S–III Structure: A_tI16_142_f

Picture of Structure; Click for Big Picture
Prototype : S
AFLOW prototype label : A_tI16_142_f
Strukturbericht designation : None
Pearson symbol : tI16
Space group number : 142
Space group symbol : $I4_{1}/acd$
AFLOW prototype command : aflow --proto=A_tI16_142_f
--params=
$a$,$c/a$,$x_{1}$


Other elements with this structure

  • Se (Se–VII, prepared at 450 K and 20 GPa)

  • The S–III phase is found when sulfur is pressurized above 36 GPa at 300 K. At 300 K it is stable up to 83 GPa. This data was taken at 12 GPa and 300 K.

Body-centered Tetragonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \left(\frac{3}{8} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} +x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +2x_{1}\right) \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{S} \\ \mathbf{B}_{2} & = & \left(\frac{3}{8} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} - x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - 2x_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{S} \\ \mathbf{B}_{3} & = & \left(\frac{1}{8} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} - x_{1}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}}- \frac{1}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{S} \\ \mathbf{B}_{4} & = & \left(\frac{1}{8} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} +x_{1}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{7}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{S} \\ \mathbf{B}_{5} & = & \left(\frac{5}{8} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{7}{8} - x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - 2x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{S} \\ \mathbf{B}_{6} & = & \left(\frac{5}{8} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{7}{8} +x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +2x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{S} \\ \mathbf{B}_{7} & = & \left(\frac{7}{8} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{5}{8} +x_{1}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{5}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{S} \\ \mathbf{B}_{8} & = & \left(\frac{7}{8} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{5}{8} - x_{1}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{5}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{S} \\ \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_tI16_142_f --params=

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