AFLOW Prototype: A_hP4_194_f
Prototype | : | C |
AFLOW prototype label | : | A_hP4_194_f |
Strukturbericht designation | : | None |
Pearson symbol | : | hP4 |
Space group number | : | 194 |
Space group symbol | : | $\text{P6}_{3}\text{/mmc}$ |
AFLOW prototype command | : | aflow --proto=A_hP4_194_f --params=$a$,$c/a$,$z_{1}$ |
idealstructure, where the nearest-neighbor environment of each atom is the same as in diamond, is achieved when we take $c/a = \sqrt{8/3}$ and $z_{1}=1/16$. Alternatively, we can take $z_{1}=3/16$, in which case the origin is at the center of a C–C bond aligned in the [0001] direction. When $z_{1}=0$ this structure becomes a set of graphitic sheets, but not true hexagonal graphite (A9).
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+\frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{C} \\ \mathbf{B}_{2}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{C} \\ \mathbf{B}_{3}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{C} \\ \mathbf{B}_{4}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \left(\frac12 - z_{1}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \text{C} \\ \end{array} \]