Wurtzite (ZnS, $B4$) Structure: AB_hP4_186_b_b

Picture of Structure; Click for Big Picture
Prototype : ZnS
AFLOW prototype label : AB_hP4_186_b_b
Strukturbericht designation : $B4$
Pearson symbol : hP4
Space group number : 186
Space group symbol : $\mbox{P6}_{3}\mbox{mc}$
AFLOW prototype command : aflow --proto=AB_hP4_186_b_b
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$


Other compounds with this structure

  • ZnO, SiC, AlN, CdSe, BN, C (hexagonal diamond)

  • This is the hexagonal analog of the zincblende lattice, i.e. the stacking of the ZnS dimers 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 Bk (BN) structure. Note that we have arbitrarily chosen the $z_{1}$ parameter for the zinc atoms to be zero.

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:

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

References

  • E. H. Kisi and M. M. Elcombe, u parameters for the wurtzite structure of ZnS and ZnO using powder neutron diffraction, Acta Crystallogr. 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).

Geometry files


Prototype Generator

aflow --proto=AB_hP4_186_b_b --params=

Species:

Running:

Output: