Ag$_{3}$LiIr$_{2}$O$_{6}$ Structure: A3B2CD6_mC24_12_ag_h_c_ij-001
| Prototype | Ag$_{3}$Ir$_{2}$LiO$_{6}$ |
| AFLOW prototype label | A3B2CD6_mC24_12_ag_h_c_ij-001 |
| ICSD | 10616 |
| Pearson symbol | mC24 |
| Space group number | 12 |
| Space group symbol | $C2/m$ |
| AFLOW prototype command |
aflow --proto=A3B2CD6_mC24_12_ag_h_c_ij-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
Other compounds with this structure
Ag$_{3}$LiRu$_{2}$O$_{6}$, Cu$_{3}$LiIr$_{2}$O$_{6}$, H$_{3}$LiIr$_{2}$O$_{6}$
- Some authors designate H$_{3}$LiIr$_{2}$O$_{6}$ as the prototype for this structure, but as it is much easier to locate silver atoms than hydrogen we use Ag$_{3}$LiIr$_{2}$O$_{6}$.
- We have rearranged the primitive vectors of (Bette, 2019).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ag I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (2c) | Li I |
| $\mathbf{B_{3}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $b y_{3} \,\mathbf{\hat{y}}$ | (4g) | Ag II |
| $\mathbf{B_{4}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- b y_{3} \,\mathbf{\hat{y}}$ | (4g) | Ag II |
| $\mathbf{B_{5}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4h) | Ir I |
| $\mathbf{B_{6}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4h) | Ir I |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O I |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O I |
| $\mathbf{B_{9}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O II |
| $\mathbf{B_{11}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O II |
| $\mathbf{B_{12}}$ | = | $\left(x_{6} + y_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O II |
References
- S. Bette, T. Takayama, V. Duppel, A. Poulain, H. Takagi, and R. E. Dinnebier, Crystal structure and stacking faults in the layered honeycomb, delafossite-type materials Ag$_{3}$LiIr$_{2}$O$_{6}$ and Ag$_{3}$LiRu$_{2}$O$_{6}$, Dalton Transactions 48, 9250–9259 (2019), doi:10.1039/c9dt01789e.
Prototype Generator
aflow --proto=A3B2CD6_mC24_12_ag_h_c_ij --params=$a,b/a,c/a,\beta,y_{3},y_{4},x_{5},z_{5},x_{6},y_{6},z_{6}$