Cinnabar ($B9$) Structure: AB_hP6_154_a_b

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Prototype : HgS
AFLOW prototype label : AB_hP6_154_a_b
Strukturbericht designation : $B9$
Pearson symbol : hP6
Space group number : 154
Space group symbol : $\mbox{P3}_{2}\mbox{21}$
AFLOW prototype command : aflow --proto=AB_hP6_154_a_b
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$


Other compounds with this structure

  • HgO

Trigonal 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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& x_{1} \, \mathbf{a}_{1} + \frac23 \, \mathbf{a}_{3}& =& \frac12 \, x_{1} \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, x_{1} \, a \, \mathbf{\hat{y}} +\frac23 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \mbox{Hg} \\ \mathbf{B}_{2} & =& x_{1} \, \mathbf{a}_{2} + \frac13 \, \mathbf{a}_{3}& =& \frac12 \, x_{1} \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, x_{1} \, a \, \mathbf{\hat{y}} +\frac13 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \mbox{Hg} \\ \mathbf{B}_{3} & =& - x_{1} \, \mathbf{a}_{1} - x_{1} \, \mathbf{a}_{2}& =& - x_{1} \, a \, \mathbf{\hat{x}}& \left(3a\right) & \mbox{Hg} \\ \mathbf{B}_{4} & =& x_{2} \, \mathbf{a}_{1} + \frac16 \, \mathbf{a}_{3}& =& \frac12 \, x_{2} \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, x_{2} \, a \, \mathbf{\hat{y}} +\frac16 \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{S} \\ \mathbf{B}_{5} & =& x_{2} \, \mathbf{a}_{2} + \frac56 \, \mathbf{a}_{3}& =& \frac12 \, x_{2} \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, x_{2} \, a \, \mathbf{\hat{y}} +\frac56 \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{S} \\ \mathbf{B}_{6} & =& - x_{2} \, \mathbf{a}_{1} - x_{2} \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& - x_{2} \, a \, \mathbf{\hat{x}} + \frac12 \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{S} \\ \end{array} \]

References

  • P. Auvray and F. Genet, Affinement de la structure cristalline du cinabre alpha–HgS, Bull. Soc. fr. Minéral. Crystallogr. 96, 218–219 (1973).

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_hP6_154_a_b --params=

Species:

Running:

Output: