CsV$_{8}$Sb$_{12}$ Structure: AB12C8_oF84_69_a_2g2n_fgl-001
| Prototype | CsV$_{8}$Sb$_{12}$ |
| AFLOW prototype label | AB12C8_oF84_69_a_2g2n_fgl-001 |
| Pearson symbol | oF84 |
| Space group number | 69 |
| Space group symbol | $Fmmm$ |
| AFLOW prototype command |
aflow --proto=AB12C8_oF84_69_a_2g2n_fgl-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}$ |
- The AFLOW prototype label protocol rotates the reported axes, taking $\rightarrow$ b $\rightarrow$ c $\rightarrow$ a.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Cs I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8f) | V I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8f) | V I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (8g) | Sb I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (8g) | Sb I |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}$ | (8g) | Sb II |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}$ | (8g) | Sb II |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}$ | (8g) | V II |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}$ | (8g) | V II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | V III |
| $\mathbf{B_{11}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | V III |
| $\mathbf{B_{12}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | V III |
| $\mathbf{B_{13}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | V III |
| $\mathbf{B_{14}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+c z_{7} \,\mathbf{\hat{z}}$ | (16n) | Sb III |
| $\mathbf{B_{15}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+c z_{7} \,\mathbf{\hat{z}}$ | (16n) | Sb III |
| $\mathbf{B_{16}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- c z_{7} \,\mathbf{\hat{z}}$ | (16n) | Sb III |
| $\mathbf{B_{17}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- c z_{7} \,\mathbf{\hat{z}}$ | (16n) | Sb III |
| $\mathbf{B_{18}}$ | = | $- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sb IV |
| $\mathbf{B_{19}}$ | = | $\left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sb IV |
| $\mathbf{B_{20}}$ | = | $\left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sb IV |
| $\mathbf{B_{21}}$ | = | $- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sb IV |
References
- Q. Yin, Z. Tu, C. Gong, S. Tian, and H. Lei, Structures and Physical Properties of V-Based Kagome Metals CsV$_{6}$Sb$_{6}$ and CsV$_{8}$Sb$_{12}$, Chinese Phys. Lett. 38, 127401 (2021), doi:10.1088/0256-307X/38/12/127401.
Found in
- X. Liu, X. Zhang, J. Jiao, R. Zhang, K. Chen, Y. Wang, Y. Ye, Z. Yu, C. Jiang, X. Wang, L. Shu, B. Lv, G. Li, and Y. Guo, Emergent dynamical Kondo coherence and competing magnetic order in a correlated kagome flat-band metal CsCr$_{6}$Sb$_{6}$ (2025), doi:10.48550/arXiv.2508.08580. ArXiv:2508.08580 [cond-mat.str-el].
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=AB12C8_oF84_69_a_2g2n_fgl --params=$a,b/a,c/a,x_{3},x_{4},x_{5},x_{6},x_{7},z_{7},x_{8},z_{8}$