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Orthorhombic Co₄Al₁₃ Structure (Approximate Quasicrystal): A13B4_oP102_31_17a11b_8a2b-001

Orthorhombic · space group Pmn21 (No. 31) · Pearson oP102

Symmetry elements and Wyckoff positions (interactive)

Orthorhombic Co₄Al₁₃ Structure (Approximate Quasicrystal): A13B4_oP102_31_17a11b_8a2b-001 in Pmn21

Setting

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Model atom x

x = 0.10, y = 0.17, z = 0.08

Unit cell

Lattice constants: a = 8.158 Å, b = 12.342 Å, c = 14.452 Å; α = 90.00°, β = 90.00°, γ = 90.00°
Cell volume: 1455.1 Å³
Atoms in the conventional cell: 102 (Al 78, Co 24)
Formula units Z: 6
Pearson symbol: oP102 — orthorhombic, primitive lattice, 102 atoms per conventional cell
Symmetry operations: 4 per cell

Crystallographic sites

Site	Element	Wyckoff	Multiplicity	x	y	z
Al10	Al	2a	2	0.0000	0.4010	0.1491
Al1	Al	2a	2	0.0000	0.9945	0.8151
Al11	Al	2a	2	0.0000	0.6837	0.6749
Al12	Al	2a	2	0.0000	0.5900	0.3960
Al13	Al	2a	2	0.0000	0.5271	0.0054
Al14	Al	2a	2	0.0000	0.5986	0.2149
Al15	Al	2a	2	0.0000	0.7111	0.9668
Al16	Al	2a	2	0.0000	0.1047	0.2380
Al17	Al	2a	2	0.0000	0.4179	0.5881
Al2	Al	2a	2	0.0000	0.0914	0.9569
Al3	Al	2a	2	0.0000	0.9053	0.6226
Al4	Al	2a	2	0.0000	0.9085	0.4431
Al5	Al	2a	2	0.0000	0.1394	0.6728
Al6	Al	2a	2	0.0000	0.8113	0.1564
Al7	Al	2a	2	0.0000	0.8092	0.8360
Al8	Al	2a	2	0.0000	0.2520	0.4140
Al9	Al	2a	2	0.0000	0.4070	0.8520
Co29	Co	2a	2	0.0000	0.8978	0.0000
Co30	Co	2a	2	0.0000	0.0901	0.5114
Co31	Co	2a	2	0.0000	0.1977	0.8250
Co32	Co	2a	2	0.0000	0.7720	0.3167
Co33	Co	2a	2	0.0000	0.5986	0.8248
Co34	Co	2a	2	0.0000	0.4119	0.3137
Co35	Co	2a	2	0.0000	0.7309	0.5180
Co36	Co	2a	2	0.0000	0.2877	0.0076
Al18	Al	4b	4	0.2135	0.2138	0.0996
Al19	Al	4b	4	0.2138	0.9020	0.2831
Al20	Al	4b	4	0.2401	0.0829	0.4088
Al21	Al	4b	4	0.2534	0.2550	0.9172
Al22	Al	4b	4	0.2251	0.9810	0.0935
Al23	Al	4b	4	0.2214	0.2229	0.5500
Al24	Al	4b	4	0.2259	0.5885	0.5422
Al25	Al	4b	4	0.2244	0.2946	0.7352
Al26	Al	4b	4	0.2291	0.4220	0.4252
Al27	Al	4b	4	0.2133	0.5174	0.7338
Al28	Al	4b	4	0.2319	0.2763	0.2849
Co37	Co	4b	4	0.2257	0.9099	0.7346
Co38	Co	4b	4	0.2181	0.5969	0.0984

The multiplicity and the Wyckoff letter say how many copies of the site the group makes in one cell and on which kind of symmetry element the site sits; the 102 atoms drawn above are these sites multiplied by all 4 operations. Press Wyckoff under Colour to see the sites, and tick a symmetry element on the left to see which atoms lie on it.

How to read the label

A13B4_oP102_31_17a11b_8a2b-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol oP102, then the space-group number 31, then the Wyckoff letters occupied by each element in turn (Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Al: 2a; Co: 2a; Co: 2a; Co: 2a; Co: 2a; Co: 2a; Co: 2a; Co: 2a; Co: 2a; Al: 4b; Al: 4b; Al: 4b; Al: 4b; Al: 4b; Al: 4b; Al: 4b; Al: 4b; Al: 4b; Al: 4b; Al: 4b; Co: 4b; Co: 4b). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Note: Approximate Quasicrystal.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A13B4_oP102_31_17a11b_8a2b-001 (M. J. Mehl et al., Comput. Mater. Sci. 136, S1 (2017); D. Hicks et al., ibid. 161, S1 (2019) and 199, 110450 (2021); S. Eckert et al., ibid. 240, 112988 (2024)). Symmetry elements, Wyckoff assignment and the diagram are computed on this page from the group operations.

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