Mayenite (12 CaO$\cdot$7Al$_{2}$O$_{3}$, $K7_4$, C12A7) Structure: A7B12C19_cI152_220_ac_2d_bce-001
| Prototype | Al$_{14}$Ca$_{12}$O$_{33}$ |
| AFLOW prototype label | A7B12C19_cI152_220_ac_2d_bce-001 |
| Strukturbericht designation | $K7_{4}$ |
| Mineral name | mayenite |
| ICSD | 24100 |
| Pearson symbol | cI152 |
| Space group number | 220 |
| Space group symbol | $I\overline{4}3d$ |
| AFLOW prototype command |
aflow --proto=A7B12C19_cI152_220_ac_2d_bce-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}$ |
- We present the structure determined by (Boysen, 2007) with data taken at 293K. This slightly differs from the original determination of (Büssem, 1936), which was given the $K7_{4}$ designation by (Gottfried, 1938). In the original work, the calcium atoms were thought to be located at a single (24d) site. Newer findings show that calcium is split between two (24d) sites, with the site we have labeled Ca-I having 87.5% of the atoms and Ca-II the remainder, although presumably only one of the two sites is occupied in any pair.
- All studies show that the O-I (12a) site is only partially occupied: if this is occupied 1/6 of the time we get the proper stoichiometry, though (Boysen, 2007) found the occupation was 0.251 at 293K, dropping as the temperature decreased.
- This structure is often referred to in the literature as C12A7 to distinguish it from other CaO/Al$_{2}$O$_{3}$ compounds.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12a) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}$ | (12a) | Al I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}$ | (12a) | Al I |
| $\mathbf{B_{5}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (12a) | Al I |
| $\mathbf{B_{6}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (12a) | Al I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{4}a \,\mathbf{\hat{z}}$ | (12b) | O I |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12b) | O I |
| $\mathbf{B_{9}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12b) | O I |
| $\mathbf{B_{10}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12b) | O I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (12b) | O I |
| $\mathbf{B_{12}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (12b) | O I |
| $\mathbf{B_{13}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16c) | Al II |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16c) | Al II |
| $\mathbf{B_{15}}$ | = | $- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16c) | Al II |
| $\mathbf{B_{16}}$ | = | $- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16c) | Al II |
| $\mathbf{B_{17}}$ | = | $\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Al II |
| $\mathbf{B_{18}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Al II |
| $\mathbf{B_{19}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Al II |
| $\mathbf{B_{20}}$ | = | $- 2 x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Al II |
| $\mathbf{B_{21}}$ | = | $2 x_{4} \, \mathbf{a}_{1}+2 x_{4} \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16c) | O II |
| $\mathbf{B_{22}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(2 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16c) | O II |
| $\mathbf{B_{23}}$ | = | $- \left(2 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16c) | O II |
| $\mathbf{B_{24}}$ | = | $- \left(2 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16c) | O II |
| $\mathbf{B_{25}}$ | = | $\left(2 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | O II |
| $\mathbf{B_{26}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | O II |
| $\mathbf{B_{27}}$ | = | $- 2 x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | O II |
| $\mathbf{B_{28}}$ | = | $- 2 x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | O II |
| $\mathbf{B_{29}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{30}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{31}}$ | = | $x_{5} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}$ | (24d) | Ca I |
| $\mathbf{B_{32}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{33}}$ | = | $\left(x_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{34}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{35}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{36}}$ | = | $- \left(x_{5} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{37}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{38}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{39}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{40}}$ | = | $- x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24d) | Ca I |
| $\mathbf{B_{41}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{42}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{43}}$ | = | $x_{6} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}$ | (24d) | Ca II |
| $\mathbf{B_{44}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{45}}$ | = | $\left(x_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{46}}$ | = | $- \left(x_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{47}}$ | = | $\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{48}}$ | = | $- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{49}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{50}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{51}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{52}}$ | = | $- x_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (24d) | Ca II |
| $\mathbf{B_{53}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{54}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{55}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{56}}$ | = | $- \left(y_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{57}}$ | = | $\left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{58}}$ | = | $- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{59}}$ | = | $\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{60}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{61}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{62}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{63}}$ | = | $- \left(x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{64}}$ | = | $\left(x_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- \left(y_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{65}}$ | = | $\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{66}}$ | = | $\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{67}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{68}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{69}}$ | = | $\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{70}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{71}}$ | = | $\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{72}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{73}}$ | = | $\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{74}}$ | = | $- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{75}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
| $\mathbf{B_{76}}$ | = | $\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O III |
References
- H. Boysen, M. Lerch, A. Stys, and A. Senyshyn, Structure and oxygen mobility in mayenite (Ca$_{12}$Al$_{14}$O$_{33}$): a high-temperature neutron powder diffraction study, Acta Crystallogr. Sect. B 63, 675–682 (2007), doi:10.1107/S0108768107030005.
- W. Büssem and A. Eitel, Die Struktur des Pentacalciumtrialuminats, Zeitschrift für Kristallographie 95, 175–188 (1936).
- C. Gottfried, ed., Strukturbericht Band IV 1936 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1938).
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A7B12C19_cI152_220_ac_2d_bce --params=$a,x_{3},x_{4},x_{5},x_{6},x_{7},y_{7},z_{7}$