Hexagonal Graphite ($A9$) Structure: A_hP4_194_bc-001
| Prototype | C |
| AFLOW prototype label | A_hP4_194_bc-001 |
| Strukturbericht designation | $A9$ |
| Mineral name | graphite |
| ICSD | 76767 |
| CCDC | 1637294 |
| Pearson symbol | hP4 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=A_hP4_194_bc-001
--params=$a, \allowbreak c/a$ |
Other compounds with this structure
LiB
- According to (Wyckoff, 1963), hexagonal graphite may be either flat, space group $P6_{3}/mmc$ #194 (this structure) or buckled, space group $P6_{3}mc$ #186. We assign the $A9$ Strukturbericht designation to the unbuckled structure shown here.
- Experimentally, a rhombohedral ($R\overline{3}m$) graphite structure is also observed.
- Carbon can also be found in nature as cubic diamond ($A4$), lonsdaleite (hexagonal diamond}, and buckminsterfullerene (C$_{60}$).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2b) | C I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2b) | C I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | C II |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | C II |
References
- P. Trucano and R. Chen, Structure of graphite by neutron diffraction, Nature 258, 136–137 (1975), doi:10.1038/258136a0.
- R. G. W. Wyckoff, Crystal Structure, vol. 1 (Interscience, New York, London, Sydney, 1963).
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
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_hP4_194_bc --params=$a,c/a$