Atomic structure solution of the complex quasicrystal approximant Al₇₇Rh₁₅Ru₈ from electron diffraction data

The crystal structure of the novel Al₇₇Rh₁₅Ru₈ phase (which is an approximant of decagonal quasicrystals) was determined using modern direct methods (MDM) applied to automated electron diffraction tomography (ADT) data. The Al₇₇Rh₁₅Ru₈ E-phase is orthorhombic [Pbma, a = 23.40 (5), b = 16.20 (4) and c = 20.00 (5) Å] and has one of the most complicated intermetallic structures solved solely by electron diffraction methods. Its structural model consists of 78 unique atomic positions in the unit cell (19 Rh/Ru and 59 Al). Precession electron diffraction (PED) patterns and high-resolution electron microscopy (HRTEM) images were used for the validation of the proposed atomic model. The structure of the E-phase is described using hierarchical packing of polyhedra and a single type of tiling in the form of a parallelogram. Based on this description, the structure of the E-phase is compared with that of the ε₆-phase formed in Al–Rh–Ru at close compositions.

Computing details

Data collection: ADT module; cell refinement: ADT3D; data reduction: own developed routines; program(s) used to solve structure: MDM inplemented in SIR2014; program(s) used to refine structure: SHELXL2013 (Sheldrick, 2013).

Figures

(I)

Crystal data

Al46Ru14	V = 7582 (30) Å^3
Mr = 2656.11	Z = 8
?, ?	F(000) = 3233
a = 23.40 (5) Å	Dx = 4.654 Mg m^−3
b = 16.20 (4) Å	? radiation, λ = 0.0197 Å
c = 20.00 (5) Å	µ = 0.02 mm^−1
α = 90°	T = 293 K
β = 90°	Nanocrystal
γ = 90°	× × mm

Data collection

FEI Tecnai F30 ST diffractometer	θmax = 0.6°, θmin = 0.04°
electron precession and ADT scans	h = ?→?
3851 independent reflections	k = ?→?
3433 reflections with I > 2σ(I)	l = ?→?

Refinement

Refinement on F^2	269 parameters
Least-squares matrix: full	0 restraints
R[F^2 > 2σ(F^2)] = 0.322	w = 1/[σ^2(Fo^2) + (0.2P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.634	(Δ/σ)max = 0.217
S = 2.11	Δρmax = 0.69 e Å^−3
3851 reflections	Δρmin = −1.19 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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Ru1	0.7509 (5)	0.7500	0.4039 (6)	0.043 (3)*
Ru2	0.9381 (4)	0.7500	0.0931 (5)	0.025 (3)*
Ru3	0.7525 (6)	0.7500	−0.2131 (7)	0.055 (4)*
Ru4	0.7500	0.5000	0.4046 (6)	0.055 (4)*
Ru5	0.9468 (5)	0.2500	0.0900 (6)	0.045 (4)*
Ru6	0.8039 (4)	0.6199 (6)	0.5972 (4)	0.050 (3)*
Ru7	0.8882 (4)	0.1315 (6)	−0.0995 (4)	0.047 (3)*
Ru8	0.8862 (3)	0.3807 (5)	0.2843 (4)	0.036 (2)*
Ru9	0.7500	0.5000	−0.2174 (5)	0.023 (3)*
Ru10	0.9387 (4)	0.4987 (7)	0.0974 (4)	0.051 (3)*
Ru11	0.8042 (3)	0.6190 (5)	0.2130 (4)	0.035 (2)*
Ru12	0.9193 (4)	0.6189 (6)	0.4039 (4)	0.044 (3)*
Ru13	0.8850 (4)	0.3827 (6)	0.5223 (5)	0.057 (3)*
Ru14	1.0600 (5)	0.7500	0.2887 (5)	0.033 (3)*
Ru15	0.9441 (4)	0.5014 (6)	0.7053 (4)	0.043 (2)*
Ru16	0.7500	0.5000	0.0283 (7)	0.054 (4)*
Ru17	0.7501 (5)	0.7500	0.0173 (6)	0.037 (3)*
Ru18	1.0547 (5)	0.2500	0.2830 (6)	0.049 (4)*
Ru19	0.8885 (4)	0.6578 (7)	−0.0928 (4)	0.055 (3)*
Al1	0.9215 (10)	0.6130 (16)	0.0138 (12)	0.053 (7)*
Al2	1.0258 (12)	0.2500	0.3979 (13)	0.022 (7)*
Al3	0.4899 (9)	0.6177 (13)	0.0968 (9)	0.028 (6)*
Al4	0.4789 (7)	0.5993 (11)	0.4127 (7)	0.006 (4)*
Al5	0.8080 (8)	0.6175 (13)	−0.1675 (10)	0.027 (5)*
Al6	0.9656 (11)	0.7500	−0.0268 (13)	0.021 (7)*
Al7	0.7861 (16)	0.7500	0.5261 (19)	0.061 (11)*
Al8	0.7777 (17)	0.7500	0.278 (2)	0.067 (12)*
Al9	0.9045 (9)	0.3740 (15)	0.1615 (11)	0.041 (6)*
Al10	0.6598 (13)	0.7500	0.0959 (13)	0.028 (8)*
Al11	0.8986 (11)	0.6269 (18)	0.1543 (13)	0.062 (8)*
Al12	0.8638 (14)	0.7500	0.4003 (15)	0.041 (9)*
Al13	0.6850 (13)	0.625 (2)	−0.1760 (15)	0.074 (9)*
Al14	0.7500	0.5000	0.1742 (16)	0.040 (9)*
Al15	0.7970 (19)	0.7500	−0.096 (2)	0.076 (14)*
Al16	0.8832 (12)	0.5123 (19)	−0.0898 (13)	0.066 (9)*
Al17	0.968 (3)	0.7500	0.231 (3)	0.12 (2)*
Al18	0.5865 (8)	0.6158 (12)	0.0298 (9)	0.023 (5)*
Al19	0.8402 (9)	0.5027 (14)	0.7200 (10)	0.031 (5)*
Al20	0.5709 (18)	0.7500	0.238 (2)	0.080 (13)*
Al21	1.0274 (13)	0.2500	0.1550 (15)	0.036 (8)*
Al22	0.7583 (11)	0.6350 (19)	0.1085 (12)	0.059 (8)*
Al23	0.8200 (17)	0.7500	0.151 (2)	0.070 (12)*
Al24	0.8091 (13)	0.7500	0.6589 (15)	0.039 (9)*
Al25	0.6977 (9)	0.6248 (14)	−0.0198 (10)	0.033 (6)*
Al26	0.7502 (8)	0.6276 (13)	0.7071 (9)	0.029 (5)*
Al27	0.650 (2)	0.7500	0.322 (3)	0.104 (17)*
Al28	0.5782 (10)	0.6654 (17)	0.4054 (10)	0.044 (7)*
Al29	0.7021 (13)	0.671 (2)	0.5908 (14)	0.076 (9)*
Al30	0.9340 (13)	0.2500	−0.0472 (15)	0.034 (8)*
Al31	0.9394 (10)	0.5065 (15)	0.4799 (11)	0.042 (6)*
Al32	0.8848 (14)	0.658 (2)	0.5197 (16)	0.091 (10)*
Al33	0.8904 (9)	0.6648 (15)	0.2906 (10)	0.037 (6)*
Al34	0.5074 (8)	0.6392 (13)	0.2917 (9)	0.023 (5)*
Al35	0.4230 (8)	0.6116 (13)	0.2148 (10)	0.029 (5)*
Al36	0.8993 (9)	0.6372 (16)	0.6555 (11)	0.042 (6)*
Al37	0.8576 (10)	0.7500	0.0167 (13)	0.017 (7)*
Al38	1.0096 (12)	0.6251 (18)	0.1067 (13)	0.062 (8)*
Al39	1.0000	0.5000	0.0000	0.017 (7)*
Al40	0.9805 (10)	0.4925 (16)	0.2017 (12)	0.051 (7)*
Al41	0.5876 (14)	0.7500	0.5804 (16)	0.046 (9)*
Al42	1.0014 (11)	0.6425 (17)	0.4744 (12)	0.057 (7)*
Al43	0.6840 (12)	0.7500	−0.0920 (13)	0.027 (8)*
Al44	0.7500	0.5000	−0.1019 (15)	0.043 (9)*
Al45	0.6566 (17)	0.7500	0.4727 (19)	0.068 (12)*
Al46	1.0851 (18)	0.7500	0.172 (2)	0.075 (13)*
Al47	0.8861 (10)	0.3801 (16)	0.6606 (12)	0.046 (7)*
Al48	0.7018 (13)	0.665 (2)	0.2183 (15)	0.087 (10)*
Al49	0.9979 (14)	0.631 (2)	0.3181 (16)	0.090 (10)*
Al50	0.8083 (15)	0.608 (2)	−0.0211 (17)	0.097 (11)*
Al51	0.8777 (16)	0.502 (2)	0.5877 (16)	0.097 (12)*
Al52	0.9345 (18)	0.489 (3)	0.348 (2)	0.128 (15)*
Al53	0.669 (2)	0.7500	0.708 (2)	0.087 (15)*
Al54	0.8414 (11)	0.5009 (17)	0.0792 (12)	0.057 (7)*
Al55	0.8673 (14)	0.503 (2)	0.2198 (16)	0.090 (11)*
Al56	0.7500	0.5000	0.622 (2)	0.088 (15)*
Al57	1.1382 (15)	0.2500	0.2064 (18)	0.054 (10)*
Al58	0.0809 (18)	0.905 (3)	0.214 (2)	0.129 (15)*
Al59	0.9705 (14)	0.7500	0.3914 (16)	0.045 (9)*

Bond lengths (Å)

Ru1—Al7	2.58 (4)	Al11—Al38	2.77 (4)
Ru1—Al8	2.60 (4)	Al11—Al33	2.80 (3)
Ru1—Al45	2.60 (4)	Al11—Al54	2.87 (4)
Ru1—Al12	2.64 (4)	Al12—Ru12^i	2.49 (2)
Ru1—Al27	2.87 (5)	Al12—Al59	2.50 (5)
Ru2—Al37	2.42 (3)	Al12—Al33	2.67 (3)
Ru2—Al6	2.48 (3)	Al12—Al33^i	2.67 (3)
Ru2—Al11^i	2.52 (3)	Al12—Al32	2.85 (4)
Ru2—Al11	2.52 (3)	Al12—Al32^i	2.85 (4)
Ru2—Al38	2.64 (3)	Al13—Ru7^xx	2.30 (3)
Ru2—Al38^i	2.64 (3)	Al13—Al58^xix	2.59 (5)
Ru2—Al1^i	2.75 (3)	Al13—Al43	2.64 (3)
Ru2—Al1	2.75 (3)	Al13—Al26^ii	2.79 (3)
Ru2—Al17	2.84 (6)	Al14—Ru11^v	2.433 (14)
Ru3—Al53^ii	2.51 (5)	Al14—Al22	2.56 (3)
Ru3—Al26^ii	2.55 (2)	Al14—Al22^v	2.56 (3)
Ru3—Al26^iii	2.55 (2)	Al15—Al5^i	2.59 (3)
Ru3—Al15	2.56 (4)	Al15—Ru19^i	2.61 (4)
Ru3—Al57^iv	2.56 (4)	Al15—Al43	2.65 (5)
Ru3—Al5	2.67 (2)	Al15—Al57^iv	2.68 (5)
Ru3—Al5^i	2.67 (2)	Al15—Al37	2.67 (5)
Ru3—Al13	2.68 (3)	Al15—Al50^i	2.76 (4)
Ru3—Al13^i	2.68 (3)	Al15—Al50	2.76 (4)
Ru3—Al24^ii	2.88 (3)	Al16—Ru7^vii	2.34 (3)
Ru5—Al21	2.29 (3)	Al16—Al50	2.72 (5)
Ru5—Al6^iv	2.41 (3)	Al17—Al33	2.58 (5)
Ru5—Al10^v	2.50 (3)	Al17—Al33^i	2.58 (5)
Ru5—Al3^v	2.61 (2)	Al17—Al49	2.69 (5)
Ru5—Al3^vi	2.61 (2)	Al17—Al49^i	2.69 (5)
Ru5—Al18^vi	2.60 (2)	Al18—Ru10^v	2.37 (2)
Ru5—Al18^v	2.60 (2)	Al18—Ru5^v	2.60 (2)
Ru5—Al9	2.66 (2)	Al18—Al9^v	2.65 (3)
Ru5—Al9^vii	2.66 (2)	Al18—Ru7^xx	2.67 (2)
Ru5—Al30	2.76 (3)	Al18—Al30^v	2.71 (3)
Ru6—Al56	2.370 (15)	Al18—Al54^v	2.72 (3)
Ru6—Al24	2.445 (19)	Al18—Al25	2.79 (3)
Ru6—Al29	2.52 (3)	Al18—Al39^v	2.82 (2)
Ru6—Al26	2.54 (2)	Al19—Ru9^xxi	2.45 (2)
Ru6—Al32	2.53 (3)	Al19—Al47	2.55 (3)
Ru6—Al36	2.53 (2)	Al19—Al58^xiv	2.77 (5)
Ru6—Al7	2.58 (2)	Al19—Al51	2.79 (4)
Ru6—Al51	2.58 (4)	Al20—Al27	2.51 (7)
Ru7—Al13^vi	2.30 (3)	Al20—Ru8^xx	2.52 (3)
Ru7—Al16^vii	2.34 (3)	Al20—Ru8^v	2.52 (3)
Ru7—Al38^viii	2.40 (3)	Al20—Al34	2.57 (4)
Ru7—Al30	2.44 (2)	Al20—Al34^i	2.57 (4)
Ru7—Al58^ix	2.47 (4)	Al20—Al9^v	2.59 (4)
Ru7—Al46^iv	2.48 (3)	Al20—Al9^xx	2.59 (4)
Ru7—Al25^vi	2.57 (2)	Al20—Al21^v	2.83 (5)
Ru7—Al43^v	2.56 (2)	Al21—Al3^vi	2.47 (3)
Ru7—Al18^vi	2.67 (2)	Al21—Al3^v	2.47 (3)
Ru8—Al27^v	2.40 (3)	Al21—Al6^iv	2.57 (4)
Ru8—Al55	2.41 (4)	Al21—Al20^v	2.83 (5)
Ru8—Al52	2.45 (4)	Al21—Al35^v	2.79 (3)
Ru8—Al9	2.49 (2)	Al21—Al35^vi	2.79 (3)
Ru8—Al34^v	2.52 (2)	Al21—Ru19^iv	2.77 (3)
Ru8—Al20^v	2.52 (3)	Al21—Ru19^viii	2.77 (3)
Ru8—Al48^v	2.56 (3)	Al21—Al57	2.79 (5)
Ru8—Al28^v	2.67 (2)	Al22—Al23	2.51 (4)
Ru9—Al44	2.31 (3)	Al22—Al48	2.61 (4)
Ru9—Al19^x	2.45 (2)	Al23—Al22^i	2.51 (4)
Ru9—Al19^ii	2.45 (2)	Al23—Ru11^i	2.48 (2)
Ru9—Al5^v	2.54 (2)	Al23—Al11^i	2.71 (4)
Ru9—Al5	2.54 (2)	Al23—Al37	2.83 (5)
Ru9—Al26^x	2.56 (2)	Al24—Ru6^i	2.445 (19)
Ru9—Al26^ii	2.56 (2)	Al24—Al26^i	2.60 (3)
Ru9—Al13^v	2.66 (3)	Al24—Al26	2.60 (3)
Ru9—Al13	2.66 (3)	Al24—Al36^i	2.79 (3)
Ru10—Al40	2.31 (3)	Al24—Al36	2.79 (3)
Ru10—Al54	2.30 (3)	Al24—Ru3^xxi	2.88 (3)
Ru10—Al18^v	2.37 (2)	Al25—Al43	2.51 (3)
Ru10—Al39	2.419 (10)	Al25—Ru7^xx	2.57 (2)
Ru10—Al3^v	2.52 (2)	Al25—Al50	2.60 (4)
Ru10—Al9	2.52 (3)	Al26—Ru3^xxi	2.55 (2)
Ru10—Al1	2.53 (3)	Al26—Ru9^xxi	2.56 (2)
Ru10—Al11	2.55 (3)	Al26—Al56	2.67 (4)
Ru10—Al38	2.64 (3)	Al26—Al29	2.68 (3)
Ru11—Al22	2.36 (3)	Al26—Al53	2.74 (4)
Ru11—Al55	2.39 (4)	Al26—Al13^xxi	2.79 (3)
Ru11—Al14	2.433 (14)	Al26—Al5^xxi	2.85 (3)
Ru11—Al23	2.48 (2)	Al27—Ru8^v	2.40 (3)
Ru11—Al11	2.51 (3)	Al27—Ru8^xx	2.40 (3)
Ru11—Al48	2.51 (3)	Al27—Al28^i	2.73 (5)
Ru11—Al8	2.56 (2)	Al27—Al28	2.73 (5)
Ru11—Al33	2.65 (2)	Al27—Al48	2.77 (5)
Ru12—Al52	2.40 (5)	Al27—Al48^i	2.77 (5)
Ru12—Al42	2.41 (3)	Al28—Ru13^v	2.61 (2)
Ru12—Al59	2.45 (2)	Al28—Ru8^v	2.67 (2)
Ru12—Al31	2.42 (3)	Al28—Al45	2.66 (4)
Ru12—Al33	2.48 (2)	Al28—Al28^i	2.74 (5)
Ru12—Al12	2.49 (2)	Al28—Al2^v	2.80 (3)
Ru12—Al49	2.52 (3)	Al28—Al52^v	2.77 (5)
Ru12—Al32	2.53 (3)	Al28—Al34	2.85 (3)
Ru13—Al51	2.34 (4)	Al29—Al29^i	2.57 (7)
Ru13—Al31	2.52 (3)	Al29—Ru13^v	2.60 (3)
Ru13—Al41^v	2.53 (2)	Al29—Al47^v	2.62 (4)
Ru13—Al45^v	2.56 (2)	Al29—Al53	2.77 (5)
Ru13—Al29^v	2.60 (3)	Al29—Al45	2.89 (5)
Ru13—Al28^v	2.61 (2)	Al30—Ru7^vii	2.44 (2)
Ru13—Al42^xi	2.69 (3)	Al30—Al46^iv	2.53 (5)
Ru13—Al47	2.77 (3)	Al30—Al38^iv	2.69 (3)
Ru14—Al46	2.42 (4)	Al30—Al38^viii	2.69 (3)
Ru14—Al49^i	2.48 (4)	Al30—Al18^v	2.71 (3)
Ru14—Al49	2.48 (4)	Al30—Al18^vi	2.71 (3)
Ru14—Al53^xii	2.56 (5)	Al30—Al6^iv	2.78 (4)
Ru14—Al17	2.44 (6)	Al31—Al51	2.59 (4)
Ru14—Al47^xiii	2.66 (3)	Al31—Al42	2.64 (4)
Ru14—Al47^xi	2.66 (3)	Al31—Al52	2.65 (5)
Ru14—Al41^xii	2.70 (3)	Al31—Al4^xii	2.78 (3)
Ru15—Al58^xiv	2.32 (4)	Al32—Al36	2.76 (4)
Ru15—Al19	2.45 (2)	Al32—Al4^xii	2.76 (4)
Ru15—Al35^xii	2.45 (2)	Al32—Al32^i	2.97 (7)
Ru15—Al47	2.55 (3)	Al33—Al49	2.63 (4)
Ru15—Al49^xi	2.58 (4)	Al33—Al33^i	2.76 (5)
Ru15—Al40^xi	2.57 (3)	Al34—Ru18^v	2.32 (2)
Ru15—Al36	2.63 (3)	Al34—Ru8^v	2.52 (2)
Ru15—Al34^xii	2.68 (2)	Al34—Al35	2.54 (3)
Ru15—Al51	2.82 (4)	Al34—Ru15^xviii	2.68 (2)
Ru16—Al54^v	2.37 (3)	Al34—Al36^xviii	2.74 (3)
Ru16—Al54	2.37 (3)	Al34—Al52^v	2.73 (5)
Ru16—Al50	2.43 (4)	Al34—Al40^v	2.81 (3)
Ru16—Al50^v	2.43 (4)	Al35—Ru15^xviii	2.45 (2)
Ru16—Al25	2.55 (2)	Al35—Al57^v	2.66 (3)
Ru16—Al25^v	2.55 (2)	Al35—Ru19^xvii	2.68 (2)
Ru16—Al44	2.60 (3)	Al35—Ru18^v	2.68 (2)
Ru16—Al22	2.72 (3)	Al35—Al36^xviii	2.68 (3)
Ru16—Al22^v	2.72 (3)	Al35—Al21^v	2.79 (3)
Ru16—Al14	2.92 (4)	Al35—Al5^xvii	2.85 (3)
Ru17—Al37	2.52 (3)	Al36—Al4^xii	2.39 (3)
Ru17—Al25^i	2.48 (2)	Al36—Ru18^xi	2.45 (3)
Ru17—Al25	2.48 (2)	Al36—Al51	2.63 (4)
Ru17—Al15	2.52 (4)	Al36—Al35^xii	2.68 (3)
Ru17—Al22^i	2.61 (3)	Al36—Al34^xii	2.74 (3)
Ru17—Al22	2.61 (3)	Al36—Al2^xi	2.75 (3)
Ru17—Al10	2.63 (3)	Al37—Al1^i	2.68 (3)
Ru17—Al43	2.68 (3)	Al37—Al50^i	2.68 (4)
Ru17—Al50	2.78 (4)	Al37—Al50	2.68 (4)
Ru17—Al50^i	2.78 (4)	Al37—Ru19^i	2.75 (2)
Ru18—Al34^vi	2.32 (2)	Al38—Ru7^xxii	2.40 (3)
Ru18—Al34^v	2.32 (2)	Al38—Al30^iv	2.69 (3)
Ru18—Al2	2.39 (3)	Al38—Al58^xxiii	2.76 (5)
Ru18—Al36^xi	2.45 (3)	Al39—Ru10^iv	2.419 (10)
Ru18—Al36^xv	2.45 (3)	Al39—Al1^iv	2.61 (3)
Ru18—Al57	2.48 (4)	Al39—Al3^xvi	2.73 (2)
Ru18—Al21	2.64 (3)	Al39—Al3^v	2.73 (2)
Ru18—Al35^vi	2.68 (2)	Al39—Al18^xvi	2.82 (2)
Ru18—Al35^v	2.68 (2)	Al39—Al18^v	2.82 (2)
Ru19—Al1	2.38 (3)	Al40—Ru15^xi	2.57 (3)
Ru19—Al16	2.36 (3)	Al40—Al55	2.68 (4)
Ru19—Al3^xvi	2.46 (2)	Al40—Al34^v	2.81 (3)
Ru19—Al5	2.49 (2)	Al40—Al3^v	2.84 (3)
Ru19—Al50	2.50 (4)	Al41—Ru13^v	2.53 (2)
Ru19—Al15	2.61 (4)	Al41—Ru13^xx	2.53 (2)
Ru19—Al35^xvi	2.68 (2)	Al41—Al45	2.69 (5)
Ru19—Al6	2.69 (2)	Al41—Ru14^xviii	2.70 (3)
Ru19—Al37	2.75 (2)	Al41—Al47^xx	2.72 (3)
Ru19—Al57^iv	2.79 (3)	Al41—Al47^v	2.72 (3)
Ru19—Al21^iv	2.77 (3)	Al41—Al59^xviii	2.80 (5)
Ru19—Ru19^i	2.99 (2)	Al42—Al4^xii	2.42 (3)
Al1—Al6	2.58 (3)	Al42—Al59	2.51 (4)
Al1—Al39	2.61 (3)	Al42—Ru13^xi	2.69 (3)
Al1—Al37	2.68 (3)	Al43—Al25^i	2.51 (3)
Al1—Al3^xvi	2.73 (3)	Al43—Ru7^xx	2.56 (2)
Al1—Al50	2.74 (4)	Al43—Ru7^v	2.56 (2)
Al1—Al16	2.79 (4)	Al43—Al13^i	2.64 (3)
Al1—Al38	2.78 (4)	Al43—Al46^xvii	2.81 (5)
Al2—Al4^v	2.462 (19)	Al44—Al5^v	2.68 (3)
Al2—Al4^vi	2.462 (19)	Al44—Al50	2.75 (4)
Al2—Al36^xi	2.75 (3)	Al44—Al50^v	2.75 (4)
Al2—Al36^xv	2.75 (3)	Al45—Ru13^xx	2.56 (2)
Al2—Al28^vi	2.80 (3)	Al45—Ru13^v	2.56 (2)
Al2—Al28^v	2.80 (3)	Al45—Al28^i	2.66 (4)
Al3—Ru19^xvii	2.46 (2)	Al45—Al29^i	2.89 (5)
Al3—Al21^v	2.47 (3)	Al46—Ru7^xxii	2.48 (3)
Al3—Ru10^v	2.52 (2)	Al46—Ru7^iv	2.48 (3)
Al3—Ru5^v	2.61 (2)	Al46—Al30^iv	2.53 (5)
Al3—Al6^xvii	2.62 (3)	Al46—Al58^xxiv	2.65 (5)
Al3—Al18	2.63 (3)	Al46—Al58^xxiii	2.65 (5)
Al3—Al39^v	2.73 (2)	Al46—Al43^xvi	2.81 (5)
Al3—Al1^xvii	2.73 (3)	Al47—Al51	2.46 (4)
Al3—Al9^v	2.79 (3)	Al47—Ru14^xi	2.66 (3)
Al3—Al35	2.83 (3)	Al47—Al53^v	2.65 (4)
Al3—Al40^v	2.84 (3)	Al47—Al29^v	2.62 (4)
Al4—Al36^xviii	2.39 (3)	Al47—Al58^xiv	2.65 (5)
Al4—Al42^xviii	2.42 (3)	Al47—Al41^v	2.72 (3)
Al4—Al2^v	2.462 (19)	Al47—Al49^xi	2.75 (4)
Al4—Al28	2.56 (3)	Al48—Ru8^v	2.56 (3)
Al4—Al34	2.59 (2)	Al48—Al48^i	2.75 (7)
Al4—Al31^xviii	2.78 (3)	Al48—Al9^v	2.81 (4)
Al4—Al32^xviii	2.76 (4)	Al49—Al59	2.50 (4)
Al4—Al52^v	2.80 (5)	Al49—Ru15^xi	2.58 (4)
Al5—Al15	2.59 (3)	Al49—Al47^xi	2.75 (4)
Al5—Al57^iv	2.61 (3)	Al49—Al52	2.80 (5)
Al5—Al44	2.68 (3)	Al50—Al54	2.76 (4)
Al5—Al35^xvi	2.85 (3)	Al52—Al34^v	2.73 (5)
Al5—Al26^ii	2.85 (3)	Al52—Al4^v	2.80 (5)
Al6—Ru5^iv	2.41 (3)	Al52—Al28^v	2.77 (5)
Al6—Al1^i	2.58 (3)	Al53—Ru3^xxi	2.51 (5)
Al6—Al21^iv	2.57 (4)	Al53—Ru14^xviii	2.56 (5)
Al6—Al3^xvi	2.62 (3)	Al53—Al47^v	2.65 (4)
Al6—Al3^xix	2.62 (3)	Al53—Al47^xx	2.65 (4)
Al6—Ru19^i	2.69 (2)	Al53—Al26^i	2.74 (4)
Al6—Al37	2.67 (4)	Al53—Al29^i	2.77 (5)
Al6—Al30^iv	2.78 (4)	Al54—Al18^v	2.72 (3)
Al7—Ru6^i	2.58 (2)	Al56—Ru6^v	2.370 (15)
Al7—Al29^i	2.68 (4)	Al56—Al26^v	2.67 (4)
Al7—Al29	2.68 (4)	Al57—Ru3^iv	2.56 (4)
Al7—Al32	2.75 (5)	Al57—Al5^iv	2.61 (3)
Al7—Al32^i	2.75 (5)	Al57—Al5^viii	2.61 (3)
Al7—Al24	2.71 (5)	Al57—Al35^vi	2.66 (3)
Al8—Al48	2.54 (5)	Al57—Al35^v	2.66 (3)
Al8—Al48^i	2.54 (5)	Al57—Al15^iv	2.68 (5)
Al8—Ru11^i	2.56 (2)	Al57—Ru19^viii	2.79 (3)
Al8—Al23	2.72 (6)	Al57—Ru19^iv	2.79 (3)
Al9—Al55	2.55 (4)	Al58—Ru15^xxv	2.32 (4)
Al9—Al20^v	2.59 (4)	Al58—Ru7^ix	2.47 (4)
Al9—Al18^v	2.65 (3)	Al58—Al13^xxvi	2.59 (5)
Al9—Al40	2.74 (3)	Al58—Al46^xxvii	2.65 (5)
Al9—Al3^v	2.79 (3)	Al58—Al47^xxv	2.65 (5)
Al9—Al48^v	2.81 (4)	Al58—Al38^xxviii	2.76 (5)
Al9—Al10^v	2.83 (3)	Al58—Al19^xxv	2.77 (5)
Al10—Ru5^v	2.50 (3)	Al59—Ru12^i	2.45 (2)
Al10—Al9^v	2.83 (3)	Al59—Al42^i	2.51 (4)
Al10—Al9^xx	2.83 (3)	Al59—Al49^i	2.50 (4)
Al11—Al55	2.51 (4)	Al59—Al41^xii	2.80 (5)
Al11—Al23	2.71 (4)

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