Boracite (Mg$_{3}$B$_{7}$ClO$_{13}$) Structure: A7BC3D13_cF192_219_ce_a_d_bh-001
| Prototype | B$_{7}$ClMg$_{3}$O$_{13}$ |
| AFLOW prototype label | A7BC3D13_cF192_219_ce_a_d_bh-001 |
| Mineral name | boracite |
| ICSD | 22009 |
| Pearson symbol | cF192 |
| Space group number | 219 |
| Space group symbol | $F\overline{4}3c$ |
| AFLOW prototype command |
aflow --proto=A7BC3D13_cF192_219_ce_a_d_bh-001
--params=$a, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
Other compounds with this structure
Cr$_{3}$B$_{7}$BrO$_{13}$, Cr$_{3}$B$_{7}$ClO$_{13}$, Cr$_{3}$B$_{7}$IO$_{13}$, Fe$_{3}$B$_{7}$BrO$_{13}$, Fe$_{3}$B$_{7}$ClO$_{13}$, Fe$_{3}$B$_{7}$IO$_{13}$, Mg$_{3}$B$_{7}$BrO$_{13}$, Mg$_{3}$B$_{7}$ClO$_{13}$, Mg$_{3}$B$_{7}$IO$_{13}$, Mn$_{3}$B$_{7}$BrO$_{13}$, Mn$_{3}$B$_{7}$ClO$_{13}$, Mn$_{3}$B$_{7}$IO$_{13}$
- Experimental data was obtained at 400$^\circ$C.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (8a) | Cl I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (8a) | Cl I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24c) | B I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24c) | B I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24c) | B I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24c) | B I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (24c) | B I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24c) | B I |
| $\mathbf{B_{11}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Mg I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Mg I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Mg I |
| $\mathbf{B_{14}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Mg I |
| $\mathbf{B_{15}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mg I |
| $\mathbf{B_{16}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mg I |
| $\mathbf{B_{17}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32e) | B II |
| $\mathbf{B_{18}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- 3 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32e) | B II |
| $\mathbf{B_{19}}$ | = | $x_{5} \, \mathbf{a}_{1}- 3 x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32e) | B II |
| $\mathbf{B_{20}}$ | = | $- 3 x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32e) | B II |
| $\mathbf{B_{21}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32e) | B II |
| $\mathbf{B_{22}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(3 x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32e) | B II |
| $\mathbf{B_{23}}$ | = | $- \left(3 x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32e) | B II |
| $\mathbf{B_{24}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(3 x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32e) | B II |
| $\mathbf{B_{25}}$ | = | $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{26}}$ | = | $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{27}}$ | = | $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{28}}$ | = | $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{29}}$ | = | $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{30}}$ | = | $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{31}}$ | = | $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{32}}$ | = | $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{33}}$ | = | $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{34}}$ | = | $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{35}}$ | = | $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{36}}$ | = | $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{37}}$ | = | $\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{38}}$ | = | $\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{39}}$ | = | $- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{40}}$ | = | $\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{41}}$ | = | $\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{42}}$ | = | $\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{43}}$ | = | $\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{44}}$ | = | $- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{45}}$ | = | $\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{46}}$ | = | $- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{47}}$ | = | $\left(- x_{6} + y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
| $\mathbf{B_{48}}$ | = | $\left(x_{6} - y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (96h) | O II |
References
- S. Sueno, J. R. Clark, J. J. Papike, and J. A. Konnert, Crystal-Structure Refinement of Cubic Boracite, Am. Mineral. 58, 691–697 (1973).
Prototype Generator
aflow --proto=A7BC3D13_cF192_219_ce_a_d_bh --params=$a,x_{5},x_{6},y_{6},z_{6}$