The C32 (ideal omega) Structure

Last modified 11 April 2001

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This is the hexagonal omega phase. There is also a trigonal omega (C6) phase.

For more details about the omega phase and materials which form in the omega phase, see S.K. Sikka, Y.K. Vohra, and R. Chidambaram, Progress in Materials Science 27, 245-310 (1982). Most omega phase intermetallic alloys are disordered.

One interesting thing about this structure is that the B-B distance is smaller than the Al-B distance for every c/a ratio. So if c/a is small enough the structure looks like a set of inter-penetrating Boron triangular planes and Aluminum chains. If c/a = 3^-1/3 the Al-Al distance along (001) is the same as the B-B distance in the plane, and, for that matter, the B-B distance in the (001) direction. This value (0.577) is close to the value (3/8)^1/2 (0.612) where the trigonal omega phase can transform to the body-centered cubic (A2) lattice, which probably explains the close connection between the omega and bcc phases.

The other interesting thing about this structure is that the Boron atoms form graphite-like sheets.

Prototype: AlB₂
Pearson Symbol: hP3
Strukturbericht Designation: C32
Space Group: P6/mmm (Cartesian and lattice coordinate listings available)
Number: 191
Other systems with this structure: Ti (metastable), MgB₂, Be₂Hf, CeHg₂
Primitive Vectors:
- A₁ = ½ a X - ½ 3^½ a Y
- A₂ = ½ a X + ½ 3^½ a Y
- A₃ = c Z
Basis Vectors:
- B₁ = 0 (Al)
- B₂ = 1/3 A₁ + 2/3 A₂ + 1/2 A₃ = 1/2 a X + 3^-½/2 a Y + 1/2 c Z (B)
- B₃ = 2/3 A₁ + 1/3 A₂ + 1/2 A₃ = 1/2 a X - 3^-½/2 a Y + 1/2 c Z (B)

See these vectors in a better notation.

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