RbAlF$_{4}$ II Structure: AB4C_tP12_127_a_eg_c-001
| Prototype | AlF$_{4}$Rb |
| AFLOW prototype label | AB4C_tP12_127_a_eg_c-001 |
| ICSD | 54121 |
| Pearson symbol | tP12 |
| Space group number | 127 |
| Space group symbol | $P4/mbm$ |
| AFLOW prototype command |
aflow --proto=AB4C_tP12_127_a_eg_c-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak x_{4}$ |
- (Bulou, 1982) identify three phases of RbAlF$_{4}$:
- Above 553K RbAlF$_{4}$ I has the tetragonal TlAlF$_{4}$ ($H0_{8}$) structure.
- Between 282 and 553K RbAlF$_{4}$ II is tetragonal, space group $P4/mbm$ #127 (this structure).
- Below 282K RbAlF$_{4}$ III is orthorhombic, space group $Pmmn$ #59.
- The different structures are distinguished by the tilt of the AlF$_{6}$ octahedra.
- We use Bulou and Nouet's data for RbAlF$_{4}$ II at 293K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (2a) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2c) | Rb I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2c) | Rb I |
| $\mathbf{B_{5}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | F I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | F I |
| $\mathbf{B_{7}}$ | = | $- z_{3} \, \mathbf{a}_{3}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | F I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4e) | F I |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (4g) | F II |
| $\mathbf{B_{10}}$ | = | $- x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (4g) | F II |
| $\mathbf{B_{11}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (4g) | F II |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (4g) | F II |
References
- A. Bulou and J. Nouet, Structural phase transitions in ferroelastic RbAlF$_{4}$. I. DSC, X-ray powder diffraction investigations and neutron powder profile refinement of the structures, J. Phys. C: Solid State Phys. 15, 183–196 (1982), doi:10.1088/0022-3719/15/2/004.
Prototype Generator
aflow --proto=AB4C_tP12_127_a_eg_c --params=$a,c/a,z_{3},x_{4}$