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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.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108767313005035/dm5040sup1.cif
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108767313005035/dm5040Isup2.hkl
Contains datablock I

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S0108767313005035/dm5040sup3.pdf
Supplementary information

pdf

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°
Mr = ?γ = 90°
?, Pa3V = ? Å3
a = 40.54050 ÅZ = ?
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°
Mr = ?γ = 90°
?, Pa3V = ? Å3
a = 40.54050 ÅZ = ?
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
xyzUiso*/UeqOcc. (<1)
Pd10.09485 (8)0.09485 (8)0.09485 (8)0.003200*
Al20.1308 (4)0.0944 (4)0.0381 (4)0.005000*
Al30.0585 (4)0.0946 (4)0.0386 (4)0.004600*
Al40.1516 (4)0.1300 (4)0.0949 (4)0.004600*
Al50.0948 (4)0.1515 (4)0.0597 (4)0.004600*
Pd60.40400 (9)0.40400 (9)0.40400 (9)0.008100*
Al70.4612 (4)0.4387 (4)0.4051 (4)0.012000*
Al80.4043 (4)0.4619 (4)0.3680 (4)0.002000*
Al90.3698 (4)0.4025 (4)0.3458 (4)0.012000*
Al100.4389 (4)0.4046 (4)0.3487 (4)0.012000*
Pd110.25036 (9)0.34485 (10)0.19066 (9)0.005700*
Al120.2868 (4)0.3453 (4)0.1326 (4)0.014800*
Al130.3459 (4)0.2472 (4)0.2142 (5)0.014800*
Al140.2503 (4)0.4026 (4)0.2255 (4)0.009600*
Al150.1915 (4)0.3809 (4)0.1905 (4)0.009600*
Al160.3074 (4)0.3101 (4)0.1894 (4)0.014800*
Al170.2508 (4)0.2898 (4)0.2264 (4)0.006000*
Al180.3074 (4)0.3804 (4)0.1899 (4)0.014800*
Al190.2160 (4)0.3474 (4)0.1333 (4)0.009600*
Al200.2490 (4)0.4013 (4)0.1564 (4)0.009600*
Al210.2861 (4)0.3468 (4)0.2471 (4)0.014800*
Al220.1935 (4)0.3102 (4)0.1902 (4)0.014800*
Al230.2492 (4)0.2876 (5)0.1557 (4)0.014800*
Pd240.34558 (9)0.49947 (11)0.24956 (10)0.008300*
Al250.2514 (4)0.2123 (4)0.0366 (4)0.010400*
Al260.4019 (5)0.4640 (4)0.2491 (4)0.010400*
Al270.3793 (4)0.4985 (4)0.3065 (4)0.012000*
Al280.2881 (4)0.4654 (4)0.2491 (4)0.012000*
Al290.1930 (4)0.1181 (4)0.0004 (4)0.012000*
Al300.3461 (4)0.4437 (4)0.2840 (4)0.010400*
Al310.3457 (4)0.4426 (4)0.2158 (4)0.010400*
Al320.2834 (4)0.1540 (4)0.0569 (4)0.010400*
Al330.2132 (4)0.1562 (4)0.0572 (4)0.010400*
Al340.1921 (4)0.1897 (4)0.0007 (4)0.010400*
Al350.3056 (4)0.1904 (4)0.0001 (4)0.010400*
Al360.2489 (4)0.0980 (5)0.0352 (4)0.010400*
Pd370.40403 (9)0.09507 (9)0.09482 (9)0.006100*
Al380.4391 (4)0.0940 (4)0.0384 (4)0.007000*
Al390.1299 (4)0.4040 (4)0.0383 (4)0.007600*
Al400.3692 (4)0.0969 (4)0.0380 (4)0.007600*
Al410.0595 (4)0.4051 (4)0.0375 (4)0.007000*
Al420.0944 (4)0.4614 (4)0.0600 (4)0.007000*
Al430.4616 (4)0.1301 (4)0.0957 (4)0.007600*
Al440.4043 (4)0.1518 (4)0.0607 (4)0.007000*
Al450.1522 (4)0.3699 (4)0.0951 (4)0.007600*
Al460.3477 (4)0.1309 (4)0.0954 (4)0.007000*
Al470.4047 (4)0.1521 (4)0.1314 (4)0.007600*
Al480.1520 (4)0.4391 (4)0.0946 (4)0.007600*
Al490.0951 (4)0.3472 (4)0.0605 (4)0.007000*
Pd500.50004 (10)0.25064 (9)0.15386 (9)0.004400*
Al510.3062 (4)0.3107 (4)0.0003 (4)0.009000*
Al520.4989 (4)0.1934 (4)0.1882 (4)0.009100*
Al530.4638 (4)0.2495 (4)0.0970 (4)0.009000*
Al540.4985 (4)0.3065 (4)0.1190 (4)0.009100*
Al550.5359 (4)0.2490 (4)0.2103 (4)0.009000*
Al560.4998 (4)0.1930 (4)0.1203 (4)0.009100*
Al570.4436 (4)0.2836 (4)0.1542 (4)0.009000*
Al580.4417 (4)0.2141 (4)0.1543 (4)0.009100*
Al590.2151 (4)0.3465 (4)0.0582 (4)0.009100*
Al600.2841 (4)0.3448 (4)0.0568 (4)0.009000*
Al610.2502 (4)0.4030 (4)0.0342 (4)0.009000*
Al620.4650 (4)0.2496 (4)0.2105 (4)0.009100*
Pd630.49994 (9)0.44058 (9)0.15447 (8)0.006900*
Al640.3822 (4)0.3091 (4)0.0010 (4)0.011900*
Al650.4633 (4)0.4390 (4)0.2120 (4)0.011900*
Al660.5340 (4)0.4421 (4)0.2129 (4)0.011900*
Al670.4425 (4)0.4024 (4)0.0353 (4)0.011900*
Al680.4756 (4)0.3449 (4)0.0579 (4)0.008100*
Al690.4431 (4)0.4768 (4)0.1556 (4)0.008100*
Al700.4986 (4)0.3836 (4)0.1198 (4)0.008100*
Al710.5003 (4)0.4976 (4)0.1184 (4)0.011900*
Al720.4974 (4)0.3108 (4)0.0004 (5)0.011900*
Al730.4439 (4)0.4055 (4)0.1546 (4)0.011900*
Al740.4051 (5)0.3453 (4)0.0567 (4)0.011900*
Al750.4653 (4)0.4400 (4)0.0964 (4)0.011900*
Cr760.0000000.0000000.0000000.015000*0.7600
Al760.0000000.0000000.0000000.015000*0.2400
Al770.47737 (18)0.44032 (18)0.0002 (2)0.007000*0.1200
Cr770.47737 (18)0.44032 (18)0.0002 (2)0.007000*0.8800
Al780.03635 (18)0.03635 (18)0.03635 (18)0.006000*0.0400
Cr780.03635 (18)0.03635 (18)0.03635 (18)0.006000*0.9600
Al790.5000000.0000000.0000000.007000*0.4600
Cr790.5000000.0000000.0000000.007000*0.5400
Fe800.46330 (13)0.46330 (13)0.46330 (13)0.002000*0.7500
Pd800.46330 (13)0.46330 (13)0.46330 (13)0.002000*0.2500
Fe810.46332 (16)0.03661 (16)0.03672 (16)0.013200*0.7600
Pd810.46332 (16)0.03661 (16)0.03672 (16)0.013200*0.2400
Fe820.3452 (2)0.4405 (2)0.0954 (2)0.017000*0.8900
Pd820.3452 (2)0.4405 (2)0.0954 (2)0.017000*0.1100
Al830.3114 (5)0.4078 (7)0.0598 (5)0.048000*
Al840.3817 (7)0.4086 (7)0.0601 (7)0.081000*
Al850.3458 (5)0.4624 (5)0.0387 (5)0.045000*
Al860.3078 (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
Al870.3447 (5)0.4619 (5)0.1520 (5)0.025000*
Al880.4008 (7)0.4398 (7)0.1181 (7)0.077000*
Al890.3692 (7)0.4957 (7)0.0937 (7)0.075000*
Fe900.4990 (2)0.19166 (13)0.0003 (2)0.011700*0.9100
Pd900.4990 (2)0.19166 (13)0.0003 (2)0.011700*0.0900
Al910.2894 (5)0.0563 (5)0.0003 (5)0.041000*
Al920.2136 (5)0.4439 (7)0.0026 (7)0.054000*
Al930.3446 (4)0.0345 (4)0.0338 (4)0.007000*
Al940.1584 (7)0.4661 (7)0.0348 (7)0.065000*
Al950.4991 (7)0.4817 (5)0.2521 (5)0.048000*
Al960.4670 (8)0.4680 (8)0.3470 (8)0.105000*
Al970.4688 (10)0.1527 (10)0.0323 (10)0.152000*
Cr980.1531 (2)0.2497 (2)0.0947 (2)0.001000*0.8000
Al980.1531 (2)0.2497 (2)0.0947 (2)0.001000*0.2000
Al990.1918 (2)0.2162 (2)0.0607 (2)0.015000*0.2800
Cr990.1918 (2)0.2162 (2)0.0607 (2)0.015000*0.7200
Al1000.1748 (8)0.2803 (8)0.0502 (8)0.132000*
Al1010.1331 (2)0.1906 (2)0.0953 (2)0.007000*0.1500
Cr1010.1331 (2)0.1906 (2)0.0953 (2)0.007000*0.8500
Al1020.1322 (2)0.3076 (2)0.0952 (2)0.004000*0.2100
Cr1020.1322 (2)0.3076 (2)0.0952 (2)0.004000*0.7900
Al1030.2480 (2)0.1194 (2)0.0962 (2)0.008000*0.2300
Cr1030.2480 (2)0.1194 (2)0.0962 (2)0.008000*0.7700
Al1040.1912 (10)0.2897 (10)0.1164 (10)0.160000*0.3800
Cr1040.1912 (10)0.2897 (10)0.1164 (10)0.160000*0.2700
Fe1050.1555 (2)0.7506 (2)0.0956 (4)0.021000*0.9800
Pd1050.1555 (2)0.7506 (2)0.0956 (4)0.021000*0.0200
Al1060.3088 (4)0.2842 (4)0.1317 (4)0.014000*
Al1070.3087 (4)0.2844 (4)0.0586 (4)0.025000*0.7700
Cr1070.3087 (4)0.2844 (4)0.0586 (4)0.025000*0.2300
Al1080.3837 (4)0.2834 (4)0.0608 (4)0.025000*0.8300
Cr1080.3837 (4)0.2834 (4)0.0608 (4)0.025000*0.1700
Al1090.4034 (4)0.2477 (4)0.1180 (4)0.023000*0.8900
Cr1090.4034 (4)0.2477 (4)0.1180 (4)0.023000*0.1100
Al1100.3087 (5)0.2128 (5)0.0597 (5)0.034000*
Al1110.3446 (5)0.2258 (5)0.1524 (4)0.034000*
Al1120.3672 (7)0.1931 (7)0.0976 (7)0.067000*
Fe1130.4047 (4)0.3455 (2)0.2498 (2)0.024000*
Cr1130.4047 (4)0.3455 (2)0.2498 (2)0.024000*0.0000
Al1140.4421 (4)0.3802 (4)0.2141 (4)0.018000*
Al1150.4054 (4)0.3663 (4)0.3083 (4)0.013000*
Al1160.3846 (4)0.4039 (4)0.2495 (4)0.019000*
Al1170.3464 (4)0.3445 (4)0.2263 (4)0.016000*
Al1180.4392 (4)0.3104 (4)0.2143 (4)0.012000*
Al1190.4388 (5)0.3102 (5)0.2841 (5)0.038000*
Al1200.3823 (4)0.2882 (4)0.2501 (4)0.023000*
Pd1210.03787 (10)0.15382 (10)0.03341 (10)0.010600*
Pd1220.15498 (9)0.34383 (9)0.03828 (10)0.001200*
Pd1230.49979 (10)0.40696 (9)0.36725 (9)0.006500*
Pd1240.46348 (11)0.15417 (11)0.15351 (10)0.012300*
Pd1250.44313 (10)0.49909 (11)0.21630 (10)0.012900*
Pd1260.43854 (9)0.38408 (9)0.09501 (10)0.008800*
Pd1270.46130 (10)0.34462 (10)0.34335 (10)0.009400*
Pd1280.25334 (9)0.38382 (9)0.09498 (10)0.006400*
Pd1290.34485 (11)0.15618 (11)0.03799 (11)0.016100*
Pd1300.21331 (9)0.44028 (9)0.19174 (9)0.006800*
Pd1310.09127 (9)0.36632 (9)0.00029 (11)0.011400*
Pd1320.28893 (9)0.44069 (10)0.18784 (9)0.008500*
Pd1330.19040 (10)0.40743 (11)0.05541 (10)0.011700*
Pd1340.19072 (9)0.40400 (9)0.13116 (9)0.005300*
Pd1350.31200 (11)0.28740 (11)0.24952 (10)0.015600*
Pd1360.30892 (10)0.09278 (11)0.05660 (10)0.010100*
Pd1370.15265 (10)0.15458 (10)0.03373 (11)0.012900*
Pd1380.21235 (10)0.25038 (9)0.00257 (11)0.008800*
Pd1390.43897 (10)0.30740 (10)0.09494 (11)0.010000*
Pd1400.19126 (10)0.09605 (10)0.05993 (10)0.008800*
Pd1410.46242 (11)0.34524 (10)0.15668 (10)0.010800*
Fe1420.28543 (11)0.24948 (11)0.19141 (12)0.009700*0.2600
Pd1420.28543 (11)0.24948 (11)0.19141 (12)0.009700*0.7400
Fe1430.50141 (13)0.28711 (12)0.05893 (12)0.007800*0.5100
Pd1430.50141 (13)0.28711 (12)0.05893 (12)0.007800*0.4900
Fe1440.44322 (12)0.49968 (13)0.40016 (12)0.012500*0.3700
Pd1440.44322 (12)0.49968 (13)0.40016 (12)0.012500*0.6300
Fe1450.49849 (14)0.28713 (13)0.24931 (11)0.019000*0.2200
Pd1450.49849 (14)0.28713 (13)0.24931 (11)0.019000*0.7800
Fe1460.34478 (11)0.34920 (11)0.03828 (11)0.008400*0.1600
Pd1460.34478 (11)0.34920 (11)0.03828 (11)0.008400*0.8400
Fe1470.49981 (12)0.09886 (11)0.05776 (11)0.007300*0.3200
Pd1470.49981 (12)0.09886 (11)0.05776 (11)0.007300*0.6800
Fe1480.15417 (14)0.34369 (13)0.15351 (14)0.008800*0.4500
Pd1480.15417 (14)0.34369 (13)0.15351 (14)0.008800*0.5500
Fe1490.40154 (13)0.44069 (12)0.00331 (13)0.009200*0.4500
Pd1490.40154 (13)0.44069 (12)0.00331 (13)0.009200*0.5500
Fe1500.44148 (12)0.19141 (12)0.09361 (13)0.004700*0.4300
Pd1500.44148 (12)0.19141 (12)0.09361 (13)0.004700*0.5700
Fe1510.40261 (13)0.44054 (13)0.18868 (12)0.014200*0.3600
Pd1510.40261 (13)0.44054 (13)0.18868 (12)0.014200*0.6400
Fe1520.43821 (12)0.49800 (13)0.09582 (13)0.010100*0.4700
Pd1520.43821 (12)0.49800 (13)0.09582 (13)0.010100*0.5300
Fe1530.40714 (14)0.44205 (13)0.30777 (13)0.011600*0.4500
Pd1530.40714 (14)0.44205 (13)0.30777 (13)0.011600*0.5500
Pd1540.15344 (17)0.15344 (17)0.15344 (17)0.011000*0.2800
Fe1540.15344 (17)0.15344 (17)0.15344 (17)0.011000*0.7200
Fe1550.24809 (13)0.30790 (16)0.09506 (16)0.008700*0.5800
Pd1550.24809 (13)0.30790 (16)0.09506 (16)0.008700*0.4200
Fe1560.30852 (14)0.40455 (14)0.25214 (13)0.014900*0.3600
Pd1560.30852 (14)0.40455 (14)0.25214 (13)0.014900*0.6400
Pd1570.21000 (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
Fe1580.40291 (16)0.25131 (13)0.19141 (16)0.015000*0.4500
Pd1580.40291 (16)0.25131 (13)0.19141 (16)0.015000*0.5500
Cr1590.0963 (2)0.2494 (2)0.0002 (2)0.008000*0.9900
Al1590.0963 (2)0.2494 (2)0.0002 (2)0.008000*0.0100
Cr1600.4035 (4)0.2486 (2)0.0013 (2)0.019000*0.6000
Fe1600.4035 (4)0.2486 (2)0.0013 (2)0.019000*0.4000
Fe1610.3445 (4)0.3445 (4)0.3445 (4)0.057000*0.9100
Pd1610.3445 (4)0.3445 (4)0.3445 (4)0.057000*0.0900
Fe1620.3470 (2)0.3444 (2)0.1534 (2)0.021000*0.8000
Cr1620.3470 (2)0.3444 (2)0.1534 (2)0.021000*0.2000
Cr1630.24888 (18)0.1904 (2)0.0955 (2)0.002000*0.3000
Fe1630.24888 (18)0.1904 (2)0.0955 (2)0.002000*0.7000
Al1640.0602 (4)0.2148 (4)0.0364 (4)0.009000*
Al1650.4990 (4)0.3805 (4)0.3086 (4)0.016000*
Al1660.2270 (4)0.4421 (4)0.0947 (4)0.010000*
Al1670.1915 (4)0.5005 (4)0.1184 (4)0.013000*
Al1680.2488 (4)0.4763 (4)0.1540 (4)0.008000*
Al1690.4037 (4)0.3463 (4)0.1326 (4)0.014000*
Al1700.1900 (4)0.1900 (4)0.1900 (4)?
Al1710.2497 (4)0.2140 (5)0.1531 (5)0.022000*
Al1720.3092 (5)0.3092 (5)0.3092 (5)0.029000*
Al1730.2086 (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
Al1740.0964 (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
Al1750.2834 (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
Al1760.2869 (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
Al1770.2306 (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
Al1780.3678 (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
Al1790.0964 (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
Al1800.5259 (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
Al1810.3824 (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
Al1820.3466 (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
Al1830.5371 (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
Al1840.4253 (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
Al1850.4365 (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
Al1860.4403 (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
Al1870.4658 (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?
Mr?
Crystal system, space group?, Pa3
Temperature (K)?
a, b, c (Å)40.54050, 40.54050, 40.54050
α, β, γ (°)90, 90, 90
V3)?
Z?
Radiation type?, λ = ? Å
µ (mm1)?
Crystal size (mm) × ×
Data collection
Diffractometer?
Absorption correction?
No. of measured, independent and
observed (?) reflections
?, ?, ?
Rint?
Refinement
R[F2 > 2σ(F2)], wR(F2), S ?, ?, ?
No. of reflections?
No. of parameters?
No. of restraints?
Δρmax, Δρmin (e Å3)?, ?

 

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