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Crystal Lab › Prototype structures › Hexagonal

Al₂₃V₄

Hexagonal · space group P63/mmc (No. 194) · Pearson hP54

Symmetry elements and Wyckoff positions (interactive)

Al₂₃V₄ in P63/mmc

Setting
Loading the group…
x = 0.10, y = 0.17, z = 0.08

Unit cell

Lattice constants
a = 7.692 Å, b = 7.692 Å, c = 17.040 Å; α = 90.00°, β = 90.00°, γ = 120.00°
Cell volume
873.1 ų
Atoms in the conventional cell
54 (V 8, Al 46)
Formula units Z
2
Pearson symbol
hP54 — hexagonal / trigonal, primitive lattice, 54 atoms per conventional cell
Symmetry operations
24 per cell

Crystallographic sites

SiteElementWyckoffMultiplicityxyz
V6V2a20.00000.00000.0000
Al1Al4f40.33330.66670.6170
Al2Al6h60.12600.25200.2500
V7V6h60.78100.56200.2500
Al3Al12k120.21300.42600.0290
Al4Al12k120.12400.24800.6180
Al5Al12k120.45500.91000.1660

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 54 atoms drawn above are these sites multiplied by all 24 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

A23B4_hP54_194_fh3k_ah-001: the stoichiometry comes first (A, B, C… are the elements in alphabetical order of their site labels), then the Pearson symbol hP54, then the space-group number 194, then the Wyckoff letters occupied by each element in turn (V: 2a; Al: 4f; Al: 6h; V: 6h; Al: 12k; Al: 12k; Al: 12k). Two structures with the same label are the same arrangement with different cell parameters or coordinates.

Source

Coordinates and cell from the AFLOW Encyclopedia of Crystallographic Prototypes, entry A23B4_hP54_194_fh3k_ah-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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