KO Structure: AB_oC16_64_e_f-002
| Prototype | KO |
| AFLOW prototype label | AB_oC16_64_e_f-002 |
| ICSD | 25527 |
| CCDC | 1601181 |
| Pearson symbol | oC16 |
| Space group number | 64 |
| Space group symbol | $Cmce$ |
| AFLOW prototype command |
aflow --proto=AB_oC16_64_e_f-002
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak z_{2}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- \left(y_{1} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{2}}$ | = | $\left(y_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{3}}$ | = | $\left(y_{1} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{4}}$ | = | $- \left(y_{1} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8e) | K I |
| $\mathbf{B_{5}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{6}}$ | = | $\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{7}}$ | = | $- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{8}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (8f) | O I |
References
- H. Föppl, Die Kristallstrukturen der Alkaliperoxyde, Z. Anorganische und Allgemeine Chemie 291, 12–50 (1957), doi:10.1002/zaac.19572910104.
First cited in
- H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters, X. Campilongo, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4, Comp. Mat. Sci. 240, 112988 (2024). (doi=10.1016/j.commatsci.2021.110450)
Geometry files
Prototype Generator
aflow --proto=AB_oC16_64_e_f --params=$a,b/a,c/a,y_{1},y_{2},z_{2}$