Lonsdaleite (Hexagonal Diamond) Structure: A_hP4_194_f-001
| Prototype | C |
| AFLOW prototype label | A_hP4_194_f-001 |
| Mineral name | lonsdaleite |
| ICSD | 66465 |
| Pearson symbol | hP4 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=A_hP4_194_f-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}$ |
Other compounds with this structure
Ge (hexagonal), H (hexagonal), N (hexagonal), O (hexagonal), Si (hexagonal)
- Hexagonal diamond was named lonsdaleite in honor of Kathleen Lonsdale.
- This structure is related to the hcp ($A3$) structure 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 ($A9$), as the stacking differs.
- (Yoshiasa, 2003) does not have an ICSD entry for Lonsdaleite, so we use the one provided for (Ownby, 1992).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (4f) | C I |
| $\mathbf{B_{2}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | C I |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (4f) | C I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | C I |
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.
- P. D. Ownby, X. Yang, and J. Liu, Calculated X-ray Diffraction Data for Diamond Polytypes, J. Am. Ceram. Soc. 75, 1876–1883 (1992), doi:10.1111/j.1151-2916.1992.tb07211.x.
Prototype Generator
aflow --proto=A_hP4_194_f --params=$a,c/a,z_{1}$