Paratellurite (αTeO$_{2}$) Structure: A2B_tP12_92_b_a-002
| Prototype | O$_{2}$Te |
| AFLOW prototype label | A2B_tP12_92_b_a-002 |
| Mineral name | paratellurite |
| ICSD | 202792 |
| Pearson symbol | tP12 |
| Space group number | 92 |
| Space group symbol | $P4_12_12$ |
| AFLOW prototype command |
aflow --proto=A2B_tP12_92_b_a-002
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}$ |
Other compounds with this structure
$\gamma$-SnF$_{2}$
- TeO$_{2}$ has been observed in three different forms (Ceriotti, 2006; Liu, 2016):
- $\alpha$–TeO$_{2}$, paratellurite (this structure) is the ground state
- $\beta$–TeO$_{2}$, tellurite is stable under ambient conditions and is the most commonly observed phase
- $\gamma$–TeO$_{2}$ is metastable, and forms at 663K in the $\beta$–SnF$_{2}$ structure.
- Paratellurite and $\alpha$-cristobalite ($C30$) have the same AFLOW prototype label, A2B_tP12_92_b_a. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}$ | (4a) | Te I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | Te I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Te I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Te I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{7}}$ | = | $- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{8}}$ | = | $\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{9}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{10}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{11}}$ | = | $y_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{12}}$ | = | $- y_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
References
- P. A. Thomas, The crystal structure and absolute optical chirality of paratellurite, α-TeO$_{2}$, J. Phys. C: Solid State Phys. 21, 4611–4627 (1988), doi:10.1016/S0022-3697(00)00012-3.
- X. Liu, T. Mashimo1, N. Kawai1, T. Sekine, Z. Zeng, and X. Zhou, Phase transition and equation of state of paratellurite (TeO$_{2}$) under high pressure, Mater. Res. Express 3, 076206 (2016), doi:10.1088/2053-1591/3/7/076206.
Found in
- M. Ceriotti, F. Pietrucci, and M. Bernasconi, {\em Ab initio} study of the vibrational properties of crystalline TeO$_{2}$: The $\alpha$, $\beta$, and $\gamma$ phases, Phys. Rev. B 73, 104304 (2006), doi:10.1103/PhysRevB.73.104304.
Prototype Generator
aflow --proto=A2B_tP12_92_b_a --params=$a,c/a,x_{1},x_{2},y_{2},z_{2}$