Structure of ν-Al80.61Cr10.71Fe8.68, a giant hexagonal approximant of a quasicrystal determined by a combination of electron microscopy and X-ray diffraction

Kuo, K.H.; Mo, Z.M.; Zhou, H.Y.

doi:10.1107/S0108768199015761

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Structure of ν-Al_80.61Cr_10.71Fe_8.68, a giant hexagonal approximant of a quasicrystal determined by a combination of electron microscopy and X-ray diffraction

Z. M. Mo, H. Y. Zhou and K. H. Kuo

ν-Al_80.61Cr_10.71Fe_8.68, P6₃/m (No. 176), a = 40.68 (7), c = 12.546 (1) Å, V = 17 983 (8) Å³, atoms/cell = 1184.56, D_x = 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 F_o > 4σ(F_o). 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-Al_4.32Mn [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.

Keywords: Aluminium–chromium–iron; Electron microscopy; X-ray diffraction.

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Supporting information

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

(word) top

Crystal data top

Al_477.44Cr_63.42Fe_51.42	D_x = 3.518 Mg m⁻³
M_r = 19051.3	Mo Kα radiation, λ = 0.71069 Å
Hexagonal, P6₃/m	Cell parameters from 23 reflections
Hall symbol: -P 6c	θ = 9–23.5°
a = 40.68 (7) Å	µ = 5.03 mm⁻¹
c = 12.546 (1) Å	T = 293 K
V = 17983 (8) Å³	Needle, grey
Z = 2	0.6 × 0.12 × 0.1 mm
F(000) = 18433

Data collection top

Rigaku AFC5R diffractometer	R_int = 0.086
Graphite monochromator	θ_max = 26.0°, θ_min = 1.5°
ω–2θ scans	h = 0→50
Absorption correction: ψ scan (North et al., 1968)	k = 0→50
T_min = 0.481, T_max = 0.593	l = 0→15
12684 measured reflections	3 standard reflections every 500 reflections
12273 independent reflections	intensity decay: 0.6%
3854 reflections with I > 2σ(I)

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F² > 2σ(F²)] = 0.075	Secondary atom site location: difference Fourier map
wR(F²) = 0.207	Calculated w = 1/[σ²(F_o²) + (0.0778P)²] where P = (F_o² + 2F_c²)/3
S = 1.09	(Δ/σ)_max = 0.001
5453 reflections	Δρ_max = 1.61 e Å⁻³
474 parameters	Δρ_min = −1.30 e Å⁻³

Crystal data top

Al_477.44Cr_63.42Fe_51.42	Z = 2
M_r = 19051.3	Mo Kα radiation
Hexagonal, P6₃/m	µ = 5.03 mm⁻¹
a = 40.68 (7) Å	T = 293 K
c = 12.546 (1) Å	0.6 × 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)	R_int = 0.086
T_min = 0.481, T_max = 0.593	3 standard reflections every 500 reflections
12684 measured reflections	intensity decay: 0.6%
12273 independent reflections

Refinement top

R[F² > 2σ(F²)] = 0.075	474 parameters
wR(F²) = 0.207	0 restraints
S = 1.09	Δρ_max = 1.61 e Å⁻³
5453 reflections	Δρ_min = −1.30 e Å⁻³

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Al1	0.0000	0.0000	0.2500	0.003 (10)*	0.47
Cr1	0.0000	0.0000	0.2500	0.003 (10)*	0.015
Fe1	0.0000	0.0000	0.2500	0.003 (10)*	0.015
Al2	0.0000	0.0000	0.1099 (18)	0.001 (4)*	0.50
Al3	0.6667	0.3333	0.0426 (9)	0.005 (2)*
Cr4	0.03193 (15)	0.90723 (14)	0.2500	0.0037 (11)*
Cr5	0.18049 (15)	0.85053 (15)	0.2500	0.0050 (12)*
Cr6	0.33670 (14)	0.02076 (15)	0.2500	0.0061 (12)*
Cr7	0.59667 (14)	0.15519 (14)	0.2500	0.0042 (12)*
Cr8	0.75065 (15)	0.09767 (15)	0.2500	0.0084 (12)*
Cr9	0.84274 (15)	0.21868 (14)	0.2500	0.0049 (13)*
Cr10	0.94010 (16)	0.18129 (15)	0.2500	0.0060 (12)*
Cr11	0.99335 (14)	0.15933 (14)	0.2500	0.0028 (11)*
Cr12	0.03669 (15)	0.75047 (15)	0.2500	0.0089 (12)*	0.5
Fe12	0.03669 (15)	0.75047 (15)	0.2500	0.0089 (12)*	0.5
Cr13	0.06812 (15)	0.66065 (15)	0.2500	0.0081 (12)*	0.5
Fe13	0.06812 (15)	0.66065 (15)	0.2500	0.0081 (12)*	0.5
Cr14	0.12878 (15)	0.87186 (15)	0.2500	0.0090 (12)*	0.5
Fe14	0.12878 (15)	0.87186 (15)	0.2500	0.0090 (12)*	0.5
Cr15	0.14507 (19)	0.71979 (18)	0.2500	0.010 (2)*	0.3
Fe15	0.14507 (19)	0.71979 (18)	0.2500	0.010 (2)*	0.3
Al15	0.14507 (19)	0.71979 (18)	0.2500	0.010 (2)*	0.4
Cr16	0.27105 (17)	0.52623 (17)	0.2500	0.008 (2)*	0.31
Fe16	0.27105 (17)	0.52623 (17)	0.2500	0.008 (2)*	0.31
Al16	0.27105 (17)	0.52623 (17)	0.2500	0.008 (2)*	0.38
Cr17	0.27959 (16)	0.81464 (16)	0.2500	0.0100 (12)*	0.5
Fe17	0.27959 (16)	0.81464 (16)	0.2500	0.0100 (12)*	0.5
Cr18	0.31882 (15)	0.94934 (15)	0.2500	0.0093 (12)*	0.5
Fe18	0.31882 (15)	0.94934 (15)	0.2500	0.0093 (12)*	0.5
Cr19	0.37904 (16)	0.77809 (17)	0.2500	0.010 (2)*	0.405
Fe19	0.37904 (16)	0.77809 (17)	0.2500	0.010 (2)*	0.405
Al19	0.37904 (16)	0.77809 (17)	0.2500	0.010 (2)*	0.19
Cr20	0.46032 (14)	1.05536 (14)	0.2500	0.0080 (11)*	0.5
Fe20	0.46032 (14)	1.05536 (14)	0.2500	0.0080 (11)*	0.5
Cr21	0.49307 (14)	0.96621 (14)	0.2500	0.0056 (12)*	0.5
Fe21	0.49307 (14)	0.96621 (14)	0.2500	0.0056 (12)*	0.5
Cr22	0.62837 (15)	0.06518 (15)	0.2500	0.0078 (11)*	0.5
Fe22	0.62837 (15)	0.06518 (15)	0.2500	0.0078 (11)*	0.5
Cr23	0.80862 (14)	0.30749 (14)	0.2500	0.0089 (12)*	0.5
Fe23	0.80862 (14)	0.30749 (14)	0.2500	0.0089 (12)*	0.5
Cr24	0.84853 (14)	0.06002 (14)	0.2500	0.0083 (11)*	0.5
Fe24	0.84853 (14)	0.06002 (14)	0.2500	0.0083 (11)*	0.5
Cr25	0.9647 (2)	0.0358 (2)	0.2500	0.019 (3)*	0.24
Fe25	0.9647 (2)	0.0358 (2)	0.2500	0.019 (3)*	0.24
Al25	0.9647 (2)	0.0358 (2)	0.2500	0.019 (3)*	0.52
Al26	0.0567 (3)	0.5951 (3)	0.2500	0.007 (2)*
Al27	0.0722 (3)	0.8798 (3)	0.2500	0.011 (2)*
Al28	0.0881 (3)	0.7318 (3)	0.2500	0.004 (2)*
Al29	0.0962 (3)	0.9616 (3)	0.2500	0.024 (3)*
Al30	0.1081 (3)	0.8020 (3)	0.2500	0.002 (2)*
Al31	0.1538 (3)	0.9409 (3)	0.2500	0.015 (3)*
Al32	0.2147 (5)	0.7549 (5)	0.2500	0.040 (6)*	0.84
Al33	0.2234 (3)	0.8253 (3)	0.2500	0.012 (2)*
Al34	0.2475 (3)	0.9053 (3)	0.2500	0.007 (2)*
Al35	0.3039 (3)	0.8842 (3)	0.2500	0.013 (2)*
Al36	0.3120 (3)	0.7186 (3)	0.2500	0.0043 (19)*
Al37	0.3896 (3)	1.0029 (3)	0.2500	0.010 (2)*
Al38	0.4117 (3)	0.9089 (3)	0.2500	0.020 (4)*	0.83
Cr38	0.4117 (3)	0.9089 (3)	0.2500	0.020 (4)*	0.085
Fe38	0.4117 (3)	0.9089 (3)	0.2500	0.020 (4)*	0.085
Al39	0.4298 (3)	0.7613 (3)	0.2500	0.027 (4)*	0.76
Cr39	0.4298 (3)	0.7613 (3)	0.2500	0.027 (4)*	0.12
Fe39	0.4298 (3)	0.7613 (3)	0.2500	0.027 (4)*	0.12
Al40	0.4412 (3)	0.9843 (3)	0.2500	0.006 (2)*
Al41	0.4606 (3)	0.8424 (3)	0.2500	0.016 (2)*
Al42	0.4614 (4)	0.6740 (4)	0.2500	0.037 (4)*
Al43	0.5321 (3)	0.0969 (3)	0.2500	0.011 (2)*
Al44	0.5459 (3)	0.1706 (3)	0.2500	0.011 (2)*
Al45	0.5583 (3)	0.0238 (3)	0.2500	0.005 (2)*
Al46	0.6207 (3)	0.0018 (3)	0.2500	0.005 (2)*
Al47	0.6476 (3)	0.1361 (3)	0.2500	0.012 (2)*
Al48	0.6680 (3)	0.2091 (3)	0.2500	0.013 (2)*
Al49	0.6991 (3)	0.1178 (3)	0.2500	0.010 (3)*	0.87
Cr49	0.6991 (3)	0.1178 (3)	0.2500	0.010 (3)*	0.065
Fe49	0.6991 (3)	0.1178 (3)	0.2500	0.010 (3)*	0.065
Al50	0.7159 (3)	0.3462 (3)	0.2500	0.010 (2)*
Al51	0.7259 (3)	0.0290 (3)	0.2500	0.011 (2)*
Al52	0.7355 (3)	0.2554 (3)	0.2500	0.020 (3)*
Al53	0.7708 (3)	0.1682 (3)	0.2500	0.014 (3)*	0.92
Cr53	0.7708 (3)	0.1682 (3)	0.2500	0.014 (3)*	0.04
Fe53	0.7708 (3)	0.1682 (3)	0.2500	0.014 (3)*	0.04
Al54	0.7828 (3)	0.0071 (3)	0.2500	0.008 (2)*
Al55	0.7909 (3)	0.2372 (3)	0.2500	0.011 (2)*
Al56	0.8048 (3)	0.0856 (3)	0.2500	0.011 (2)*
Al57	0.8804 (3)	0.3484 (3)	0.2500	0.004 (2)*
Al58	0.8834 (3)	0.1897 (3)	0.2500	0.007 (2)*
Al59	0.9010 (3)	0.0398 (3)	0.2500	0.013 (2)*
Al60	0.9088 (3)	0.2744 (3)	0.2500	0.011 (2)*
Al61	0.9207 (3)	0.1107 (3)	0.2500	0.010 (2)*
Al62	0.9656 (3)	0.2497 (3)	0.2500	0.006 (2)*
Fe63	0.14240 (8)	0.61874 (8)	0.0633 (3)	0.0044 (6)*
Fe64	0.70289 (9)	0.23518 (8)	0.0733 (3)	0.0087 (7)*
Fe65	0.73475 (8)	0.35062 (8)	0.0534 (2)	0.0051 (6)*
Cr66	0.73951 (9)	0.12994 (9)	0.0766 (3)	0.0031 (7)*
Cr67	0.07945 (9)	0.76160 (9)	0.0748 (3)	0.0077 (7)*	0.5
Fe67	0.07945 (9)	0.76160 (9)	0.0748 (3)	0.0077 (7)*	0.5
Cr68	0.39138 (10)	0.89074 (10)	0.0530 (3)	0.0060 (11)*	0.405
Fe68	0.39138 (10)	0.89074 (10)	0.0530 (3)	0.0060 (11)*	0.405
Al68	0.39138 (10)	0.89074 (10)	0.0530 (3)	0.0060 (11)*	0.19
Cr69	0.42939 (9)	1.01312 (9)	0.0754 (3)	0.0060 (7)*	0.5
Fe69	0.42939 (9)	1.01312 (9)	0.0754 (3)	0.0060 (7)*	0.5
Cr70	0.89035 (9)	0.07075 (9)	0.0751 (3)	0.0075 (8)*	0.5
Fe70	0.89035 (9)	0.07075 (9)	0.0751 (3)	0.0075 (8)*	0.5
Cr71	0.98087 (16)	0.04531 (16)	0.0464 (5)	0.0241 (18)*	0.235
Fe71	0.98087 (16)	0.04531 (16)	0.0464 (5)	0.0241 (18)*	0.235
Al71	0.98087 (16)	0.04531 (16)	0.0464 (5)	0.0241 (18)*	0.53
Al72	0.0028 (2)	0.8395 (2)	0.1365 (6)	0.0115 (17)*
Al73	0.00492 (19)	0.2216 (2)	0.1341 (6)	0.0087 (16)*
Al74	0.00535 (18)	0.74239 (18)	0.0569 (6)	0.0090 (15)*
Al75	0.02462 (19)	0.16719 (19)	0.0693 (6)	0.0133 (17)*
Al76	0.02517 (19)	0.68767 (19)	0.1361 (6)	0.0063 (15)*
Al77	0.0326 (2)	0.9590 (2)	0.1458 (7)	0.0240 (19)*
Al78	0.04435 (19)	0.63116 (19)	0.0694 (6)	0.0107 (15)*
Al79	0.05941 (19)	0.9144 (2)	0.0651 (6)	0.0141 (16)*
Al80	0.0613 (2)	0.8159 (2)	0.1347 (6)	0.0081 (16)*
Al81	0.09837 (18)	0.70722 (19)	0.0614 (6)	0.0086 (14)*
Al82	0.1180 (2)	0.6554 (2)	0.1371 (6)	0.0120 (16)*
Al83	0.11879 (18)	0.89340 (18)	0.0705 (5)	0.0066 (14)*
Al84	0.13639 (19)	0.83721 (19)	0.0647 (6)	0.0108 (15)*
Al85	0.1531 (2)	0.78225 (19)	0.1377 (7)	0.0116 (17)*
Al86	0.16097 (19)	0.56140 (19)	0.1375 (6)	0.0075 (15)*
Al87	0.1641 (2)	0.4319 (2)	0.0717 (7)	0.0201 (18)*
Al88	0.17214 (14)	0.73356 (14)	0.0587 (5)	0.0114 (17)*	0.71
Cr88	0.17214 (14)	0.73356 (14)	0.0587 (5)	0.0114 (17)*	0.145
Fe88	0.17214 (14)	0.73356 (14)	0.0587 (5)	0.0114 (17)*	0.145
Al89	0.1939 (2)	0.9138 (2)	0.1328 (6)	0.0068 (15)*
Al90	0.1959 (2)	0.6898 (2)	0.1335 (6)	0.0108 (16)*
Al91	0.2077 (2)	0.6312 (2)	0.0557 (6)	0.0165 (16)*
Al92	0.21199 (18)	0.85803 (18)	0.0677 (6)	0.0083 (14)*
Al93	0.27552 (19)	0.97233 (19)	0.1327 (6)	0.0081 (16)*
Al94	0.29474 (18)	0.91707 (18)	0.0670 (6)	0.0088 (14)*
Al95	0.33166 (18)	1.04641 (17)	0.0702 (6)	0.0073 (14)*
Al96	0.3370 (2)	0.8499 (2)	0.1370 (7)	0.018 (3)*	0.87
Al97	0.35193 (18)	0.99159 (18)	0.0641 (6)	0.0082 (14)*
Al98	0.3655 (2)	0.7136 (2)	0.1311 (6)	0.0130 (17)*
Al99	0.3731 (2)	0.9386 (2)	0.1358 (5)	0.0099 (16)*
Al100	0.40795 (19)	1.06524 (19)	0.1359 (6)	0.0062 (15)*
Al101	0.41792 (17)	0.65273 (17)	0.0537 (6)	0.0070 (14)*
Al102	0.43661 (18)	0.72931 (18)	0.0562 (6)	0.0102 (15)*
Al103	0.44743 (18)	0.95708 (18)	0.0581 (7)	0.0115 (16)*
Al104	0.4674 (2)	0.9068 (2)	0.1327 (6)	0.0113 (16)*
Al105	0.48329 (18)	1.08619 (18)	0.0552 (6)	0.0077 (14)*
Al106	0.4982 (3)	0.7256 (3)	0.0922 (8)	0.022 (3)*	0.84
Al107	0.5017 (2)	1.03015 (19)	0.1359 (6)	0.0063 (15)*
Al108	0.52460 (18)	0.97830 (18)	0.0694 (6)	0.0074 (14)*
Al109	0.56637 (18)	0.13897 (18)	0.0605 (6)	0.0102 (15)*
Al110	0.5870 (2)	0.0899 (2)	0.1357 (6)	0.0136 (17)*
Al111	0.60568 (19)	0.03463 (19)	0.0692 (6)	0.0121 (15)*
Al112	0.61537 (19)	0.21344 (19)	0.1374 (6)	0.0088 (16)*
Al113	0.64393 (19)	0.16902 (18)	0.0623 (6)	0.0116 (15)*
Al114	0.66306 (19)	0.10882 (19)	0.0598 (6)	0.0115 (15)*
Al115	0.68393 (19)	0.28295 (19)	0.1195 (5)	0.0069 (14)*
Al116	0.6846 (2)	0.0569 (2)	0.1367 (6)	0.0092 (15)*
Al117	0.7194 (2)	0.1849 (2)	0.1306 (6)	0.0075 (16)*
Al118	0.75885 (18)	0.07369 (18)	0.0572 (6)	0.0105 (15)*
Al119	0.76254 (18)	0.31908 (18)	0.1378 (6)	0.0076 (15)*
Al120	0.77458 (17)	0.26177 (17)	0.0657 (6)	0.0062 (14)*
Al121	0.79724 (19)	0.20399 (19)	0.0641 (6)	0.0100 (15)*
Al122	0.8140 (2)	0.1486 (2)	0.1390 (6)	0.0109 (17)*
Al123	0.81693 (19)	0.05171 (19)	0.0574 (6)	0.0122 (15)*
Al124	0.83502 (19)	0.33443 (19)	0.0656 (6)	0.0114 (15)*
Al125	0.8548 (2)	0.2817 (2)	0.1369 (6)	0.0111 (16)*
Al126	0.8731 (2)	0.1260 (2)	0.1361 (6)	0.0095 (16)*
Al127	0.87326 (17)	0.22510 (18)	0.0701 (6)	0.0067 (14)*
Al128	0.90992 (19)	0.01769 (19)	0.0560 (6)	0.0125 (15)*
Al129	0.93007 (19)	0.20256 (19)	0.0696 (6)	0.0108 (15)*
Al130	0.94878 (19)	0.14683 (19)	0.0656 (6)	0.0099 (15)*
Al131	0.9664 (2)	0.0919 (2)	0.1375 (6)	0.0152 (17)*

Experimental details

Crystal data
Chemical formula	Al_477.44Cr_63.42Fe_51.42
M_r	19051.3
Crystal system, space group	Hexagonal, P6₃/m
Temperature (K)	293
a, c (Å)	40.68 (7), 12.546 (1)
V (Å³)	17983 (8)
Z	2
Radiation type	Mo Kα
µ (mm⁻¹)	5.03
Crystal size (mm)	0.6 × 0.12 × 0.1

Data collection
Diffractometer	Rigaku AFC5R diffractometer
Absorption correction	ψ scan (North et al., 1968)
T_min, T_max	0.481, 0.593
No. of measured, independent and observed [I > 2σ(I)] reflections	12684, 12273, 3854
R_int	0.086
(sin θ/λ)_max (Å⁻¹)	0.617

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.075, 0.207, 1.09
No. of reflections	5453
No. of parameters	474
Δρ_max, Δρ_min (e Å⁻³)	1.61, −1.30

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

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