Ag$_{2}$O$_{3}$ Structure: A2B3_oF40_43_b_ab-001
| Prototype | Ag$_{2}$O$_{3}$ |
| AFLOW prototype label | A2B3_oF40_43_b_ab-001 |
| ICSD | 59193 |
| Pearson symbol | oF40 |
| Space group number | 43 |
| Space group symbol | $Fdd2$ |
| AFLOW prototype command |
aflow --proto=A2B3_oF40_43_b_ab-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- This structure is a distortion of the D5$_{5}$ Ag$_{2}$O$_{3}$ structure (A2B3_cP10_224_b_d), although (Standke, 1986) does not seem to be aware of the earlier work. This is most likely closer to the correct structure for Ag$_{2}$O$_{3}$ than the D5$_{5}$ structure is.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (8a) | O I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8a) | O I |
| $\mathbf{B_{3}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16b) | Ag I |
| $\mathbf{B_{4}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16b) | Ag I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Ag I |
| $\mathbf{B_{6}}$ | = | $\left(x_{2} + y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Ag I |
| $\mathbf{B_{7}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16b) | O II |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16b) | O II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | O II |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} + y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | O II |
References
- B. Standke and M. Jansen, Darstellung und Kristallstruktur von Ag$_{2}$O$_{3}$, Z. Anorganische und Allgemeine Chemie 535, 39–46 (1986), doi:10.1002/zaac.1986535040.
Prototype Generator
aflow --proto=A2B3_oF40_43_b_ab --params=$a,b/a,c/a,z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$