KCNS ($F5_{9}$) Structure: ABCD_oP16_57_d_c_d_d

Picture of Structure; Click for Big Picture
Prototype : KCNS
AFLOW prototype label : ABCD_oP16_57_d_c_d_d
Strukturbericht designation : $F5_{9}$
Pearson symbol : oP16
Space group number : 57
Space group symbol : $\mbox{Pbcm}$
AFLOW prototype command : aflow --proto=ABCD_oP16_57_d_c_d_d
--params=
$a$,$b/a$,$c/a$,$x_{1}$,$x_{2}$,$y_{2}$,$x_{3}$,$y_{3}$,$x_{4}$,$y_{4}$


Simple Orthorhombic primitive vectors:

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

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}+ \frac14 \, \mathbf{a}_{2}& =&x_{1} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}& \left(4c\right) & \mbox{K} \\ \mathbf{B}_{2} & =&- x_{1} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&- x_{1} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{K} \\ \mathbf{B}_{3} & =&- x_{1} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}& =&- x_{1} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}& \left(4c\right) & \mbox{K} \\ \mathbf{B}_{4} & =&x_{1} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&x_{1} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4c\right) & \mbox{K} \\ \mathbf{B}_{5} & =&x_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&x_{2} \, a \, \mathbf{\hat{x}}+ y_{2} \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{C} \\ \mathbf{B}_{6} & =&- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&- x_{2} \, a \, \mathbf{\hat{x}}- y_{2} \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{C} \\ \mathbf{B}_{7} & =&- x_{2} \, \mathbf{a}_{1}+ \left(\frac12 + y_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&- x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{C} \\ \mathbf{B}_{8} & =&x_{2} \, \mathbf{a}_{1}+ \left(\frac12 - y_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{C} \\ \mathbf{B}_{9} & =&x_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{N} \\ \mathbf{B}_{10} & =&- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{N} \\ \mathbf{B}_{11} & =&- x_{3} \, \mathbf{a}_{1}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{3}\right) \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{N} \\ \mathbf{B}_{12} & =&x_{3} \, \mathbf{a}_{1}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{3}\right) \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{N} \\ \mathbf{B}_{13} & =&x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{S} \\ \mathbf{B}_{14} & =&- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{S} \\ \mathbf{B}_{15} & =&- x_{4} \, \mathbf{a}_{1}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&- x_{4} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{4}\right) \, b \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{S} \\ \mathbf{B}_{16} & =&x_{4} \, \mathbf{a}_{1}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&x_{4} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{4}\right) \, b \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{S} \\ \end{array} \]

References

  • D. J. Cookson, M. M. Elcombe, and T. R. Finlayson, Phonon dispersion relations for potassium thiocyanate at and above room temperature, J. Phys.: Condens. Matter 4, 7851–7864 (1992), doi:10.1088/0953-8984/4/39/001.

Found in

  • E. Nakamura, Y. Shiozaki, E. Nakamura, and T. Mitsui, SpringerMaterials (Springer–Verlag GmbH, Heidelberg, 2005).

Geometry files


Prototype Generator

aflow --proto=ABCD_oP16_57_d_c_d_d --params=

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