Weberite (Na$_{2}$MgAlF$_{7}$) Structure: AB7CD2_oI44_24_a_c3d_b_ab-001
| Prototype | AlF$_{7}$MgNa$_{2}$ |
| AFLOW prototype label | AB7CD2_oI44_24_a_c3d_b_ab-001 |
| Mineral name | weberite |
| ICSD | 33512 |
| Pearson symbol | oI44 |
| Space group number | 24 |
| Space group symbol | $I2_12_12_1$ |
| AFLOW prototype command |
aflow --proto=AB7CD2_oI44_24_a_c3d_b_ab-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Na I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Na I |
| $\mathbf{B_{5}}$ | = | $y_{3} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}$ | (4b) | Mg I |
| $\mathbf{B_{6}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4b) | Mg I |
| $\mathbf{B_{7}}$ | = | $y_{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}$ | (4b) | Na II |
| $\mathbf{B_{8}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4b) | Na II |
| $\mathbf{B_{9}}$ | = | $\left(z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4c) | F I |
| $\mathbf{B_{10}}$ | = | $- \left(z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4c) | F I |
| $\mathbf{B_{11}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8d) | F II |
| $\mathbf{B_{12}}$ | = | $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- b \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8d) | F II |
| $\mathbf{B_{13}}$ | = | $\left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8d) | F II |
| $\mathbf{B_{14}}$ | = | $- \left(y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | F II |
| $\mathbf{B_{15}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8d) | F III |
| $\mathbf{B_{16}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- b \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8d) | F III |
| $\mathbf{B_{17}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8d) | F III |
| $\mathbf{B_{18}}$ | = | $- \left(y_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | F III |
| $\mathbf{B_{19}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8d) | F IV |
| $\mathbf{B_{20}}$ | = | $\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- b \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8d) | F IV |
| $\mathbf{B_{21}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8d) | F IV |
| $\mathbf{B_{22}}$ | = | $- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8d) | F IV |
References
- O. Knop, T. S. Cameron, and K. Jochem, What is the True Space Group of Weberite?, J. Solid State Chem. 43, 213–221 (1982), doi:10.1016/0022-4596(82)90231-6.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=AB7CD2_oI44_24_a_c3d_b_ab --params=$a,b/a,c/a,x_{1},x_{2},y_{3},y_{4},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8}$