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ν-Al80.61Cr10.71Fe8.68, P63/m (No. 176), a = 40.68 (7), c = 12.546 (1) Å, V = 17 983 (8) Å3, atoms/cell = 1184.56, Dx = 3.518 g cm−3, λ(Mo Kα) = 0.71069 Å, μ = 5.032 mm−1, F(000) = 18 433, T = 293 K, final R = 0.075 for 3854 reflections with Fo > 4σ(Fo). The [001] high-resolution electron-microscopic image of the ν-AlCrFe phase clearly shows similar local characteristics to those given by the complex icosahedral cluster found in somewhat smaller hexagonal approximant structures, such as κ-Al76Cr18Ni6 [a = 17.674 (3), c = 12.516 (3) Å; Sato et al. (1997). Acta Cryst. C53, 1531–1533; Marsh (1998). Acta Cryst. B54, 925–926] and λ-Al4.32Mn [a = 28.382 (9), c = 12.389 (2) Å; Kreiner & Franzen (1997). J. Alloys Compd. 261, 83–104]. Using the known atomic distribution of this icosahedral cluster in the κ and λ phases as the starting point, the structure of the ν phase, a hexagonal intermetallic compound with probably the largest a parameter, was solved by X-ray single-crystal diffraction using direct methods. As in κ and λ phases, almost all TM (transition metal) atoms in the complex icosahedral cluster are icosahedrally coordinated. However, contrary to the λ structure in which about 98% of the TM atoms have icosahedral coordination, the TM atoms in the ν structure also form capped pentagonal prisms in the region between these complex icosahedral clusters, yielding an average icosahedral coordination of about 70% for TM atoms. After rapid solidification, the ν phase occurs together with a decagonal quasicrystal with a periodicity of about 12.5 Å along its tenfold axis and thus also consists of six layers, two flat ones each sandwiched between two puckered layers in mirror reflection, stacked along the c axis.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768199015761/zh0020sup1.cif
Contains datablocks word, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768199015761/zh0020sup2.hkl
Contains datablock word

Computing details top

Data collection: Rigaku/AFC Diffractometer Control Software; cell refinement: Rigaku/AFC Diffractometer Control Software; data reduction: TEXSAN; program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
(word) top
Crystal data top
Al477.44Cr63.42Fe51.42Dx = 3.518 Mg m3
Mr = 19051.3Mo Kα radiation, λ = 0.71069 Å
Hexagonal, P63/mCell parameters from 23 reflections
Hall symbol: -P 6cθ = 9–23.5°
a = 40.68 (7) ŵ = 5.03 mm1
c = 12.546 (1) ÅT = 293 K
V = 17983 (8) Å3Needle, grey
Z = 20.6 × 0.12 × 0.1 mm
F(000) = 18433
Data collection top
Rigaku AFC5R
diffractometer
Rint = 0.086
Graphite monochromatorθmax = 26.0°, θmin = 1.5°
ω–2θ scansh = 050
Absorption correction: ψ scan
(North et al., 1968)
k = 050
Tmin = 0.481, Tmax = 0.593l = 015
12684 measured reflections3 standard reflections every 500 reflections
12273 independent reflections intensity decay: 0.6%
3854 reflections with I > 2σ(I)
Refinement top
Refinement on F20 restraints
Least-squares matrix: fullPrimary atom site location: structure-invariant direct methods
R[F2 > 2σ(F2)] = 0.075Secondary atom site location: difference Fourier map
wR(F2) = 0.207Calculated w = 1/[σ2(Fo2) + (0.0778P)2]
where P = (Fo2 + 2Fc2)/3
S = 1.09(Δ/σ)max = 0.001
5453 reflectionsΔρmax = 1.61 e Å3
474 parametersΔρmin = 1.30 e Å3
Crystal data top
Al477.44Cr63.42Fe51.42Z = 2
Mr = 19051.3Mo Kα radiation
Hexagonal, P63/mµ = 5.03 mm1
a = 40.68 (7) ÅT = 293 K
c = 12.546 (1) Å0.6 × 0.12 × 0.1 mm
V = 17983 (8) Å3
Data collection top
Rigaku AFC5R
diffractometer
3854 reflections with I > 2σ(I)
Absorption correction: ψ scan
(North et al., 1968)
Rint = 0.086
Tmin = 0.481, Tmax = 0.5933 standard reflections every 500 reflections
12684 measured reflections intensity decay: 0.6%
12273 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.075474 parameters
wR(F2) = 0.2070 restraints
S = 1.09Δρmax = 1.61 e Å3
5453 reflectionsΔρmin = 1.30 e Å3
Special details top

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Al10.00000.00000.25000.003 (10)*0.47
Cr10.00000.00000.25000.003 (10)*0.015
Fe10.00000.00000.25000.003 (10)*0.015
Al20.00000.00000.1099 (18)0.001 (4)*0.50
Al30.66670.33330.0426 (9)0.005 (2)*
Cr40.03193 (15)0.90723 (14)0.25000.0037 (11)*
Cr50.18049 (15)0.85053 (15)0.25000.0050 (12)*
Cr60.33670 (14)0.02076 (15)0.25000.0061 (12)*
Cr70.59667 (14)0.15519 (14)0.25000.0042 (12)*
Cr80.75065 (15)0.09767 (15)0.25000.0084 (12)*
Cr90.84274 (15)0.21868 (14)0.25000.0049 (13)*
Cr100.94010 (16)0.18129 (15)0.25000.0060 (12)*
Cr110.99335 (14)0.15933 (14)0.25000.0028 (11)*
Cr120.03669 (15)0.75047 (15)0.25000.0089 (12)*0.5
Fe120.03669 (15)0.75047 (15)0.25000.0089 (12)*0.5
Cr130.06812 (15)0.66065 (15)0.25000.0081 (12)*0.5
Fe130.06812 (15)0.66065 (15)0.25000.0081 (12)*0.5
Cr140.12878 (15)0.87186 (15)0.25000.0090 (12)*0.5
Fe140.12878 (15)0.87186 (15)0.25000.0090 (12)*0.5
Cr150.14507 (19)0.71979 (18)0.25000.010 (2)*0.3
Fe150.14507 (19)0.71979 (18)0.25000.010 (2)*0.3
Al150.14507 (19)0.71979 (18)0.25000.010 (2)*0.4
Cr160.27105 (17)0.52623 (17)0.25000.008 (2)*0.31
Fe160.27105 (17)0.52623 (17)0.25000.008 (2)*0.31
Al160.27105 (17)0.52623 (17)0.25000.008 (2)*0.38
Cr170.27959 (16)0.81464 (16)0.25000.0100 (12)*0.5
Fe170.27959 (16)0.81464 (16)0.25000.0100 (12)*0.5
Cr180.31882 (15)0.94934 (15)0.25000.0093 (12)*0.5
Fe180.31882 (15)0.94934 (15)0.25000.0093 (12)*0.5
Cr190.37904 (16)0.77809 (17)0.25000.010 (2)*0.405
Fe190.37904 (16)0.77809 (17)0.25000.010 (2)*0.405
Al190.37904 (16)0.77809 (17)0.25000.010 (2)*0.19
Cr200.46032 (14)1.05536 (14)0.25000.0080 (11)*0.5
Fe200.46032 (14)1.05536 (14)0.25000.0080 (11)*0.5
Cr210.49307 (14)0.96621 (14)0.25000.0056 (12)*0.5
Fe210.49307 (14)0.96621 (14)0.25000.0056 (12)*0.5
Cr220.62837 (15)0.06518 (15)0.25000.0078 (11)*0.5
Fe220.62837 (15)0.06518 (15)0.25000.0078 (11)*0.5
Cr230.80862 (14)0.30749 (14)0.25000.0089 (12)*0.5
Fe230.80862 (14)0.30749 (14)0.25000.0089 (12)*0.5
Cr240.84853 (14)0.06002 (14)0.25000.0083 (11)*0.5
Fe240.84853 (14)0.06002 (14)0.25000.0083 (11)*0.5
Cr250.9647 (2)0.0358 (2)0.25000.019 (3)*0.24
Fe250.9647 (2)0.0358 (2)0.25000.019 (3)*0.24
Al250.9647 (2)0.0358 (2)0.25000.019 (3)*0.52
Al260.0567 (3)0.5951 (3)0.25000.007 (2)*
Al270.0722 (3)0.8798 (3)0.25000.011 (2)*
Al280.0881 (3)0.7318 (3)0.25000.004 (2)*
Al290.0962 (3)0.9616 (3)0.25000.024 (3)*
Al300.1081 (3)0.8020 (3)0.25000.002 (2)*
Al310.1538 (3)0.9409 (3)0.25000.015 (3)*
Al320.2147 (5)0.7549 (5)0.25000.040 (6)*0.84
Al330.2234 (3)0.8253 (3)0.25000.012 (2)*
Al340.2475 (3)0.9053 (3)0.25000.007 (2)*
Al350.3039 (3)0.8842 (3)0.25000.013 (2)*
Al360.3120 (3)0.7186 (3)0.25000.0043 (19)*
Al370.3896 (3)1.0029 (3)0.25000.010 (2)*
Al380.4117 (3)0.9089 (3)0.25000.020 (4)*0.83
Cr380.4117 (3)0.9089 (3)0.25000.020 (4)*0.085
Fe380.4117 (3)0.9089 (3)0.25000.020 (4)*0.085
Al390.4298 (3)0.7613 (3)0.25000.027 (4)*0.76
Cr390.4298 (3)0.7613 (3)0.25000.027 (4)*0.12
Fe390.4298 (3)0.7613 (3)0.25000.027 (4)*0.12
Al400.4412 (3)0.9843 (3)0.25000.006 (2)*
Al410.4606 (3)0.8424 (3)0.25000.016 (2)*
Al420.4614 (4)0.6740 (4)0.25000.037 (4)*
Al430.5321 (3)0.0969 (3)0.25000.011 (2)*
Al440.5459 (3)0.1706 (3)0.25000.011 (2)*
Al450.5583 (3)0.0238 (3)0.25000.005 (2)*
Al460.6207 (3)0.0018 (3)0.25000.005 (2)*
Al470.6476 (3)0.1361 (3)0.25000.012 (2)*
Al480.6680 (3)0.2091 (3)0.25000.013 (2)*
Al490.6991 (3)0.1178 (3)0.25000.010 (3)*0.87
Cr490.6991 (3)0.1178 (3)0.25000.010 (3)*0.065
Fe490.6991 (3)0.1178 (3)0.25000.010 (3)*0.065
Al500.7159 (3)0.3462 (3)0.25000.010 (2)*
Al510.7259 (3)0.0290 (3)0.25000.011 (2)*
Al520.7355 (3)0.2554 (3)0.25000.020 (3)*
Al530.7708 (3)0.1682 (3)0.25000.014 (3)*0.92
Cr530.7708 (3)0.1682 (3)0.25000.014 (3)*0.04
Fe530.7708 (3)0.1682 (3)0.25000.014 (3)*0.04
Al540.7828 (3)0.0071 (3)0.25000.008 (2)*
Al550.7909 (3)0.2372 (3)0.25000.011 (2)*
Al560.8048 (3)0.0856 (3)0.25000.011 (2)*
Al570.8804 (3)0.3484 (3)0.25000.004 (2)*
Al580.8834 (3)0.1897 (3)0.25000.007 (2)*
Al590.9010 (3)0.0398 (3)0.25000.013 (2)*
Al600.9088 (3)0.2744 (3)0.25000.011 (2)*
Al610.9207 (3)0.1107 (3)0.25000.010 (2)*
Al620.9656 (3)0.2497 (3)0.25000.006 (2)*
Fe630.14240 (8)0.61874 (8)0.0633 (3)0.0044 (6)*
Fe640.70289 (9)0.23518 (8)0.0733 (3)0.0087 (7)*
Fe650.73475 (8)0.35062 (8)0.0534 (2)0.0051 (6)*
Cr660.73951 (9)0.12994 (9)0.0766 (3)0.0031 (7)*
Cr670.07945 (9)0.76160 (9)0.0748 (3)0.0077 (7)*0.5
Fe670.07945 (9)0.76160 (9)0.0748 (3)0.0077 (7)*0.5
Cr680.39138 (10)0.89074 (10)0.0530 (3)0.0060 (11)*0.405
Fe680.39138 (10)0.89074 (10)0.0530 (3)0.0060 (11)*0.405
Al680.39138 (10)0.89074 (10)0.0530 (3)0.0060 (11)*0.19
Cr690.42939 (9)1.01312 (9)0.0754 (3)0.0060 (7)*0.5
Fe690.42939 (9)1.01312 (9)0.0754 (3)0.0060 (7)*0.5
Cr700.89035 (9)0.07075 (9)0.0751 (3)0.0075 (8)*0.5
Fe700.89035 (9)0.07075 (9)0.0751 (3)0.0075 (8)*0.5
Cr710.98087 (16)0.04531 (16)0.0464 (5)0.0241 (18)*0.235
Fe710.98087 (16)0.04531 (16)0.0464 (5)0.0241 (18)*0.235
Al710.98087 (16)0.04531 (16)0.0464 (5)0.0241 (18)*0.53
Al720.0028 (2)0.8395 (2)0.1365 (6)0.0115 (17)*
Al730.00492 (19)0.2216 (2)0.1341 (6)0.0087 (16)*
Al740.00535 (18)0.74239 (18)0.0569 (6)0.0090 (15)*
Al750.02462 (19)0.16719 (19)0.0693 (6)0.0133 (17)*
Al760.02517 (19)0.68767 (19)0.1361 (6)0.0063 (15)*
Al770.0326 (2)0.9590 (2)0.1458 (7)0.0240 (19)*
Al780.04435 (19)0.63116 (19)0.0694 (6)0.0107 (15)*
Al790.05941 (19)0.9144 (2)0.0651 (6)0.0141 (16)*
Al800.0613 (2)0.8159 (2)0.1347 (6)0.0081 (16)*
Al810.09837 (18)0.70722 (19)0.0614 (6)0.0086 (14)*
Al820.1180 (2)0.6554 (2)0.1371 (6)0.0120 (16)*
Al830.11879 (18)0.89340 (18)0.0705 (5)0.0066 (14)*
Al840.13639 (19)0.83721 (19)0.0647 (6)0.0108 (15)*
Al850.1531 (2)0.78225 (19)0.1377 (7)0.0116 (17)*
Al860.16097 (19)0.56140 (19)0.1375 (6)0.0075 (15)*
Al870.1641 (2)0.4319 (2)0.0717 (7)0.0201 (18)*
Al880.17214 (14)0.73356 (14)0.0587 (5)0.0114 (17)*0.71
Cr880.17214 (14)0.73356 (14)0.0587 (5)0.0114 (17)*0.145
Fe880.17214 (14)0.73356 (14)0.0587 (5)0.0114 (17)*0.145
Al890.1939 (2)0.9138 (2)0.1328 (6)0.0068 (15)*
Al900.1959 (2)0.6898 (2)0.1335 (6)0.0108 (16)*
Al910.2077 (2)0.6312 (2)0.0557 (6)0.0165 (16)*
Al920.21199 (18)0.85803 (18)0.0677 (6)0.0083 (14)*
Al930.27552 (19)0.97233 (19)0.1327 (6)0.0081 (16)*
Al940.29474 (18)0.91707 (18)0.0670 (6)0.0088 (14)*
Al950.33166 (18)1.04641 (17)0.0702 (6)0.0073 (14)*
Al960.3370 (2)0.8499 (2)0.1370 (7)0.018 (3)*0.87
Al970.35193 (18)0.99159 (18)0.0641 (6)0.0082 (14)*
Al980.3655 (2)0.7136 (2)0.1311 (6)0.0130 (17)*
Al990.3731 (2)0.9386 (2)0.1358 (5)0.0099 (16)*
Al1000.40795 (19)1.06524 (19)0.1359 (6)0.0062 (15)*
Al1010.41792 (17)0.65273 (17)0.0537 (6)0.0070 (14)*
Al1020.43661 (18)0.72931 (18)0.0562 (6)0.0102 (15)*
Al1030.44743 (18)0.95708 (18)0.0581 (7)0.0115 (16)*
Al1040.4674 (2)0.9068 (2)0.1327 (6)0.0113 (16)*
Al1050.48329 (18)1.08619 (18)0.0552 (6)0.0077 (14)*
Al1060.4982 (3)0.7256 (3)0.0922 (8)0.022 (3)*0.84
Al1070.5017 (2)1.03015 (19)0.1359 (6)0.0063 (15)*
Al1080.52460 (18)0.97830 (18)0.0694 (6)0.0074 (14)*
Al1090.56637 (18)0.13897 (18)0.0605 (6)0.0102 (15)*
Al1100.5870 (2)0.0899 (2)0.1357 (6)0.0136 (17)*
Al1110.60568 (19)0.03463 (19)0.0692 (6)0.0121 (15)*
Al1120.61537 (19)0.21344 (19)0.1374 (6)0.0088 (16)*
Al1130.64393 (19)0.16902 (18)0.0623 (6)0.0116 (15)*
Al1140.66306 (19)0.10882 (19)0.0598 (6)0.0115 (15)*
Al1150.68393 (19)0.28295 (19)0.1195 (5)0.0069 (14)*
Al1160.6846 (2)0.0569 (2)0.1367 (6)0.0092 (15)*
Al1170.7194 (2)0.1849 (2)0.1306 (6)0.0075 (16)*
Al1180.75885 (18)0.07369 (18)0.0572 (6)0.0105 (15)*
Al1190.76254 (18)0.31908 (18)0.1378 (6)0.0076 (15)*
Al1200.77458 (17)0.26177 (17)0.0657 (6)0.0062 (14)*
Al1210.79724 (19)0.20399 (19)0.0641 (6)0.0100 (15)*
Al1220.8140 (2)0.1486 (2)0.1390 (6)0.0109 (17)*
Al1230.81693 (19)0.05171 (19)0.0574 (6)0.0122 (15)*
Al1240.83502 (19)0.33443 (19)0.0656 (6)0.0114 (15)*
Al1250.8548 (2)0.2817 (2)0.1369 (6)0.0111 (16)*
Al1260.8731 (2)0.1260 (2)0.1361 (6)0.0095 (16)*
Al1270.87326 (17)0.22510 (18)0.0701 (6)0.0067 (14)*
Al1280.90992 (19)0.01769 (19)0.0560 (6)0.0125 (15)*
Al1290.93007 (19)0.20256 (19)0.0696 (6)0.0108 (15)*
Al1300.94878 (19)0.14683 (19)0.0656 (6)0.0099 (15)*
Al1310.9664 (2)0.0919 (2)0.1375 (6)0.0152 (17)*

Experimental details

Crystal data
Chemical formulaAl477.44Cr63.42Fe51.42
Mr19051.3
Crystal system, space groupHexagonal, P63/m
Temperature (K)293
a, c (Å)40.68 (7), 12.546 (1)
V3)17983 (8)
Z2
Radiation typeMo Kα
µ (mm1)5.03
Crystal size (mm)0.6 × 0.12 × 0.1
Data collection
DiffractometerRigaku AFC5R
diffractometer
Absorption correctionψ scan
(North et al., 1968)
Tmin, Tmax0.481, 0.593
No. of measured, independent and
observed [I > 2σ(I)] reflections
12684, 12273, 3854
Rint0.086
(sin θ/λ)max1)0.617
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.075, 0.207, 1.09
No. of reflections5453
No. of parameters474
Δρmax, Δρmin (e Å3)1.61, 1.30

Computer programs: Rigaku/AFC Diffractometer Control Software, TEXSAN, SHELXS97 (Sheldrick, 1990), SHELXL97 (Sheldrick, 1997).

 

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