γ-Se ($A8$) Structure: A_hP3_152_a-001
Other compounds with this structure
Te, SeTe, Se$_{3}$Te
- There are a variety of naming conventions for selenium:
- (Cherin, 1967) refers to this structure as
trigonal selenium.
(Donohue, 1982) refers to it as the $\alpha$–Se structure, calling what we designate $\alpha$–Se and $\beta$–Se ($A_{l}$) asmonoclinic $\alpha$
andmonoclinic $\beta$,
respectively. - When $x=1/3$ this reduces to the $A_{i}$ ($\beta$–Po) or $A10$ ($\alpha$–Hg) structure.
- If, in addition, $c=\sqrt{6} \, a$, then the structure becomes fcc ($A1$).
- On the other hand, if $c=\sqrt{3/2} \, a$, then the structure becomes simple cubic ($A_{h}$).
- This structure can also be found in the enantiomorphic space group $P3_{2}12$ #153.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{1} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3a) | Se I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{2}+\frac{2}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{1} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{2}{3}c \,\mathbf{\hat{z}}$ | (3a) | Se I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (3a) | Se I |
References
- P. Cherin and P. Unger, The crystal structure of trigonal selenium, Inorg. Chem. 6, 1589–1591 (1967), doi:10.1021/ic50054a037.
Found in
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=A_hP3_152_a --params=$a,c/a,x_{1}$