Stannoidite (Cu8(Fe,Zn)3Sn2S12) Structure: A8B2C12D2E_oI50_23_bcfk_i_3k_j_a

Picture of Structure; Click for Big Picture
Prototype : Cu8(Fe,Zn)3Sn2S12
AFLOW prototype label : A8B2C12D2E_oI50_23_bcfk_i_3k_j_a
Strukturbericht designation : None
Pearson symbol : oI50
Space group number : 23
Space group symbol : $I222$
AFLOW prototype command : aflow --proto=A8B2C12D2E_oI50_23_bcfk_i_3k_j_a
--params=
$a$,$b/a$,$c/a$,$x_{4}$,$z_{5}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$


  • The composition of the Zn (2a) site is actually Zn0.85Fe0.15.

Body-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Zn} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(2b\right) & \mbox{Cu I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Cu II} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Cu III} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Cu III} \\ \mathbf{B}_{6} & = & z_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} & = & z_{5}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Fe} \\ \mathbf{B}_{7} & = & -z_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} & = & -z_{5}c \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Fe} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{Sn} \\ \mathbf{B}_{9} & = & \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}b \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(4j\right) & \mbox{Sn} \\ \mathbf{B}_{10} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(x_{7}+y_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{Cu IV} \\ \mathbf{B}_{11} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{Cu IV} \\ \mathbf{B}_{12} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{Cu IV} \\ \mathbf{B}_{13} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{Cu IV} \\ \mathbf{B}_{14} & = & \left(y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(x_{8}+y_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S I} \\ \mathbf{B}_{15} & = & \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S I} \\ \mathbf{B}_{16} & = & \left(y_{8}-z_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S I} \\ \mathbf{B}_{17} & = & \left(-y_{8}-z_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S I} \\ \mathbf{B}_{18} & = & \left(y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(x_{9}+y_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S II} \\ \mathbf{B}_{19} & = & \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(-x_{9}-y_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S II} \\ \mathbf{B}_{20} & = & \left(y_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S II} \\ \mathbf{B}_{21} & = & \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(x_{9}-y_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S II} \\ \mathbf{B}_{22} & = & \left(y_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}+z_{10}\right) \, \mathbf{a}_{2} + \left(x_{10}+y_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S III} \\ \mathbf{B}_{23} & = & \left(-y_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}+z_{10}\right) \, \mathbf{a}_{2} + \left(-x_{10}-y_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S III} \\ \mathbf{B}_{24} & = & \left(y_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-x_{10}+y_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S III} \\ \mathbf{B}_{25} & = & \left(-y_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(x_{10}-y_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(8k\right) & \mbox{S III} \\ \end{array} \]

References

  • Y. Kudoh and Y. Takéuchi, The superstructure of stannoidite, Zeitschrift für Kristallographie – Crystalline Materials 144, 145–160 (1976), doi:10.1524/zkri.1976.144.16.145.

Geometry files


Prototype Generator

aflow --proto=A8B2C12D2E_oI50_23_bcfk_i_3k_j_a --params=

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