θ-AlF$_{3}$ Structure: AB3_tP64_129_2cdi_2cfhijk-001
| Prototype | AlF$_{3}$ |
| AFLOW prototype label | AB3_tP64_129_2cdi_2cfhijk-001 |
| ICSD | 79814 |
| Pearson symbol | tP64 |
| Space group number | 129 |
| Space group symbol | $P4/nmm$ |
| AFLOW prototype command |
aflow --proto=AB3_tP64_129_2cdi_2cfhijk-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}$ |
- AlF$_{3}$ has a variety of polymorphs (Le Bail, 2006) including:
- $\alpha$–AlF$_{3}$, which takes the rhombohedral FeF$_{3}$ ($D0_{12}$) structure.
- $\beta$–AlF$_{3}$ has a body-centered orthorhombic structure.
- $\eta$–AlF$_{3}$ has the $\beta$–AlH$_{3}$ structure.
- $\kappa$–AlF$_{3}$ is tetragonal structure.
- $\theta$–AlF$_{3}$ (this structure), also known as $\tau$–AlF$_{3}$, is a larger tetragonal structure.
- Above 713K AlF$_{3}$ transforms into the cubic ReO$_{3}$ ($D0_{9}$) structure (Morelock, 2014).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2c) | F I |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2c) | F I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2c) | F II |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2c) | F II |
| $\mathbf{B_{9}}$ | = | $0$ | = | $0$ | (4d) | Al III |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4d) | Al III |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (4d) | Al III |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4d) | Al III |
| $\mathbf{B_{13}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4f) | F III |
| $\mathbf{B_{14}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4f) | F III |
| $\mathbf{B_{15}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (4f) | F III |
| $\mathbf{B_{16}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (4f) | F III |
| $\mathbf{B_{17}}$ | = | $x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | F IV |
| $\mathbf{B_{18}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | F IV |
| $\mathbf{B_{19}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | F IV |
| $\mathbf{B_{20}}$ | = | $- x_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | F IV |
| $\mathbf{B_{21}}$ | = | $- x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | F IV |
| $\mathbf{B_{22}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | F IV |
| $\mathbf{B_{23}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | F IV |
| $\mathbf{B_{24}}$ | = | $x_{7} \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | F IV |
| $\mathbf{B_{25}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Al IV |
| $\mathbf{B_{26}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Al IV |
| $\mathbf{B_{27}}$ | = | $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Al IV |
| $\mathbf{B_{28}}$ | = | $y_{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Al IV |
| $\mathbf{B_{29}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Al IV |
| $\mathbf{B_{30}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Al IV |
| $\mathbf{B_{31}}$ | = | $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Al IV |
| $\mathbf{B_{32}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Al IV |
| $\mathbf{B_{33}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | F V |
| $\mathbf{B_{34}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | F V |
| $\mathbf{B_{35}}$ | = | $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | F V |
| $\mathbf{B_{36}}$ | = | $y_{9} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | F V |
| $\mathbf{B_{37}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | F V |
| $\mathbf{B_{38}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | F V |
| $\mathbf{B_{39}}$ | = | $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | F V |
| $\mathbf{B_{40}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | F V |
| $\mathbf{B_{41}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8j) | F VI |
| $\mathbf{B_{42}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8j) | F VI |
| $\mathbf{B_{43}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8j) | F VI |
| $\mathbf{B_{44}}$ | = | $x_{10} \, \mathbf{a}_{1}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8j) | F VI |
| $\mathbf{B_{45}}$ | = | $- x_{10} \, \mathbf{a}_{1}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8j) | F VI |
| $\mathbf{B_{46}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8j) | F VI |
| $\mathbf{B_{47}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8j) | F VI |
| $\mathbf{B_{48}}$ | = | $- x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8j) | F VI |
| $\mathbf{B_{49}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{50}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{51}}$ | = | $- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{52}}$ | = | $y_{11} \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{53}}$ | = | $- x_{11} \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{54}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{55}}$ | = | $\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{56}}$ | = | $- y_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{57}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{58}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{59}}$ | = | $\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{60}}$ | = | $- y_{11} \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{61}}$ | = | $x_{11} \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{62}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{63}}$ | = | $- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
| $\mathbf{B_{64}}$ | = | $y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16k) | F VII |
References
- N. Herron, D. L. Thorn, R. L. Harlow, G. A. Jones, J. B. Parise, J. A. Fernandez-Baca, and T. Vogt, Preparation and Structural Characterization of Two New Phases of Aluminum Trifluoride, Chem. Mater. 7, 75–83 (1995), doi:10.1021/cm00049a013.
- C. R. Morelock, J. C. Hancock, and A. P. Wilkinson, Thermal expansion and phase transitions of α-AlF$_{3}$, J. Solid State Chem. 219, 143–147 (2014), doi:10.1016/j.jssc.2014.07.031.
Found in
- A. L. Bail and F. Calvayrac, Hypothetical AlF$_{3}$ crystal structures, J. Solid State Chem. 179, 3159–3166 (2006), doi:10.1016/j.jssc.2006.06.010.
Prototype Generator
aflow --proto=AB3_tP64_129_2cdi_2cfhijk --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{6},x_{7},y_{8},z_{8},y_{9},z_{9},x_{10},z_{10},x_{11},y_{11},z_{11}$