High-Temperature Sr$_{4}$Al$_{6}$O$_{16}$S Structure: A6B28CD8_cI86_197_e_c2f_a_2c-001
| Prototype | Al$_{6}$O$_{16}$SSr$_{4}$ |
| AFLOW prototype label | A6B28CD8_cI86_197_e_c2f_a_2c-001 |
| ICSD | 236132 |
| CCDC | 1535840 |
| Pearson symbol | cI86 |
| Space group number | 197 |
| Space group symbol | $I23$ |
| AFLOW prototype command |
aflow --proto=A6B28CD8_cI86_197_e_c2f_a_2c-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}$ |
- This is the high temperature structure of Sr$_{4}$Al$_{6}$O$_{16}$S. Below $≈ 520$K it transforms into the orthorhombic Ca$_{4}$Al$_{6}$O$_{16}$S structure.
- There is disorder in this structure:
- The Sr-I and Sr-II sites are 56% and 44% occupied, respectively. These are the paired atoms in the diagram. Only one site in each pair is occupied.
- The O-I (8c) site and the O-III (24f) site are 26.3% and 24.6% occupied. These are the atoms around the sulfur atom. Only four of the sixteen available oxygen sites around each sulfer atom are occupied.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | S I |
| $\mathbf{B_{2}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | O I |
| $\mathbf{B_{3}}$ | = | $- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | O I |
| $\mathbf{B_{4}}$ | = | $- 2 x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | O I |
| $\mathbf{B_{5}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | O I |
| $\mathbf{B_{6}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Sr I |
| $\mathbf{B_{7}}$ | = | $- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Sr I |
| $\mathbf{B_{8}}$ | = | $- 2 x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Sr I |
| $\mathbf{B_{9}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Sr I |
| $\mathbf{B_{10}}$ | = | $2 x_{4} \, \mathbf{a}_{1}+2 x_{4} \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{11}}$ | = | $- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{12}}$ | = | $- 2 x_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{13}}$ | = | $- 2 x_{4} \, \mathbf{a}_{1}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (12e) | Al I |
| $\mathbf{B_{15}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (12e) | Al I |
| $\mathbf{B_{16}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12e) | Al I |
| $\mathbf{B_{17}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12e) | Al I |
| $\mathbf{B_{18}}$ | = | $x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{z}}$ | (12e) | Al I |
| $\mathbf{B_{19}}$ | = | $- x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{z}}$ | (12e) | Al I |
| $\mathbf{B_{20}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{21}}$ | = | $- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{22}}$ | = | $\left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{23}}$ | = | $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{24}}$ | = | $\left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{25}}$ | = | $- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{26}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{27}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{28}}$ | = | $\left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{29}}$ | = | $- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{30}}$ | = | $- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{31}}$ | = | $\left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24f) | O II |
| $\mathbf{B_{32}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{33}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{34}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{35}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{36}}$ | = | $\left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{37}}$ | = | $- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{38}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{39}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{40}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{41}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{42}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
| $\mathbf{B_{43}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24f) | O III |
References
- H. Banno, S. Ichikawa, S. Takeda, T. Asaka, M. Colas, P. Thomas, and K. Fukuda, Crystal structures and polymorphism of Sr$_{4}$[Al$_{6}$O$_{12}$]SO$_{4}$, J. Ceram. Soc. Japan 125, 364–370 (2017), doi:10.2109/jcersj2.17008.
Found in
- ICSD, Inorganic Crystal Structure Database. ID 236132.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A6B28CD8_cI86_197_e_c2f_a_2c --params=$a,x_{2},x_{3},x_{4},x_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7}$