The hexagonal ω (C32) Structure
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 This is the hexagonal ω phase. There is also a trigonal ω (C6) phase.
 For more details about the ω phase and materials
which form in the ω phase, see S.K. Sikka, Y.K. Vohra,
and R. Chidambaram, Progress in Materials Science
27, 245310 (1982). Most ω phase
intermetallic alloys are disordered.
 One interesting thing about this structure is that the
BB distance is smaller than the AlB distance for every c/a
ratio. So if c/a is small enough the structure looks like a
set of interpenetrating Boron triangular planes and Aluminum
chains. If c/a = 3^{1/3} the AlAl
distance along (001) is the same as the BB distance in the
plane, and, for that matter, the BB distance in the (001)
direction. This value (0.577) is close to the value
(3/8)^{1/2} (0.612) where the trigonal ω phase can transform to
the bodycentered cubic (A2) lattice,
which probably explains the close connection between the
ω and bcc phases.
 The other interesting thing about this structure is that
the Boron atoms form graphitelike
sheets. For this reason, as of 7 Feb 2003, we've moved
this structure into the sp^{2} section of
the Carbon and Related Structures page.
 Prototype: AlB_{2}
 Pearson Symbol: hP3
 Strukturbericht Designation: C32
 Space Group: P6/mmm (Cartesian and lattice coordinate listings
available)
 Number: 191

Reference: Villars and
Calvert, Pearson's Handbook, Vol. I, p. 656.
 Other systems with this structure: Ti (metastable),
MgB_{2}, Be_{2}Hf, CeHg_{2}

Primitive Vectors:
A_{1} 
_{ }=_{ } 
½ a X  ½
3^{1/2} a
Y_{ } 
A_{2} 
_{ }=_{ } 
½ a X + ½
3^{1/2} a
Y_{ } 
A_{3} 
_{ }=_{ } 
c
Z_{ }^{ } 

Basis Vectors:
B_{1} 
_{ }=_{ } 

_{ }0_{ } 

_{ }(Al)_{ } 
_{ }(1a) 
B_{2} 
_{ }=_{ } 
1/3 A_{1} + 2/3
A_{2} + ½
A_{3} 
_{ }=_{ } 
½_{ }aX +
12^{½} a Y + ½
c Z 
_{ }(B)_{ } 
_{ }(2d) 
B_{3} 
_{ }=_{ } 
2/3 A_{1} + 1/3
A_{2} + ½
A_{3} 
_{ }=_{ } 
½ a_{ }X 
12^{½} a Y + ½
c Z 
_{ }(B)_{ } 
_{ }(2d) 
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