Magnetoplumbite (PbFe$_{12}$O$_{19}$) Structure: A12B19C_hP64_194_ab2fk_efh2k_c-001
| Prototype | Fe$_{12}$O$_{19}$Pb |
| AFLOW prototype label | A12B19C_hP64_194_ab2fk_efh2k_c-001 |
| Mineral name | magnetoplumbite |
| ICSD | 36259 |
| Pearson symbol | hP64 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=A12B19C_hP64_194_ab2fk_efh2k_c-001
--params=$a, \allowbreak c/a, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}$ |
Other compounds with this structure
PbAl$_{12}$O$_{19}$, PbGa$_{12}$O$_{19}$, PbMn$_{12}$O$_{19}$, Pb(Co, Ti)$_{12}$O$_{19}$, BaAl$_{12}$O$_{19}$, BaFe$_{12}$O$_{19}$, BaGa$_{12}$O$_{19}$, BaMn$_{12}$O$_{19}$, Ba(Co, Ti)$_{12}$O$_{19}$, CaAl$_{12}$O$_{19}$, CaGa$_{12}$O$_{19}$, CaMn$_{12}$O$_{19}$, Ca(Co, Ti)$_{12}$O$_{19}$, SrAl$_{12}$O$_{19}$, SrGa$_{12}$O$_{19}$, SrMn$_{12}$O$_{19}$, Sr(Co, Ti)$_{12}$O$_{19}$
- 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).
- We did not find an ICSD or CCDC entry for (Simsa, 1994). We use the ICSD entry from the early work of (Adelskoeld, 1938).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Fe I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Fe I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2b) | Fe II |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2b) | Fe II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Pb I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Pb I |
| $\mathbf{B_{7}}$ | = | $z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{8}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{9}}$ | = | $- z_{4} \, \mathbf{a}_{3}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{10}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4f) | Fe III |
| $\mathbf{B_{12}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | Fe III |
| $\mathbf{B_{13}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4f) | Fe III |
| $\mathbf{B_{14}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | Fe III |
| $\mathbf{B_{15}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4f) | Fe IV |
| $\mathbf{B_{16}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | Fe IV |
| $\mathbf{B_{17}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (4f) | Fe IV |
| $\mathbf{B_{18}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | Fe IV |
| $\mathbf{B_{19}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4f) | O II |
| $\mathbf{B_{20}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | O II |
| $\mathbf{B_{21}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (4f) | O II |
| $\mathbf{B_{22}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | O II |
| $\mathbf{B_{23}}$ | = | $x_{8} \, \mathbf{a}_{1}+2 x_{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{24}}$ | = | $- 2 x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{25}}$ | = | $x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{8} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{26}}$ | = | $- x_{8} \, \mathbf{a}_{1}- 2 x_{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{27}}$ | = | $2 x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{28}}$ | = | $- x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{8} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O III |
| $\mathbf{B_{29}}$ | = | $x_{9} \, \mathbf{a}_{1}+2 x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{30}}$ | = | $- 2 x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{31}}$ | = | $x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{32}}$ | = | $- x_{9} \, \mathbf{a}_{1}- 2 x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{33}}$ | = | $2 x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{34}}$ | = | $- x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{35}}$ | = | $2 x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{36}}$ | = | $- x_{9} \, \mathbf{a}_{1}- 2 x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{37}}$ | = | $- x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{38}}$ | = | $- 2 x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{39}}$ | = | $x_{9} \, \mathbf{a}_{1}+2 x_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{40}}$ | = | $x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | Fe V |
| $\mathbf{B_{41}}$ | = | $x_{10} \, \mathbf{a}_{1}+2 x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{42}}$ | = | $- 2 x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{43}}$ | = | $x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{44}}$ | = | $- x_{10} \, \mathbf{a}_{1}- 2 x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{45}}$ | = | $2 x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{46}}$ | = | $- x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{47}}$ | = | $2 x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{48}}$ | = | $- x_{10} \, \mathbf{a}_{1}- 2 x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{49}}$ | = | $- x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{50}}$ | = | $- 2 x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{51}}$ | = | $x_{10} \, \mathbf{a}_{1}+2 x_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{52}}$ | = | $x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O IV |
| $\mathbf{B_{53}}$ | = | $x_{11} \, \mathbf{a}_{1}+2 x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{54}}$ | = | $- 2 x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{55}}$ | = | $x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{56}}$ | = | $- x_{11} \, \mathbf{a}_{1}- 2 x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{57}}$ | = | $2 x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{58}}$ | = | $- x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{59}}$ | = | $2 x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{60}}$ | = | $- x_{11} \, \mathbf{a}_{1}- 2 x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{61}}$ | = | $- x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{62}}$ | = | $- 2 x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{63}}$ | = | $x_{11} \, \mathbf{a}_{1}+2 x_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O V |
| $\mathbf{B_{64}}$ | = | $x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12k) | O V |
References
- R. Gerber, Z. Šimša, 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. Hä{ßner, and R. Niewa, High-entropy oxide phases with magnetoplumbite structure, Ceram. Int. 45, 12942–12948 (2019), doi:10.1016/j.ceramint.2019.03.221.
- V. Adelskoeld, X-ray studies on magneto plumbite PbO(Fe$_{2}$O$_{3}$)$_{6}$ and other substances resembling β-alumina Na$_{2}$O(Al$_{2}$O$_{3}$)$_{11}$, Arkiv för Kemi, Mineralogi och Geologi 12, 1–9 (1938).
Prototype Generator
aflow --proto=A12B19C_hP64_194_ab2fk_efh2k_c --params=$a,c/a,z_{4},z_{5},z_{6},z_{7},x_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11}$