Cr-233 Quasi-One-Dimensional Superconductor (K$_{2}$Cr$_{3}$As$_{3}$) Structure: A3B3C2_hP16_187_jk_jk_ak-001
| Prototype | As$_{3}$Cr$_{3}$K$_{2}$ |
| AFLOW prototype label | A3B3C2_hP16_187_jk_jk_ak-001 |
| ICSD | 35909 |
| Pearson symbol | hP16 |
| Space group number | 187 |
| Space group symbol | $P\overline{6}m2$ |
| AFLOW prototype command |
aflow --proto=A3B3C2_hP16_187_jk_jk_ak-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}$ |
Other compounds with this structure
Cs$_{2}$Cr$_{3}$As$_{3}$, K$_{2}$Mo$_{3}$As$_{3}$, Rb$_{2}$Cr$_{3}$As$_{3}$, Rb$_{2}$Mo$_{3}$As$_{3}$
- Cr-233 designates a class of structures of the form A$_{2}$B$_{2}$As$_{3}$, where the
A
atoms form one-dimensional chains. Several of these compounds have been found to superconduct at temperatures on the order of 5-10K. - The ICSD entry is for Rb$_{2}$Mo$_{3}$As$_{3}$ from (Zhao, 2020). The ICSD entry lists that as the prototype, but (Bao, 2015) obviously found K$_{2}$Cr$_{3}$As$_{3}$ earlier, so we continue using it as our prototype.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | K I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- \sqrt{3}a x_{2} \,\mathbf{\hat{y}}$ | (3j) | As I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}$ | = | $\frac{3}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}$ | (3j) | As I |
| $\mathbf{B_{4}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- \frac{3}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}$ | (3j) | As I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- \sqrt{3}a x_{3} \,\mathbf{\hat{y}}$ | (3j) | Cr I |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (3j) | Cr I |
| $\mathbf{B_{7}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (3j) | Cr I |
| $\mathbf{B_{8}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | As II |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}+2 x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | As II |
| $\mathbf{B_{10}}$ | = | $- 2 x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | As II |
| $\mathbf{B_{11}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | Cr II |
| $\mathbf{B_{12}}$ | = | $x_{5} \, \mathbf{a}_{1}+2 x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{5} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | Cr II |
| $\mathbf{B_{13}}$ | = | $- 2 x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{5} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | Cr II |
| $\mathbf{B_{14}}$ | = | $x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | K II |
| $\mathbf{B_{15}}$ | = | $x_{6} \, \mathbf{a}_{1}+2 x_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | K II |
| $\mathbf{B_{16}}$ | = | $- 2 x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3k) | K II |
References
- J.-K. Bao, J.-Y. Liu, C.-W. Ma, Z.-H. Meng, Z.-T. Tang, Y.-L. Sun, H.-F. Zhai, H. Jiang, H. Bai, C.-M. Feng, Z.-A. Xu, and G.-H. Cao, Superconductivity in Quasi-One-Dimensional K$_{2}$Cr$_{3}$As$_{3}$ with Significant Electron Correlations, Phys. Rev. X 5, 011013 (2015), doi:10.1103/PhysRevX.5.011013.
- K. Zhao, Q.-G. Mu, B.-B. Ruan, M.-H. Zhou, Q.-S. Yang, T. Liu, B.-J. Pan, S. Zhang, G.-F. Chen, and Z.-A. Ren, A New Quasi-One-Dimensional Ternary Molybdenum Pnictide Rb$_{2}$Mo$_{3}$As$_{3}$ with Superconducting Transition at 10.5K, Chin. Phys. Lett. 37, 097401 (2020), doi:10.1088/0256-307X/37/9/097401.
Found in
- Q.-G. Mu, B.-B. Ruan, K. Zhao, B.-J. Pan, T. Liu, L. Shan, G.-F. Chen, and Z.-A. Ren, Superconductivity at 10.4 K in a novel quasi-one-dimensional ternary molybdenum pnictide K$_{2}$Mo$_{3}$As$_{3}$, Science Bulletin 63, 952–956 (2008), doi:10.1016/j.scib.2018.06.011.
Prototype Generator
aflow --proto=A3B3C2_hP16_187_jk_jk_ak --params=$a,c/a,x_{2},x_{3},x_{4},x_{5},x_{6}$