KAg(CN)2 ($F5_{10}$) Structure: AB2CD2_hP36_163_h_i_bf_i

Picture of Structure; Click for Big Picture
Prototype : KAg(CN)2
AFLOW prototype label : AB2CD2_hP36_163_h_i_bf_i
Strukturbericht designation : $F5_{10}$
Pearson symbol : hP36
Space group number : 163
Space group symbol : $\mbox{P}\bar{3}\mbox{1c}$
AFLOW prototype command : aflow --proto=AB2CD2_hP36_163_h_i_bf_i
--params=
$a$,$c/a$,$z_2$,$x_3$,$x_4$,$y_4$,$z_4$,$x_5$,$y_5$,$z_5$


Trigonal Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 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(2b\right) & \mbox{K I} \\ \mathbf{B_2} & = & \frac12 \, \mathbf{a}_{3} & = & \frac12 \, c \,\mathbf{\hat{z}} & \left(2b\right) & \mbox{K I} \\ \mathbf{B_3} & =& \frac13 \, \mathbf{a}_{1} + \frac23 \, \mathbf{a}_{2} + z_2 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} +z_2 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{K II} \\ \mathbf{B_4} & =& \frac13 \, \mathbf{a}_{1} + \frac23 \, \mathbf{a}_{2} + \left(\frac12 - z_2\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} +\left(\frac12 - z_2\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{K II} \\ \mathbf{B_5} & =& \frac23 \, \mathbf{a}_{1} + \frac13 \, \mathbf{a}_{2} - z_2 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} -z_2 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{K II} \\ \mathbf{B_6} & =& \frac23 \, \mathbf{a}_{1} + \frac13 \, \mathbf{a}_{2} + \left(\frac12 + z_2\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}} +\left(\frac12 + z_2\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{K II} \\ \mathbf{B_7} & =& x_3 \, \mathbf{a}_{1} - x_3 \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& - \sqrt{3} \, x_3 \, a \, \mathbf{\hat{y}} + \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ag} \\ \mathbf{B_8} & =& x_3 \, \mathbf{a}_{1} + 2 x_3 \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& \frac32 \, x_3 \, a \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, x_3 \, a \, \mathbf{\hat{y}} + \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ag} \\ \mathbf{B_9} & =& -2 x_3 \, \mathbf{a}_{1} - x_3 \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& - \frac32 \, x_3 \, a \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, x_3 \, a \, \mathbf{\hat{y}} + \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ag} \\ \mathbf{B}_{10} & =& - x_3 \, \mathbf{a}_{1} + x_3 \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& \sqrt{3} \, x_3 \, a \, \mathbf{\hat{y}} + \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ag} \\ \mathbf{B}_{11} & =& - x_3 \, \mathbf{a}_{1} - 2 x_3 \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& - \frac32 \, x_3 \, a \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, x_3 \, a \, \mathbf{\hat{y}} + \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ag} \\ \mathbf{B}_{12} & =& 2 x_3 \, \mathbf{a}_{1} + x_3 \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& \frac32 \, x_3 \, a \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, x_3 \, a \, \mathbf{\hat{y}} + \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Ag} \\ \mathbf{B}_{13} & =& x_4 \, \mathbf{a}_{1} + y_4 \, \mathbf{a}_{2} + z_4 \, \mathbf{a}_{3}& =& \frac12 \, \left(x_4 + y_4\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, \left(y_4 - x_4\right) \, a \, \mathbf{\hat{y}}+ z_4 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{14} & =& - y_4 \, \mathbf{a}_{1} + \left(x_4 - y_4\right) \, \mathbf{a}_{2} + z_4 \, \mathbf{a}_{3}& =& \frac12 \, \left(x_4 - 2 y_4\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, x_4 \, a \, \mathbf{\hat{y}}+ z_4 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{15} & =& \left(y_4 - x_4\right) \, \mathbf{a}_{1} - x_4 \, \mathbf{a}_{2} + z_4 \, \mathbf{a}_{3}& =& \frac12 \, \left(y_4 - 2 x_4\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, y_4 \, a \, \mathbf{\hat{y}}+ z_4 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{16} & =& - y_4 \, \mathbf{a}_{1} - x_4 \, \mathbf{a}_{2} + \left(\frac12 - z_4\right) \, \mathbf{a}_{3}& =& - \frac12 \, \left(x_4 + y_4\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, \left(y_4 - x_4\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_4\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{17} & =& \left( y_4 - x_4\right) \, \mathbf{a}_{1} + y_4 \, \mathbf{a}_{2} + \left(\frac12 - z_4\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(2 y_4 - x_4\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, x_4 \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_4\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{18} & =& x_4 \, \mathbf{a}_{1} + \left(x_4-y_4\right) \, \mathbf{a}_{2} + \left(\frac12 - z_4\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(2 x_4 - y_4\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, y_4 \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_4\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{19} & =& - x_4 \, \mathbf{a}_{1} - y_4 \, \mathbf{a}_{2} - z_4 \, \mathbf{a}_{3}& =& - \frac12 \, \left(x_4 + y_4\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, \left(x_4 - y_4\right) \, a \, \mathbf{\hat{y}}- z_4 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{20} & =& y_4 \, \mathbf{a}_{1} + \left(y_4 - x_4\right) \, \mathbf{a}_{2} - z_4 \, \mathbf{a}_{3}& =& \frac12 \, \left(2 y_4 - x_4\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, x_4 \, a \, \mathbf{\hat{y}}- z_4 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{21} & =& \left(x_4 - y_4\right) \, \mathbf{a}_{1} + x_4 \, \mathbf{a}_{2} - z_4 \, \mathbf{a}_{3}& =& \frac12 \, \left(2 x_4 - y_4\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, y_4 \, a \, \mathbf{\hat{y}}- z_4 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{22} & =& y_4 \, \mathbf{a}_{1} + x_4 \, \mathbf{a}_{2} + \left(\frac12 + z_4\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(x_4 + y_4\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, \left(x_4 - y_4\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_4\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{23} & =& \left( x_4 - y_4\right) \, \mathbf{a}_{1} - y_4 \, \mathbf{a}_{2} + \left(\frac12 + z_4\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(x_4 - 2 y_4\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, x_4 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_4\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{24} & =& - x_4 \, \mathbf{a}_{1} + \left(y_4 - x_4\right) \, \mathbf{a}_{2} + \left(\frac12 + z_4\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(y_4 - 2 x_4\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, y_4 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_4\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{C} \\ \mathbf{B}_{25} & =& x_5 \, \mathbf{a}_{1} + y_5 \, \mathbf{a}_{2} + z_5 \, \mathbf{a}_{3}& =& \frac12 \, \left(x_5 + y_5\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, \left(y_5 - x_5\right) \, a \, \mathbf{\hat{y}}+ z_5 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{26} & =& - y_5 \, \mathbf{a}_{1} + \left(x_5 - y_5\right) \, \mathbf{a}_{2} + z_5 \, \mathbf{a}_{3}& =& \frac12 \, \left(x_5 - 2 y_5\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, x_5 \, a \, \mathbf{\hat{y}}+ z_5 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{27} & =& \left(y_5 - x_5\right) \, \mathbf{a}_{1} - x_5 \, \mathbf{a}_{2} + z_5 \, \mathbf{a}_{3}& =& \frac12 \, \left(y_5 - 2 x_5\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, y_5 \, a \, \mathbf{\hat{y}}+ z_5 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{28} & =& - y_5 \, \mathbf{a}_{1} - x_5 \, \mathbf{a}_{2} + \left(\frac12 - z_5\right) \, \mathbf{a}_{3}& =& - \frac12 \, \left(x_5 + y_5\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, \left(y_5 - x_5\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_5\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{29} & =& \left( y_5 - x_5\right) \, \mathbf{a}_{1} + y_5 \, \mathbf{a}_{2} + \left(\frac12 - z_5\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(2 y_5 - x_5\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, x_5 \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_5\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{30} & =& x_5 \, \mathbf{a}_{1} + \left(x_5-y_5\right) \, \mathbf{a}_{2} + \left(\frac12 - z_5\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(2 x_5 - y_5\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, y_5 \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_5\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{31} & =& - x_5 \, \mathbf{a}_{1} - y_5 \, \mathbf{a}_{2} - z_5 \, \mathbf{a}_{3}& =& - \frac12 \, \left(x_5 + y_5\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, \left(x_5 - y_5\right) \, a \, \mathbf{\hat{y}}- z_5 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{32} & =& y_5 \, \mathbf{a}_{1} + \left(y_5 - x_5\right) \, \mathbf{a}_{2} - z_5 \, \mathbf{a}_{3}& =& \frac12 \, \left(2 y_5 - x_5\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, x_5 \, a \, \mathbf{\hat{y}}- z_5 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{33} & =& \left(x_5 - y_5\right) \, \mathbf{a}_{1} + x_5 \, \mathbf{a}_{2} - z_5 \, \mathbf{a}_{3}& =& \frac12 \, \left(2 x_5 - y_5\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, y_5 \, a \, \mathbf{\hat{y}}- z_5 \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{34} & =& y_5 \, \mathbf{a}_{1} + x_5 \, \mathbf{a}_{2} + \left(\frac12 + z_5\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(x_5 + y_5\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, \left(x_5 - y_5\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_5\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{35} & =& \left( x_5 - y_5\right) \, \mathbf{a}_{1} - y_5 \, \mathbf{a}_{2} + \left(\frac12 + z_5\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(x_5 - 2 y_5\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, x_5 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_5\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \mathbf{B}_{36} & =& - x_5 \, \mathbf{a}_{1} + \left(y_5 - x_5\right) \, \mathbf{a}_{2} + \left(\frac12 + z_5\right) \, \mathbf{a}_{3}& =& \frac12 \, \left(y_5 - 2 x_5\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, y_5 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_5\right) \, c \, \mathbf{\hat{z}}& \left(12i\right) & \mbox{N} \\ \end{array} \]

References

  • J. L. Hoard, The Crystal Structure of Potassium Silver Cyanide, Zeitschrift für Kristallographie – Crystalline Materials 84, 231–255 (1933), doi:10.1524/zkri.1933.84.1.231.

Found in

  • P. Villars, Material Phases Data System ((MPDS), CH–6354 Vitznau, Switzerland, 2014). Accessed through the Springer Materials site.

Geometry files


Prototype Generator

aflow --proto=AB2CD2_hP36_163_h_i_bf_i --params=

Species:

Running:

Output: