Hexagonal ω ($C32$) Structure: AB2_hP3_191_a_d-001
| Prototype | AlB$_{2}$ |
| AFLOW prototype label | AB2_hP3_191_a_d-001 |
| Strukturbericht designation | $C32$ |
| Mineral name | ω-phase |
| ICSD | 99639 |
| Pearson symbol | hP3 |
| Space group number | 191 |
| Space group symbol | $P6/mmm$ |
| AFLOW prototype command |
aflow --proto=AB2_hP3_191_a_d-001
--params=$a, \allowbreak c/a$ |
Other compounds with this structure
AgB$_{2}$, AuB$_{2}$, BaGa$_{2}$, BaSi$_{2}$, Be$_{2}$Hf, Be$_{2}$Zr, CaGa$_{2}$, CrB$_{2}$, DyGa$_{2}$, ErB$_{2}$, ErGa$_{2}$, EuGa$_{2}$, GdGa$_{2}$, HfB$_{2}$, HgLa$_{2}$, HoB$_{2}$, HoGa$_{2}$, LaCu$_{2}$, LaGa$_{2}$, LuB$_{2}$, MgB$_{2}$, MnB$_{2}$, MoB$_{2}$, NaHg$_{2}$, NbB$_{2}$, NdGa$_{2}$, OsB$_{2}$, PrGa$_{2}$, PuB$_{2}$, PuB$_{2}$, RuB$_{2}$, ScB$_{2}$, SmGa$_{2}$, SrGa$_{2}$, TaB$_{2}$, TbB$_{2}$, TbGa$_{2}$, ThAg$_{2}$, ThAl$_{2}$, ThCd$_{2}$, ThCu$_{2}$, ThNi$_{2}$, ThZn$_{2}$, TiU2$_{2}$, TlB$_{2}$, UB$_{2}$, $\beta$-UGa$_{2}$, UHg$_{2}$, USi$_{2}$, UZr$_{2}$, VB$_{2}$, YGa$_{2}$, ZrB$_{2}$
- 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).
- Many $\omega$ phase intermetallic alloys are disordered, we list some of the ordered structures here.
- 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 $c/a = 1/\sqrt{3}$ the Al-Al distance along (001) is the same as the B-B distance in the plane, and the B-B distance in the (001) direction. This value 0.577 is close to the value $\sqrt{3/8} \, (≈ 0.612)$ 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.
- In the current sample (Burkhardt, 2004) the aluminum (1a) site has 10% vacancies.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | B I |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | B I |
References
- U. Burkhardt, V. Gurin, F. Haarmann, H. Borrmann, and W. Schnelle, On the electronic and structural properties of aluminum diboride Al$_{0.9}$B$_2$, J. Solid State Chem. 177, 389–394 (2004), doi:10.1016/j.jssc.2002.12.001.
Found in
- S. K. Sikka, Y. K. Vohra, and R. Chidambaram, Omega Phase in Materials, Prog. Mater. Sci. 27, 245–310 (1982), doi:10.1016/0079-6425(82)90002-0.
Prototype Generator
aflow --proto=AB2_hP3_191_a_d --params=$a,c/a$