NaS2 Structure : AB2_tI48_122_cd_2e

Picture of Structure; Click for Big Picture
Prototype : NaS2
AFLOW prototype label : AB2_tI48_122_cd_2e
Strukturbericht designation : None
Pearson symbol : tI48
Space group number : 122
Space group symbol : $I\bar{4}2d$
AFLOW prototype command : aflow --proto=AB2_tI48_122_cd_2e
--params=
$a$,$c/a$,$z_{1}$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


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} & = & z_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2} & = & z_{1}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Na I} \\ \mathbf{B}_{2} & = & -z_{1} \, \mathbf{a}_{1}-z_{1} \, \mathbf{a}_{2} & = & -z_{1}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Na I} \\ \mathbf{B}_{3} & = & \left(\frac{3}{4} - z_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - z_{1}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{1}\right)c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Na I} \\ \mathbf{B}_{4} & = & \left(\frac{3}{4} +z_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{1}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Na I} \\ \mathbf{B}_{5} & = & \frac{3}{8} \, \mathbf{a}_{1} + \left(\frac{1}{8} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Na II} \\ \mathbf{B}_{6} & = & \frac{7}{8} \, \mathbf{a}_{1} + \left(\frac{1}{8} - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Na II} \\ \mathbf{B}_{7} & = & \left(\frac{7}{8} - x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{3} & = & - \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Na II} \\ \mathbf{B}_{8} & = & \left(\frac{7}{8} +x_{2}\right) \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Na II} \\ \mathbf{B}_{9} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S I} \\ \mathbf{B}_{10} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S I} \\ \mathbf{B}_{11} & = & \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S I} \\ \mathbf{B}_{12} & = & \left(x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S I} \\ \mathbf{B}_{13} & = & \left(\frac{3}{4} +y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S I} \\ \mathbf{B}_{14} & = & \left(\frac{3}{4} - y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S I} \\ \mathbf{B}_{15} & = & \left(\frac{3}{4} - x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S I} \\ \mathbf{B}_{16} & = & \left(\frac{3}{4} +x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S I} \\ \mathbf{B}_{17} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S II} \\ \mathbf{B}_{18} & = & \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S II} \\ \mathbf{B}_{19} & = & \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S II} \\ \mathbf{B}_{20} & = & \left(x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S II} \\ \mathbf{B}_{21} & = & \left(\frac{3}{4} +y_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} + y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S II} \\ \mathbf{B}_{22} & = & \left(\frac{3}{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} - y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S II} \\ \mathbf{B}_{23} & = & \left(\frac{3}{4} - x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4} - y_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S II} \\ \mathbf{B}_{24} & = & \left(\frac{3}{4} +x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4} + y_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{S II} \\ \end{array} \]

References

  • R. Tegman, The Crystal Structure of Sodium Tetrasulphide, Na2S4, Acta Crystallogr. Sect. B Struct. Sci. 29, 1463–1469 (1973), doi:10.1107/S0567740873004735.

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.

Geometry files


Prototype Generator

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