—Al10^xiv	70.7	Cu1^xxxiv—Al11—Cu1^xxvi	112.0
Al7—Al1—Al10^xiv	115.5	Al13^xxxiv—Al11—Cu1^xxvi	112.0
Cu4^xvi—Al1—Cr2^xxiv	143.0	Al13^xxvi—Al11—Cu1^xxvi	0.0
Al6^xiv—Al1—Cr2^xxiv	126.7	Cu4^xxii—Al11—Cu2^viii	79.2
Al13—Al1—Cr2^xxiv	98.7	Cu4—Al11—Cu2^viii	79.2
Cu1—Al1—Cr2^xxiv	98.7	Cu4^xxxiii—Al11—Cu2^viii	79.2
Al7—Al1—Cr2^xxiv	63.3	Al13^xxv—Al11—Cu2^viii	106.8
Al10^xiv—Al1—Cr2^xxiv	150.3	Cu1^xxv—Al11—Cu2^viii	106.8
Cu4^xvi—Al1—Cr1^xxiii	111.6	Cu1^xxxiv—Al11—Cu2^viii	106.8
Al6^xiv—Al1—Cr1^xxiii	61.4	Al13^xxxiv—Al11—Cu2^viii	106.8
Al13—Al1—Cr1^xxiii	114.3	Al13^xxvi—Al11—Cu2^viii	106.8
Cu1—Al1—Cr1^xxiii	114.3	Cu1^xxvi—Al11—Cu2^viii	106.8
Al7—Al1—Cr1^xxiii	59.2	Cu4^xxii—Al11—Al4^vi	131.9
Al10^xiv—Al1—Cr1^xxiii	58.6	Cu4—Al11—Al4^vi	54.2
Cr2^xxiv—Al1—Cr1^xxiii	105.3	Cu4^xxxiii—Al11—Al4^vi	65.3
Cu4^xvi—Al1—Al8^xxvii	104.3	Al13^xxv—Al11—Al4^vi	54.1
Al6^xiv—Al1—Al8^xxvii	86.3	Cu1^xxv—Al11—Al4^vi	54.1
Al13—Al1—Al8^xxvii	122.8	Cu1^xxxiv—Al11—Al4^vi	129.5
Cu1—Al1—Al8^xxvii	122.8	Al13^xxxiv—Al11—Al4^vi	129.5
Al7—Al1—Al8^xxvii	63.3	Al13^xxvi—Al11—Al4^vi	118.1
Al10^xiv—Al1—Al8^xxvii	153.5	Cu1^xxvi—Al11—Al4^vi	118.1
Cr2^xxiv—Al1—Al8^xxvii	55.4	Cu2^viii—Al11—Al4^vi	53.1
Cr1^xxiii—Al1—Al8^xxvii	121.2	Cu4^xxii—Al11—Al4^xxxv	65.3
Cu4^xvi—Al1—Al3	148.4	Cu4—Al11—Al4^xxxv	131.9
Al6^xiv—Al1—Al3	113.1	Cu4^xxxiii—Al11—Al4^xxxv	54.2
Al13—Al1—Al3	92.7	Al13^xxv—Al11—Al4^xxxv	118.1
Cu1—Al1—Al3	92.7	Cu1^xxv—Al11—Al4^xxxv	118.1
Al7—Al1—Al3	62.9	Cu1^xxxiv—Al11—Al4^xxxv	54.1
Al10^xiv—Al1—Al3	94.5	Al13^xxxiv—Al11—Al4^xxxv	54.1
Cr2^xxiv—Al1—Al3	57.6	Al13^xxvi—Al11—Al4^xxxv	129.5
Cr1^xxiii—Al1—Al3	56.0	Cu1^xxvi—Al11—Al4^xxxv	129.5
Al8^xxvii—Al1—Al3	106.6	Cu2^viii—Al11—Al4^xxxv	53.1
Al3^vii—Al2—Cu4	98.2	Al4^vi—Al11—Al4^xxxv	87.7

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

Footnotes

¹The composition of the minor phase is almost binary. There are three phases in the relevant compositional region of Al–Cu. Although at the annealing temperature of 923 K the ɛ_2Cu phase would be expected in equilibrium with f, this was not confirmed by powder XRD. The binary ζ_1Cu phase is formed in a lower temperature range in the solid state, but it could be stabilized by the addition of Cr. Alternatively it could undergo transformation from ɛ_2Cu during cooling.

Acknowledgements

The authors thank C. Thomas for alloy preparation.

References

Balanetskyy, S., Grushko, B. & Velikanova, T. Y. (2004). Z. Kristallogr. Cryst. Mater. 219, 779–781. CrossRef CAS Google Scholar
Bergerhoff, G., Berndt, M., Brandenburg, K. & Degen, T. (1999). Acta Cryst. B55, 147–156. Web of Science CrossRef CAS IUCr Journals Google Scholar
Christensen, J. (2004). Licentiate thesis, Stockholm University, Sweden. Google Scholar
Christensen, J., Oleynikov, P., HovmÖller, S. & Zou, S. (2004). Ferroelectrics, 305, 273–277. CrossRef CAS Google Scholar
Grushko, B. (2017). J. Alloys Compd. 729, 426–437. CrossRef CAS Google Scholar
Grushko, B., Kowalski, W., Pavlyuchkov, D., Przepiórzyński, B. & Surowiec, M. (2008). J. Alloys Compd. 460, 299–304. CrossRef CAS Google Scholar
Grushko, B., Pavlyuchkov, D., Mi, S. & Balanetskyy, S. (2016). J. Alloys Compd. 677, 148–162. CrossRef CAS Google Scholar
Gulay, L. D. & Harbrecht, B. (2004). J. Alloys Compd. 367, 103–108. CrossRef ICSD CAS Google Scholar
He, Z. B., Zou, X. D., Hovmöller, S., Oleynikov, P. & Kuo, K. H. (2007). Ultramicroscopy, 107, 495–500. Web of Science CrossRef ICSD PubMed CAS Google Scholar
Kowalski, W., Grushko, B., Pavlyuchkov, D. & Surowiec, M. (2010). J. Alloys Compd. 496, 129–134. CrossRef CAS Google Scholar
Kreiner, G. & Franzen, H. F. (1997). J. Alloys Compd. 261, 83–104. CrossRef ICSD CAS Google Scholar
Meshi, L., Grushko, B. & Ezersky, V. (2009). J. Alloys Compd. 488, 108–111. Web of Science CrossRef CAS Google Scholar
Mo, Z. M. & Kuo, K. H. (2000). Mater. Sci. Eng. A, 294–296, 242–245. CrossRef Google Scholar
Oleynikov, P. (2011). Cryst. Res. Technol. 46, 569–579. Web of Science CrossRef CAS Google Scholar
Rodrigues-Carvajal, J. (1998). FULLPROF, Version 0.2. Laboratoire Léon Brillouin, Saclay, France. Google Scholar
Samuha, S., Grushko, B. & Meshi, L. (2016). J. Alloys Compd. 670, 18–24. CrossRef CAS Google Scholar
Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. (1984). Phys. Rev. Lett. 53, 1951–1953. CrossRef CAS Web of Science Google Scholar
Sugiyama, K., Saito, H. & Hiraga, K. (2002). J. Alloys Compd. 342, 148–152. Web of Science CrossRef CAS Google Scholar
Tasci, E. S., de la Flor, G., Orobengoa, D., Capillas, C., Perez-Mato, J. M. & Aroyo, M. I. (2012). EPJ Web Conf. 22, 9. Google Scholar
Uziel, A., Bram, A. I., Venkert, A., Kiv, A. E., Fuks, D. & Meshi, L. (2015). J. Alloys Compd. 648, 353–359. CrossRef CAS Google Scholar
Yaniv, G., Fuks, D. & Meshi, L. (2018). Intermetallics, 100, 44–51. CrossRef CAS Google Scholar
Yaniv, G., Vidal, D., Fuks, D. & Meshi, L. (2020). Metals, 10, 422. CrossRef Google Scholar
Zhang, H., He, Z. B., Oleynikov, P., Zou, X. D., Hovmöller, S. & Kuo, K. H. (2006). Acta Cryst. B62, 16–25. Web of Science CrossRef CAS IUCr Journals Google Scholar
Zhang, H., Wang, S. J., Wang, S. C., Li, Z. C., Hovmöller, S. & Zou, X. D. (2008). J. Comput. Theor. Nanosci. 5, 2. Google Scholar
Zhang, H., Zou, X. D., Oleynikov, P. & Hovmöller, S. (2005). Philos. Mag. 86, 5. Google Scholar

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Volume 55| Part 1| February 2022| Pages 74-79

https://doi.org/10.1107/S1600576721011961

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