Zabuyelite (Li$_{2}$CO$_{3}$) Structure: AB2C3_mC24_15_e_f_ef-001
| Prototype | CLi$_{2}$O$_{3}$ |
| AFLOW prototype label | AB2C3_mC24_15_e_f_ef-001 |
| Mineral name | zabuyelite |
| ICSD | 100324 |
| Pearson symbol | mC24 |
| Space group number | 15 |
| Space group symbol | $C2/c$ |
| AFLOW prototype command |
aflow --proto=AB2C3_mC24_15_e_f_ef-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | C I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | C I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Li I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c \left(z_{3} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Li I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Li I |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c \left(z_{3} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | Li I |
| $\mathbf{B_{9}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c \left(z_{4} - \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{11}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c \left(z_{4} + \frac{1}{2}\right) \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \sin{\beta} \,\mathbf{\hat{z}}$ | (8f) | O II |
References
- H. Effenberger and J. Zemann, Verfeinerung der Kristallstruktur des Lithiumkarbonates, Li$_{2}$CO$_{3}$, Z. Kristallogr. 150, 133–138 (1979).
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=AB2C3_mC24_15_e_f_ef --params=$a,b/a,c/a,\beta,y_{1},y_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4}$