α-CuZrF$_{6}$ Structure: AB12C_cF56_202_a_h_b-001
| Prototype | CuF$_{6}$Zr |
| AFLOW prototype label | AB12C_cF56_202_a_h_b-001 |
| ICSD | 30115 |
| Pearson symbol | cF56 |
| Space group number | 202 |
| Space group symbol | $Fm\overline{3}$ |
| AFLOW prototype command |
aflow --proto=AB12C_cF56_202_a_h_b-001
--params=$a, \allowbreak y_{3}, \allowbreak z_{3}$ |
- CuZrF$_{6}$ exists in four forms, depending on the temperature. Structures below 500K show evidence of a Jahn-Teller distortion.
- $\alpha'$–CuZrF$_{6}$ is the high temperature cubic form. Evidence from (Propach, 1978) shows this to be stable above $≈ 450$K. We use the lattice constant at 500K.
- $\alpha$–CuZrF$_{6}$ (this structure) is stable above 383K. The fluorine (6f) sites are doubled, with only one of each pair occupied. We use data taken at 393K.
- $\beta$–CuZrF$_{6}$ is stable between 353 and 383K. In this case the Jahn-Teller distortion is locked in, so there are only six fluorine sites, all fully occupied.
- $\gamma$–CuZrF$_{6}$ is stable below 353K. Again each fluorine site is only half-filled.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Cu I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Zr I |
| $\mathbf{B_{3}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48h) | F I |
| $\mathbf{B_{4}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48h) | F I |
| $\mathbf{B_{5}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48h) | F I |
| $\mathbf{B_{6}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48h) | F I |
| $\mathbf{B_{7}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (48h) | F I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (48h) | F I |
| $\mathbf{B_{9}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (48h) | F I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (48h) | F I |
| $\mathbf{B_{11}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (48h) | F I |
| $\mathbf{B_{12}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (48h) | F I |
| $\mathbf{B_{13}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (48h) | F I |
| $\mathbf{B_{14}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (48h) | F I |
References
- V. Propach and F. Steffens, Über die Strukturen der CuZrF$_{6}$-Modifikationen - Neutronenbeugungsuntersuchungen an den Kristallpulvern, Z. Krystallogr. 33, 268–274 (1978), doi:10.1515/znb-1978-0304.
Prototype Generator
aflow --proto=AB12C_cF56_202_a_h_b --params=$a,y_{3},z_{3}$