Lonsdaleite (Hexagonal Diamond) Structure: A_hP4_194_f

Picture of Structure; Click for Big Picture
Prototype : C
AFLOW prototype label : A_hP4_194_f
Strukturbericht designation : None
Pearson symbol : hP4
Space group number : 194
Space group symbol : $\mbox{P6}_{3}\mbox{/mmc}$
AFLOW prototype command : aflow --proto=A_hP4_194_f
--params=
$a$,$c/a$,$z_{1}$


Other elements with this structure

  • Si (Hexagonal)

  • Hexagonal diamond was named lonsdaleite in honor of Kathleen Lonsdale. This is related to the hcp (A3) lattice in the same way that diamond (A4) is related to the fcc lattice (A1). It can also be obtained from wurtzite (B4) by replacing both the Zn and S atoms by carbon. The ideal structure, 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).

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:

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

References

  • A. Yoshiasa, Y. Murai, O. Ohtaka, and T. Katsura, Detailed Structures of Hexagonal Diamond (lonsdaleite) and Wurtzite–type BN, Jpn. J. Appl. Phys 42, 1694–1704 (2003), doi:10.1143/JJAP.42.1694.

Geometry files


Prototype Generator

aflow --proto=A_hP4_194_f --params=

Species:

Running:

Output: