Wurtzite (ZnS, $B4$) Structure: AB_hP4_186_b_b-001
| Prototype | SZn |
| AFLOW prototype label | AB_hP4_186_b_b-001 |
| Strukturbericht designation | $B4$ |
| Mineral name | wurtzite |
| ICSD | 67453 |
| CCDC | 1629447 |
| Pearson symbol | hP4 |
| Space group number | 186 |
| Space group symbol | $P6_3mc$ |
| AFLOW prototype command |
aflow --proto=AB_hP4_186_b_b-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}$ |
Other compounds with this structure
β-AgI, AlN, BN, BeO, CdS, CdSe, CdSe, CuH, β-CuI, GaN, InN, MgTe, γ-MnS, γ-MnSe, SiC, ZnO, ZnSe
- This is the hexagonal analog of zincblende ($B3$), i.e. the stacking of the ZnS dimers along the (0001) direction is ABABAB… Replacing both the Zn and S atoms by C (or Si) gives the hexagonal diamond structure. The
ideal
structure, where the nearest-neighbor environment of each atom is the same as in zincblende, is achieved when we take $c/a=\sqrt{8/3}$ and $z_{2}=1/8$. In the extreme case $z_{2}=1/2$ this structure becomes the BN ($B_{k}$) structure. - Space group $P6_{3}$ #186 is polar, so there is no fixed origin for the $z$ axis. We have arbitrarily chosen the $z_{2}$ parameter for the zinc atoms to be zero.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (2b) | S I |
| $\mathbf{B_{2}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | S I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2b) | Zn I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Zn I |
References
- E. H. Kisi and M. M. Elcombe, $u$ parameters for the wurtzite structure of ZnS and ZnO using powder neutron diffraction, Acta Crystallogr. Sect. C 45, 1867–1870 (1989), doi:10.1107/S0108270189004269.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
First cited in
- 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)
Geometry files
Prototype Generator
aflow --proto=AB_hP4_186_b_b --params=$a,c/a,z_{1},z_{2}$