Deltalumite (δ-alumina, Al$_{2}$O$_{3}$) Structure: A3B4_tP84_115_acef3g3j3k_6j6k-001
| Prototype | Al$_{2}$O$_{3}$ |
| AFLOW prototype label | A3B4_tP84_115_acef3g3j3k_6j6k-001 |
| Mineral name | deltalumite |
| ICSD | 40200 |
| Pearson symbol | tP84 |
| Space group number | 115 |
| Space group symbol | $P\overline{4}m2$ |
| AFLOW prototype command |
aflow --proto=A3B4_tP84_115_acef3g3j3k_6j6k-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak z_{24}, \allowbreak x_{25}, \allowbreak z_{25}$ |
- Alumina comes in a variety of forms. In the Encyclopedia we have:
- Corundum, or $\alpha$-alumina ($D5_{1}$) is the mineral usual found in nature.
- $\beta$-alumina ($D5_{6}$)
- We describe $\gamma$-alumina ($D5_{7}$) using Fe$_{2}$O$_{3}$ as the prototype.
- $\delta$-alumina (this structure) is a tetragonal distortion of the spinel structure. It is found in nature as deltalumite.
- $\kappa$–Al$_{2}$O$_{3}$.
- Only 5/6 of the aluminum (4j) and (4k) sites in deltalumite are occupied, giving the observed alumina stoichiometry, Al$_{2}$O$_{3}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1c) | Al II |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Al III |
| $\mathbf{B_{4}}$ | = | $- z_{3} \, \mathbf{a}_{3}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Al III |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2f) | Al IV |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2f) | Al IV |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2g) | Al V |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{5} \,\mathbf{\hat{z}}$ | (2g) | Al V |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (2g) | Al VI |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{6} \,\mathbf{\hat{z}}$ | (2g) | Al VI |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (2g) | Al VII |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{7} \,\mathbf{\hat{z}}$ | (2g) | Al VII |
| $\mathbf{B_{13}}$ | = | $x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (4j) | Al VIII |
| $\mathbf{B_{14}}$ | = | $- x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (4j) | Al VIII |
| $\mathbf{B_{15}}$ | = | $- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (4j) | Al VIII |
| $\mathbf{B_{16}}$ | = | $x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (4j) | Al VIII |
| $\mathbf{B_{17}}$ | = | $x_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (4j) | Al IX |
| $\mathbf{B_{18}}$ | = | $- x_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (4j) | Al IX |
| $\mathbf{B_{19}}$ | = | $- x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (4j) | Al IX |
| $\mathbf{B_{20}}$ | = | $x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (4j) | Al IX |
| $\mathbf{B_{21}}$ | = | $x_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (4j) | Al X |
| $\mathbf{B_{22}}$ | = | $- x_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (4j) | Al X |
| $\mathbf{B_{23}}$ | = | $- x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (4j) | Al X |
| $\mathbf{B_{24}}$ | = | $x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (4j) | Al X |
| $\mathbf{B_{25}}$ | = | $x_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (4j) | O I |
| $\mathbf{B_{26}}$ | = | $- x_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (4j) | O I |
| $\mathbf{B_{27}}$ | = | $- x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (4j) | O I |
| $\mathbf{B_{28}}$ | = | $x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (4j) | O I |
| $\mathbf{B_{29}}$ | = | $x_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+c z_{12} \,\mathbf{\hat{z}}$ | (4j) | O II |
| $\mathbf{B_{30}}$ | = | $- x_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+c z_{12} \,\mathbf{\hat{z}}$ | (4j) | O II |
| $\mathbf{B_{31}}$ | = | $- x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (4j) | O II |
| $\mathbf{B_{32}}$ | = | $x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (4j) | O II |
| $\mathbf{B_{33}}$ | = | $x_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+c z_{13} \,\mathbf{\hat{z}}$ | (4j) | O III |
| $\mathbf{B_{34}}$ | = | $- x_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+c z_{13} \,\mathbf{\hat{z}}$ | (4j) | O III |
| $\mathbf{B_{35}}$ | = | $- x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (4j) | O III |
| $\mathbf{B_{36}}$ | = | $x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (4j) | O III |
| $\mathbf{B_{37}}$ | = | $x_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+c z_{14} \,\mathbf{\hat{z}}$ | (4j) | O IV |
| $\mathbf{B_{38}}$ | = | $- x_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+c z_{14} \,\mathbf{\hat{z}}$ | (4j) | O IV |
| $\mathbf{B_{39}}$ | = | $- x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (4j) | O IV |
| $\mathbf{B_{40}}$ | = | $x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (4j) | O IV |
| $\mathbf{B_{41}}$ | = | $x_{15} \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+c z_{15} \,\mathbf{\hat{z}}$ | (4j) | O V |
| $\mathbf{B_{42}}$ | = | $- x_{15} \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+c z_{15} \,\mathbf{\hat{z}}$ | (4j) | O V |
| $\mathbf{B_{43}}$ | = | $- x_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (4j) | O V |
| $\mathbf{B_{44}}$ | = | $x_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (4j) | O V |
| $\mathbf{B_{45}}$ | = | $x_{16} \, \mathbf{a}_{1}+z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+c z_{16} \,\mathbf{\hat{z}}$ | (4j) | O VI |
| $\mathbf{B_{46}}$ | = | $- x_{16} \, \mathbf{a}_{1}+z_{16} \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}+c z_{16} \,\mathbf{\hat{z}}$ | (4j) | O VI |
| $\mathbf{B_{47}}$ | = | $- x_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (4j) | O VI |
| $\mathbf{B_{48}}$ | = | $x_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (4j) | O VI |
| $\mathbf{B_{49}}$ | = | $x_{17} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (4k) | Al XI |
| $\mathbf{B_{50}}$ | = | $- x_{17} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (4k) | Al XI |
| $\mathbf{B_{51}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (4k) | Al XI |
| $\mathbf{B_{52}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (4k) | Al XI |
| $\mathbf{B_{53}}$ | = | $x_{18} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (4k) | Al XII |
| $\mathbf{B_{54}}$ | = | $- x_{18} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (4k) | Al XII |
| $\mathbf{B_{55}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (4k) | Al XII |
| $\mathbf{B_{56}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (4k) | Al XII |
| $\mathbf{B_{57}}$ | = | $x_{19} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (4k) | Al XIII |
| $\mathbf{B_{58}}$ | = | $- x_{19} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (4k) | Al XIII |
| $\mathbf{B_{59}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (4k) | Al XIII |
| $\mathbf{B_{60}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (4k) | Al XIII |
| $\mathbf{B_{61}}$ | = | $x_{20} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (4k) | O VII |
| $\mathbf{B_{62}}$ | = | $- x_{20} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (4k) | O VII |
| $\mathbf{B_{63}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (4k) | O VII |
| $\mathbf{B_{64}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (4k) | O VII |
| $\mathbf{B_{65}}$ | = | $x_{21} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $a x_{21} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (4k) | O VIII |
| $\mathbf{B_{66}}$ | = | $- x_{21} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $- a x_{21} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (4k) | O VIII |
| $\mathbf{B_{67}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{21} \,\mathbf{\hat{y}}- c z_{21} \,\mathbf{\hat{z}}$ | (4k) | O VIII |
| $\mathbf{B_{68}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{21} \,\mathbf{\hat{y}}- c z_{21} \,\mathbf{\hat{z}}$ | (4k) | O VIII |
| $\mathbf{B_{69}}$ | = | $x_{22} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $a x_{22} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (4k) | O IX |
| $\mathbf{B_{70}}$ | = | $- x_{22} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $- a x_{22} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (4k) | O IX |
| $\mathbf{B_{71}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{22} \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{22} \,\mathbf{\hat{y}}- c z_{22} \,\mathbf{\hat{z}}$ | (4k) | O IX |
| $\mathbf{B_{72}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{22} \,\mathbf{\hat{y}}- c z_{22} \,\mathbf{\hat{z}}$ | (4k) | O IX |
| $\mathbf{B_{73}}$ | = | $x_{23} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $a x_{23} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (4k) | O X |
| $\mathbf{B_{74}}$ | = | $- x_{23} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $- a x_{23} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (4k) | O X |
| $\mathbf{B_{75}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{23} \, \mathbf{a}_{2}- z_{23} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{23} \,\mathbf{\hat{y}}- c z_{23} \,\mathbf{\hat{z}}$ | (4k) | O X |
| $\mathbf{B_{76}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{23} \, \mathbf{a}_{2}- z_{23} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{23} \,\mathbf{\hat{y}}- c z_{23} \,\mathbf{\hat{z}}$ | (4k) | O X |
| $\mathbf{B_{77}}$ | = | $x_{24} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $a x_{24} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (4k) | O XI |
| $\mathbf{B_{78}}$ | = | $- x_{24} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $- a x_{24} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (4k) | O XI |
| $\mathbf{B_{79}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{24} \, \mathbf{a}_{2}- z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{24} \,\mathbf{\hat{y}}- c z_{24} \,\mathbf{\hat{z}}$ | (4k) | O XI |
| $\mathbf{B_{80}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{24} \, \mathbf{a}_{2}- z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{24} \,\mathbf{\hat{y}}- c z_{24} \,\mathbf{\hat{z}}$ | (4k) | O XI |
| $\mathbf{B_{81}}$ | = | $x_{25} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $a x_{25} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (4k) | O XII |
| $\mathbf{B_{82}}$ | = | $- x_{25} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $- a x_{25} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (4k) | O XII |
| $\mathbf{B_{83}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{25} \, \mathbf{a}_{2}- z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{25} \,\mathbf{\hat{y}}- c z_{25} \,\mathbf{\hat{z}}$ | (4k) | O XII |
| $\mathbf{B_{84}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{25} \, \mathbf{a}_{2}- z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{25} \,\mathbf{\hat{y}}- c z_{25} \,\mathbf{\hat{z}}$ | (4k) | O XII |
References
- Y. Repelin and E. Husson, Etudes structurales d'alumines de transition. I-alumines gamma et delta, Mater. Res. Bull. 25, 611–621 (1990), doi:10.1016/0025-5408(90)90027-Y.
Found in
- I. V. Pekov, I. P. Anikin, N. V. Chukanov, D. I. Belakovskiy, V. O. Yapaskurt, E. G. Sidorov, S. N. Britvin, and N. V. Zubkova, Deltalumite, a New Natural Modification of Alumina with a Spinel-Type Structure, Geol. Ore Deposits 62, 608–617 (2020), doi:10.1134/S1075701520070089. Translated from the Russian text: Zapiski Rossiiskogo Mineralogicheskogo Obshchestva 5, 45-58 (2019).
Prototype Generator
aflow --proto=A3B4_tP84_115_acef3g3j3k_6j6k --params=$a,c/a,z_{3},z_{4},z_{5},z_{6},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},z_{12},x_{13},z_{13},x_{14},z_{14},x_{15},z_{15},x_{16},z_{16},x_{17},z_{17},x_{18},z_{18},x_{19},z_{19},x_{20},z_{20},x_{21},z_{21},x_{22},z_{22},x_{23},z_{23},x_{24},z_{24},x_{25},z_{25}$