Hexagonal Graphite (A9) Crystal Structure: A_hP4_194_bc
| Prototype | : | C |
| AFLOW prototype label | : | A_hP4_194_bc |
| Strukturbericht designation | : | $A9$ |
| Pearson symbol | : | hP4 |
| Space group number | : | 194 |
| Space group symbol | : | $\mbox{P6}_{3}\mbox{/mmc}$ |
| AFLOW prototype command | : | aflow --proto=A_hP4_194_bc --params=$a,c/a$ |
Other compounds with this structure
- LiB
- According to (Wyckoff, 1963), hexagonal graphite may be either flat, space group P63/mmc (#194) or buckled, space group P63mc (#186). If it is buckled, the buckling parameter is small, less than 1/20 of the
c
parameter of the hexagonal unit cell. We will assign the A9 Strukturbericht designation to the unbuckled structure. Experimentally, a rhombohedral (R3m) graphite structure is also observed.
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:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &\frac14 \, \mathbf{a}_{3}& = &\frac14 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{C I} \\ \mathbf{B}_{2}& = &\frac34 \, \mathbf{a}_{3}& = &\frac34 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{C I} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{C II} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{C II} \\ \end{array} \]References
- P. Trucano and R. Chen, Structure of graphite by neutron diffraction, Nature 258, 136–137 (1975), doi:10.1038/258136a0.
- R. W. G. Wyckoff, Crystal Structures Vol. 1 (Wiley, 1963), 2nd edn.
Found in
- R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).