Magnetoplumbite (PbFe12O19) Structure : A12B19C_hP64_194_ab2fk_efh2k_d

Picture of Structure; Click for Big Picture
Prototype : Fe12O19Pb
AFLOW prototype label : A12B19C_hP64_194_ab2fk_efh2k_d
Strukturbericht designation : None
Pearson symbol : hP64
Space group number : 194
Space group symbol : $P6_{3}/mmc$
AFLOW prototype command : aflow --proto=A12B19C_hP64_194_ab2fk_efh2k_d
--params=
$a$,$c/a$,$z_{4}$,$z_{5}$,$z_{6}$,$z_{7}$,$x_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$


Other compounds with this structure

  • PbAl12O19, PbGa12O19, PbMn12O19, Pb(Co,Ti)12O19, BaAl12O19, BaGa12O19, BaMn12O19, Ba(Co,Ti)12O19, CaAl12O19, CaGa12O19, CaMn12O19, Ca(Co,Ti)12O19, SrAl12O19, SrGa12O19, SrMn12O19, and Sr(Co,Ti)12O19

  • In addition to the listed compounds, the lead and iron sites may be alloyed with a wide variety of metals and semi–metals resulting in high–entropy phases (Vinnik, 2019).

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

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(2a\right) & \mbox{Fe I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Fe I} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Fe II} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Fe II} \\ \mathbf{B}_{5} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Pb} \\ \mathbf{B}_{6} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{Pb} \\ \mathbf{B}_{7} & = & z_{4} \, \mathbf{a}_{3} & = & z_{4}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & -z_{4} \, \mathbf{a}_{3} & = & -z_{4}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Fe III} \\ \mathbf{B}_{12} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Fe III} \\ \mathbf{B}_{13} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Fe III} \\ \mathbf{B}_{14} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Fe III} \\ \mathbf{B}_{15} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Fe IV} \\ \mathbf{B}_{16} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Fe IV} \\ \mathbf{B}_{17} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Fe IV} \\ \mathbf{B}_{18} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Fe IV} \\ \mathbf{B}_{19} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{O II} \\ \mathbf{B}_{20} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{O II} \\ \mathbf{B}_{21} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{O II} \\ \mathbf{B}_{22} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{O II} \\ \mathbf{B}_{23} & = & x_{8} \, \mathbf{a}_{1} + 2x_{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{8}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{8}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{24} & = & -2x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{8}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{8}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{25} & = & x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{8}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{26} & = & -x_{8} \, \mathbf{a}_{1}-2x_{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{8}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{8}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{27} & = & 2x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{8}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{8}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{28} & = & -x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \sqrt{3}x_{8}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{O III} \\ \mathbf{B}_{29} & = & x_{9} \, \mathbf{a}_{1} + 2x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{9}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{30} & = & -2x_{9} \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{9}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{31} & = & x_{9} \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{32} & = & -x_{9} \, \mathbf{a}_{1}-2x_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{9}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{33} & = & 2x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{9}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{34} & = & -x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & \sqrt{3}x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{35} & = & 2x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{9}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{36} & = & -x_{9} \, \mathbf{a}_{1}-2x_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{9}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{37} & = & -x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \sqrt{3}x_{9}a \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{38} & = & -2x_{9} \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{9}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{9}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{39} & = & x_{9} \, \mathbf{a}_{1} + 2x_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{9}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{9}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{40} & = & x_{9} \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & -\sqrt{3}x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{9}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Fe V} \\ \mathbf{B}_{41} & = & x_{10} \, \mathbf{a}_{1} + 2x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{10}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{42} & = & -2x_{10} \, \mathbf{a}_{1}-x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{10}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{43} & = & x_{10} \, \mathbf{a}_{1}-x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{10}a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{44} & = & -x_{10} \, \mathbf{a}_{1}-2x_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{10}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{45} & = & 2x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{10}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{46} & = & -x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & \sqrt{3}x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{47} & = & 2x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{10}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{48} & = & -x_{10} \, \mathbf{a}_{1}-2x_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{10}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{49} & = & -x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \sqrt{3}x_{10}a \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{50} & = & -2x_{10} \, \mathbf{a}_{1}-x_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{10}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{10}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{10}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{51} & = & x_{10} \, \mathbf{a}_{1} + 2x_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{10}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{10}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{10}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{52} & = & x_{10} \, \mathbf{a}_{1}-x_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{10}\right) \, \mathbf{a}_{3} & = & -\sqrt{3}x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{10}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O IV} \\ \mathbf{B}_{53} & = & x_{11} \, \mathbf{a}_{1} + 2x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{11}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{54} & = & -2x_{11} \, \mathbf{a}_{1}-x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{11}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{55} & = & x_{11} \, \mathbf{a}_{1}-x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{11}a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{56} & = & -x_{11} \, \mathbf{a}_{1}-2x_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{11}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{57} & = & 2x_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{11}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{58} & = & -x_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & \sqrt{3}x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{59} & = & 2x_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{11}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}}-z_{11}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{60} & = & -x_{11} \, \mathbf{a}_{1}-2x_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{11}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}}-z_{11}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{61} & = & -x_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \sqrt{3}x_{11}a \, \mathbf{\hat{y}}-z_{11}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{62} & = & -2x_{11} \, \mathbf{a}_{1}-x_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{11}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{11}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{11}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{63} & = & x_{11} \, \mathbf{a}_{1} + 2x_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{11}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{11}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{11}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \mathbf{B}_{64} & = & x_{11} \, \mathbf{a}_{1}-x_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{11}\right) \, \mathbf{a}_{3} & = & -\sqrt{3}x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{11}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O V} \\ \end{array} \]

References

  • R. Gerber, Z. \vSimša, and L. Jenšovský, A note on the magnetoplumbite crystal structure, Czech. J. Phys. 44, 937–940 (1994), doi:10.1007/BF01715487.
  • D. A. Vinnik, E. A. Trofimov, V. E. Zhivulin, O. V. Zaitseva, S. A. Gudkova, A. Y. Starikov, D. A. Zherebtsov, A. A. Kirsanova, M. Häßner, and R. Niewa, High–entropy oxide phases with magnetoplumbite structure, Ceram. Int. 45, 12942–12948 (2019), doi:10.1016/j.ceramint.2019.03.221.

Geometry files


Prototype Generator

aflow --proto=A12B19C_hP64_194_ab2fk_efh2k_d --params=

Species:

Running:

Output: