Li$_{7}$Ge$_{2}$ Structure: A2B7_oC36_65_gj_achipq-001
| Prototype | Ge$_{2}$Li$_{7}$ |
| AFLOW prototype label | A2B7_oC36_65_gj_achipq-001 |
| ICSD | 42063 |
| Pearson symbol | oC36 |
| Space group number | 65 |
| Space group symbol | $Cmmm$ |
| AFLOW prototype command |
aflow --proto=A2B7_oC36_65_gj_achipq-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{5}, \allowbreak y_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak x_{8}, \allowbreak y_{8}$ |
Other compounds with this structure
Li$_{7}$Sn$_{2}$
- We have shifted the origin by 1/2 ({\bf a}$_{1}$ + {\bf a}$_{2}$) from that used by (Hopf, 1972).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2c) | Li II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (4g) | Ge I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (4g) | Ge I |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Li III |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Li III |
| $\mathbf{B_{7}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}$ | = | $b y_{5} \,\mathbf{\hat{y}}$ | (4i) | Li IV |
| $\mathbf{B_{8}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}$ | = | $- b y_{5} \,\mathbf{\hat{y}}$ | (4i) | Li IV |
| $\mathbf{B_{9}}$ | = | $- y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4j) | Ge II |
| $\mathbf{B_{10}}$ | = | $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- b y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4j) | Ge II |
| $\mathbf{B_{11}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}$ | (8p) | Li V |
| $\mathbf{B_{12}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}$ | (8p) | Li V |
| $\mathbf{B_{13}}$ | = | $- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}$ | (8p) | Li V |
| $\mathbf{B_{14}}$ | = | $\left(x_{7} + y_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}$ | (8p) | Li V |
| $\mathbf{B_{15}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8q) | Li VI |
| $\mathbf{B_{16}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8q) | Li VI |
| $\mathbf{B_{17}}$ | = | $- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8q) | Li VI |
| $\mathbf{B_{18}}$ | = | $\left(x_{8} + y_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8q) | Li VI |
References
- W. Hopf, W. Müller, and H. Schäfer, Die Struktur der Phase Li$_{7}$Ge$_{2}$, Z. Naturforsch. B 27, 1157–1160 (1972), doi:10.1515/znb-1972-1009.
Prototype Generator
aflow --proto=A2B7_oC36_65_gj_achipq --params=$a,b/a,c/a,x_{3},x_{4},y_{5},y_{6},x_{7},y_{7},x_{8},y_{8}$