Manganese-leonite [K$_{2}$Mn(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, $H4_{23}$] Structure: A8B2CD15E2_mC112_12_2i3j_j_ac_g4i5j_2i-001
| Prototype | H$_{8}$K$_{2}$MnO$_{12}$S$_{2}$ |
| AFLOW prototype label | A8B2CD15E2_mC112_12_2i3j_j_ac_g4i5j_2i-001 |
| Strukturbericht designation | $H4_{23}$ |
| Mineral name | manganese-leonite |
| ICSD | 92700 |
| Pearson symbol | mC112 |
| Space group number | 12 |
| Space group symbol | $C2/m$ |
| AFLOW prototype command |
aflow --proto=A8B2CD15E2_mC112_12_2i3j_j_ac_g4i5j_2i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}$ |
Other compounds with this structure
(NH$_{2}$)$_{2}$Co(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, (NH$_{2}$)$_{2}$Cu(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, (NH$_{2}$)$_{2}$Fe(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, (NH$_{2}$)$_{2}$Mg(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, (NH$_{2}$)$_{2}$Mn(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cd$_{2}$Co(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cd$_{2}$Cu(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cd$_{2}$Fe(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cd$_{2}$Mg(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cd$_{2}$Mn(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cs$_{2}$Co(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cs$_{2}$Cu(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cs$_{2}$Fe(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cs$_{2}$Mg(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Cs$_{2}$Mn(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, K$_{2}$Co(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, K$_{2}$Cu(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, K$_{2}$Fe(SO$_{4}$)$_{2}\cdot$4H$_{2}$O (mereiterite), K$_{2}$Mg(SO$_{4}$)$_{2}\cdot$4H$_{2}$O (leonite), Rb$_{2}$Co(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Rb$_{2}$Cu(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Rb$_{2}$Fe(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Rb$_{2}$Mg(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Rb$_{2}$Mn(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Tl$_{2}$Co(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Tl$_{2}$Cu(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Tl$_{2}$Fe(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Tl$_{2}$Mg(SO$_{4}$)$_{2}\cdot$4H$_{2}$O, Tl$_{2}$Mn(SO$_{4}$)$_{2}\cdot$4H$_{2}$O
- Manganese-leonite is found in three forms:
- A low-temperature structure, stable below 168K.
- An intermediate-temperature structure, stable in between 168 and 205K.
- This room temperature structure, Strukturbericht $H4_{23}$, stable above 205K.
- Properly the prototype of leonite is K$_{2}$Mg(SO$_{4}$)$_{2}$·4H$_{2}$O, but (Herrmann, 1943) gives manganese-leonite Strukturbericht symbol $H4_{23}$, so we will use Mn-leonite as the prototype.
- Unlike the lower temperature structures, this leonite structure is characterized by the disorder of the second sulfate group, centered on atom S-II (Hertweck, 2001). The oxygen sites around S-II, labeled O-VII, O-VIII, and O-IX in our notation, are only occupied 50% of the time. (Anspach, 1939), who did the original determination of this structure, was not able to see the disorder and so gives an ordered structure for both sulfates.
- We use the structure determined by (Hertweck, 2001) at room temperature, 293K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (2c) | Mn II |
| $\mathbf{B_{3}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $b y_{3} \,\mathbf{\hat{y}}$ | (4g) | O I |
| $\mathbf{B_{4}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- b y_{3} \,\mathbf{\hat{y}}$ | (4g) | O I |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | H I |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | H I |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | H II |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | H II |
| $\mathbf{B_{9}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O II |
| $\mathbf{B_{10}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O II |
| $\mathbf{B_{11}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O III |
| $\mathbf{B_{12}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O III |
| $\mathbf{B_{13}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O IV |
| $\mathbf{B_{14}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O IV |
| $\mathbf{B_{15}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O V |
| $\mathbf{B_{16}}$ | = | $- x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O V |
| $\mathbf{B_{17}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | S I |
| $\mathbf{B_{18}}$ | = | $- x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | S I |
| $\mathbf{B_{19}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | S II |
| $\mathbf{B_{20}}$ | = | $- x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- \left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | S II |
| $\mathbf{B_{21}}$ | = | $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + y_{12}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H III |
| $\mathbf{B_{22}}$ | = | $- \left(x_{12} + y_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}- c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H III |
| $\mathbf{B_{23}}$ | = | $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} + y_{12}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}- c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H III |
| $\mathbf{B_{24}}$ | = | $\left(x_{12} + y_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H III |
| $\mathbf{B_{25}}$ | = | $\left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H IV |
| $\mathbf{B_{26}}$ | = | $- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}- c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H IV |
| $\mathbf{B_{27}}$ | = | $- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}- c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H IV |
| $\mathbf{B_{28}}$ | = | $\left(x_{13} + y_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H IV |
| $\mathbf{B_{29}}$ | = | $\left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H V |
| $\mathbf{B_{30}}$ | = | $- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}- c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H V |
| $\mathbf{B_{31}}$ | = | $- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}- c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H V |
| $\mathbf{B_{32}}$ | = | $\left(x_{14} + y_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | H V |
| $\mathbf{B_{33}}$ | = | $\left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} + y_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | K I |
| $\mathbf{B_{34}}$ | = | $- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- \left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}- c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | K I |
| $\mathbf{B_{35}}$ | = | $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- \left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}- c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | K I |
| $\mathbf{B_{36}}$ | = | $\left(x_{15} + y_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | K I |
| $\mathbf{B_{37}}$ | = | $\left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}+\left(x_{16} + y_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VI |
| $\mathbf{B_{38}}$ | = | $- \left(x_{16} + y_{16}\right) \, \mathbf{a}_{1}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- \left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}- c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VI |
| $\mathbf{B_{39}}$ | = | $- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}- \left(x_{16} + y_{16}\right) \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- \left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}- c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VI |
| $\mathbf{B_{40}}$ | = | $\left(x_{16} + y_{16}\right) \, \mathbf{a}_{1}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}+c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VI |
| $\mathbf{B_{41}}$ | = | $\left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} + y_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\left(a x_{17} + c z_{17} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+c z_{17} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VII |
| $\mathbf{B_{42}}$ | = | $- \left(x_{17} + y_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $- \left(a x_{17} + c z_{17} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}- c z_{17} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VII |
| $\mathbf{B_{43}}$ | = | $- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} + y_{17}\right) \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $- \left(a x_{17} + c z_{17} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}- c z_{17} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VII |
| $\mathbf{B_{44}}$ | = | $\left(x_{17} + y_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\left(a x_{17} + c z_{17} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}+c z_{17} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VII |
| $\mathbf{B_{45}}$ | = | $\left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} + y_{18}\right) \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\left(a x_{18} + c z_{18} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}+c z_{18} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VIII |
| $\mathbf{B_{46}}$ | = | $- \left(x_{18} + y_{18}\right) \, \mathbf{a}_{1}- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $- \left(a x_{18} + c z_{18} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}- c z_{18} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VIII |
| $\mathbf{B_{47}}$ | = | $- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}- \left(x_{18} + y_{18}\right) \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $- \left(a x_{18} + c z_{18} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}- c z_{18} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VIII |
| $\mathbf{B_{48}}$ | = | $\left(x_{18} + y_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\left(a x_{18} + c z_{18} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}+c z_{18} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O VIII |
| $\mathbf{B_{49}}$ | = | $\left(x_{19} - y_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} + y_{19}\right) \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}+c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O IX |
| $\mathbf{B_{50}}$ | = | $- \left(x_{19} + y_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} - y_{19}\right) \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $- \left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}- c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O IX |
| $\mathbf{B_{51}}$ | = | $- \left(x_{19} - y_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} + y_{19}\right) \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $- \left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}- c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O IX |
| $\mathbf{B_{52}}$ | = | $\left(x_{19} + y_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} - y_{19}\right) \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}+c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O IX |
| $\mathbf{B_{53}}$ | = | $\left(x_{20} - y_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} + y_{20}\right) \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}+c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O X |
| $\mathbf{B_{54}}$ | = | $- \left(x_{20} + y_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} - y_{20}\right) \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $- \left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}- c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O X |
| $\mathbf{B_{55}}$ | = | $- \left(x_{20} - y_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} + y_{20}\right) \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $- \left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}- c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O X |
| $\mathbf{B_{56}}$ | = | $\left(x_{20} + y_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} - y_{20}\right) \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}+c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O X |
References
- B. Hertweck, G. Giester, and E. Libowitzky, The crystal structures of the low-temperature phases of leonite-type compounds, K$_{2}$Me(SO$_{4}$)$_{2}$$\cdot$4H$_{2}$O (Me$^{2+}$ = Mg, Mn, Fe), Am. Mineral. 86, 1282–1292 (2001), doi:10.2138/am-2001-1016.
- H. Anspach, Die Struktur von Mn-Leonit, Z. Kristallogr. 101, 39–77 (1939), doi:10.1524/zkri.1939.101.1.39.
- K. Herrmann, ed., Strukturbericht Band VII 1939 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1943).
Prototype Generator
aflow --proto=A8B2CD15E2_mC112_12_2i3j_j_ac_g4i5j_2i --params=$a,b/a,c/a,\beta,y_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20}$