K2CdPb Structure: AB2C_oC16_40_a_2b_b

Picture of Structure; Click for Big Picture
Prototype : K2CdPb
AFLOW prototype label : AB2C_oC16_40_a_2b_b
Strukturbericht designation : None
Pearson symbol : oC16
Space group number : 40
Space group symbol : $Ama2$
AFLOW prototype command : aflow --proto=AB2C_oC16_40_a_2b_b
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$y_{2}$,$z_{2}$,$y_{3}$,$z_{3}$,$y_{4}$,$z_{4}$


Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & -z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Cd} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Cd} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{K I} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{K I} \\ \mathbf{B}_{5} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{K II} \\ \mathbf{B}_{6} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{K II} \\ \mathbf{B}_{7} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(y_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Pb} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Pb} \\ \end{array} \]

References

  • R. Matthes and H.–U. Schuster, Synthese und Struktur der Phasen K2CdSn und K2CdPb/ Synthesis and Structure of the Phase K2CdSn and K2CdPb, Z. Naturforsch. B 34, 541–543 (1979), doi:10.1515/znb-1979-0403.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=AB2C_oC16_40_a_2b_b --params=

Species:

Running:

Output: