Cronstedtite {Fe(Fe,Si)[(OH)$_{2}$O]O$_{3}$OH, $S5_{7}$} Structure: AB3C2D_hR7_160_a_b_2a_a-001
| Prototype | FeO$_{3}$(OH)$_{2}$Si |
| AFLOW prototype label | AB3C2D_hR7_160_a_b_2a_a-001 |
| Strukturbericht designation | $S5_{7}$ |
| Mineral name | cronstedtite |
| ICSD | 161270 |
| Pearson symbol | hR7 |
| Space group number | 160 |
| Space group symbol | $R3m$ |
| AFLOW prototype command |
aflow --proto=AB3C2D_hR7_160_a_b_2a_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak z_{5}$ |
- 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, and the O (3b) site has 2/3 occupation.
- 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.
- The ICSD entry gives $a$=3.16Å, but (Hendricks, 1939) finds 5.48Å. The ICSD value is apparently a misinterpretaion of Hendricks's Figure 2.
- This is the final structure given a Strukturbericht designation.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (1a) | Fe I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (1a) | OH I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (1a) | OH II |
| $\mathbf{B_{4}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (1a) | Si I |
| $\mathbf{B_{5}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | O I |
| $\mathbf{B_{6}}$ | = | $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | O I |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | O I |
References
- S. B. Hendricks, Random structures of layer minerals as illustrated by cronstedite (2FeO$\cdot$Fe$_{2}$O$_{3}$$\cdot$SiO$_{2}$$\cdot$2H$_{2}$O). Possible iron content of kaolin, Am. Mineral. 24, 529–539 (1939).
- C. Frondel, Polytypism in Cronstedtite, Am. Mineral. 47, 781–783 (1962).
Found in
- K. Herrmann, ed., Strukturbericht Band VII 1939 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1943).
Prototype Generator
aflow --proto=AB3C2D_hR7_160_a_b_2a_a --params=$a,c/a,x_{1},x_{2},x_{3},x_{4},x_{5},z_{5}$