Hexagonal Graphite ($A9$) Crystal Structure: A_hP4_194_bc

Picture of Structure; Click for Big Picture
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).

Geometry files


Prototype Generator

aflow --proto=A_hP4_194_bc --params=

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