S–II Structure: A_hP9_154_bc

Picture of Structure; Click for Big Picture
Prototype : S
AFLOW prototype label : A_hP9_154_bc
Strukturbericht designation : None
Pearson symbol : hP9
Space group number : 154
Space group symbol : $P3_{2}21$
AFLOW prototype command : aflow --proto=A_hP9_154_bc
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$y_{2}$,$z_{2}$


  • The S–II phase is found when sulfur is heated and pressurized above 3 GPa. This data was taken at 5.8 GPa and 800 K.

Trigonal 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} & = & x_{1} \, \mathbf{a}_{1} + \frac{1}{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{S I} \\ \mathbf{B}_{2} & = & x_{1} \, \mathbf{a}_{2} + \frac{5}{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{5}{6}c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{S I} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{S I} \\ \mathbf{B}_{4} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{2}+y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{2}+y_{2}\right)a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{S II} \\ \mathbf{B}_{5} & = & -y_{2} \, \mathbf{a}_{1} + \left(x_{2}-y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{2}{3} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{2}-y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \left(\frac{2}{3} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{S II} \\ \mathbf{B}_{6} & = & \left(-x_{2}+y_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{3} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(-x_{2}+\frac{1}{2}y_{2}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{3} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{S II} \\ \mathbf{B}_{7} & = & y_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{2}+y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{2}-y_{2}\right)a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{S II} \\ \mathbf{B}_{8} & = & \left(x_{2}-y_{2}\right) \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{3} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{2}-y_{2}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{3} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{S II} \\ \mathbf{B}_{9} & = & -x_{2} \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{2}{3} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(-x_{2}+\frac{1}{2}y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{2}a \, \mathbf{\hat{y}} + \left(\frac{2}{3} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(6c\right) & \mbox{S II} \\ \end{array} \]

References

  • O. Degtyareva, E. Gregoryanz, M. Somayazulu, P. Dera, H. Mao, and R. J. Hemley, Novel chain structures in group VI elements, Nat. Mater. 4, 152–155 (2005), doi:10.1038/nmat1294.

Geometry files


Prototype Generator

aflow --proto=A_hP9_154_bc --params=

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