β-ThCl$_{4}$ Structure: A4B_tI20_141_h_a-001
| Prototype | Cl$_{4}$Th |
| AFLOW prototype label | A4B_tI20_141_h_a-001 |
| ICSD | 26197 |
| Pearson symbol | tI20 |
| Space group number | 141 |
| Space group symbol | $I4_1/amd$ |
| AFLOW prototype command |
aflow --proto=A4B_tI20_141_h_a-001
--params=$a, \allowbreak c/a, \allowbreak y_{2}, \allowbreak z_{2}$ |
- $\beta$–ThCl$_{4}$ is stable above 405$^\circ$C. Below that temperature it transforms into $\alpha$–ThCl$_{4}$. (Mason, 1974)
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (4a) | Th I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (4a) | Th I |
| $\mathbf{B_{3}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16h) | Cl I |
| $\mathbf{B_{4}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16h) | Cl I |
| $\mathbf{B_{5}}$ | = | $z_{2} \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | Cl I |
| $\mathbf{B_{6}}$ | = | $z_{2} \, \mathbf{a}_{1}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | Cl I |
| $\mathbf{B_{7}}$ | = | $\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (16h) | Cl I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (16h) | Cl I |
| $\mathbf{B_{9}}$ | = | $- z_{2} \, \mathbf{a}_{1}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | Cl I |
| $\mathbf{B_{10}}$ | = | $- z_{2} \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | Cl I |
References
- K. Mucker, G. S. Smith, Q. Johnson, and R. E. Elson, Refinement of the Crystal Structure of ThCl$_{4}$, Acta Crystallogr. Sect. B 25, 2362–2365 (1969), doi:10.1107/S056774086900570X.
Found in
- J. T. Mason, M. C. Jha, and P. Chiotti, Crystal Structures of the ThCl$_{4}$ Polymorphs, J. Less-Common Met. 34, 143–151 (1974), doi:10.1016/0022-5088(74)90224-0.
Prototype Generator
aflow --proto=A4B_tI20_141_h_a --params=$a,c/a,y_{2},z_{2}$