Steklite [KAl(SO$_{4}$)$_{2}$, $H3_{2}$] Structure: ABC8D2_hP12_150_a_b_dg_d-001
| Prototype | AlKO$_{8}$S$_{2}$ |
| AFLOW prototype label | ABC8D2_hP12_150_a_b_dg_d-001 |
| Strukturbericht designation | $H3_{2}$ |
| Mineral name | steklite |
| ICSD | 60170 |
| Pearson symbol | hP12 |
| Space group number | 150 |
| Space group symbol | $P321$ |
| AFLOW prototype command |
aflow --proto=ABC8D2_hP12_150_a_b_dg_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
NH$_{4}$(Al, Fe)(SO$_{4}$)$_{2}$ (godovikovite), KCr(SO$_{4}$)$_{2}$, RbCr(SO$_{4}$)$_{2}$
- This has been a rather difficult structure to follow through the literature. (Villars, 2016) quotes the structure given by (Manoli, 1970), but gives the space group as $P\overline{3}$ #147. (Murashko, 2013) lists the space group as both $P312$ #149 and $P321$ #150, as well as listing obviously incorrect Wyckoff positions.
- (West, 2008) states that the simple structure is in $P\overline{3}$ but that it may be doubled along the $c$ axis and be in space group $P321$.
- After correcting Murashko's results, we find that all of these interpretations yield essentially the same structure in a given layer, and only differ as the structure is reflected through the $z = 0$ plane. As it is not clear which structure is correct, we will use the original $H3_{2}$ structure given by (Hermann, 1937).
- Steklite is the name of the mineral form of this compound (Murashko, 2013). (Hermann, 1937) simply calls it Wasserfreier Alaun (anhydrous alum). For hydrated alum, KAl(SO$_{4}$)$_{2}$·12H$_{2}$O, see the $H4_{13}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | K I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2d) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2d) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2d) | S I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2d) | S I |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{8}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{10}}$ | = | $y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{11}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (6g) | O II |
| $\mathbf{B_{12}}$ | = | $- x_{5} \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (6g) | O II |
References
- L. Vegard and A. Maurstad, Die Kristallstruktur der wasserfreien Alaune R'R(S0$_{4}$)$_{2}$, Z. Kristallogr. 69, 519–532 (1929), doi:10.1524/zkri.1929.69.1.519.
- L. Vegard and A. Maurstad, Die Kristallstruktur der wasserfreien Alaune R'R(S0$_{4}$)$_{2}$, Skrifter utgitt av det Norske Videnskaps-Akademi i Oslo pp. 1–24 (1928).
- D. V. West, Q. Huang, H. W. Zandbergen, T. M. McQueen, and R. J. Cava, Structural disorder, octahedral coordination and two-dimensional ferromagnetism in anhydrous alums, J. Solid State Chem. 181, 2768–2775 (2008), doi:10.1016/j.jssc.2008.07.006.
- M. N. Murashko, I. V. Pekov, S. V. Krivovichev, A. P. Chernyatyeva, V. O. Yapaskurt, A. E. Zadov, and M. E. Zelensky, Steklite, KAl(SO$_{4}$)$_{2}$: A finding at the Tolbachik Volcano, Kamchatka, Russia, validating its status as a mineral species and crystal structure, Geol. Ore Deposits 55, 594–600 (2013), doi:10.1134/S1075701513070088.
- P. Villars, KAl(SO4)2 (KAl[SO4]2 trig1) Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database).
- J. M. Manoli, P. Herpin, and G. Pannetier, Structure cristalline du sulfate double d'aluminium et de potassium, Bull. Soc. Chim. Frace pp. 98–101 (1970).
Found in
- P. P. Ewald and C. Hermann, eds., Strukturbericht 1913-1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=ABC8D2_hP12_150_a_b_dg_d --params=$a,c/a,z_{3},z_{4},x_{5},y_{5},z_{5}$