Mercury Cyanide [Hg(CN)2, $F1_{1}$] Structure : A2BC2_tI40_122_e_d_e

Picture of Structure; Click for Big Picture
Prototype : C2HgN2
AFLOW prototype label : A2BC2_tI40_122_e_d_e
Strukturbericht designation : $F1_{1}$
Pearson symbol : tI40
Space group number : 122
Space group symbol : $I\bar{4}2d$
AFLOW prototype command : aflow --proto=A2BC2_tI40_122_e_d_e
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


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

References

  • O. Reckeweg and A. Simon, X–Ray and Raman Investigations on Cyanides of Mono– and Divalent Metals and Synthesis, Crystal Structure and Raman Spectrum of Tl5(CO3)2(CN), Z. Naturforsch. B 57, 895–900 (2002), doi:10.1515/znb-2002-0809.

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aflow --proto=A2BC2_tI40_122_e_d_e --params=

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