γ-Na$_{2}$Ti$_{3}$Cl$_{8}$ Structure: A8B2C3_hR13_160_2a2b_2a_b-001
| Prototype | Cl$_{8}$Na$_{2}$Ti$_{3}$ |
| AFLOW prototype label | A8B2C3_hR13_160_2a2b_2a_b-001 |
| ICSD | 259123 |
| Pearson symbol | hR13 |
| Space group number | 160 |
| Space group symbol | $R3m$ |
| AFLOW prototype command |
aflow --proto=A8B2C3_hR13_160_2a2b_2a_b-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}$ |
- Na$_{2}$Ti$_{3}$Cl$_{8}$ can be found in three different phases (Hänni, 2017):
- $\gamma$–Na$_{2}$Ti$_{3}$Cl$_{8}$, below 210K (heating) or 190K (cooling) (this structure).
- $\beta$–Na$_{2}$Ti$_{3}$Cl$_{8}$ is found between 190 and 210K when samples are cooled. It is in the $R\overline{3}m$ space group, but we have no atomic positions.
- $\alpha$–Na$_{2}$Ti$_{3}$Cl$_{8}$, above 190/210K, is in the Na$_{2}$Mn$_{3}$Cl$_{8}$ structure.
- (Hänni, 2017) give the lattice constants of $\gamma$–Na$_{2}$Ti$_{3}$Cl$_{8}$ at 2K, and the atomic positions at 1.6K.
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (1a) | Cl I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (1a) | Cl II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (1a) | Na I |
| $\mathbf{B_{4}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (1a) | Na II |
| $\mathbf{B_{5}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | Cl III |
| $\mathbf{B_{6}}$ | = | $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | Cl III |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | Cl III |
| $\mathbf{B_{8}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (3b) | Cl IV |
| $\mathbf{B_{9}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (3b) | Cl IV |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (3b) | Cl IV |
| $\mathbf{B_{11}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (3b) | Ti I |
| $\mathbf{B_{12}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (3b) | Ti I |
| $\mathbf{B_{13}}$ | = | $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (3b) | Ti I |
References
- N. Hänni, M. Frontzek, J. Hauser, D. Cheptiakov, and K. Krämer, Low Temperature Phases of Na$_{2}$Ti$_{3}$Cl$_{8}$ Revisited, Z. Anorganische und Allgemeine Chemie 643, 2063–2069 (2017), doi:10.1002/zaac.201700331.
Prototype Generator
aflow --proto=A8B2C3_hR13_160_2a2b_2a_b --params=$a,c/a,x_{1},x_{2},x_{3},x_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7}$