Ca$_{14}$Zn$_{6}$Al$_{10}$O$_{35}$ Structure: A12B14C35D4_cF260_196_abeg_2ef_cef2h_e-001
| Prototype | Al$_{10}$Ca$_{14}$O$_{35}$Zn$_{6}$ |
| AFLOW prototype label | A12B14C35D4_cF260_196_abeg_2ef_cef2h_e-001 |
| ICSD | 50292 |
| Pearson symbol | cF260 |
| Space group number | 196 |
| Space group symbol | $F23$ |
| AFLOW prototype command |
aflow --proto=A12B14C35D4_cF260_196_abeg_2ef_cef2h_e-001
--params=$a, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}, \allowbreak x_{9}, \allowbreak x_{10}, \allowbreak x_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}$ |
- All of the sites labeled
aluminum
are actual 5 parts aluminum and 1 part zinc, giving the observed stoichiometry.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Al II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (4c) | O I |
| $\mathbf{B_{4}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Al III |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- 3 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Al III |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}- 3 x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Al III |
| $\mathbf{B_{7}}$ | = | $- 3 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Al III |
| $\mathbf{B_{8}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Ca I |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- 3 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Ca I |
| $\mathbf{B_{10}}$ | = | $x_{5} \, \mathbf{a}_{1}- 3 x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Ca I |
| $\mathbf{B_{11}}$ | = | $- 3 x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Ca I |
| $\mathbf{B_{12}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Ca II |
| $\mathbf{B_{13}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- 3 x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Ca II |
| $\mathbf{B_{14}}$ | = | $x_{6} \, \mathbf{a}_{1}- 3 x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Ca II |
| $\mathbf{B_{15}}$ | = | $- 3 x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Ca II |
| $\mathbf{B_{16}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (16e) | O II |
| $\mathbf{B_{17}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- 3 x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (16e) | O II |
| $\mathbf{B_{18}}$ | = | $x_{7} \, \mathbf{a}_{1}- 3 x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (16e) | O II |
| $\mathbf{B_{19}}$ | = | $- 3 x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (16e) | O II |
| $\mathbf{B_{20}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Zn I |
| $\mathbf{B_{21}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- 3 x_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Zn I |
| $\mathbf{B_{22}}$ | = | $x_{8} \, \mathbf{a}_{1}- 3 x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Zn I |
| $\mathbf{B_{23}}$ | = | $- 3 x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Zn I |
| $\mathbf{B_{24}}$ | = | $- x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}$ | (24f) | Ca III |
| $\mathbf{B_{25}}$ | = | $x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}$ | (24f) | Ca III |
| $\mathbf{B_{26}}$ | = | $x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{y}}$ | (24f) | Ca III |
| $\mathbf{B_{27}}$ | = | $- x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{y}}$ | (24f) | Ca III |
| $\mathbf{B_{28}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{z}}$ | (24f) | Ca III |
| $\mathbf{B_{29}}$ | = | $- x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{z}}$ | (24f) | Ca III |
| $\mathbf{B_{30}}$ | = | $- x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}$ | (24f) | O III |
| $\mathbf{B_{31}}$ | = | $x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}$ | (24f) | O III |
| $\mathbf{B_{32}}$ | = | $x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{y}}$ | (24f) | O III |
| $\mathbf{B_{33}}$ | = | $- x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{y}}$ | (24f) | O III |
| $\mathbf{B_{34}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{35}}$ | = | $- x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{36}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Al IV |
| $\mathbf{B_{37}}$ | = | $x_{11} \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Al IV |
| $\mathbf{B_{38}}$ | = | $x_{11} \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Al IV |
| $\mathbf{B_{39}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Al IV |
| $\mathbf{B_{40}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (24g) | Al IV |
| $\mathbf{B_{41}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Al IV |
| $\mathbf{B_{42}}$ | = | $\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+a z_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{43}}$ | = | $\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+a z_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{44}}$ | = | $\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}- a z_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{45}}$ | = | $- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}- a z_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{46}}$ | = | $\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{1}+\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $a z_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+a y_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{47}}$ | = | $- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $a z_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- a y_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{48}}$ | = | $\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a z_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+a y_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{49}}$ | = | $\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a z_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}- a y_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{50}}$ | = | $\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{2}+\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $a y_{12} \,\mathbf{\hat{x}}+a z_{12} \,\mathbf{\hat{y}}+a x_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{51}}$ | = | $\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a y_{12} \,\mathbf{\hat{x}}+a z_{12} \,\mathbf{\hat{y}}- a x_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{52}}$ | = | $- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(- x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{3}$ | = | $a y_{12} \,\mathbf{\hat{x}}- a z_{12} \,\mathbf{\hat{y}}- a x_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{53}}$ | = | $\left(x_{12} + y_{12} - z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - y_{12} + z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a y_{12} \,\mathbf{\hat{x}}- a z_{12} \,\mathbf{\hat{y}}+a x_{12} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{54}}$ | = | $\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+a z_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{55}}$ | = | $\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+a z_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{56}}$ | = | $\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}- a z_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{57}}$ | = | $- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}- a z_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{58}}$ | = | $\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{1}+\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $a z_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+a y_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{59}}$ | = | $- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $a z_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- a y_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{60}}$ | = | $\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a z_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}+a y_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{61}}$ | = | $\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a z_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- a y_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{62}}$ | = | $\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{2}+\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}+a z_{13} \,\mathbf{\hat{y}}+a x_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{63}}$ | = | $\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}+a z_{13} \,\mathbf{\hat{y}}- a x_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{64}}$ | = | $- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(- x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}- a z_{13} \,\mathbf{\hat{y}}- a x_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{65}}$ | = | $\left(x_{13} + y_{13} - z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - y_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}- a z_{13} \,\mathbf{\hat{y}}+a x_{13} \,\mathbf{\hat{z}}$ | (48h) | O V |
References
- V. D. Barbanyagre, T. I. Timoshenko, A. M. Il'inets, and V. M. Shamshurov, Calcium aluminozincates of Ca$_{x}$Al$_{y}$Zn$_{k}$O$_{n}$ composition, Powder Diff. 12, 22–26 (1997), doi:10.1017/S0885715600009398.
Found in
- ICSD, Inorganic Crystal Structure Database. ID 50292.
Prototype Generator
aflow --proto=A12B14C35D4_cF260_196_abeg_2ef_cef2h_e --params=$a,x_{4},x_{5},x_{6},x_{7},x_{8},x_{9},x_{10},x_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13}$