Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A_hP4_186_ab

  • 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)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

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 : $\text{P6}_{3}\text{mc}$
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:

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

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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