Cronstedtite {Fe(Fe,Si)[(OH)2,O]O3, $S5_{7}$} Structure : AB3C2D_hR7_160_a_b_2a_a

Picture of Structure; Click for Big Picture
Prototype : FeO3(OH)2Si
AFLOW prototype label : AB3C2D_hR7_160_a_b_2a_a
Strukturbericht designation : $S5_{7}$
Pearson symbol : hR7
Space group number : 160
Space group symbol : $R3m$
AFLOW prototype command : aflow --proto=AB3C2D_hR7_160_a_b_2a_a
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$z_{5}$


  • This particular structure of cronstedtite (also spelled cronstedite) is technically cronstedtite–3R, as there are three layers in the hexagonal cell, repeated in rhombohedral order. It is characterized by a high degree of disorder. The site we have labeled Si is better written as (Si,Fe), and the site labeled OH–I is actually [(OH)2,O]. In addition the pure iron site, Fe (1a), is only occupied 90% of the time.
  • As noted by (Frondel, 1962), there are a large number of varieties of cronstedtite, which each type having a different stacking sequence in the hexagonal cell.
  • (Sterling, 1939) and (Hermann, 1943) put this structure in space group $R3$ #146, but the coordinates given by Sterling resolve to space group $R3m$ #160, and so we list this structure there.
  • This is the final structure given a Strukturbericht designation.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Fe} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{OH I} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{OH II} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Si} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{O} \\ \mathbf{B}_{6} & = & z_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{5}+z_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{O} \\ \mathbf{B}_{7} & = & x_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{5}+z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{O} \\ \end{array} \]

References

  • S. B. Hendricks, Random structures of layer minerals as illustrated by cronstedite (2FeO·Fe2O3·SiO2·2H2O). Possible iron content of kaolin, Am. Mineral. 24, 529–539 (1939).
  • C. Frondel, Polytypism in Cronstedtite, Am. Mineral. 47, 781–783 (1962).

Found in

  • K. Herrmann, ed., Strukturbericht Band VII 1939 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1943).

Geometry files


Prototype Generator

aflow --proto=AB3C2D_hR7_160_a_b_2a_a --params=

Species:

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