K$_{3}$CrO$_{8}$ Structure: AB3C8_tI24_121_a_bd_2i-001
| Prototype | CrK$_{3}$O$_{8}$ |
| AFLOW prototype label | AB3C8_tI24_121_a_bd_2i-001 |
| ICSD | 9356 |
| Pearson symbol | tI24 |
| Space group number | 121 |
| Space group symbol | $I\overline{4}2m$ |
| AFLOW prototype command |
aflow --proto=AB3C8_tI24_121_a_bd_2i-001
--params=$a, \allowbreak c/a, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
Zr$_{3}$GeO$_{8}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Cr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | K I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | K II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | K II |
| $\mathbf{B_{5}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8i) | O I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8i) | O I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8i) | O I |
| $\mathbf{B_{8}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8i) | O I |
| $\mathbf{B_{9}}$ | = | $\left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+2 x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8i) | O II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- 2 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8i) | O II |
| $\mathbf{B_{11}}$ | = | $- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8i) | O II |
| $\mathbf{B_{12}}$ | = | $\left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8i) | O II |
References
- R. Stomberg, Least-Squares Refinement of the Crystal Structure of Potassium Peroxochromate, Acta Chem. Scand. 17, 1563–1566 (1963), doi:10.3891/acta.chem.scand.17-1563.
Prototype Generator
aflow --proto=AB3C8_tI24_121_a_bd_2i --params=$a,c/a,x_{4},z_{4},x_{5},z_{5}$