A complex pseudo-decagonal quasicrystal approximant, Al₃₇(Co,Ni)_15.5, solved by rotation electron diffraction

Electron diffraction is a complementary technique to single-crystal X-ray diffraction and powder X-ray diffraction for structure solution of unknown crystals. Crystals too small to be studied by single-crystal X-ray diffraction or too complex to be solved by powder X-ray diffraction can be studied by electron diffraction. The main drawbacks of electron diffraction have been the difficulties in collecting complete three-dimensional electron diffraction data by conventional electron diffraction methods and the very time-consuming data collection. In addition, the intensities of electron diffraction suffer from dynamical scattering. Recently, a new electron diffraction method, rotation electron diffraction (RED), was developed, which can overcome the drawbacks and reduce dynamical effects. A complete three-dimensional electron diffraction data set can be collected from a sub-micrometre-sized single crystal in less than 2 h. Here the RED method is applied for ab initio structure determination of an unknown complex intermetallic phase, the pseudo-decagonal (PD) quasicrystal approximant Al_37.0(Co,Ni)_15.5, denoted as PD2. RED shows that the crystal is F-centered, with a = 46.4, b = 64.6, c = 8.2 Å. However, as with other approximants in the PD series, the reflections with odd l indices are much weaker than those with l even, so it was decided to first solve the PD2 structure in the smaller, primitive unit cell. The basic structure of PD2 with unit-cell parameters a = 23.2, b = 32.3, c = 4.1 Å and space group Pnmm has been solved in the present study. The structure with c = 8.2 Å will be taken up in the near future. The basic structure contains 55 unique atoms (17 Co/Ni and 38 Al) and is one of the most complex structures solved by electron diffraction. PD2 is built of characteristic 2 nm wheel clusters with fivefold rotational symmetry, which agrees with results from high-resolution electron microscopy images. Simulated electron diffraction patterns for the structure model are in good agreement with the experimental electron diffraction patterns obtained by RED.

Computing details

Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

Figures

(I)

Crystal data

Al18.50Co7.75Ni0	γ = 90°
Mr = 956.75	V = 3075.7 (2) Å^3
a = 23.2010 (3) Å	Z = 8
b = 32.3100 (3) Å	F(000) = 5282
c = 4.1030 (3) Å	Dx = 4.132 Mg m^−3
α = 90°	µ = 0.00 mm^−1
β = 90°	T = 293 K

Data collection

Radiation source: fine-focus sealed tube	Rint = 0.332
Graphite monochromator	θmax = 0.7°, θmin = 0.1°
8073 measured reflections	h = −22→23
1799 independent reflections	k = −32→32
1738 reflections with I > 2σ(I)	l = −4→4

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.429	Secondary atom site location: difference Fourier map
wR(F^2) = 0.702	w = 1/[σ^2(Fo^2) + (0.1P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 4.16	(Δ/σ)max = 0.435
1799 reflections	Δρmax = 1.98 e Å^−3
156 parameters	Δρmin = −2.56 e Å^−3

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

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 (Ų)

	x	y	z	Uiso*/Ueq
Co1	0.5322 (8)	0.3655 (5)	0.7500	0.011 (5)*
Co2	0.1625 (8)	0.5570 (4)	0.2500	0.000 (4)*
Co3	0.1506 (11)	0.3217 (7)	−0.7500	0.036 (6)*
Co4	0.483 (3)	0.2500	0.2500	0.11 (2)*
Co5	0.0231 (12)	0.2500	−0.2500	0.014 (7)*
Co6	0.8568 (16)	0.2500	0.2500	0.036 (9)*
Co7	0.3368 (8)	0.3177 (5)	0.7500	0.007 (5)*
Co8	0.3365 (8)	0.5580 (5)	−0.2500	0.007 (5)*
Co9	0.6654 (8)	0.2968 (5)	0.2500	0.009 (5)*
Co10	0.2866 (10)	0.4383 (6)	0.2500	0.019 (5)*
Co11	0.0316 (7)	0.4842 (5)	−0.2500	0.007 (5)*
Co12	−0.0290 (7)	0.3673 (5)	−0.7500	0.003 (4)*
Co13	0.4693 (7)	0.4855 (5)	0.2500	0.000 (4)*
Co14	0.2149 (10)	0.4374 (6)	−0.2500	0.024 (6)*
Co15	0.7823 (8)	0.3225 (5)	0.2500	0.007 (4)*
Co16	0.3489 (12)	0.3730 (8)	0.2500	0.042 (7)*
Co17	0.1461 (9)	0.3701 (6)	−0.2500	0.018 (5)*
Al18	0.1242 (15)	0.4487 (10)	−0.2500	0.070 (9)*
Al19	0.3562 (7)	0.5114 (5)	0.2500	0.009 (4)*
Al20	0.1804 (19)	0.2500	−0.7500	0.062 (12)*
Al21	0.4087 (14)	0.3674 (10)	0.7500	0.068 (9)*
Al22	0.601 (2)	0.3254 (14)	0.7500	0.124 (17)*
Al23	0.1072 (11)	0.2947 (8)	−0.2500	0.046 (7)*
Al24	0.0260 (9)	0.3993 (6)	−0.2500	0.026 (5)*
Al25	0.635 (2)	0.2500	0.7500	0.084 (15)*
Al26	0.8343 (7)	0.2914 (5)	−0.2500	0.006 (4)*
Al27	0.7078 (19)	0.3135 (13)	0.7500	0.101 (12)*
Al28	0.5056 (8)	0.2895 (6)	0.7500	0.022 (5)*
Al29	0.089 (2)	0.5142 (14)	−0.7500	0.121 (16)*
Al30	0.4997 (14)	0.3206 (9)	0.2500	0.067 (9)*
Al31	0.0029 (10)	0.4357 (6)	−0.7500	0.030 (6)*
Al32	0.1978 (8)	0.4841 (5)	0.2500	0.013 (5)*
Al33	0.2614 (11)	0.5582 (7)	−0.7500	0.045 (7)*
Al34	0.7553 (18)	0.2500	0.2500	0.066 (11)*
Al35	0.0787 (14)	0.6043 (9)	0.2500	0.067 (8)*
Al36	0.301 (3)	0.2500	0.7500	0.12 (2)*
Al37	0.425 (2)	0.5191 (14)	−0.2500	0.121 (16)*
Al38	0.243 (2)	0.3192 (17)	−0.7500	0.18 (3)*
Al39	0.4982 (12)	0.4398 (7)	0.7500	0.046 (7)*
Al40	0.3023 (12)	0.6248 (8)	−1.2500	0.048 (7)*
Al41	0.2956 (10)	0.3892 (7)	0.7500	0.042 (6)*
Al42	0.1994 (9)	0.3981 (6)	−0.7500	0.025 (5)*
Al43	−0.0709 (12)	0.2500	−0.2500	0.027 (7)*
Al44	0.6113 (14)	0.4137 (10)	0.7500	0.070 (9)*
Al45	0.176 (4)	0.540 (2)	−0.2500	0.25 (4)*
Al46	0.2935 (18)	0.4836 (12)	−0.2500	0.094 (12)*
Al47	−0.0081 (12)	0.3227 (8)	−0.2500	0.055 (7)*
Al48	0.586 (3)	0.2500	0.2500	0.13 (2)*
Al49	−0.1015 (11)	0.3330 (8)	−0.7500	0.053 (7)*
Al50	0.0764 (14)	0.3650 (9)	−0.7500	0.061 (8)*
Al51	0.407 (3)	0.4230 (19)	0.2500	0.16 (2)*
Al52	0.027 (2)	0.2876 (13)	−0.7500	0.124 (17)*
Al53	0.1959 (19)	0.6177 (13)	−0.7500	0.100 (13)*
Al54	0.381 (3)	0.2500	0.7500	0.15 (3)*
Al55	0.401 (3)	0.2906 (17)	0.2500	0.16 (3)*

Bond lengths (Å)

Co1—Al22	2.05 (5)	Al26—Al43^viii	2.57 (3)
Co1—Al44	2.41 (4)	Al26—Al26^v	2.68 (3)
Co1—Al39	2.53 (3)	Al26—Al49^vii	2.87 (2)
Co1—Al28	2.53 (2)	Al26—Al49^viii	2.87 (2)
Co1—Al30	2.62 (2)	Al26—Al53^xiii	3.02 (5)
Co1—Al30^i	2.62 (2)	Al26—Al27^ii	3.02 (5)
Co1—Al21	2.87 (4)	Al26—Al34^ii	3.06 (3)
Co2—Al45	2.15 (2)	Al26—Al34	3.06 (3)
Co2—Al45^i	2.15 (2)	Al27—Co9^i	2.34 (2)
Co2—Al53^i	2.11 (4)	Al27—Co15^i	2.70 (3)
Co2—Al29^i	2.19 (5)	Al27—Al40^xii	2.87 (3)
Co2—Al33^i	2.29 (3)	Al27—Al40^xiii	2.87 (3)
Co2—Al32	2.49 (2)	Al27—Al26^i	3.02 (5)
Co2—Al35	2.47 (4)	Al27—Al34	3.10 (3)
Co3—Al50	2.22 (4)	Al27—Al34^i	3.10 (3)
Co3—Al38	2.16 (6)	Al27—Al53^xii	3.15 (6)
Co3—Al20	2.42 (3)	Al28—Al30^i	2.289 (15)
Co3—Al23^ii	2.45 (2)	Al28—Al30	2.289 (15)
Co3—Al23	2.45 (2)	Al28—Co4^i	2.475 (18)
Co3—Co17	2.581 (19)	Al28—Al28^iv	2.55 (4)
Co3—Co17^ii	2.581 (19)	Al28—Al48	3.05 (5)
Co3—Al42	2.72 (3)	Al28—Al48^i	3.05 (5)
Co3—Al52	3.08 (5)	Al29—Co2^ii	2.19 (5)
Co4—Al30	2.32 (3)	Al29—Co11^ii	2.63 (3)
Co4—Al30^iii	2.32 (3)	Al29—Co11^xiv	2.80 (5)
Co4—Al28	2.475 (18)	Al29—Al32^ii	2.70 (5)
Co4—Al28^iii	2.475 (18)	Al29—Al35^ii	2.92 (5)
Co4—Al28^iv	2.475 (18)	Al29—Al45	2.99 (7)
Co4—Al28^ii	2.475 (18)	Al29—Al45^ii	2.99 (7)
Co4—Al48	2.40 (9)	Al29—Al18^ii	3.06 (4)
Co4—Al55^iii	2.31 (7)	Al29—Al31	3.23 (5)
Co4—Al55	2.31 (7)	Al29—Al31^xvi	3.37 (4)
Co5—Al43	2.18 (4)	Al30—Al28^ii	2.289 (15)
Co5—Al23	2.43 (3)	Al30—Al55	2.49 (6)
Co5—Al23^v	2.43 (3)	Al30—Co1^ii	2.62 (2)
Co5—Al52^i	2.39 (2)	Al30—Al48	3.03 (6)
Co5—Al52^vi	2.39 (2)	Al30—Al22^ii	3.12 (4)
Co5—Al52	2.39 (2)	Al30—Al21^ii	3.31 (4)
Co5—Al52^v	2.39 (2)	Al31—Al24^ii	2.424 (16)
Co5—Al47^v	2.46 (3)	Al31—Co11^ii	2.667 (17)
Co5—Al47	2.46 (3)	Al31—Co11^xiv	2.71 (3)
Co6—Al34	2.35 (5)	Al31—Al50	2.85 (4)
Co6—Al26^v	2.504 (12)	Al31—Al35^xiv	3.08 (3)
Co6—Al26^i	2.504 (12)	Al31—Al35^xv	3.08 (3)
Co6—Al26	2.504 (12)	Al31—Al29^xvi	3.37 (4)
Co6—Al26^iii	2.504 (12)	Al31—Al29^xiv	3.37 (4)
Co6—Al43^vii	2.65 (3)	Al32—Co14^i	2.578 (16)
Co6—Al43^viii	2.65 (3)	Al32—Al33^i	2.81 (3)
Co6—Al49^vii	2.85 (3)	Al32—Al42^i	2.78 (3)
Co6—Al49^ix	2.85 (3)	Al32—Al29^i	2.70 (5)
Co6—Co15^iii	2.91 (3)	Al32—Al45^i	2.77 (5)
Co6—Co15	2.91 (3)	Al32—Al45	2.77 (5)
Co7—Al54	2.42 (4)	Al32—Al18^i	2.91 (3)
Co7—Al36	2.34 (3)	Al32—Al46^i	3.02 (3)
Co7—Al21	2.32 (4)	Al33—Co2^ii	2.29 (3)
Co7—Al55^i	2.68 (4)	Al33—Al53	2.45 (5)
Co7—Al55	2.68 (4)	Al33—Al19^ii	2.67 (3)
Co7—Al41	2.50 (3)	Al33—Co8^ii	2.69 (2)
Co7—Co16^i	2.74 (2)	Al33—Al32^ii	2.81 (3)
Co7—Co16	2.74 (2)	Al33—Al45^ii	2.91 (6)
Co7—Al38^i	2.98 (4)	Al33—Al45	2.91 (6)
Co7—Al38^x	2.98 (4)	Al33—Al44^xii	3.09 (4)
Co8—Al40^i	2.30 (3)	Al33—Al40^i	3.12 (3)
Co8—Al37	2.40 (5)	Al33—Al40	3.12 (3)
Co8—Al44^xi	2.55 (2)	Al33—Al46^ii	3.25 (3)
Co8—Al44^xii	2.55 (2)	Al34—Co15^iii	2.43 (2)
Co8—Al46	2.60 (4)	Al34—Co9^iii	2.58 (4)
Co8—Al19	2.585 (14)	Al34—Al26^i	3.06 (3)
Co8—Al19^ii	2.585 (14)	Al34—Al26^iii	3.06 (3)
Co8—Al33	2.69 (2)	Al34—Al26^v	3.06 (3)
Co8—Al33^i	2.69 (2)	Al34—Al27^iii	3.10 (3)
Co9—Al27	2.34 (2)	Al34—Al27^iv	3.10 (3)
Co9—Al27^ii	2.34 (2)	Al35—Al24^xv	2.43 (4)
Co9—Al48	2.39 (6)	Al35—Co12^xiv	2.53 (2)
Co9—Al40^xiii	2.64 (3)	Al35—Co12^xv	2.53 (2)
Co9—Al34	2.58 (4)	Al35—Al53^i	2.75 (5)
Co9—Al22^ii	2.71 (3)	Al35—Al47^xv	2.87 (4)
Co9—Al22	2.71 (3)	Al35—Al49^xv	2.93 (3)
Co9—Al25^ii	2.645 (17)	Al35—Al49^xiv	2.93 (3)
Co9—Al25	2.645 (17)	Al35—Al29^i	2.92 (5)
Co9—Co15	2.84 (3)	Al35—Al31^xiv	3.08 (3)
Co10—Al42^i	2.40 (3)	Al35—Al31^xv	3.08 (3)
Co10—Co16	2.56 (3)	Al36—Al54	1.87 (10)
Co10—Al46^i	2.53 (2)	Al36—Co7^iv	2.34 (3)
Co10—Al46	2.53 (2)	Al36—Al38^v	3.31 (5)
Co10—Al32	2.54 (3)	Al36—Al38^x	3.31 (5)
Co10—Al41^ii	2.601 (18)	Al36—Al38^iii	3.31 (5)
Co10—Al41	2.601 (18)	Al36—Al38^i	3.31 (5)
Co10—Co14	2.64 (2)	Al37—Co13^xii	2.46 (5)
Co10—Co14^i	2.64 (2)	Al37—Co13^ii	2.54 (3)
Co10—Al51	2.85 (6)	Al37—Al19^ii	2.61 (3)
Co10—Al19	2.86 (3)	Al37—Al44^xi	3.10 (4)
Co11—Al18	2.44 (4)	Al37—Al44^xii	3.10 (4)
Co11—Al29^i	2.63 (3)	Al37—Al39^xi	3.03 (4)
Co11—Al29	2.63 (3)	Al37—Al39^xii	3.03 (4)
Co11—Al31	2.667 (17)	Al37—Al39^ii	3.08 (5)
Co11—Al31^i	2.667 (17)	Al37—Al46	3.25 (6)
Co11—Al31^xiv	2.71 (3)	Al38—Al42	2.75 (6)
Co11—Al29^xiv	2.80 (5)	Al38—Co7^ii	2.98 (4)
Co11—Co11^xiv	2.72 (2)	Al38—Co7^xvii	2.98 (4)
Co11—Co11^xv	2.72 (2)	Al38—Co16^ii	3.00 (6)
Co11—Al24	2.75 (3)	Al38—Al41^ii	3.29 (5)
Co12—Al49	2.02 (3)	Al38—Al41^xvii	3.29 (5)
Co12—Al31	2.33 (3)	Al38—Al36^xvii	3.31 (5)
Co12—Al50	2.45 (4)	Al38—Al36^ii	3.31 (5)
Co12—Al35^xiv	2.53 (2)	Al39—Co13^xi	2.53 (3)
Co12—Al35^xv	2.53 (2)	Al39—Co13^i	2.614 (18)
Co12—Al47^ii	2.555 (19)	Al39—Al44	2.76 (4)
Co12—Al47	2.555 (19)	Al39—Al37^xi	3.03 (4)
Co12—Al24	2.628 (16)	Al39—Al37^xii	3.03 (4)
Co12—Al24^ii	2.628 (16)	Al39—Al37^i	3.08 (5)
Co12—Al52	2.88 (4)	Al39—Al51	2.99 (5)
Co13—Al39^xi	2.53 (3)	Al39—Al51^i	2.99 (5)
Co13—Al37^xii	2.46 (5)	Al40—Co8^ii	2.30 (3)
Co13—Al37^i	2.54 (3)	Al40—Co9^xiii	2.64 (3)
Co13—Al37	2.54 (3)	Al40—Co15^xiii	2.60 (3)
Co13—Al39^ii	2.614 (18)	Al40—Al27^xii	2.87 (3)
Co13—Al39	2.614 (18)	Al40—Al27^xiii	2.87 (3)
Co13—Al51	2.48 (6)	Al40—Al33^ii	3.12 (3)
Co13—Co13^xi	2.67 (2)	Al40—Al44^xii	3.13 (3)
Co13—Co13^xii	2.67 (2)	Al40—Al44^xiii	3.13 (3)
Co13—Al19	2.76 (2)	Al40—Al53^ii	3.22 (4)
Co14—Al18	2.14 (4)	Al40—Al53	3.22 (4)
Co14—Al46	2.36 (4)	Al41—Co16^i	2.45 (2)
Co14—Al42	2.439 (15)	Al41—Co14^i	2.43 (3)
Co14—Al42^i	2.439 (15)	Al41—Co10^i	2.601 (18)
Co14—Al41^ii	2.43 (3)	Al41—Al42^i	3.05 (2)
Co14—Al32	2.578 (16)	Al41—Al42^x	3.05 (2)
Co14—Al32^ii	2.578 (16)	Al41—Al46^i	3.05 (5)
Co14—Co10^ii	2.64 (2)	Al41—Al38^i	3.29 (5)
Co14—Co17	2.70 (3)	Al41—Al38^x	3.29 (5)
Co15—Al34	2.43 (2)	Al42—Co10^ii	2.40 (3)
Co15—Al26	2.583 (15)	Al42—Co14^ii	2.439 (15)
Co15—Al26^i	2.583 (15)	Al42—Co17^ii	2.561 (18)
Co15—Al40^xiii	2.60 (3)	Al42—Al32^ii	2.78 (3)
Co15—Al27^ii	2.70 (3)	Al42—Al50	3.05 (4)
Co15—Al27	2.70 (3)	Al42—Al41^ii	3.05 (2)
Co15—Al49^vii	2.72 (3)	Al42—Al41^xvii	3.05 (2)
Co15—Al53^xii	2.86 (3)	Al42—Al18^ii	3.15 (3)
Co15—Al53^xiii	2.86 (3)	Al43—Al26^xviii	2.57 (3)
Co16—Al51	2.11 (6)	Al43—Al26^xix	2.57 (3)
Co16—Al55	2.92 (6)	Al43—Co6^xx	2.65 (3)
Co16—Al41^ii	2.45 (2)	Al43—Co6^xix	2.65 (3)
Co16—Al41	2.45 (2)	Al43—Al47	2.76 (3)
Co16—Al21	2.48 (3)	Al43—Al47^v	2.76 (3)
Co16—Al21^ii	2.48 (3)	Al43—Al52^i	3.29 (4)
Co16—Co7^ii	2.74 (2)	Al43—Al52	3.29 (4)
Co16—Al38^i	3.00 (6)	Al43—Al52^v	3.29 (4)
Co17—Al42^i	2.561 (18)	Al43—Al52^vi	3.29 (4)
Co17—Al42	2.561 (18)	Al44—Al19^xi	2.53 (4)
Co17—Al18	2.59 (4)	Al44—Co8^xi	2.55 (2)
Co17—Co3^i	2.581 (19)	Al44—Co8^xii	2.55 (2)
Co17—Al50	2.62 (2)	Al44—Al37^xi	3.10 (4)
Co17—Al50^i	2.62 (2)	Al44—Al37^xii	3.10 (4)
Co17—Al23	2.60 (3)	Al44—Al33^xii	3.09 (4)
Co17—Al24	2.94 (3)	Al44—Al40^xii	3.13 (3)
Al18—Al24	2.78 (4)	Al44—Al40^xiii	3.13 (3)
Al18—Al32	2.91 (3)	Al45—Co2^ii	2.15 (2)
Al18—Al32^ii	2.91 (3)	Al45—Al32^ii	2.77 (5)
Al18—Al42	3.15 (3)	Al45—Al33^i	2.91 (6)
Al18—Al42^i	3.15 (3)	Al45—Al29^i	2.99 (7)
Al18—Al29^i	3.06 (4)	Al45—Al53^i	3.28 (7)
Al18—Al29	3.06 (4)	Al45—Al53	3.28 (7)
Al18—Al45	3.18 (8)	Al45—Al46	3.27 (9)
Al19—Al44^xi	2.53 (4)	Al46—Co10^ii	2.53 (2)
Al19—Al37^i	2.61 (3)	Al46—Al19^ii	2.67 (3)
Al19—Al37	2.61 (3)	Al46—Al32^ii	3.02 (3)
Al19—Co8^i	2.585 (14)	Al46—Al41^ii	3.05 (5)
Al19—Al33^i	2.67 (3)	Al46—Al33^i	3.25 (3)
Al19—Al46	2.67 (3)	Al47—Al52	2.48 (3)
Al19—Al46^i	2.67 (3)	Al47—Al52^i	2.48 (3)
Al19—Al51	3.09 (7)	Al47—Co12^i	2.555 (19)
Al20—Co3^vi	2.42 (3)	Al47—Al35^xv	2.87 (4)
Al20—Al38	2.67 (6)	Al47—Al49	3.00 (3)
Al20—Al38^vi	2.67 (6)	Al47—Al49^i	3.00 (3)
Al20—Al23^vi	3.03 (3)	Al47—Al50^i	3.15 (3)
Al20—Al23^ii	3.03 (3)	Al48—Al25^ii	2.35 (4)
Al20—Al23^v	3.03 (3)	Al48—Co9^iii	2.39 (6)
Al20—Al23	3.03 (3)	Al48—Al30^iii	3.03 (6)
Al21—Co16^i	2.48 (3)	Al48—Al28^iii	3.05 (5)
Al21—Al41	2.72 (4)	Al48—Al28^ii	3.05 (5)
Al21—Al51^i	2.73 (4)	Al48—Al28^iv	3.05 (5)
Al21—Al51	2.73 (4)	Al48—Al22^iii	3.20 (4)
Al21—Al55	3.22 (4)	Al49—Co15^xx	2.72 (3)
Al21—Al55^i	3.22 (4)	Al49—Co6^xx	2.85 (3)
Al21—Al39	3.13 (4)	Al49—Al26^xx	2.87 (2)
Al21—Al30	3.31 (4)	Al49—Al26^xix	2.87 (2)
Al21—Al30^i	3.31 (4)	Al49—Al35^xv	2.93 (3)
Al22—Al27	2.52 (6)	Al49—Al35^xiv	2.93 (3)
Al22—Al25	2.56 (5)	Al49—Al47^ii	3.00 (3)
Al22—Al28	2.49 (5)	Al49—Al52	3.32 (5)
Al22—Co9^i	2.71 (3)	Al49—Al53^xvi	3.40 (4)
Al22—Al44	2.87 (6)	Al49—Al53^xiv	3.40 (4)
Al22—Al48	3.20 (4)	Al50—Co17^ii	2.62 (2)
Al22—Al48^i	3.20 (4)	Al50—Al24^ii	2.61 (2)
Al22—Al30^i	3.12 (4)	Al50—Al52	2.75 (5)
Al22—Al30	3.12 (4)	Al50—Al47^ii	3.15 (3)
Al23—Co3^i	2.45 (2)	Al50—Al23^ii	3.14 (3)
Al23—Al47	2.82 (4)	Al51—Al21^ii	2.73 (4)
Al23—Al52	2.78 (3)	Al51—Al39^ii	2.99 (5)
Al23—Al52^i	2.78 (3)	Al51—Al41^ii	3.48 (5)
Al23—Al23^v	2.89 (5)	Al52—Co5^ii	2.39 (2)
Al23—Al20^i	3.03 (3)	Al52—Al47^ii	2.48 (3)
Al23—Al50^i	3.14 (3)	Al52—Al52^vi	2.43 (8)
Al23—Al50	3.14 (3)	Al52—Al23^ii	2.78 (3)
Al24—Al31^i	2.424 (16)	Al52—Al43^ii	3.29 (4)
Al24—Al31	2.424 (16)	Al53—Co2^ii	2.11 (4)
Al24—Al35^xv	2.43 (4)	Al53—Al35^ii	2.75 (5)
Al24—Al47	2.60 (3)	Al53—Co15^xii	2.86 (3)
Al24—Al50	2.61 (2)	Al53—Co15^xiii	2.86 (3)
Al24—Al50^i	2.61 (2)	Al53—Al26^xiii	3.02 (5)
Al24—Co12^i	2.628 (16)	Al53—Al27^xii	3.15 (6)
Al25—Al48^i	2.35 (4)	Al53—Al45^ii	3.28 (7)
Al25—Al48	2.35 (4)	Al53—Al40^i	3.22 (4)
Al25—Al22^iv	2.56 (5)	Al53—Al49^xvi	3.40 (4)
Al25—Al27	2.66 (5)	Al54—Co7^iv	2.42 (4)
Al25—Al27^iv	2.66 (5)	Al54—Al55^i	2.48 (3)
Al25—Co9^i	2.645 (18)	Al54—Al55^iii	2.48 (3)
Al25—Co9^iii	2.645 (18)	Al54—Al55^iv	2.48 (3)
Al25—Co9^iv	2.645 (18)	Al54—Al55	2.48 (3)
Al25—Al28^iv	3.26 (5)	Al55—Co7^ii	2.68 (4)
Al25—Al28	3.26 (5)	Al55—Al54^ii	2.48 (3)
Al26—Co6^ii	2.504 (12)	Al55—Al21^ii	3.22 (4)
Al26—Co15^ii	2.583 (15)

Symmetry codes: (i) x, y, z+1; (ii) x, y, z−1; (iii) x, −y+1/2, −z+1/2; (iv) x, −y+1/2, −z+3/2; (v) x, −y+1/2, −z−1/2; (vi) x, −y+1/2, −z−3/2; (vii) x+1, y, z+1; (viii) x+1, y, z; (ix) x+1, −y+1/2, −z−1/2; (x) x, y, z+2; (xi) −x+1, −y+1, −z+1; (xii) −x+1, −y+1, −z; (xiii) −x+1, −y+1, −z−1; (xiv) −x, −y+1, −z−1; (xv) −x, −y+1, −z; (xvi) −x, −y+1, −z−2; (xvii) x, y, z−2; (xviii) x−1, −y+1/2, −z−1/2; (xix) x−1, y, z; (xx) x−1, y, z−1.