Hexagonal $\omega$ ($C32$) Structure: AB2_hP3_191_a_d

Picture of Structure; Click for Big Picture
Prototype : AlB2
AFLOW prototype label : AB2_hP3_191_a_d
Strukturbericht designation : $C32$
Pearson symbol : hP3
Space group number : 191
Space group symbol : $\mbox{P6/mmm}$
AFLOW prototype command : aflow --proto=AB2_hP3_191_a_d
--params=
$a$,$c/a$


Other compounds with this structure

  • Ti (metastable), MgB2, Be2Hf, CeHg2, AgB2, Ag2Th, Al2Th, AuB2, B2Cr, B2Er, B2Hf, B2Ho, B2Lu, B2Mg, B2Mn, B2Mo, B2Nb, B2Os, B2Pu, B2Pu, B2Ru, B2Sc, B2Ta, B2Tb, B2Tl, B2U, B2V, B2Zr, BaGa2, BaSi2, Be2Hf, Be2Zr, CaGa2, Cd2Th, Cu2La, Cu2Th, DyGa2, ErGa2, EuGa2, Ga2Gd, Ga2Ho, Ga2La, Ga2Nd, Ga2Pr, Ga2Sm, Ga2Sr, Ga2Tb, Ga2U, Ga2Y, HgLa2, Hg2Na, Hg2U, Ni2Th, ThZn2, TiU22

  • 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 (Sikka, 1982). Most $\omega$ phase intermetallic alloys are disordered. In this structure the B–B distance is smaller than the Al–B distance for every $c/a$ ratio. If $c/a$ is small enough the structure looks like a set of inter-penetrating boron triangular planes and aluminium chains. If $c/a= 1/\sqrt3$ 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 $\sqrt{3/8} \left(\approx 0.612\right)$ 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.

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Al} \\ \mathbf{B}_{2} & =&\frac13 \mathbf{a}_{1}+ \frac23 \mathbf{a}_{2}+ \frac12 \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \mbox{B} \\ \mathbf{B}_{3} & =&\frac23 \mathbf{a}_{1}+ \frac13 \mathbf{a}_{2}+ \frac12 \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \mbox{B} \\ \end{array} \]

References

  • U. Burkhardt, V. Gurin, F. Haarmann, H. Borrmann, W. Schnelle, A. Yaresko, and Y. Grin, On the electronic and structural properties of aluminum diboride Al0.9B2, J. Solid State Chem. 177, 389–394 (2004), doi:10.1016/j.jssc.2002.12.001.

Geometry files


Prototype Generator

aflow --proto=AB2_hP3_191_a_d --params=

Species:

Running:

Output: