research papers
Structure solution of the Al69.2Cu20Cr10.8 ϕ phase
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
The stable ϕ phase that forms below ∼923 K around the Al69.2Cu20.0Cr10.8 composition was found to be hexagonal [P63, a = 11.045 (2), c = 12.688 (2) Å] and isostructural to the earlier reported Al6.2Cu2Re X phase [Samuha, Grushko & Meshi (2016). J. Alloys Compd. 670, 18–24]. Using the structural model of the latter, a successful of the XRD data for Al69.5Cu20.0Cr10.5 was performed. Both ϕ and X were found to be structurally related to the Al72.6Cu11.0Cr16.4 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 Al72.6Cu11.0Cr16.4 and the κ phases of Al67.4Cu14.3Cr18.3 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 of the XRD data based on the structural model of the isostructural Al6.2Cu2Re 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.
2. Experimental
An Al69.5Cu20.0Cr10.5 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 Kα radiation. The measurements were performed within the 2θ range from 5 to 100° with a step size of 0.02° and a of 10 s per step. The FULLPROF software (Rodrigues-Carvajal, 1998) was used to analyze the XRD data.
(SEM), powder XRD and (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 CuFor 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. of the ϕ phase structure
The SEM examinations of the Al69.5Cu20.0Cr10.5 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 ∼Al45.4Cu53.7Cr0.9. 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 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 of the Al–Cu–Re X phase was deduced by Samuha et al. (2016) through the application of on the PED tomography data and refined against the powder XRD data by the Rietveld method.
unit-cell parameters and intensity distribution in the PED patterns of theThese 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 ζ1Cu [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 Al69.5Cu20.0Cr10.5 and Al65Cu25Re10 in the Al–Cu–Cr and Al–Cu–Re phase diagrams, respectively, whereas the Al6.2Cu2Re (Al67.4Cu21.7Cr10.9) 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 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 ζ1Cu 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 Al69.5Cu20.0Cr10.5, 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 Al65.2Cu23.9Re10.9 – richer in Cu and poorer in Al]. This idea was not confirmed by the 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 are summarized in Table 1; the atomic positions and displacement parameters are presented in Table 2.
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The agreement factors for the Rp = 2.66%, Rwp = 3.49%, RBragg = 6.66% (of the ϕ phase) and RBragg = 0.788% (of Al3Cu4). The calculated and observed XRD profiles and the difference between them, as obtained following the are shown in Fig. 3. The interatomic distances are listed in Table 3. The occupancy process led to the realistic stoichiometry of Al69.2Cu20.0Cr10.8 and exhibited convergence.
were
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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 + 51/2)/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 method, based on the extraction of atomic positions of the unknown structure of an approximant of a (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 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 amplitudes and phases of reflections from a series of related approximants. Zhang et al. (2005) found that the strong reflections that are close to each other in have similar amplitudes and phases for all the approximants in the series. Therefore, the 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).
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
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):
Using equation (1), a new set of h, k indexes of ϕ was obtained simply by re-indexing the h, k indexes of ζ (aϕ/aζ ≃ 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
Next, the , 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 phases of the strongest reflections of ζ should be modified by a shift of the origin, compatible with the 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 phases were calculated using equation (2):
phases, which mainly determine the atomic positions in a structure, were modified according to their symmetry. For structurally related compounds, the relations of the phases of the strongest reflections are close (Christensen, 2004Following 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 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.
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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).
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.
4. Conclusions
69.5Cu20.0Cr10.5 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 Al6.2Cu2Re X phase. Using the strong-reflections approach, these phases were found to be structurally related to the Al72.6Cu11.0Cr16.4 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.
of the powder XRD data for the AlSupporting information
CCDC reference: 2121302
https://doi.org/10.1107/S1600576721011961/tu5013sup1.cif
contains datablocks global, I. DOI:Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S1600576721011961/tu5013sup2.hkl
Al63.64Cr10Cu18.38 | V = 1330.5 (3) Å3 |
Mr = 3405.19 | Z = 1 |
Hexagonal, P63 | Dx = 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 |
Rigaku diffractometer | Scan method: step |
Radiation source: X-ray tube | 2θmin = 4.998°, 2θmax = 99.998°, 2θstep = 0.020° |
C monochromator |
Rp = 2.614 | 4751 data points |
Rwp = 3.455 | 74 parameters |
Rexp = 1.598 | 0 restraints |
RBragg = 6.626 |
x | y | z | Uiso*/Ueq | 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)* |
Cr1—Al8 | 2.2976 | Al1—Al10xiv | 2.7155 |
Cr1—Al5i | 2.4454 | Al1—Cr2xxiv | 2.8393 |
Cr1—Al4 | 2.5363 | Al1—Cr1xxiii | 2.8910 |
Cr1—Al5 | 2.5389 | Al1—Al8xxvii | 2.8971 |
Cr1—Al2ii | 2.7046 | Al1—Al3 | 2.9293 |
Cr1—Al3iii | 2.7327 | Al2—Al3vii | 2.4961 |
Cr1—Al10iv | 2.7467 | Al2—Al9iv | 2.6026 |
Cr1—Al7iii | 2.7483 | Al2—Al6xi | 2.6278 |
Cr1—Al6iv | 2.7899 | Al2—Al3viii | 2.6902 |
Cr1—Al9v | 2.8464 | Al2—Cr1xxviii | 2.7047 |
Cr1—Al1iii | 2.8911 | Al2—Al12vii | 2.7721 |
Cr2—Al8 | 2.6657 | Al2—Cu3vii | 2.7721 |
Cr2—Al8iv | 2.6657 | Al2—Al8xxviii | 2.7874 |
Cr2—Al8i | 2.6657 | Al2—Al7viii | 2.8133 |
Cr2—Al3vi | 2.7781 | Al2—Al9 | 2.8260 |
Cr2—Al3vii | 2.7781 | Al3—Al9xxiv | 2.4424 |
Cr2—Al3viii | 2.7780 | Al3—Al3xviii | 2.4913 |
Cr2—Al1vi | 2.8394 | Al3—Al3xiv | 2.4913 |
Cr2—Al1vii | 2.8394 | Al3—Al2xxiv | 2.4961 |
Cr2—Al1viii | 2.8394 | Al3—Cr3xxiv | 2.5006 |
Cr2—Al7vii | 2.8885 | Al3—Al2xiii | 2.6902 |
Cr2—Al7vi | 2.8885 | Al3—Cr1xxiii | 2.7327 |
Cr2—Al7viii | 2.8885 | Al3—Al7xiv | 2.7557 |
Cr3—Al6ix | 2.4143 | Al3—Cr2xxiv | 2.7781 |
Cr3—Al6x | 2.4143 | Al3—Al7 | 2.9241 |
Cr3—Al6xi | 2.4143 | Al4—Cu4xxvii | 2.4374 |
Cr3—Al3vi | 2.5006 | Al4—Al13viii | 2.4678 |
Cr3—Al3vii | 2.5006 | Al4—Cu1viii | 2.4678 |
Cr3—Al3viii | 2.5006 | Al4—Cu2xxix | 2.4958 |
Cr3—Al9i | 2.5296 | Al4—Al12iii | 2.6197 |
Cr3—Al9 | 2.5296 | Al4—Cu3iii | 2.6197 |
Cr3—Al9iv | 2.5296 | Al4—Al10iv | 2.6438 |
Cr3—Al2i | 2.7101 | Al4—Al9v | 2.7778 |
Cr3—Al2iv | 2.7101 | Al4—Al11v | 2.8373 |
Cr3—Al2 | 2.7101 | Al4—Cu4v | 2.8780 |
Cu1—Al10xii | 2.2869 | Al4—Al8 | 2.9258 |
Cu1—Al4xiii | 2.4678 | Al5—Cr1iv | 2.4454 |
Cu1—Al7xiv | 2.5077 | Al5—Al7iii | 2.6650 |
Cu1—Al11xv | 2.5577 | Al5—Al6i | 2.6784 |
Cu1—Cu3 | 2.5663 | Al5—Al6iv | 2.7139 |
Cu1—Al12 | 2.5663 | Al5—Al10i | 2.8523 |
Cu1—Al1 | 2.6293 | Al5—Al5i | 2.8788 |
Cu1—Al9xv | 2.6383 | Al5—Al5iv | 2.8788 |
Cu1—Cu4xv | 2.7138 | Al6—Cr3xxx | 2.4143 |
Cu1—Cu4xvi | 2.7204 | Al6—Al1xviii | 2.5454 |
Al13—Al10xii | 2.2869 | Al6—Al2xxx | 2.6278 |
Al13—Al4xiii | 2.4678 | Al6—Al5iv | 2.6784 |
Al13—Al7xiv | 2.5077 | Al6—Al5i | 2.7139 |
Al13—Al11xv | 2.5577 | Al6—Al9xxxi | 2.7167 |
Al13—Cu3 | 2.5663 | Al6—Al9xxx | 2.7516 |
Al13—Al12 | 2.5663 | Al6—Cr1i | 2.7899 |
Al13—Al1 | 2.6293 | Al6—Al7xviii | 2.8723 |
Al13—Al9xv | 2.6383 | Al6—Al6i | 2.9614 |
Al13—Cu4xv | 2.7138 | Al6—Al6iv | 2.9614 |
Al13—Cu4xvi | 2.7204 | Al7—Al13xviii | 2.5077 |
Cu2—Al4xvii | 2.4958 | Al7—Cu1xviii | 2.5077 |
Cu2—Al4i | 2.4958 | Al7—Al12xviii | 2.6226 |
Cu2—Al4xiv | 2.4958 | Al7—Cu3xviii | 2.6226 |
Cu2—Al12xviii | 2.5334 | Al7—Al5xxiii | 2.6650 |
Cu2—Cu3xviii | 2.5334 | Al7—Cr1xxiii | 2.7482 |
Cu2—Cu3xix | 2.5334 | Al7—Al3xviii | 2.7557 |
Cu2—Al12xix | 2.5334 | Al7—Al2xiii | 2.8133 |
Cu2—Cu3xx | 2.5335 | Al7—Al6xiv | 2.8723 |
Cu2—Al12xx | 2.5335 | Al7—Cr2xxiv | 2.8885 |
Cu2—Al11xxi | 2.7415 | Al8—Al9v | 2.7598 |
Cu2—Al10 | 2.7943 | Al8—Al2ii | 2.7873 |
Cu2—Al10xxii | 2.7943 | Al8—Al1vi | 2.8971 |
Cu3—Cu2xii | 2.5334 | Al8—Al7vi | 2.9248 |
Cu3—Al3 | 2.5936 | Al9—Al3vii | 2.4424 |
Cu3—Al4xxiii | 2.6197 | Al9—Al2i | 2.6027 |
Cu3—Al7xiv | 2.6226 | Al9—Al13xxvi | 2.6384 |
Cu3—Al10xii | 2.6841 | Al9—Cu1xxvi | 2.6384 |
Cu3—Cu4xxiv | 2.6863 | Al9—Al6ix | 2.7167 |
Cu3—Al10xiv | 2.7342 | Al9—Al6xi | 2.7516 |
Cu3—Al2xxiv | 2.7720 | Al9—Al8xxxii | 2.7598 |
Cu3—Al4xviii | 2.9261 | Al9—Al4xxxii | 2.7778 |
Al12—Cu2xii | 2.5334 | Al9—Cr1xxxii | 2.8463 |
Al12—Al3 | 2.5936 | Al10—Al13xx | 2.2869 |
Al12—Al4xxiii | 2.6197 | Al10—Cu1xx | 2.2869 |
Al12—Al7xiv | 2.6226 | Al10—Cu4xxx | 2.5319 |
Al12—Al10xii | 2.6841 | Al10—Al4i | 2.6438 |
Al12—Cu4xxiv | 2.6863 | Al10—Al12xx | 2.6842 |
Al12—Al10xiv | 2.7342 | Al10—Cu3xx | 2.6842 |
Al12—Al2xxiv | 2.7720 | Al10—Al1xviii | 2.7156 |
Al12—Al4xviii | 2.9261 | Al10—Cu3xviii | 2.7341 |
Cu4—Al4vi | 2.4374 | Al10—Al12xviii | 2.7341 |
Cu4—Al1xxv | 2.4569 | Al10—Cr1i | 2.7467 |
Cu4—Al11 | 2.4687 | Al10—Al5iv | 2.8524 |
Cu4—Al2 | 2.5044 | Al11—Cu4xxii | 2.4687 |
Cu4—Al9 | 2.5139 | Al11—Cu4xxxiii | 2.4688 |
Cu4—Al10xi | 2.5319 | Al11—Al13xxv | 2.5577 |
Cu4—Al12vii | 2.6863 | Al11—Cu1xxv | 2.5577 |
Cu4—Cu3vii | 2.6863 | Al11—Cu1xxxiv | 2.5577 |
Cu4—Al13xxvi | 2.7137 | Al11—Al13xxxiv | 2.5577 |
Cu4—Cu1xxvi | 2.7137 | Al11—Al13xxvi | 2.5577 |
Cu4—Al13xxv | 2.7204 | Al11—Cu1xxvi | 2.5577 |
Cu4—Cu1xxv | 2.7204 | Al11—Cu2viii | 2.7415 |
Al1—Cu4xvi | 2.4570 | Al11—Al4vi | 2.8373 |
Al1—Al6xiv | 2.5454 | Al11—Al4xxxv | 2.8373 |
Al1—Al7 | 2.6602 | ||
Al8—Cr1—Al5i | 81.1 | Al3vii—Al2—Al9iv | 103.1 |
Al8—Cr1—Al4 | 74.3 | Cu4—Al2—Al9iv | 133.9 |
Al5i—Cr1—Al4 | 81.3 | Al3vii—Al2—Al6xi | 103.1 |
Al8—Cr1—Al5 | 79.3 | Cu4—Al2—Al6xi | 73.0 |
Al5i—Cr1—Al5 | 70.5 | Al9iv—Al2—Al6xi | 62.6 |
Al4—Cr1—Al5 | 143.9 | Al3vii—Al2—Al3viii | 57.3 |
Al8—Cr1—Al2ii | 67.2 | Cu4—Al2—Al3viii | 153.9 |
Al5i—Cr1—Al2ii | 136.0 | Al9iv—Al2—Al3viii | 54.9 |
Al4—Cr1—Al2ii | 116.0 | Al6xi—Al2—Al3viii | 102.1 |
Al5—Cr1—Al2ii | 74.1 | Al3vii—Al2—Cr1xxviii | 107.7 |
Al8—Cr1—Al3iii | 111.4 | Cu4—Al2—Cr1xxviii | 143.4 |
Al5i—Cr1—Al3iii | 164.5 | Al9iv—Al2—Cr1xxviii | 64.8 |
Al4—Cr1—Al3iii | 93.2 | Al6xi—Al2—Cr1xxviii | 123.4 |
Al5—Cr1—Al3iii | 119.5 | Al3viii—Al2—Cr1xxviii | 60.9 |
Al2ii—Cr1—Al3iii | 59.3 | Al3vii—Al2—Cr3 | 57.2 |
Al8—Cr1—Al10iv | 126.3 | Cu4—Al2—Cr3 | 105.9 |
Al5i—Cr1—Al10iv | 66.4 | Al9iv—Al2—Cr3 | 56.8 |
Al4—Cr1—Al10iv | 59.9 | Al6xi—Al2—Cr3 | 53.8 |
Al5—Cr1—Al10iv | 123.2 | Al3viii—Al2—Cr3 | 55.2 |
Al2ii—Cr1—Al10iv | 157.6 | Cr1xxviii—Al2—Cr3 | 109.7 |
Al3iii—Cr1—Al10iv | 98.4 | Al3vii—Al2—Al12vii | 58.7 |
Al8—Cr1—Al7iii | 121.3 | Cu4—Al2—Al12vii | 61.0 |
Al5i—Cr1—Al7iii | 117.6 | Al9iv—Al2—Al12vii | 160.6 |
Al4—Cr1—Al7iii | 155.7 | Al6xi—Al2—Al12vii | 124.8 |
Al5—Cr1—Al7iii | 60.4 | Al3viii—Al2—Al12vii | 106.1 |
Al2ii—Cr1—Al7iii | 62.1 | Cr1xxviii—Al2—Al12vii | 111.8 |
Al3iii—Cr1—Al7iii | 64.5 | Cr3—Al2—Al12vii | 110.8 |
Al10iv—Cr1—Al7iii | 111.7 | Al3vii—Al2—Cu3vii | 58.7 |
Al8—Cr1—Al6iv | 131.6 | Cu4—Al2—Cu3vii | 61.0 |
Al5i—Cr1—Al6iv | 61.1 | Al9iv—Al2—Cu3vii | 160.6 |
Al4—Cr1—Al6iv | 123.4 | Al6xi—Al2—Cu3vii | 124.8 |
Al5—Cr1—Al6iv | 61.0 | Al3viii—Al2—Cu3vii | 106.1 |
Al2ii—Cr1—Al6iv | 120.5 | Cr1xxviii—Al2—Cu3vii | 111.8 |
Al3iii—Cr1—Al6iv | 111.7 | Cr3—Al2—Cu3vii | 110.8 |
Al10iv—Cr1—Al6iv | 66.5 | Al12vii—Al2—Cu3vii | 0.0 |
Al7iii—Cr1—Al6iv | 62.5 | Al3vii—Al2—Al8xxviii | 155.4 |
Al8—Cr1—Al9v | 63.9 | Cu4—Al2—Al8xxviii | 106.3 |
Al5i—Cr1—Al9v | 134.0 | Al9iv—Al2—Al8xxviii | 61.5 |
Al4—Cr1—Al9v | 61.8 | Al6xi—Al2—Al8xxviii | 87.1 |
Al5—Cr1—Al9v | 125.7 | Al3viii—Al2—Al8xxviii | 98.9 |
Al2ii—Cr1—Al9v | 55.8 | Cr1xxviii—Al2—Al8xxviii | 49.4 |
Al3iii—Cr1—Al9v | 51.9 | Cr3—Al2—Al8xxviii | 116.8 |
Al10iv—Cr1—Al9v | 110.8 | Al12vii—Al2—Al8xxviii | 132.4 |
Al7iii—Cr1—Al9v | 106.1 | Cu3vii—Al2—Al8xxviii | 132.4 |
Al6iv—Cr1—Al9v | 163.5 | Al3vii—Al2—Al7viii | 62.2 |
Al8—Cr1—Al1iii | 174.1 | Cu4—Al2—Al7viii | 114.8 |
Al5i—Cr1—Al1iii | 104.8 | Al9iv—Al2—Al7viii | 111.3 |
Al4—Cr1—Al1iii | 106.3 | Al6xi—Al2—Al7viii | 163.4 |
Al5—Cr1—Al1iii | 102.6 | Al3viii—Al2—Al7viii | 64.1 |
Al2ii—Cr1—Al1iii | 107.7 | Cr1xxviii—Al2—Al7viii | 59.7 |
Al3iii—Cr1—Al1iii | 62.7 | Cr3—Al2—Al7viii | 109.7 |
Al10iv—Cr1—Al1iii | 57.5 | Al12vii—Al2—Al7viii | 56.0 |
Al7iii—Cr1—Al1iii | 56.2 | Cu3vii—Al2—Al7viii | 56.0 |
Al6iv—Cr1—Al1iii | 53.2 | Al8xxviii—Al2—Al7viii | 103.6 |
Al9v—Cr1—Al1iii | 111.0 | Al3vii—Al2—Al9 | 54.2 |
Al8—Cr2—Al8iv | 73.5 | Cu4—Al2—Al9 | 55.9 |
Al8—Cr2—Al8i | 73.5 | Al9iv—Al2—Al9 | 107.4 |
Al8iv—Cr2—Al8i | 73.5 | Al6xi—Al2—Al9 | 60.5 |
Al8—Cr2—Al3vi | 118.2 | Al3viii—Al2—Al9 | 99.0 |
Al8iv—Cr2—Al3vi | 114.2 | Cr1xxviii—Al2—Al9 | 159.6 |
Al8i—Cr2—Al3vi | 167.0 | Cr3—Al2—Al9 | 54.3 |
Al8—Cr2—Al3vii | 167.0 | Al12vii—Al2—Al9 | 68.9 |
Al8iv—Cr2—Al3vii | 118.2 | Cu3vii—Al2—Al9 | 68.9 |
Al8i—Cr2—Al3vii | 114.2 | Al8xxviii—Al2—Al9 | 145.6 |
Al3vi—Cr2—Al3vii | 53.3 | Al7viii—Al2—Al9 | 110.6 |
Al8—Cr2—Al3viii | 114.2 | Al9xxiv—Al3—Al3xviii | 108.1 |
Al8iv—Cr2—Al3viii | 167.0 | Al9xxiv—Al3—Al3xiv | 116.5 |
Al8i—Cr2—Al3viii | 118.2 | Al3xviii—Al3—Al3xiv | 60.0 |
Al3vi—Cr2—Al3viii | 53.3 | Al9xxiv—Al3—Al2xxiv | 69.8 |
Al3vii—Cr2—Al3viii | 53.3 | Al3xviii—Al3—Al2xxiv | 116.1 |
Al8—Cr2—Al1vi | 63.4 | Al3xiv—Al3—Al2xxiv | 65.3 |
Al8iv—Cr2—Al1vi | 71.2 | Al9xxiv—Al3—Cr3xxiv | 61.5 |
Al8i—Cr2—Al1vi | 130.1 | Al3xviii—Al3—Cr3xxiv | 60.1 |
Al3vi—Cr2—Al1vi | 62.9 | Al3xiv—Al3—Cr3xxiv | 60.1 |
Al3vii—Cr2—Al1vi | 113.2 | Al2xxiv—Al3—Cr3xxiv | 65.7 |
Al3viii—Cr2—Al1vi | 102.2 | Al9xxiv—Al3—Cu3 | 77.8 |
Al8—Cr2—Al1vii | 130.1 | Al3xviii—Al3—Cu3 | 174.1 |
Al8iv—Cr2—Al1vii | 63.4 | Al3xiv—Al3—Cu3 | 118.3 |
Al8i—Cr2—Al1vii | 71.2 | Al2xxiv—Al3—Cu3 | 66.0 |
Al3vi—Cr2—Al1vii | 102.2 | Cr3xxiv—Al3—Cu3 | 124.7 |
Al3vii—Cr2—Al1vii | 62.9 | Al9xxiv—Al3—Al12 | 77.8 |
Al3viii—Cr2—Al1vii | 113.2 | Al3xviii—Al3—Al12 | 174.1 |
Al1vi—Cr2—Al1vii | 119.7 | Al3xiv—Al3—Al12 | 118.3 |
Al8—Cr2—Al1viii | 71.2 | Al2xxiv—Al3—Al12 | 66.0 |
Al8iv—Cr2—Al1viii | 130.1 | Cr3xxiv—Al3—Al12 | 124.7 |
Al8i—Cr2—Al1viii | 63.4 | Cu3—Al3—Al12 | 0.0 |
Al3vi—Cr2—Al1viii | 113.2 | Al9xxiv—Al3—Al2xiii | 60.7 |
Al3vii—Cr2—Al1viii | 102.2 | Al3xviii—Al3—Al2xiii | 57.4 |
Al3viii—Cr2—Al1viii | 62.9 | Al3xiv—Al3—Al2xiii | 109.5 |
Al1vi—Cr2—Al1viii | 119.7 | Al2xxiv—Al3—Al2xiii | 120.4 |
Al1vii—Cr2—Al1viii | 119.7 | Cr3xxiv—Al3—Al2xiii | 62.8 |
Al8—Cr2—Al7vii | 124.1 | Cu3—Al3—Al2xiii | 127.0 |
Al8iv—Cr2—Al7vii | 63.4 | Al12—Al3—Al2xiii | 127.0 |
Al8i—Cr2—Al7vii | 121.6 | Al9xxiv—Al3—Cr1xxiii | 66.5 |
Al3vi—Cr2—Al7vii | 58.2 | Al3xviii—Al3—Cr1xxiii | 106.9 |
Al3vii—Cr2—Al7vii | 62.1 | Al3xiv—Al3—Cr1xxiii | 166.9 |
Al3viii—Cr2—Al7vii | 104.1 | Al2xxiv—Al3—Cr1xxiii | 125.7 |
Al1vi—Cr2—Al7vii | 70.0 | Cr3xxiv—Al3—Cr1xxiii | 115.5 |
Al1vii—Cr2—Al7vii | 55.3 | Cu3—Al3—Cr1xxiii | 74.6 |
Al1viii—Cr2—Al7vii | 164.3 | Al12—Al3—Cr1xxiii | 74.6 |
Al8—Cr2—Al7vi | 63.4 | Al2xiii—Al3—Cr1xxiii | 59.8 |
Al8iv—Cr2—Al7vi | 121.6 | Al9xxiv—Al3—Al7xiv | 126.1 |
Al8i—Cr2—Al7vi | 124.1 | Al3xviii—Al3—Al7xiv | 116.7 |
Al3vi—Cr2—Al7vi | 62.1 | Al3xiv—Al3—Al7xiv | 67.5 |
Al3vii—Cr2—Al7vi | 104.1 | Al2xxiv—Al3—Al7xiv | 64.6 |
Al3viii—Cr2—Al7vi | 58.2 | Cr3xxiv—Al3—Al7xiv | 118.4 |
Al1vi—Cr2—Al7vi | 55.3 | Cu3—Al3—Al7xiv | 58.6 |
Al1vii—Cr2—Al7vi | 164.3 | Al12—Al3—Al7xiv | 58.6 |
Al1viii—Cr2—Al7vi | 70.0 | Al2xiii—Al3—Al7xiv | 173.1 |
Al7vii—Cr2—Al7vi | 111.8 | Cr1xxiii—Al3—Al7xiv | 122.1 |
Al8—Cr2—Al7viii | 121.6 | Al9xxiv—Al3—Cr2xxiv | 170.7 |
Al8iv—Cr2—Al7viii | 124.1 | Al3xviii—Al3—Cr2xxiv | 63.4 |
Al8i—Cr2—Al7viii | 63.4 | Al3xiv—Al3—Cr2xxiv | 63.4 |
Al3vi—Cr2—Al7viii | 104.1 | Al2xxiv—Al3—Cr2xxiv | 116.4 |
Al3vii—Cr2—Al7viii | 58.2 | Cr3xxiv—Al3—Cr2xxiv | 113.7 |
Al3viii—Cr2—Al7viii | 62.1 | Cu3—Al3—Cr2xxiv | 110.7 |
Al1vi—Cr2—Al7viii | 164.3 | Al12—Al3—Cr2xxiv | 110.7 |
Al1vii—Cr2—Al7viii | 70.0 | Al2xiii—Al3—Cr2xxiv | 110.2 |
Al1viii—Cr2—Al7viii | 55.3 | Cr1xxiii—Al3—Cr2xxiv | 111.5 |
Al7vii—Cr2—Al7viii | 111.8 | Al7xiv—Al3—Cr2xxiv | 62.9 |
Al7vi—Cr2—Al7viii | 111.8 | Al9xxiv—Al3—Al7 | 112.6 |
Al6ix—Cr3—Al6x | 75.7 | Al3xviii—Al3—Al7 | 60.6 |
Al6ix—Cr3—Al6xi | 75.7 | Al3xiv—Al3—Al7 | 110.9 |
Al6x—Cr3—Al6xi | 75.7 | Al2xxiv—Al3—Al7 | 176.2 |
Al6ix—Cr3—Al3vi | 109.5 | Cr3xxiv—Al3—Al7 | 112.5 |
Al6x—Cr3—Al3vi | 114.6 | Cu3—Al3—Al7 | 117.1 |
Al6xi—Cr3—Al3vi | 169.1 | Al12—Al3—Al7 | 117.1 |
Al6ix—Cr3—Al3vii | 114.6 | Al2xiii—Al3—Al7 | 60.0 |
Al6x—Cr3—Al3vii | 169.1 | Cr1xxiii—Al3—Al7 | 58.0 |
Al6xi—Cr3—Al3vii | 109.5 | Al7xiv—Al3—Al7 | 114.7 |
Al3vi—Cr3—Al3vii | 59.8 | Cr2xxiv—Al3—Al7 | 60.8 |
Al6ix—Cr3—Al3viii | 169.1 | Cu4xxvii—Al4—Al13viii | 67.4 |
Al6x—Cr3—Al3viii | 109.5 | Cu4xxvii—Al4—Cu1viii | 67.4 |
Al6xi—Cr3—Al3viii | 114.6 | Al13viii—Al4—Cu1viii | 0.0 |
Al3vi—Cr3—Al3viii | 59.8 | Cu4xxvii—Al4—Cu2xxix | 84.9 |
Al3vii—Cr3—Al3viii | 59.8 | Al13viii—Al4—Cu2xxix | 118.1 |
Al6ix—Cr3—Al9i | 67.6 | Cu1viii—Al4—Cu2xxix | 118.1 |
Al6x—Cr3—Al9i | 66.6 | Cu4xxvii—Al4—Cr1 | 138.6 |
Al6xi—Cr3—Al9i | 132.2 | Al13viii—Al4—Cr1 | 111.5 |
Al3vi—Cr3—Al9i | 58.1 | Cu1viii—Al4—Cr1 | 111.5 |
Al3vii—Cr3—Al9i | 113.0 | Cu2xxix—Al4—Cr1 | 124.6 |
Al3viii—Cr3—Al9i | 105.1 | Cu4xxvii—Al4—Al12iii | 142.1 |
Al6ix—Cr3—Al9 | 66.6 | Al13viii—Al4—Al12iii | 116.8 |
Al6x—Cr3—Al9 | 132.2 | Cu1viii—Al4—Al12iii | 116.8 |
Al6xi—Cr3—Al9 | 67.6 | Cu2xxix—Al4—Al12iii | 59.3 |
Al3vi—Cr3—Al9 | 105.1 | Cr1—Al4—Al12iii | 77.6 |
Al3vii—Cr3—Al9 | 58.1 | Cu4xxvii—Al4—Cu3iii | 142.1 |
Al3viii—Cr3—Al9 | 113.0 | Al13viii—Al4—Cu3iii | 116.8 |
Al9i—Cr3—Al9 | 119.8 | Cu1viii—Al4—Cu3iii | 116.8 |
Al6ix—Cr3—Al9iv | 132.2 | Cu2xxix—Al4—Cu3iii | 59.3 |
Al6x—Cr3—Al9iv | 67.6 | Cr1—Al4—Cu3iii | 77.6 |
Al6xi—Cr3—Al9iv | 66.6 | Al12iii—Al4—Cu3iii | 0.0 |
Al3vi—Cr3—Al9iv | 113.0 | Cu4xxvii—Al4—Al10iv | 116.1 |
Al3vii—Cr3—Al9iv | 105.1 | Al13viii—Al4—Al10iv | 175.5 |
Al3viii—Cr3—Al9iv | 58.1 | Cu1viii—Al4—Al10iv | 175.5 |
Al9i—Cr3—Al9iv | 119.8 | Cu2xxix—Al4—Al10iv | 65.8 |
Al9—Cr3—Al9iv | 119.8 | Cr1—Al4—Al10iv | 64.0 |
Al6ix—Cr3—Al2i | 61.4 | Al12iii—Al4—Al10iv | 62.6 |
Al6x—Cr3—Al2i | 124.3 | Cu3iii—Al4—Al10iv | 62.6 |
Al6xi—Cr3—Al2i | 121.0 | Cu4xxvii—Al4—Al9v | 127.2 |
Al3vi—Cr3—Al2i | 57.1 | Al13viii—Al4—Al9v | 60.0 |
Al3vii—Cr3—Al2i | 62.0 | Cu1viii—Al4—Al9v | 60.0 |
Al3viii—Cr3—Al2i | 108.6 | Cu2xxix—Al4—Al9v | 122.8 |
Al9i—Cr3—Al2i | 65.2 | Cr1—Al4—Al9v | 64.6 |
Al9—Cr3—Al2i | 59.4 | Al12iii—Al4—Al9v | 71.7 |
Al9iv—Cr3—Al2i | 166.1 | Cu3iii—Al4—Al9v | 71.7 |
Al6ix—Cr3—Al2iv | 121.0 | Al10iv—Al4—Al9v | 116.2 |
Al6x—Cr3—Al2iv | 61.4 | Cu4xxvii—Al4—Al11v | 55.2 |
Al6xi—Cr3—Al2iv | 124.3 | Al13viii—Al4—Al11v | 57.1 |
Al3vi—Cr3—Al2iv | 62.0 | Cu1viii—Al4—Al11v | 57.1 |
Al3vii—Cr3—Al2iv | 108.6 | Cu2xxix—Al4—Al11v | 61.5 |
Al3viii—Cr3—Al2iv | 57.1 | Cr1—Al4—Al11v | 160.9 |
Al9i—Cr3—Al2iv | 59.4 | Al12iii—Al4—Al11v | 93.7 |
Al9—Cr3—Al2iv | 166.1 | Cu3iii—Al4—Al11v | 93.7 |
Al9iv—Cr3—Al2iv | 65.2 | Al10iv—Al4—Al11v | 127.0 |
Al2i—Cr3—Al2iv | 112.3 | Al9v—Al4—Al11v | 96.7 |
Al6ix—Cr3—Al2 | 124.3 | Cu4xxvii—Al4—Cu4v | 104.1 |
Al6x—Cr3—Al2 | 121.0 | Al13viii—Al4—Cu4v | 60.4 |
Al6xi—Cr3—Al2 | 61.4 | Cu1viii—Al4—Cu4v | 60.4 |
Al3vi—Cr3—Al2 | 108.6 | Cu2xxix—Al4—Cu4v | 76.2 |
Al3vii—Cr3—Al2 | 57.1 | Cr1—Al4—Cu4v | 110.6 |
Al3viii—Cr3—Al2 | 62.0 | Al12iii—Al4—Cu4v | 58.3 |
Al9i—Cr3—Al2 | 166.1 | Cu3iii—Al4—Cu4v | 58.3 |
Al9—Cr3—Al2 | 65.2 | Al10iv—Al4—Cu4v | 120.0 |
Al9iv—Cr3—Al2 | 59.4 | Al9v—Al4—Cu4v | 52.7 |
Al2i—Cr3—Al2 | 112.3 | Al11v—Al4—Cu4v | 51.2 |
Al2iv—Cr3—Al2 | 112.3 | Cu4xxvii—Al4—Al8 | 99.7 |
Al10xii—Cu1—Al4xiii | 127.1 | Al13viii—Al4—Al8 | 68.2 |
Al10xii—Cu1—Al7xiv | 89.3 | Cu1viii—Al4—Al8 | 68.2 |
Al4xiii—Cu1—Al7xiv | 124.7 | Cu2xxix—Al4—Al8 | 173.5 |
Al10xii—Cu1—Al11xv | 77.9 | Cr1—Al4—Al8 | 49.1 |
Al4xiii—Cu1—Al11xv | 68.7 | Al12iii—Al4—Al8 | 117.1 |
Al7xiv—Cu1—Al11xv | 165.9 | Cu3iii—Al4—Al8 | 117.1 |
Al10xii—Cu1—Cu3 | 66.9 | Al10iv—Al4—Al8 | 107.8 |
Al4xiii—Cu1—Cu3 | 161.1 | Al9v—Al4—Al8 | 57.8 |
Al7xiv—Cu1—Cu3 | 62.2 | Al11v—Al4—Al8 | 125.0 |
Al11xv—Cu1—Cu3 | 106.6 | Cu4v—Al4—Al8 | 106.9 |
Al10xii—Cu1—Al12 | 66.9 | Cr1iv—Al5—Cr1 | 155.7 |
Al4xiii—Cu1—Al12 | 161.1 | Cr1iv—Al5—Al7iii | 136.8 |
Al7xiv—Cu1—Al12 | 62.2 | Cr1—Al5—Al7iii | 63.7 |
Al11xv—Cu1—Al12 | 106.6 | Cr1iv—Al5—Al6i | 65.8 |
Cu3—Cu1—Al12 | 0.0 | Cr1—Al5—Al6i | 129.6 |
Al10xii—Cu1—Al1 | 139.6 | Al7iii—Al5—Al6i | 103.4 |
Al4xiii—Cu1—Al1 | 89.9 | Cr1iv—Al5—Al6iv | 131.5 |
Al7xiv—Cu1—Al1 | 79.4 | Cr1—Al5—Al6iv | 64.1 |
Al11xv—Cu1—Al1 | 106.6 | Al7iii—Al5—Al6iv | 64.5 |
Cu3—Cu1—Al1 | 73.6 | Al6i—Al5—Al6iv | 66.6 |
Al12—Cu1—Al1 | 73.6 | Cr1iv—Al5—Al10i | 61.9 |
Al10xii—Cu1—Al9xv | 88.2 | Cr1—Al5—Al10i | 138.1 |
Al4xiii—Cu1—Al9xv | 65.8 | Al7iii—Al5—Al10i | 75.3 |
Al7xiv—Cu1—Al9xv | 77.4 | Al6i—Al5—Al10i | 66.5 |
Al11xv—Cu1—Al9xv | 107.6 | Al6iv—Al5—Al10i | 106.3 |
Cu3—Cu1—Al9xv | 131.6 | Cr1iv—Al5—Al5i | 115.1 |
Al12—Cu1—Al9xv | 131.6 | Cr1—Al5—Al5i | 53.2 |
Al1—Cu1—Al9xv | 125.9 | Al7iii—Al5—Al5i | 106.6 |
Al10xii—Cu1—Cu4xv | 60.1 | Al6i—Al5—Al5i | 91.2 |
Al4xiii—Cu1—Cu4xv | 67.3 | Al6iv—Al5—Al5i | 57.1 |
Al7xiv—Cu1—Cu4xv | 122.4 | Al10i—Al5—Al5i | 157.1 |
Al11xv—Cu1—Cu4xv | 55.8 | Cr1iv—Al5—Al5iv | 56.3 |
Cu3—Cu1—Cu4xv | 126.4 | Cr1—Al5—Al5iv | 112.1 |
Al12—Cu1—Cu4xv | 126.4 | Al7iii—Al5—Al5iv | 154.4 |
Al1—Cu1—Cu4xv | 154.5 | Al6i—Al5—Al5iv | 58.3 |
Al9xv—Cu1—Cu4xv | 56.0 | Al6iv—Al5—Al5iv | 90.5 |
Al10xii—Cu1—Cu4xvi | 129.6 | Al10i—Al5—Al5iv | 108.5 |
Al4xiii—Cu1—Cu4xvi | 55.8 | Al5i—Al5—Al5iv | 60.0 |
Al7xiv—Cu1—Cu4xvi | 133.5 | Cr3xxx—Al6—Al1xviii | 136.4 |
Al11xv—Cu1—Cu4xvi | 55.7 | Cr3xxx—Al6—Al2xxx | 64.9 |
Cu3—Cu1—Cu4xvi | 106.0 | Al1xviii—Al6—Al2xxx | 71.5 |
Al12—Cu1—Cu4xvi | 106.0 | Cr3xxx—Al6—Al5iv | 109.2 |
Al1—Cu1—Cu4xvi | 54.6 | Al1xviii—Al6—Al5iv | 108.4 |
Al9xv—Cu1—Cu4xvi | 121.5 | Al2xxx—Al6—Al5iv | 150.1 |
Cu4xv—Cu1—Cu4xvi | 101.3 | Cr3xxx—Al6—Al5i | 108.1 |
Al10xii—Al13—Al4xiii | 127.1 | Al1xviii—Al6—Al5i | 107.5 |
Al10xii—Al13—Al7xiv | 89.3 | Al2xxx—Al6—Al5i | 145.1 |
Al4xiii—Al13—Al7xiv | 124.7 | Al5iv—Al6—Al5i | 64.5 |
Al10xii—Al13—Al11xv | 77.9 | Cr3xxx—Al6—Al9xxxi | 58.7 |
Al4xiii—Al13—Al11xv | 68.7 | Al1xviii—Al6—Al9xxxi | 98.3 |
Al7xiv—Al13—Al11xv | 165.9 | Al2xxx—Al6—Al9xxxi | 58.3 |
Al10xii—Al13—Cu3 | 66.9 | Al5iv—Al6—Al9xxxi | 146.3 |
Al4xiii—Al13—Cu3 | 161.1 | Al5i—Al6—Al9xxxi | 88.3 |
Al7xiv—Al13—Cu3 | 62.2 | Cr3xxx—Al6—Al9xxx | 58.2 |
Al11xv—Al13—Cu3 | 106.6 | Al1xviii—Al6—Al9xxx | 102.1 |
Al10xii—Al13—Al12 | 66.9 | Al2xxx—Al6—Al9xxx | 63.3 |
Al4xiii—Al13—Al12 | 161.1 | Al5iv—Al6—Al9xxx | 88.3 |
Al7xiv—Al13—Al12 | 62.2 | Al5i—Al6—Al9xxx | 144.7 |
Al11xv—Al13—Al12 | 106.6 | Al9xxxi—Al6—Al9xxx | 106.3 |
Cu3—Al13—Al12 | 0.0 | Cr3xxx—Al6—Cr1i | 158.2 |
Al10xii—Al13—Al1 | 139.6 | Al1xviii—Al6—Cr1i | 65.4 |
Al4xiii—Al13—Al1 | 89.9 | Al2xxx—Al6—Cr1i | 136.9 |
Al7xiv—Al13—Al1 | 79.4 | Al5iv—Al6—Cr1i | 53.1 |
Al11xv—Al13—Al1 | 106.6 | Al5i—Al6—Cr1i | 54.9 |
Cu3—Al13—Al1 | 73.6 | Al9xxxi—Al6—Cr1i | 127.0 |
Al12—Al13—Al1 | 73.6 | Al9xxx—Al6—Cr1i | 126.0 |
Al10xii—Al13—Al9xv | 88.2 | Cr3xxx—Al6—Al7xviii | 127.7 |
Al4xiii—Al13—Al9xv | 65.8 | Al1xviii—Al6—Al7xviii | 58.4 |
Al7xiv—Al13—Al9xv | 77.4 | Al2xxx—Al6—Al7xviii | 98.8 |
Al11xv—Al13—Al9xv | 107.6 | Al5iv—Al6—Al7xviii | 106.4 |
Cu3—Al13—Al9xv | 131.6 | Al5i—Al6—Al7xviii | 56.9 |
Al12—Al13—Al9xv | 131.6 | Al9xxxi—Al6—Al7xviii | 70.3 |
Al1—Al13—Al9xv | 125.9 | Al9xxx—Al6—Al7xviii | 158.2 |
Al10xii—Al13—Cu4xv | 60.1 | Cr1i—Al6—Al7xviii | 58.1 |
Al4xiii—Al13—Cu4xv | 67.3 | Cr3xxx—Al6—Al6i | 52.2 |
Al7xiv—Al13—Cu4xv | 122.4 | Al1xviii—Al6—Al6i | 151.7 |
Al11xv—Al13—Cu4xv | 55.8 | Al2xxx—Al6—Al6i | 108.2 |
Cu3—Al13—Cu4xv | 126.4 | Al5iv—Al6—Al6i | 57.3 |
Al12—Al13—Cu4xv | 126.4 | Al5i—Al6—Al6i | 88.8 |
Al1—Al13—Cu4xv | 154.5 | Al9xxxi—Al6—Al6i | 105.4 |
Al9xv—Al13—Cu4xv | 56.0 | Al9xxx—Al6—Al6i | 56.6 |
Al10xii—Al13—Cu4xvi | 129.6 | Cr1i—Al6—Al6i | 109.7 |
Al4xiii—Al13—Cu4xvi | 55.8 | Al7xviii—Al6—Al6i | 145.1 |
Al7xiv—Al13—Cu4xvi | 133.5 | Cr3xxx—Al6—Al6iv | 52.2 |
Al11xv—Al13—Cu4xvi | 55.7 | Al1xviii—Al6—Al6iv | 148.3 |
Cu3—Al13—Cu4xvi | 106.0 | Al2xxx—Al6—Al6iv | 105.8 |
Al12—Al13—Cu4xvi | 106.0 | Al5iv—Al6—Al6iv | 89.5 |
Al1—Al13—Cu4xvi | 54.6 | Al5i—Al6—Al6iv | 56.1 |
Al9xv—Al13—Cu4xvi | 121.5 | Al9xxxi—Al6—Al6iv | 57.8 |
Cu4xv—Al13—Cu4xvi | 101.3 | Al9xxx—Al6—Al6iv | 104.5 |
Al4xvii—Cu2—Al4i | 103.9 | Cr1i—Al6—Al6iv | 110.3 |
Al4xvii—Cu2—Al4xiv | 103.9 | Al7xviii—Al6—Al6iv | 91.9 |
Al4i—Cu2—Al4xiv | 103.9 | Al6i—Al6—Al6iv | 60.0 |
Al4xvii—Cu2—Al12xviii | 162.8 | Al13xviii—Al7—Cu1xviii | 0.0 |
Al4i—Cu2—Al12xviii | 62.8 | Al13xviii—Al7—Al12xviii | 60.0 |
Al4xiv—Cu2—Al12xviii | 71.2 | Cu1xviii—Al7—Al12xviii | 60.0 |
Al4xvii—Cu2—Cu3xviii | 162.8 | Al13xviii—Al7—Cu3xviii | 60.0 |
Al4i—Cu2—Cu3xviii | 62.8 | Cu1xviii—Al7—Cu3xviii | 60.0 |
Al4xiv—Cu2—Cu3xviii | 71.2 | Al12xviii—Al7—Cu3xviii | 0.0 |
Al12xviii—Cu2—Cu3xviii | 0.0 | Al13xviii—Al7—Al1 | 128.0 |
Al4xvii—Cu2—Cu3xix | 71.2 | Cu1xviii—Al7—Al1 | 128.0 |
Al4i—Cu2—Cu3xix | 162.8 | Al12xviii—Al7—Al1 | 165.2 |
Al4xiv—Cu2—Cu3xix | 62.8 | Cu3xviii—Al7—Al1 | 165.2 |
Al12xviii—Cu2—Cu3xix | 118.1 | Al13xviii—Al7—Al5xxiii | 95.7 |
Cu3xviii—Cu2—Cu3xix | 118.1 | Cu1xviii—Al7—Al5xxiii | 95.7 |
Al4xvii—Cu2—Al12xix | 71.2 | Al12xviii—Al7—Al5xxiii | 84.4 |
Al4i—Cu2—Al12xix | 162.8 | Cu3xviii—Al7—Al5xxiii | 84.4 |
Al4xiv—Cu2—Al12xix | 62.8 | Al1—Al7—Al5xxiii | 105.6 |
Al12xviii—Cu2—Al12xix | 118.1 | Al13xviii—Al7—Cr1xxiii | 151.3 |
Cu3xviii—Cu2—Al12xix | 118.1 | Cu1xviii—Al7—Cr1xxiii | 151.3 |
Cu3xix—Cu2—Al12xix | 0.0 | Al12xviii—Al7—Cr1xxiii | 115.2 |
Al4xvii—Cu2—Cu3xx | 62.8 | Cu3xviii—Al7—Cr1xxiii | 115.2 |
Al4i—Cu2—Cu3xx | 71.2 | Al1—Al7—Cr1xxiii | 64.6 |
Al4xiv—Cu2—Cu3xx | 162.8 | Al5xxiii—Al7—Cr1xxiii | 55.9 |
Al12xviii—Cu2—Cu3xx | 118.1 | Al13xviii—Al7—Al3xviii | 99.8 |
Cu3xviii—Cu2—Cu3xx | 118.1 | Cu1xviii—Al7—Al3xviii | 99.8 |
Cu3xix—Cu2—Cu3xx | 118.1 | Al12xviii—Al7—Al3xviii | 57.6 |
Al12xix—Cu2—Cu3xx | 118.1 | Cu3xviii—Al7—Al3xviii | 57.6 |
Al4xvii—Cu2—Al12xx | 62.8 | Al1—Al7—Al3xviii | 107.6 |
Al4i—Cu2—Al12xx | 71.2 | Al5xxiii—Al7—Al3xviii | 121.7 |
Al4xiv—Cu2—Al12xx | 162.8 | Cr1xxiii—Al7—Al3xviii | 99.5 |
Al12xviii—Cu2—Al12xx | 118.1 | Al13xviii—Al7—Al2xiii | 120.5 |
Cu3xviii—Cu2—Al12xx | 118.1 | Cu1xviii—Al7—Al2xiii | 120.5 |
Cu3xix—Cu2—Al12xx | 118.1 | Al12xviii—Al7—Al2xiii | 61.2 |
Al12xix—Cu2—Al12xx | 118.1 | Cu3xviii—Al7—Al2xiii | 61.2 |
Cu3xx—Cu2—Al12xx | 0.0 | Al1—Al7—Al2xiii | 111.3 |
Al4xvii—Cu2—Al11xxi | 65.4 | Al5xxiii—Al7—Al2xiii | 70.5 |
Al4i—Cu2—Al11xxi | 65.4 | Cr1xxiii—Al7—Al2xiii | 58.2 |
Al4xiv—Cu2—Al11xxi | 65.4 | Al3xviii—Al7—Al2xiii | 53.2 |
Al12xviii—Cu2—Al11xxi | 98.0 | Al13xviii—Al7—Al6xiv | 104.2 |
Cu3xviii—Cu2—Al11xxi | 98.0 | Cu1xviii—Al7—Al6xiv | 104.2 |
Cu3xix—Cu2—Al11xxi | 98.0 | Al12xviii—Al7—Al6xiv | 139.3 |
Al12xix—Cu2—Al11xxi | 98.0 | Cu3xviii—Al7—Al6xiv | 139.3 |
Cu3xx—Cu2—Al11xxi | 98.0 | Al1—Al7—Al6xiv | 54.6 |
Al12xx—Cu2—Al11xxi | 98.0 | Al5xxiii—Al7—Al6xiv | 58.6 |
Al4xvii—Cu2—Al10 | 123.0 | Cr1xxiii—Al7—Al6xiv | 59.5 |
Al4i—Cu2—Al10 | 59.7 | Al3xviii—Al7—Al6xiv | 155.9 |
Al4xiv—Cu2—Al10 | 132.3 | Al2xiii—Al7—Al6xiv | 114.1 |
Al12xviii—Cu2—Al10 | 61.5 | Al13xviii—Al7—Cr2xxiv | 100.3 |
Cu3xviii—Cu2—Al10 | 61.5 | Cu1xviii—Al7—Cr2xxiv | 100.3 |
Cu3xix—Cu2—Al10 | 137.1 | Al12xviii—Al7—Cr2xxiv | 106.6 |
Al12xix—Cu2—Al10 | 137.1 | Cu3xviii—Al7—Cr2xxiv | 106.6 |
Cu3xx—Cu2—Al10 | 60.3 | Al1—Al7—Cr2xxiv | 61.4 |
Al12xx—Cu2—Al10 | 60.3 | Al5xxiii—Al7—Cr2xxiv | 163.6 |
Al11xxi—Cu2—Al10 | 124.8 | Cr1xxiii—Al7—Cr2xxiv | 107.8 |
Al4xvii—Cu2—Al10xxii | 59.7 | Al3xviii—Al7—Cr2xxiv | 58.9 |
Al4i—Cu2—Al10xxii | 132.3 | Al2xiii—Al7—Cr2xxiv | 103.7 |
Al4xiv—Cu2—Al10xxii | 123.0 | Al6xiv—Al7—Cr2xxiv | 113.4 |
Al12xviii—Cu2—Al10xxii | 137.1 | Al13xviii—Al7—Al3 | 149.3 |
Cu3xviii—Cu2—Al10xxii | 137.1 | Cu1xviii—Al7—Al3 | 149.3 |
Cu3xix—Cu2—Al10xxii | 60.3 | Al12xviii—Al7—Al3 | 103.7 |
Al12xix—Cu2—Al10xxii | 60.3 | Cu3xviii—Al7—Al3 | 103.7 |
Cu3xx—Cu2—Al10xxii | 61.5 | Al1—Al7—Al3 | 63.1 |
Al12xx—Cu2—Al10xxii | 61.5 | Al5xxiii—Al7—Al3 | 109.1 |
Al11xxi—Cu2—Al10xxii | 124.8 | Cr1xxiii—Al7—Al3 | 57.5 |
Al10—Cu2—Al10xxii | 90.6 | Al3xviii—Al7—Al3 | 51.9 |
Cu2xii—Cu3—Cu1 | 95.3 | Al2xiii—Al7—Al3 | 55.9 |
Cu2xii—Cu3—Al13 | 95.3 | Al6xiv—Al7—Al3 | 104.1 |
Cu1—Cu3—Al13 | 0.0 | Cr2xxiv—Al7—Al3 | 57.1 |
Cu2xii—Cu3—Al3 | 152.4 | Cr1—Al8—Cr2 | 161.3 |
Cu1—Cu3—Al3 | 102.7 | Cr1—Al8—Al9v | 67.8 |
Al13—Cu3—Al3 | 102.7 | Cr2—Al8—Al9v | 130.9 |
Cu2xii—Cu3—Al4xxiii | 57.9 | Cr1—Al8—Al2ii | 63.4 |
Cu1—Cu3—Al4xxiii | 129.9 | Cr2—Al8—Al2ii | 124.5 |
Al13—Cu3—Al4xxiii | 129.9 | Al9v—Al8—Al2ii | 56.0 |
Al3—Cu3—Al4xxiii | 94.6 | Cr1—Al8—Al1vi | 127.0 |
Cu2xii—Cu3—Al7xiv | 143.5 | Cr2—Al8—Al1vi | 61.2 |
Cu1—Cu3—Al7xiv | 57.8 | Al9v—Al8—Al1vi | 89.4 |
Al13—Cu3—Al7xiv | 57.8 | Al2ii—Al8—Al1vi | 64.2 |
Al3—Cu3—Al7xiv | 63.8 | Cr1—Al8—Al7vi | 136.7 |
Al4xxiii—Cu3—Al7xiv | 158.1 | Cr2—Al8—Al7vi | 62.0 |
Cu2xii—Cu3—Al10xii | 64.7 | Al9v—Al8—Al7vi | 68.9 |
Cu1—Cu3—Al10xii | 51.6 | Al2ii—Al8—Al7vi | 94.0 |
Al13—Cu3—Al10xii | 51.6 | Al1vi—Al8—Al7vi | 54.4 |
Al3—Cu3—Al10xii | 142.6 | Cr1—Al8—Al4 | 56.6 |
Al4xxiii—Cu3—Al10xii | 122.5 | Cr2—Al8—Al4 | 128.7 |
Al7xiv—Cu3—Al10xii | 78.9 | Al9v—Al8—Al4 | 58.4 |
Cu2xii—Cu3—Cu4xxiv | 79.2 | Al2ii—Al8—Al4 | 102.1 |
Cu1—Cu3—Cu4xxiv | 157.0 | Al1vi—Al8—Al4 | 145.1 |
Al13—Cu3—Cu4xxiv | 157.0 | Al7vi—Al8—Al4 | 97.8 |
Al3—Cu3—Cu4xxiv | 91.4 | Al3vii—Al9—Cu4 | 99.3 |
Al4xxiii—Cu3—Cu4xxiv | 65.7 | Al3vii—Al9—Cr3 | 60.4 |
Al7xiv—Cu3—Cu4xxiv | 115.3 | Cu4—Al9—Cr3 | 111.3 |
Al10xii—Cu3—Cu4xxiv | 106.9 | Al3vii—Al9—Al2i | 64.4 |
Cu2xii—Cu3—Al10xiv | 63.9 | Cu4—Al9—Al2i | 163.6 |
Cu1—Cu3—Al10xiv | 71.3 | Cr3—Al9—Al2i | 63.7 |
Al13—Cu3—Al10xiv | 71.3 | Al3vii—Al9—Al13xxvi | 147.5 |
Al3—Cu3—Al10xiv | 102.2 | Cu4—Al9—Al13xxvi | 63.5 |
Al4xxiii—Cu3—Al10xiv | 59.1 | Cr3—Al9—Al13xxvi | 149.9 |
Al7xiv—Cu3—Al10xiv | 119.7 | Al2i—Al9—Al13xxvi | 129.2 |
Al10xii—Cu3—Al10xiv | 94.3 | Al3vii—Al9—Cu1xxvi | 147.5 |
Cu4xxiv—Cu3—Al10xiv | 123.8 | Cu4—Al9—Cu1xxvi | 63.5 |
Cu2xii—Cu3—Al2xxiv | 130.7 | Cr3—Al9—Cu1xxvi | 149.9 |
Cu1—Cu3—Al2xxiv | 119.9 | Al2i—Al9—Cu1xxvi | 129.2 |
Al13—Cu3—Al2xxiv | 119.9 | Al13xxvi—Al9—Cu1xxvi | 0.0 |
Al3—Cu3—Al2xxiv | 55.3 | Al3vii—Al9—Al6ix | 106.5 |
Al4xxiii—Cu3—Al2xxiv | 108.6 | Cu4—Al9—Al6ix | 132.4 |
Al7xiv—Cu3—Al2xxiv | 62.8 | Cr3—Al9—Al6ix | 54.7 |
Al10xii—Cu3—Al2xxiv | 109.8 | Al2i—Al9—Al6ix | 59.2 |
Cu4xxiv—Cu3—Al2xxiv | 54.6 | Al13xxvi—Al9—Al6ix | 105.1 |
Al10xiv—Cu3—Al2xxiv | 155.4 | Cu1xxvi—Al9—Al6ix | 105.1 |
Cu2xii—Cu3—Al4xviii | 53.8 | Al3vii—Al9—Al6xi | 101.0 |
Cu1—Cu3—Al4xviii | 107.6 | Cu4—Al9—Al6xi | 70.7 |
Al13—Cu3—Al4xviii | 107.6 | Cr3—Al9—Al6xi | 54.2 |
Al3—Cu3—Al4xviii | 135.8 | Al2i—Al9—Al6xi | 112.9 |
Al4xxiii—Cu3—Al4xviii | 90.1 | Al13xxvi—Al9—Al6xi | 98.7 |
Al7xiv—Cu3—Al4xviii | 107.5 | Cu1xxvi—Al9—Al6xi | 98.7 |
Al10xii—Cu3—Al4xviii | 56.0 | Al6ix—Al9—Al6xi | 65.6 |
Cu4xxiv—Cu3—Al4xviii | 51.3 | Al3vii—Al9—Al8xxxii | 106.2 |
Al10xiv—Cu3—Al4xviii | 117.5 | Cu4—Al9—Al8xxxii | 124.3 |
Al2xxiv—Cu3—Al4xviii | 81.6 | Cr3—Al9—Al8xxxii | 124.5 |
Cu2xii—Al12—Cu1 | 95.3 | Al2i—Al9—Al8xxxii | 62.6 |
Cu2xii—Al12—Al13 | 95.3 | Al13xxvi—Al9—Al8xxxii | 68.7 |
Cu1—Al12—Al13 | 0.0 | Cu1xxvi—Al9—Al8xxxii | 68.7 |
Cu2xii—Al12—Al3 | 152.4 | Al6ix—Al9—Al8xxxii | 85.9 |
Cu1—Al12—Al3 | 102.7 | Al6xi—Al9—Al8xxxii | 145.2 |
Al13—Al12—Al3 | 102.7 | Al3vii—Al9—Al4xxxii | 94.2 |
Cu2xii—Al12—Al4xxiii | 57.9 | Cu4—Al9—Al4xxxii | 65.7 |
Cu1—Al12—Al4xxiii | 129.9 | Cr3—Al9—Al4xxxii | 154.1 |
Al13—Al12—Al4xxiii | 129.9 | Al2i—Al9—Al4xxxii | 111.4 |
Al3—Al12—Al4xxiii | 94.6 | Al13xxvi—Al9—Al4xxxii | 54.1 |
Cu2xii—Al12—Al7xiv | 143.5 | Cu1xxvi—Al9—Al4xxxii | 54.1 |
Cu1—Al12—Al7xiv | 57.8 | Al6ix—Al9—Al4xxxii | 147.3 |
Al13—Al12—Al7xiv | 57.8 | Al6xi—Al9—Al4xxxii | 135.6 |
Al3—Al12—Al7xiv | 63.8 | Al8xxxii—Al9—Al4xxxii | 63.8 |
Al4xxiii—Al12—Al7xiv | 158.1 | Al3vii—Al9—Al2 | 56.0 |
Cu2xii—Al12—Al10xii | 64.7 | Cu4—Al9—Al2 | 55.6 |
Cu1—Al12—Al10xii | 51.6 | Cr3—Al9—Al2 | 60.5 |
Al13—Al12—Al10xii | 51.6 | Al2i—Al9—Al2 | 112.0 |
Al3—Al12—Al10xii | 142.6 | Al13xxvi—Al9—Al2 | 118.6 |
Al4xxiii—Al12—Al10xii | 122.5 | Cu1xxvi—Al9—Al2 | 118.6 |
Al7xiv—Al12—Al10xii | 78.9 | Al6ix—Al9—Al2 | 109.7 |
Cu2xii—Al12—Cu4xxiv | 79.2 | Al6xi—Al9—Al2 | 56.2 |
Cu1—Al12—Cu4xxiv | 157.0 | Al8xxxii—Al9—Al2 | 158.4 |
Al13—Al12—Cu4xxiv | 157.0 | Al4xxxii—Al9—Al2 | 102.8 |
Al3—Al12—Cu4xxiv | 91.4 | Al3vii—Al9—Cr1xxxii | 61.7 |
Al4xxiii—Al12—Cu4xxiv | 65.7 | Cu4—Al9—Cr1xxxii | 112.3 |
Al7xiv—Al12—Cu4xxiv | 115.3 | Cr3—Al9—Cr1xxxii | 110.8 |
Al10xii—Al12—Cu4xxiv | 106.9 | Al2i—Al9—Cr1xxxii | 59.3 |
Cu2xii—Al12—Al10xiv | 63.9 | Al13xxvi—Al9—Cr1xxxii | 97.8 |
Cu1—Al12—Al10xiv | 71.3 | Cu1xxvi—Al9—Cr1xxxii | 97.8 |
Al13—Al12—Al10xiv | 71.3 | Al6ix—Al9—Cr1xxxii | 115.1 |
Al3—Al12—Al10xiv | 102.2 | Al6xi—Al9—Cr1xxxii | 162.6 |
Al4xxiii—Al12—Al10xiv | 59.1 | Al8xxxii—Al9—Cr1xxxii | 48.4 |
Al7xiv—Al12—Al10xiv | 119.7 | Al4xxxii—Al9—Cr1xxxii | 53.6 |
Al10xii—Al12—Al10xiv | 94.3 | Al2—Al9—Cr1xxxii | 110.3 |
Cu4xxiv—Al12—Al10xiv | 123.8 | Al13xx—Al10—Cu1xx | 0.0 |
Cu2xii—Al12—Al2xxiv | 130.7 | Al13xx—Al10—Cu4xxx | 68.3 |
Cu1—Al12—Al2xxiv | 119.9 | Cu1xx—Al10—Cu4xxx | 68.3 |
Al13—Al12—Al2xxiv | 119.9 | Al13xx—Al10—Al4i | 128.1 |
Al3—Al12—Al2xxiv | 55.3 | Cu1xx—Al10—Al4i | 128.1 |
Al4xxiii—Al12—Al2xxiv | 108.6 | Cu4xxx—Al10—Al4i | 162.8 |
Al7xiv—Al12—Al2xxiv | 62.8 | Al13xx—Al10—Al12xx | 61.6 |
Al10xii—Al12—Al2xxiv | 109.8 | Cu1xx—Al10—Al12xx | 61.6 |
Cu4xxiv—Al12—Al2xxiv | 54.6 | Cu4xxx—Al10—Al12xx | 129.2 |
Al10xiv—Al12—Al2xxiv | 155.4 | Al4i—Al10—Al12xx | 66.6 |
Cu2xii—Al12—Al4xviii | 53.8 | Al13xx—Al10—Cu3xx | 61.6 |
Cu1—Al12—Al4xviii | 107.6 | Cu1xx—Al10—Cu3xx | 61.6 |
Al13—Al12—Al4xviii | 107.6 | Cu4xxx—Al10—Cu3xx | 129.2 |
Al3—Al12—Al4xviii | 135.8 | Al4i—Al10—Cu3xx | 66.6 |
Al4xxiii—Al12—Al4xviii | 90.1 | Al12xx—Al10—Cu3xx | 0.0 |
Al7xiv—Al12—Al4xviii | 107.5 | Al13xx—Al10—Al1xviii | 123.4 |
Al10xii—Al12—Al4xviii | 56.0 | Cu1xx—Al10—Al1xviii | 123.4 |
Cu4xxiv—Al12—Al4xviii | 51.3 | Cu4xxx—Al10—Al1xviii | 55.7 |
Al10xiv—Al12—Al4xviii | 117.5 | Al4i—Al10—Al1xviii | 108.4 |
Al2xxiv—Al12—Al4xviii | 81.6 | Al12xx—Al10—Al1xviii | 175.0 |
Al4vi—Cu4—Al1xxv | 94.8 | Cu3xx—Al10—Al1xviii | 175.0 |
Al4vi—Cu4—Al11 | 70.7 | Al13xx—Al10—Cu3xviii | 140.6 |
Al1xxv—Cu4—Al11 | 115.2 | Cu1xx—Al10—Cu3xviii | 140.6 |
Al4vi—Cu4—Al2 | 97.8 | Cu4xxx—Al10—Cu3xviii | 106.5 |
Al1xxv—Cu4—Al2 | 75.1 | Al4i—Al10—Cu3xviii | 58.3 |
Al11—Cu4—Al2 | 164.6 | Al12xx—Al10—Cu3xviii | 106.6 |
Al4vi—Cu4—Al9 | 144.2 | Cu3xx—Al10—Cu3xviii | 106.6 |
Al1xxv—Cu4—Al9 | 112.0 | Al1xviii—Al10—Cu3xviii | 69.7 |
Al11—Cu4—Al9 | 114.7 | Al13xx—Al10—Al12xviii | 140.6 |
Al2—Cu4—Al9 | 68.5 | Cu1xx—Al10—Al12xviii | 140.6 |
Al4vi—Cu4—Al10xi | 127.9 | Cu4xxx—Al10—Al12xviii | 106.5 |
Al1xxv—Cu4—Al10xi | 65.9 | Al4i—Al10—Al12xviii | 58.3 |
Al11—Cu4—Al10xi | 75.2 | Al12xx—Al10—Al12xviii | 106.6 |
Al2—Cu4—Al10xi | 120.2 | Cu3xx—Al10—Al12xviii | 106.6 |
Al9—Cu4—Al10xi | 85.8 | Al1xviii—Al10—Al12xviii | 69.7 |
Al4vi—Cu4—Al12vii | 69.5 | Cu3xviii—Al10—Al12xviii | 0.0 |
Al1xxv—Cu4—Al12vii | 133.1 | Al13xx—Al10—Cr1i | 146.8 |
Al11—Cu4—Al12vii | 101.2 | Cu1xx—Al10—Cr1i | 146.8 |
Al2—Cu4—Al12vii | 64.4 | Cu4xxx—Al10—Cr1i | 114.1 |
Al9—Cu4—Al12vii | 74.9 | Al4i—Al10—Cr1i | 56.1 |
Al10xi—Cu4—Al12vii | 157.0 | Al12xx—Al10—Cr1i | 112.1 |
Al4vi—Cu4—Cu3vii | 69.5 | Cu3xx—Al10—Cr1i | 112.1 |
Al1xxv—Cu4—Cu3vii | 133.1 | Al1xviii—Al10—Cr1i | 63.9 |
Al11—Cu4—Cu3vii | 101.2 | Cu3xviii—Al10—Cr1i | 72.2 |
Al2—Cu4—Cu3vii | 64.4 | Al12xviii—Al10—Cr1i | 72.2 |
Al9—Cu4—Cu3vii | 74.9 | Al13xx—Al10—Cu2 | 95.3 |
Al10xi—Cu4—Cu3vii | 157.0 | Cu1xx—Al10—Cu2 | 95.3 |
Al12vii—Cu4—Cu3vii | 0.0 | Cu4xxx—Al10—Cu2 | 125.5 |
Al4vi—Cu4—Al13xxvi | 127.9 | Al4i—Al10—Cu2 | 54.6 |
Al1xxv—Cu4—Al13xxvi | 117.0 | Al12xx—Al10—Cu2 | 55.0 |
Al11—Cu4—Al13xxvi | 58.9 | Cu3xx—Al10—Cu2 | 55.0 |
Al2—Cu4—Al13xxvi | 128.5 | Al1xviii—Al10—Cu2 | 122.3 |
Al9—Cu4—Al13xxvi | 60.5 | Cu3xviii—Al10—Cu2 | 54.5 |
Al10xi—Cu4—Al13xxvi | 51.6 | Al12xviii—Al10—Cu2 | 54.5 |
Al12vii—Cu4—Al13xxvi | 106.7 | Cr1i—Al10—Cu2 | 107.0 |
Cu3vii—Cu4—Al13xxvi | 106.7 | Al13xx—Al10—Al5iv | 95.9 |
Al4vi—Cu4—Cu1xxvi | 127.9 | Cu1xx—Al10—Al5iv | 95.9 |
Al1xxv—Cu4—Cu1xxvi | 117.0 | Cu4xxx—Al10—Al5iv | 114.1 |
Al11—Cu4—Cu1xxvi | 58.9 | Al4i—Al10—Al5iv | 72.3 |
Al2—Cu4—Cu1xxvi | 128.5 | Al12xx—Al10—Al5iv | 79.8 |
Al9—Cu4—Cu1xxvi | 60.5 | Cu3xx—Al10—Al5iv | 79.8 |
Al10xi—Cu4—Cu1xxvi | 51.6 | Al1xviii—Al10—Al5iv | 99.1 |
Al12vii—Cu4—Cu1xxvi | 106.7 | Cu3xviii—Al10—Al5iv | 119.9 |
Cu3vii—Cu4—Cu1xxvi | 106.7 | Al12xviii—Al10—Al5iv | 119.9 |
Al13xxvi—Cu4—Cu1xxvi | 0.0 | Cr1i—Al10—Al5iv | 51.8 |
Al4vi—Cu4—Al13xxv | 56.9 | Cu2—Al10—Al5iv | 119.3 |
Al1xxv—Cu4—Al13xxv | 60.8 | Cu4xxii—Al11—Cu4 | 116.6 |
Al11—Cu4—Al13xxv | 58.8 | Cu4xxii—Al11—Cu4xxxiii | 116.6 |
Al2—Cu4—Al13xxv | 124.0 | Cu4—Al11—Cu4xxxiii | 116.6 |
Al9—Cu4—Al13xxv | 157.8 | Cu4xxii—Al11—Al13xxv | 173.9 |
Al10xi—Cu4—Al13xxv | 72.0 | Cu4—Al11—Al13xxv | 65.5 |
Al12vii—Cu4—Al13xxv | 126.1 | Cu4xxxiii—Al11—Al13xxv | 65.3 |
Cu3vii—Cu4—Al13xxv | 126.1 | Cu4xxii—Al11—Cu1xxv | 173.9 |
Al13xxvi—Cu4—Al13xxv | 102.6 | Cu4—Al11—Cu1xxv | 65.5 |
Cu1xxvi—Cu4—Al13xxv | 102.6 | Cu4xxxiii—Al11—Cu1xxv | 65.3 |
Al4vi—Cu4—Cu1xxv | 56.9 | Al13xxv—Al11—Cu1xxv | 0.0 |
Al1xxv—Cu4—Cu1xxv | 60.8 | Cu4xxii—Al11—Cu1xxxiv | 65.3 |
Al11—Cu4—Cu1xxv | 58.8 | Cu4—Al11—Cu1xxxiv | 173.9 |
Al2—Cu4—Cu1xxv | 124.0 | Cu4xxxiii—Al11—Cu1xxxiv | 65.5 |
Al9—Cu4—Cu1xxv | 157.8 | Al13xxv—Al11—Cu1xxxiv | 112.0 |
Al10xi—Cu4—Cu1xxv | 72.0 | Cu1xxv—Al11—Cu1xxxiv | 112.0 |
Al12vii—Cu4—Cu1xxv | 126.1 | Cu4xxii—Al11—Al13xxxiv | 65.3 |
Cu3vii—Cu4—Cu1xxv | 126.1 | Cu4—Al11—Al13xxxiv | 173.9 |
Al13xxvi—Cu4—Cu1xxv | 102.6 | Cu4xxxiii—Al11—Al13xxxiv | 65.5 |
Cu1xxvi—Cu4—Cu1xxv | 102.6 | Al13xxv—Al11—Al13xxxiv | 112.0 |
Al13xxv—Cu4—Cu1xxv | 0.0 | Cu1xxv—Al11—Al13xxxiv | 112.0 |
Cu4xvi—Al1—Al6xiv | 75.2 | Cu1xxxiv—Al11—Al13xxxiv | 0.0 |
Cu4xvi—Al1—Al13 | 64.6 | Cu4xxii—Al11—Al13xxvi | 65.5 |
Al6xiv—Al1—Al13 | 134.4 | Cu4—Al11—Al13xxvi | 65.3 |
Cu4xvi—Al1—Cu1 | 64.6 | Cu4xxxiii—Al11—Al13xxvi | 173.9 |
Al6xiv—Al1—Cu1 | 134.4 | Al13xxv—Al11—Al13xxvi | 112.0 |
Al13—Al1—Cu1 | 0.0 | Cu1xxv—Al11—Al13xxvi | 112.0 |
Cu4xvi—Al1—Al7 | 140.5 | Cu1xxxiv—Al11—Al13xxvi | 112.0 |
Al6xiv—Al1—Al7 | 66.9 | Al13xxxiv—Al11—Al13xxvi | 112.0 |
Al13—Al1—Al7 | 154.6 | Cu4xxii—Al11—Cu1xxvi | 65.5 |
Cu1—Al1—Al7 | 154.6 | Cu4—Al11—Cu1xxvi | 65.3 |
Cu4xvi—Al1—Al10xiv | 58.4 | Cu4xxxiii—Al11—Cu1xxvi | 173.9 |
Al6xiv—Al1—Al10xiv | 70.4 | Al13xxv—Al11—Cu1xxvi | 112.0 |
Al13—Al1—Al10xiv | 70.7 | Cu1xxv—Al11—Cu1xxvi | 112.0 |
Cu1—Al1—Al10xiv | 70.7 | Cu1xxxiv—Al11—Cu1xxvi | 112.0 |
Al7—Al1—Al10xiv | 115.5 | Al13xxxiv—Al11—Cu1xxvi | 112.0 |
Cu4xvi—Al1—Cr2xxiv | 143.0 | Al13xxvi—Al11—Cu1xxvi | 0.0 |
Al6xiv—Al1—Cr2xxiv | 126.7 | Cu4xxii—Al11—Cu2viii | 79.2 |
Al13—Al1—Cr2xxiv | 98.7 | Cu4—Al11—Cu2viii | 79.2 |
Cu1—Al1—Cr2xxiv | 98.7 | Cu4xxxiii—Al11—Cu2viii | 79.2 |
Al7—Al1—Cr2xxiv | 63.3 | Al13xxv—Al11—Cu2viii | 106.8 |
Al10xiv—Al1—Cr2xxiv | 150.3 | Cu1xxv—Al11—Cu2viii | 106.8 |
Cu4xvi—Al1—Cr1xxiii | 111.6 | Cu1xxxiv—Al11—Cu2viii | 106.8 |
Al6xiv—Al1—Cr1xxiii | 61.4 | Al13xxxiv—Al11—Cu2viii | 106.8 |
Al13—Al1—Cr1xxiii | 114.3 | Al13xxvi—Al11—Cu2viii | 106.8 |
Cu1—Al1—Cr1xxiii | 114.3 | Cu1xxvi—Al11—Cu2viii | 106.8 |
Al7—Al1—Cr1xxiii | 59.2 | Cu4xxii—Al11—Al4vi | 131.9 |
Al10xiv—Al1—Cr1xxiii | 58.6 | Cu4—Al11—Al4vi | 54.2 |
Cr2xxiv—Al1—Cr1xxiii | 105.3 | Cu4xxxiii—Al11—Al4vi | 65.3 |
Cu4xvi—Al1—Al8xxvii | 104.3 | Al13xxv—Al11—Al4vi | 54.1 |
Al6xiv—Al1—Al8xxvii | 86.3 | Cu1xxv—Al11—Al4vi | 54.1 |
Al13—Al1—Al8xxvii | 122.8 | Cu1xxxiv—Al11—Al4vi | 129.5 |
Cu1—Al1—Al8xxvii | 122.8 | Al13xxxiv—Al11—Al4vi | 129.5 |
Al7—Al1—Al8xxvii | 63.3 | Al13xxvi—Al11—Al4vi | 118.1 |
Al10xiv—Al1—Al8xxvii | 153.5 | Cu1xxvi—Al11—Al4vi | 118.1 |
Cr2xxiv—Al1—Al8xxvii | 55.4 | Cu2viii—Al11—Al4vi | 53.1 |
Cr1xxiii—Al1—Al8xxvii | 121.2 | Cu4xxii—Al11—Al4xxxv | 65.3 |
Cu4xvi—Al1—Al3 | 148.4 | Cu4—Al11—Al4xxxv | 131.9 |
Al6xiv—Al1—Al3 | 113.1 | Cu4xxxiii—Al11—Al4xxxv | 54.2 |
Al13—Al1—Al3 | 92.7 | Al13xxv—Al11—Al4xxxv | 118.1 |
Cu1—Al1—Al3 | 92.7 | Cu1xxv—Al11—Al4xxxv | 118.1 |
Al7—Al1—Al3 | 62.9 | Cu1xxxiv—Al11—Al4xxxv | 54.1 |
Al10xiv—Al1—Al3 | 94.5 | Al13xxxiv—Al11—Al4xxxv | 54.1 |
Cr2xxiv—Al1—Al3 | 57.6 | Al13xxvi—Al11—Al4xxxv | 129.5 |
Cr1xxiii—Al1—Al3 | 56.0 | Cu1xxvi—Al11—Al4xxxv | 129.5 |
Al8xxvii—Al1—Al3 | 106.6 | Cu2viii—Al11—Al4xxxv | 53.1 |
Al3vii—Al2—Cu4 | 98.2 | Al4vi—Al11—Al4xxxv | 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 ɛ2Cu phase would be expected in equilibrium with f, this was not confirmed by powder XRD. The binary ζ1Cu 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 ɛ2Cu during cooling.
Acknowledgements
The authors thank C. Thomas for alloy preparation.
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