Cluster-packing geometry for Al-based F-type icosahedral alloys

Fujita, N.; Takano, H.; Yamamoto, A.; Tsai, A.-P.

doi:10.1107/S0108767313005035

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Cluster-packing geometry for Al-based F-type icosahedral alloys

N. Fujita, H. Takano, A. Yamamoto and A.-P. Tsai

This paper presents a new, highly stable, periodic approximant to the Al-based F-type icosahedral quasicrystals, i-Al–Pd–TM (TM = transition metals). The structure of this intermetallic Al–Pd–Cr–Fe compound is determined ab initio using single-crystal X-ray diffraction, where the space group is identified to be $Pa{\overline 3}$ and the lattice constant 40.5 Å. The structure is well described as a dense packing of clusters of two kinds, which are called the pseudo-Mackay-type and the mini-Bergman-type clusters. Adjacent clusters can be markedly interpenetrated, while the structure requires no glue atoms to fill in the gaps between the clusters. It is shown that the clusters are centred at the vertices of a canonical cell tiling, which corresponds to a 2 × 2 × 2 superstructure of Henley's cubic 3/2 packing, and that the parity of each vertex determines the kind of associated cluster. The proper quasi-lattice constant for describing the cluster packing is 1/τ (τ = golden mean) times the conventional one used to describe Al-based P-type icosahedral alloys. The superstructure ordering of the present approximant turns out to be of a different kind from the P-type superstructure ordering previously reported in i-Al–Pd–Mn. The present results will greatly improve the understanding of atomic structures of F-type icosahedral quasicrystals and their approximants.

Keywords: F-type icosahedral quasicrystals; approximants; clusters; canonical cell tilings.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108767313005035/dm5040sup1.cif Contains datablock I
	Structure factor file (CIF format) https://doi.org/10.1107/S0108767313005035/dm5040Isup2.hkl Contains datablock I
	Portable Document Format (PDF) file https://doi.org/10.1107/S0108767313005035/dm5040sup3.pdf Supplementary information
	Portable Document Format (PDF) file https://doi.org/10.1107/S0108767313005035/dm5040sup4.pdf Table 7

Computing details top

(I) top

Crystal data top

?	β = 90°
M_r = ?	γ = 90°
?, Pa3	V = ? Å³
a = 40.54050 Å	Z = ?
b = 40.54050 Å	? radiation, λ = ? Å
c = 40.54050 Å	× × mm
α = 90°

Data collection top

h = ?→?	l = ?→?
k = ?→?

Refinement top

Crystal data top

?	β = 90°
M_r = ?	γ = 90°
?, Pa3	V = ? Å³
a = 40.54050 Å	Z = ?
b = 40.54050 Å	? radiation, λ = ? Å
c = 40.54050 Å	× × mm
α = 90°

Data collection top

Refinement top

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Pd1	0.09485 (8)	0.09485 (8)	0.09485 (8)	0.003200*
Al2	0.1308 (4)	0.0944 (4)	0.0381 (4)	0.005000*
Al3	0.0585 (4)	0.0946 (4)	0.0386 (4)	0.004600*
Al4	0.1516 (4)	0.1300 (4)	0.0949 (4)	0.004600*
Al5	0.0948 (4)	0.1515 (4)	0.0597 (4)	0.004600*
Pd6	0.40400 (9)	0.40400 (9)	0.40400 (9)	0.008100*
Al7	0.4612 (4)	0.4387 (4)	0.4051 (4)	0.012000*
Al8	0.4043 (4)	0.4619 (4)	0.3680 (4)	0.002000*
Al9	0.3698 (4)	0.4025 (4)	0.3458 (4)	0.012000*
Al10	0.4389 (4)	0.4046 (4)	0.3487 (4)	0.012000*
Pd11	0.25036 (9)	0.34485 (10)	0.19066 (9)	0.005700*
Al12	0.2868 (4)	0.3453 (4)	0.1326 (4)	0.014800*
Al13	0.3459 (4)	0.2472 (4)	0.2142 (5)	0.014800*
Al14	0.2503 (4)	0.4026 (4)	0.2255 (4)	0.009600*
Al15	0.1915 (4)	0.3809 (4)	0.1905 (4)	0.009600*
Al16	0.3074 (4)	0.3101 (4)	0.1894 (4)	0.014800*
Al17	0.2508 (4)	0.2898 (4)	0.2264 (4)	0.006000*
Al18	0.3074 (4)	0.3804 (4)	0.1899 (4)	0.014800*
Al19	0.2160 (4)	0.3474 (4)	0.1333 (4)	0.009600*
Al20	0.2490 (4)	0.4013 (4)	0.1564 (4)	0.009600*
Al21	0.2861 (4)	0.3468 (4)	0.2471 (4)	0.014800*
Al22	0.1935 (4)	0.3102 (4)	0.1902 (4)	0.014800*
Al23	0.2492 (4)	0.2876 (5)	0.1557 (4)	0.014800*
Pd24	0.34558 (9)	0.49947 (11)	0.24956 (10)	0.008300*
Al25	0.2514 (4)	0.2123 (4)	0.0366 (4)	0.010400*
Al26	0.4019 (5)	0.4640 (4)	0.2491 (4)	0.010400*
Al27	0.3793 (4)	0.4985 (4)	0.3065 (4)	0.012000*
Al28	0.2881 (4)	0.4654 (4)	0.2491 (4)	0.012000*
Al29	0.1930 (4)	0.1181 (4)	−0.0004 (4)	0.012000*
Al30	0.3461 (4)	0.4437 (4)	0.2840 (4)	0.010400*
Al31	0.3457 (4)	0.4426 (4)	0.2158 (4)	0.010400*
Al32	0.2834 (4)	0.1540 (4)	0.0569 (4)	0.010400*
Al33	0.2132 (4)	0.1562 (4)	0.0572 (4)	0.010400*
Al34	0.1921 (4)	0.1897 (4)	0.0007 (4)	0.010400*
Al35	0.3056 (4)	0.1904 (4)	−0.0001 (4)	0.010400*
Al36	0.2489 (4)	0.0980 (5)	0.0352 (4)	0.010400*
Pd37	0.40403 (9)	0.09507 (9)	0.09482 (9)	0.006100*
Al38	0.4391 (4)	0.0940 (4)	0.0384 (4)	0.007000*
Al39	0.1299 (4)	0.4040 (4)	0.0383 (4)	0.007600*
Al40	0.3692 (4)	0.0969 (4)	0.0380 (4)	0.007600*
Al41	0.0595 (4)	0.4051 (4)	0.0375 (4)	0.007000*
Al42	0.0944 (4)	0.4614 (4)	0.0600 (4)	0.007000*
Al43	0.4616 (4)	0.1301 (4)	0.0957 (4)	0.007600*
Al44	0.4043 (4)	0.1518 (4)	0.0607 (4)	0.007000*
Al45	0.1522 (4)	0.3699 (4)	0.0951 (4)	0.007600*
Al46	0.3477 (4)	0.1309 (4)	0.0954 (4)	0.007000*
Al47	0.4047 (4)	0.1521 (4)	0.1314 (4)	0.007600*
Al48	0.1520 (4)	0.4391 (4)	0.0946 (4)	0.007600*
Al49	0.0951 (4)	0.3472 (4)	0.0605 (4)	0.007000*
Pd50	0.50004 (10)	0.25064 (9)	0.15386 (9)	0.004400*
Al51	0.3062 (4)	0.3107 (4)	0.0003 (4)	0.009000*
Al52	0.4989 (4)	0.1934 (4)	0.1882 (4)	0.009100*
Al53	0.4638 (4)	0.2495 (4)	0.0970 (4)	0.009000*
Al54	0.4985 (4)	0.3065 (4)	0.1190 (4)	0.009100*
Al55	0.5359 (4)	0.2490 (4)	0.2103 (4)	0.009000*
Al56	0.4998 (4)	0.1930 (4)	0.1203 (4)	0.009100*
Al57	0.4436 (4)	0.2836 (4)	0.1542 (4)	0.009000*
Al58	0.4417 (4)	0.2141 (4)	0.1543 (4)	0.009100*
Al59	0.2151 (4)	0.3465 (4)	0.0582 (4)	0.009100*
Al60	0.2841 (4)	0.3448 (4)	0.0568 (4)	0.009000*
Al61	0.2502 (4)	0.4030 (4)	0.0342 (4)	0.009000*
Al62	0.4650 (4)	0.2496 (4)	0.2105 (4)	0.009100*
Pd63	0.49994 (9)	0.44058 (9)	0.15447 (8)	0.006900*
Al64	0.3822 (4)	0.3091 (4)	0.0010 (4)	0.011900*
Al65	0.4633 (4)	0.4390 (4)	0.2120 (4)	0.011900*
Al66	0.5340 (4)	0.4421 (4)	0.2129 (4)	0.011900*
Al67	0.4425 (4)	0.4024 (4)	0.0353 (4)	0.011900*
Al68	0.4756 (4)	0.3449 (4)	0.0579 (4)	0.008100*
Al69	0.4431 (4)	0.4768 (4)	0.1556 (4)	0.008100*
Al70	0.4986 (4)	0.3836 (4)	0.1198 (4)	0.008100*
Al71	0.5003 (4)	0.4976 (4)	0.1184 (4)	0.011900*
Al72	0.4974 (4)	0.3108 (4)	0.0004 (5)	0.011900*
Al73	0.4439 (4)	0.4055 (4)	0.1546 (4)	0.011900*
Al74	0.4051 (5)	0.3453 (4)	0.0567 (4)	0.011900*
Al75	0.4653 (4)	0.4400 (4)	0.0964 (4)	0.011900*
Cr76	0.000000	0.000000	0.000000	0.015000*	0.7600
Al76	0.000000	0.000000	0.000000	0.015000*	0.2400
Al77	0.47737 (18)	0.44032 (18)	−0.0002 (2)	0.007000*	0.1200
Cr77	0.47737 (18)	0.44032 (18)	−0.0002 (2)	0.007000*	0.8800
Al78	0.03635 (18)	0.03635 (18)	0.03635 (18)	0.006000*	0.0400
Cr78	0.03635 (18)	0.03635 (18)	0.03635 (18)	0.006000*	0.9600
Al79	0.500000	0.000000	0.000000	0.007000*	0.4600
Cr79	0.500000	0.000000	0.000000	0.007000*	0.5400
Fe80	0.46330 (13)	0.46330 (13)	0.46330 (13)	0.002000*	0.7500
Pd80	0.46330 (13)	0.46330 (13)	0.46330 (13)	0.002000*	0.2500
Fe81	0.46332 (16)	0.03661 (16)	0.03672 (16)	0.013200*	0.7600
Pd81	0.46332 (16)	0.03661 (16)	0.03672 (16)	0.013200*	0.2400
Fe82	0.3452 (2)	0.4405 (2)	0.0954 (2)	0.017000*	0.8900
Pd82	0.3452 (2)	0.4405 (2)	0.0954 (2)	0.017000*	0.1100
Al83	0.3114 (5)	0.4078 (7)	0.0598 (5)	0.048000*
Al84	0.3817 (7)	0.4086 (7)	0.0601 (7)	0.081000*
Al85	0.3458 (5)	0.4624 (5)	0.0387 (5)	0.045000*
Al86	0.3078 (8)	0.4079 (8)	0.1284 (8)	0.008000*	0.4500
Al86'	0.2911 (7)	0.4358 (7)	0.1186 (7)	0.008000*	0.5500
Al87	0.3447 (5)	0.4619 (5)	0.1520 (5)	0.025000*
Al88	0.4008 (7)	0.4398 (7)	0.1181 (7)	0.077000*
Al89	0.3692 (7)	0.4957 (7)	0.0937 (7)	0.075000*
Fe90	0.4990 (2)	0.19166 (13)	0.0003 (2)	0.011700*	0.9100
Pd90	0.4990 (2)	0.19166 (13)	0.0003 (2)	0.011700*	0.0900
Al91	0.2894 (5)	0.0563 (5)	0.0003 (5)	0.041000*
Al92	0.2136 (5)	0.4439 (7)	0.0026 (7)	0.054000*
Al93	0.3446 (4)	0.0345 (4)	0.0338 (4)	0.007000*
Al94	0.1584 (7)	0.4661 (7)	0.0348 (7)	0.065000*
Al95	0.4991 (7)	0.4817 (5)	0.2521 (5)	0.048000*
Al96	0.4670 (8)	0.4680 (8)	0.3470 (8)	0.105000*
Al97	0.4688 (10)	0.1527 (10)	0.0323 (10)	0.152000*
Cr98	0.1531 (2)	0.2497 (2)	0.0947 (2)	0.001000*	0.8000
Al98	0.1531 (2)	0.2497 (2)	0.0947 (2)	0.001000*	0.2000
Al99	0.1918 (2)	0.2162 (2)	0.0607 (2)	0.015000*	0.2800
Cr99	0.1918 (2)	0.2162 (2)	0.0607 (2)	0.015000*	0.7200
Al100	0.1748 (8)	0.2803 (8)	0.0502 (8)	0.132000*
Al101	0.1331 (2)	0.1906 (2)	0.0953 (2)	0.007000*	0.1500
Cr101	0.1331 (2)	0.1906 (2)	0.0953 (2)	0.007000*	0.8500
Al102	0.1322 (2)	0.3076 (2)	0.0952 (2)	0.004000*	0.2100
Cr102	0.1322 (2)	0.3076 (2)	0.0952 (2)	0.004000*	0.7900
Al103	0.2480 (2)	0.1194 (2)	0.0962 (2)	0.008000*	0.2300
Cr103	0.2480 (2)	0.1194 (2)	0.0962 (2)	0.008000*	0.7700
Al104	0.1912 (10)	0.2897 (10)	0.1164 (10)	0.160000*	0.3800
Cr104	0.1912 (10)	0.2897 (10)	0.1164 (10)	0.160000*	0.2700
Fe105	0.1555 (2)	0.7506 (2)	0.0956 (4)	0.021000*	0.9800
Pd105	0.1555 (2)	0.7506 (2)	0.0956 (4)	0.021000*	0.0200
Al106	0.3088 (4)	0.2842 (4)	0.1317 (4)	0.014000*
Al107	0.3087 (4)	0.2844 (4)	0.0586 (4)	0.025000*	0.7700
Cr107	0.3087 (4)	0.2844 (4)	0.0586 (4)	0.025000*	0.2300
Al108	0.3837 (4)	0.2834 (4)	0.0608 (4)	0.025000*	0.8300
Cr108	0.3837 (4)	0.2834 (4)	0.0608 (4)	0.025000*	0.1700
Al109	0.4034 (4)	0.2477 (4)	0.1180 (4)	0.023000*	0.8900
Cr109	0.4034 (4)	0.2477 (4)	0.1180 (4)	0.023000*	0.1100
Al110	0.3087 (5)	0.2128 (5)	0.0597 (5)	0.034000*
Al111	0.3446 (5)	0.2258 (5)	0.1524 (4)	0.034000*
Al112	0.3672 (7)	0.1931 (7)	0.0976 (7)	0.067000*
Fe113	0.4047 (4)	0.3455 (2)	0.2498 (2)	0.024000*
Cr113	0.4047 (4)	0.3455 (2)	0.2498 (2)	0.024000*	0.0000
Al114	0.4421 (4)	0.3802 (4)	0.2141 (4)	0.018000*
Al115	0.4054 (4)	0.3663 (4)	0.3083 (4)	0.013000*
Al116	0.3846 (4)	0.4039 (4)	0.2495 (4)	0.019000*
Al117	0.3464 (4)	0.3445 (4)	0.2263 (4)	0.016000*
Al118	0.4392 (4)	0.3104 (4)	0.2143 (4)	0.012000*
Al119	0.4388 (5)	0.3102 (5)	0.2841 (5)	0.038000*
Al120	0.3823 (4)	0.2882 (4)	0.2501 (4)	0.023000*
Pd121	0.03787 (10)	0.15382 (10)	0.03341 (10)	0.010600*
Pd122	0.15498 (9)	0.34383 (9)	0.03828 (10)	0.001200*
Pd123	0.49979 (10)	0.40696 (9)	0.36725 (9)	0.006500*
Pd124	0.46348 (11)	0.15417 (11)	0.15351 (10)	0.012300*
Pd125	0.44313 (10)	0.49909 (11)	0.21630 (10)	0.012900*
Pd126	0.43854 (9)	0.38408 (9)	0.09501 (10)	0.008800*
Pd127	0.46130 (10)	0.34462 (10)	0.34335 (10)	0.009400*
Pd128	0.25334 (9)	0.38382 (9)	0.09498 (10)	0.006400*
Pd129	0.34485 (11)	0.15618 (11)	0.03799 (11)	0.016100*
Pd130	0.21331 (9)	0.44028 (9)	0.19174 (9)	0.006800*
Pd131	0.09127 (9)	0.36632 (9)	0.00029 (11)	0.011400*
Pd132	0.28893 (9)	0.44069 (10)	0.18784 (9)	0.008500*
Pd133	0.19040 (10)	0.40743 (11)	0.05541 (10)	0.011700*
Pd134	0.19072 (9)	0.40400 (9)	0.13116 (9)	0.005300*
Pd135	0.31200 (11)	0.28740 (11)	0.24952 (10)	0.015600*
Pd136	0.30892 (10)	0.09278 (11)	0.05660 (10)	0.010100*
Pd137	0.15265 (10)	0.15458 (10)	0.03373 (11)	0.012900*
Pd138	0.21235 (10)	0.25038 (9)	0.00257 (11)	0.008800*
Pd139	0.43897 (10)	0.30740 (10)	0.09494 (11)	0.010000*
Pd140	0.19126 (10)	0.09605 (10)	0.05993 (10)	0.008800*
Pd141	0.46242 (11)	0.34524 (10)	0.15668 (10)	0.010800*
Fe142	0.28543 (11)	0.24948 (11)	0.19141 (12)	0.009700*	0.2600
Pd142	0.28543 (11)	0.24948 (11)	0.19141 (12)	0.009700*	0.7400
Fe143	0.50141 (13)	0.28711 (12)	0.05893 (12)	0.007800*	0.5100
Pd143	0.50141 (13)	0.28711 (12)	0.05893 (12)	0.007800*	0.4900
Fe144	0.44322 (12)	0.49968 (13)	0.40016 (12)	0.012500*	0.3700
Pd144	0.44322 (12)	0.49968 (13)	0.40016 (12)	0.012500*	0.6300
Fe145	0.49849 (14)	0.28713 (13)	0.24931 (11)	0.019000*	0.2200
Pd145	0.49849 (14)	0.28713 (13)	0.24931 (11)	0.019000*	0.7800
Fe146	0.34478 (11)	0.34920 (11)	0.03828 (11)	0.008400*	0.1600
Pd146	0.34478 (11)	0.34920 (11)	0.03828 (11)	0.008400*	0.8400
Fe147	0.49981 (12)	0.09886 (11)	0.05776 (11)	0.007300*	0.3200
Pd147	0.49981 (12)	0.09886 (11)	0.05776 (11)	0.007300*	0.6800
Fe148	0.15417 (14)	0.34369 (13)	0.15351 (14)	0.008800*	0.4500
Pd148	0.15417 (14)	0.34369 (13)	0.15351 (14)	0.008800*	0.5500
Fe149	0.40154 (13)	0.44069 (12)	0.00331 (13)	0.009200*	0.4500
Pd149	0.40154 (13)	0.44069 (12)	0.00331 (13)	0.009200*	0.5500
Fe150	0.44148 (12)	0.19141 (12)	0.09361 (13)	0.004700*	0.4300
Pd150	0.44148 (12)	0.19141 (12)	0.09361 (13)	0.004700*	0.5700
Fe151	0.40261 (13)	0.44054 (13)	0.18868 (12)	0.014200*	0.3600
Pd151	0.40261 (13)	0.44054 (13)	0.18868 (12)	0.014200*	0.6400
Fe152	0.43821 (12)	0.49800 (13)	0.09582 (13)	0.010100*	0.4700
Pd152	0.43821 (12)	0.49800 (13)	0.09582 (13)	0.010100*	0.5300
Fe153	0.40714 (14)	0.44205 (13)	0.30777 (13)	0.011600*	0.4500
Pd153	0.40714 (14)	0.44205 (13)	0.30777 (13)	0.011600*	0.5500
Pd154	0.15344 (17)	0.15344 (17)	0.15344 (17)	0.011000*	0.2800
Fe154	0.15344 (17)	0.15344 (17)	0.15344 (17)	0.011000*	0.7200
Fe155	0.24809 (13)	0.30790 (16)	0.09506 (16)	0.008700*	0.5800
Pd155	0.24809 (13)	0.30790 (16)	0.09506 (16)	0.008700*	0.4200
Fe156	0.30852 (14)	0.40455 (14)	0.25214 (13)	0.014900*	0.3600
Pd156	0.30852 (14)	0.40455 (14)	0.25214 (13)	0.014900*	0.6400
Pd157	0.21000 (14)	0.24990 (14)	0.18636 (16)	0.006300*	0.6580
Pd157'	0.1911 (4)	0.2491 (4)	0.1549 (4)	0.009000*	0.3420
Fe158	0.40291 (16)	0.25131 (13)	0.19141 (16)	0.015000*	0.4500
Pd158	0.40291 (16)	0.25131 (13)	0.19141 (16)	0.015000*	0.5500
Cr159	0.0963 (2)	0.2494 (2)	0.0002 (2)	0.008000*	0.9900
Al159	0.0963 (2)	0.2494 (2)	0.0002 (2)	0.008000*	0.0100
Cr160	0.4035 (4)	0.2486 (2)	0.0013 (2)	0.019000*	0.6000
Fe160	0.4035 (4)	0.2486 (2)	0.0013 (2)	0.019000*	0.4000
Fe161	0.3445 (4)	0.3445 (4)	0.3445 (4)	0.057000*	0.9100
Pd161	0.3445 (4)	0.3445 (4)	0.3445 (4)	0.057000*	0.0900
Fe162	0.3470 (2)	0.3444 (2)	0.1534 (2)	0.021000*	0.8000
Cr162	0.3470 (2)	0.3444 (2)	0.1534 (2)	0.021000*	0.2000
Cr163	0.24888 (18)	0.1904 (2)	0.0955 (2)	0.002000*	0.3000
Fe163	0.24888 (18)	0.1904 (2)	0.0955 (2)	0.002000*	0.7000
Al164	0.0602 (4)	0.2148 (4)	0.0364 (4)	0.009000*
Al165	0.4990 (4)	0.3805 (4)	0.3086 (4)	0.016000*
Al166	0.2270 (4)	0.4421 (4)	0.0947 (4)	0.010000*
Al167	0.1915 (4)	0.5005 (4)	0.1184 (4)	0.013000*
Al168	0.2488 (4)	0.4763 (4)	0.1540 (4)	0.008000*
Al169	0.4037 (4)	0.3463 (4)	0.1326 (4)	0.014000*
Al170	0.1900 (4)	0.1900 (4)	0.1900 (4)	?
Al171	0.2497 (4)	0.2140 (5)	0.1531 (5)	0.022000*
Al172	0.3092 (5)	0.3092 (5)	0.3092 (5)	0.029000*
Al173	0.2086 (8)	0.1610 (8)	0.1295 (8)	0.029000*	0.5300
Al173'	0.1902 (10)	0.1909 (9)	0.1204 (9)	0.029000*	0.4700
Al174	0.0964 (5)	0.2698 (5)	0.0594 (5)	0.011000*	0.7200
Al174'	0.0515 (7)	0.2840 (7)	0.0041 (7)	0.011000*	0.5400
Al175	0.2834 (7)	0.5380 (7)	0.1334 (7)	0.017000*	0.6100
Al175'	0.3139 (9)	0.4941 (9)	0.1078 (9)	0.017000*	0.3900
Al176	0.2869 (7)	0.1605 (7)	0.1314 (7)	0.038000*	0.6900
Al176'	0.1151 (15)	0.3102 (16)	0.1911 (16)	0.038000*	0.3100
Al177	0.2306 (11)	0.2496 (10)	0.0973 (13)	0.036000*	0.4530
Al177'	0.2659 (9)	0.2487 (8)	0.0952 (9)	0.036000*	0.5470
Al178	0.3678 (11)	0.2852 (11)	0.1503 (11)	0.057000*	0.5200
Al178'	0.3790 (11)	0.3079 (13)	0.1827 (11)	0.057000*	0.4800
Al179	0.0964 (7)	0.3458 (7)	0.3218 (7)	0.029000*	0.6400
Al179'	0.0996 (13)	0.3509 (13)	0.3774 (11)	0.029000*	0.3600
Al180	0.5259 (8)	0.3437 (8)	0.2504 (7)	0.031000*	0.6200
Al180'	0.3484 (13)	0.2503 (11)	−0.0147 (13)	0.031000*	0.3800
Al181	0.3824 (13)	0.3813 (13)	0.1876 (13)	0.059000*	0.4800
Al181'	0.3683 (11)	0.4001 (11)	0.1561 (11)	0.059000*	0.5200
Al182	0.3466 (10)	0.3670 (10)	0.2857 (10)	0.058000*	0.5700
Al182'	0.3129 (13)	0.3786 (13)	0.3085 (13)	0.058000*	0.4300
Al183	0.5371 (17)	0.2480 (16)	0.0218 (17)	0.015000*	0.2300
Al183'	0.5538 (7)	0.2776 (7)	0.0321 (7)	0.015000*	0.5100
Al184	0.4253 (4)	0.0003 (5)	0.0002 (5)	0.009000*	0.7600
Al184'	−0.0014 (14)	0.4007 (13)	−0.0007 (15)	0.009000*	0.2400
Al185	0.4365 (9)	0.2128 (9)	0.0366 (9)	0.067000*	0.6600
Al185'	0.3912 (17)	0.2213 (17)	0.0618 (17)	0.067000*	0.3400
Al186	0.4403 (7)	0.4773 (5)	0.0363 (7)	0.007000*	0.6100
Al186'	0.4193 (9)	0.4689 (8)	0.0510 (9)	0.007000*	0.3900
Al187	0.4658 (9)	0.4381 (9)	0.2866 (9)	0.050000*	0.5900
Al187'	0.4423 (13)	0.4010 (13)	0.2735 (13)	0.050000*	0.4100

Experimental details

Crystal data
Chemical formula	?
M_r	?
Crystal system, space group	?, Pa3
Temperature (K)	?
a, b, c (Å)	40.54050, 40.54050, 40.54050
α, β, γ (°)	90, 90, 90
V (Å³)	?
Z	?
Radiation type	?, λ = ? Å
µ (mm⁻¹)	?
Crystal size (mm)	× ×

Data collection
Diffractometer	?
Absorption correction	?
No. of measured, independent and observed (?) reflections	?, ?, ?
R_int	?

Refinement
R[F² > 2σ(F²)], wR(F²), S	?, ?, ?
No. of reflections	?
No. of parameters	?
No. of restraints	?
Δρ_max, Δρ_min (e Å⁻³)	?, ?

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