Steklite [KAl(SO4)2, $H3_{2}$] Structure : ABC8D2_hP12_150_b_a_dg_d

Picture of Structure; Click for Big Picture
Prototype : AlKO8S2
AFLOW prototype label : ABC8D2_hP12_150_b_a_dg_d
Strukturbericht designation : $H3_{2}$
Pearson symbol : hP12
Space group number : 150
Space group symbol : $P321$
AFLOW prototype command : aflow --proto=ABC8D2_hP12_150_b_a_dg_d
--params=
$a$,$c/a$,$z_{3}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$


Other compounds with this structure

  • NH4(Al,Fe)(SO4)2 (godovikovite), KCr(SO4)2, and RbCr(SO4)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(SO4)2 · 12H2O, see the $H4_{13}$ structure.

Trigonal Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{K} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Al} \\ \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{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{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{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{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{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{S} \\ \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{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{S} \\ \mathbf{B}_{7} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & -y_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & y_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{5}-y_{5}\right)a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \mathbf{B}_{12} & = & -x_{5} \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{O II} \\ \end{array} \]

References

  • L. Vegard and A. Maurstad, Die Kristallstruktur der wasserfreien Alaune $R$$R$‘‘(SO4)2, Zeitschrift für Kristallographie – Crystalline Materials 69, 519–532 (1929), doi:10.1524/zkri.1929.69.1.519.
  • L. Vegard and A. Maurstad, Die Kristallstruktur der wasserfreien Alaune R'R''(SO4)2, Skrifter utgitt av det Norske Videnskaps–Akademi i Oslo 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(SO4)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.
  • J.–M. Manoli, P. Herpin, and G. Pannetier, Structure cristalline du sulfate double d'aluminium et de potassium, Bull. Soc. Chim. France 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).

Geometry files


Prototype Generator

aflow --proto=ABC8D2_hP12_150_b_a_dg_d --params=

Species:

Running:

Output: