Buckled Graphite Structure: A_hP4_186_ab

Picture of Structure; Click for Big Picture
Prototype : C
AFLOW prototype label : A_hP4_186_ab
Strukturbericht designation : None
Pearson symbol : hP4
Space group number : 186
Space group symbol : $\mbox{P6}_{3}\mbox{mc}$
AFLOW prototype command : aflow --proto=A_hP4_186_ab
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$


  • 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. In the pictures above we give $z_{2}$ the exaggerated value of $0.1$ When $z_{2} = 0$, this structure is equivalent to unbuckled (A9) hexagonal graphite.

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &z_{1} \, \mathbf{a}_{3}& = &z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{C I} \\ \mathbf{B}_{2}& = &\left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{C I} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{C II} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{C II} \\ \end{array} \]

References

Found in

  • R. W. G. Wyckoff, Crystal Structures Vol. 1 (Wiley, 1963), 2nd edn., pp. 254.

Geometry files


Prototype Generator

aflow --proto=A_hP4_186_ab --params=

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