Clinochlore [Mg$_{3}$(Mg$_{2}$Al)(Si$_{3}$Al)O$_{10}$(OH)$_{8}$, $S5_{5}$] Structure: A3B5C4D2_mC112_15_a3ef_5f_4f_2f-001
| Prototype | Mg$_{3}$O$_{5}$(OH)$_{4}$Si$_{2}$ |
| AFLOW prototype label | A3B5C4D2_mC112_15_a3ef_5f_4f_2f-001 |
| Strukturbericht designation | $S5_{5}$ |
| Mineral name | clinochlore |
| ICSD | 26850 |
| Pearson symbol | mC112 |
| Space group number | 15 |
| Space group symbol | $C2/c$ |
| AFLOW prototype command |
aflow --proto=A3B5C4D2_mC112_15_a3ef_5f_4f_2f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}$ |
- We follow the interpretation of (McMurchy, 1934) as given by (Downs, 2003): We have labeled
Mg (4e)
are actually 2/3 magnesium and 1/3 aluminum, and the sites we have labeledSi (8f)
are 3/4 silicon and 1/4 aluminum. This does not exactly match the ICSD entry.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Mg I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4a) | Mg I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Mg II |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Mg II |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Mg III |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Mg III |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Mg IV |
| $\mathbf{B_{8}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | Mg IV |
| $\mathbf{B_{9}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Mg V |
| $\mathbf{B_{10}}$ | = | $- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c \left(z_{5} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Mg V |
| $\mathbf{B_{11}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Mg V |
| $\mathbf{B_{12}}$ | = | $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c \left(z_{5} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Mg V |
| $\mathbf{B_{13}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{14}}$ | = | $- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c \left(z_{6} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{15}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{16}}$ | = | $\left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c \left(z_{6} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{17}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{18}}$ | = | $- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + c \left(z_{7} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{19}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{20}}$ | = | $\left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c \left(z_{7} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{21}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O III |
| $\mathbf{B_{22}}$ | = | $- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + c \left(z_{8} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O III |
| $\mathbf{B_{23}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O III |
| $\mathbf{B_{24}}$ | = | $\left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c \left(z_{8} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O III |
| $\mathbf{B_{25}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O IV |
| $\mathbf{B_{26}}$ | = | $- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + c \left(z_{9} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O IV |
| $\mathbf{B_{27}}$ | = | $- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O IV |
| $\mathbf{B_{28}}$ | = | $\left(x_{9} + y_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c \left(z_{9} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O IV |
| $\mathbf{B_{29}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O V |
| $\mathbf{B_{30}}$ | = | $- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + c \left(z_{10} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O V |
| $\mathbf{B_{31}}$ | = | $- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O V |
| $\mathbf{B_{32}}$ | = | $\left(x_{10} + y_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c \left(z_{10} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O V |
| $\mathbf{B_{33}}$ | = | $\left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH I |
| $\mathbf{B_{34}}$ | = | $- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{11} + c \left(z_{11} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH I |
| $\mathbf{B_{35}}$ | = | $- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- \left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH I |
| $\mathbf{B_{36}}$ | = | $\left(x_{11} + y_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c \left(z_{11} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH I |
| $\mathbf{B_{37}}$ | = | $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + y_{12}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH II |
| $\mathbf{B_{38}}$ | = | $- \left(x_{12} + y_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{12} + c \left(z_{12} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH II |
| $\mathbf{B_{39}}$ | = | $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} + y_{12}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}- c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH II |
| $\mathbf{B_{40}}$ | = | $\left(x_{12} + y_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c \left(z_{12} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH II |
| $\mathbf{B_{41}}$ | = | $\left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH III |
| $\mathbf{B_{42}}$ | = | $- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{13} + c \left(z_{13} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH III |
| $\mathbf{B_{43}}$ | = | $- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}- c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH III |
| $\mathbf{B_{44}}$ | = | $\left(x_{13} + y_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c \left(z_{13} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH III |
| $\mathbf{B_{45}}$ | = | $\left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH IV |
| $\mathbf{B_{46}}$ | = | $- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{14} + c \left(z_{14} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH IV |
| $\mathbf{B_{47}}$ | = | $- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}- c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH IV |
| $\mathbf{B_{48}}$ | = | $\left(x_{14} + y_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c \left(z_{14} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | OH IV |
| $\mathbf{B_{49}}$ | = | $\left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} + y_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Si I |
| $\mathbf{B_{50}}$ | = | $- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{15} + c \left(z_{15} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Si I |
| $\mathbf{B_{51}}$ | = | $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- \left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}- c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Si I |
| $\mathbf{B_{52}}$ | = | $\left(x_{15} + y_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + c \left(z_{15} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Si I |
| $\mathbf{B_{53}}$ | = | $\left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}+\left(x_{16} + y_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{54}}$ | = | $- \left(x_{16} + y_{16}\right) \, \mathbf{a}_{1}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{16} + c \left(z_{16} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{55}}$ | = | $- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}- \left(x_{16} + y_{16}\right) \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- \left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}- c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{56}}$ | = | $\left(x_{16} + y_{16}\right) \, \mathbf{a}_{1}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + c \left(z_{16} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Si II |
References
- R. C. McMurchy, The Crystal Structure of the Chlorite Minerals, Z. Kristallogr. 88, 420–432 (1934), doi:10.1524/zkri.1934.88.1.420.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A3B5C4D2_mC112_15_a3ef_5f_4f_2f --params=$a,b/a,c/a,\beta,y_{2},y_{3},y_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16}$