Mg2Zn11 ($D8_{c}$) Structure: A2B11_cP39_200_f_aghij

Picture of Structure; Click for Big Picture
Prototype : Mg2Zn11
AFLOW prototype label : A2B11_cP39_200_f_aghij
Strukturbericht designation : $D8_{c}$
Pearson symbol : cP39
Space group number : 200
Space group symbol : $Pm\bar{3}$
AFLOW prototype command : aflow --proto=A2B11_cP39_200_f_aghij
--params=
$a$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$y_{6}$,$z_{6}$


Other compounds with this structure

  • Na2Cd11, Mg2Cu6Al5, Mg2Cu6Ga5, Na2Au6In5, Sc2Co7Ga4, K6Na14CdTl18, K6Na14HgTl18, K6Na14MgTl18, K6Na14ZnTl18

Simple Cubic primitive vectors:

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

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(1a\right) & \mbox{Zn I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Mg} \\ \mathbf{B}_{3} & = & -x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Mg} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} & \left(6f\right) & \mbox{Mg} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} & \left(6f\right) & \mbox{Mg} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Mg} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Mg} \\ \mathbf{B}_{8} & = & x_{3} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(6g\right) & \mbox{Zn II} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(6g\right) & \mbox{Zn II} \\ \mathbf{B}_{10} & = & x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Zn II} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Zn II} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Zn II} \\ \mathbf{B}_{13} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Zn II} \\ \mathbf{B}_{14} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Zn III} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Zn III} \\ \mathbf{B}_{16} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Zn III} \\ \mathbf{B}_{17} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Zn III} \\ \mathbf{B}_{18} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Zn III} \\ \mathbf{B}_{19} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Zn III} \\ \mathbf{B}_{20} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Zn IV} \\ \mathbf{B}_{21} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Zn IV} \\ \mathbf{B}_{22} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Zn IV} \\ \mathbf{B}_{23} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Zn IV} \\ \mathbf{B}_{24} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Zn IV} \\ \mathbf{B}_{25} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Zn IV} \\ \mathbf{B}_{26} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Zn IV} \\ \mathbf{B}_{27} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Zn IV} \\ \mathbf{B}_{28} & = & y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{29} & = & -y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{30} & = & y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{31} & = & -y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{32} & = & z_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{33} & = & z_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{34} & = & -z_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{35} & = & -z_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{36} & = & y_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} & = & y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{37} & = & -y_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} & = & -y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{38} & = & y_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} & = & y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} & \left(12j\right) & \mbox{Zn V} \\ \mathbf{B}_{39} & = & -y_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} & = & -y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} & \left(12j\right) & \mbox{Zn V} \\ \end{array} \]

References

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=A2B11_cP39_200_f_aghij --params=

Species:

Running:

Output: