Cr–233 Quasi–One–Dimensional Superconductor (K2Cr3As3) Structure : A3B3C2_hP16_187_jk_jk_ck

Picture of Structure; Click for Big Picture
Prototype : As3Cr3K2
AFLOW prototype label : A3B3C2_hP16_187_jk_jk_ck
Strukturbericht designation : None
Pearson symbol : hP16
Space group number : 187
Space group symbol : $P\bar{6}m2$
AFLOW prototype command : aflow --proto=A3B3C2_hP16_187_jk_jk_ck
--params=
$a$,$c/a$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$


Other compounds with this structure

  • Cs2Cr3As3, Rb2Cr3As3, and K2Mo3As3

  • Cr–233 designates a class of structures of the form A2B2As3, where the 'A' atoms form one–dimensional chains. Several of these compounds have been found to superconduct at temperatures on the order of 5–10 K.

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(1c\right) & \mbox{K I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} & = & -\sqrt{3}x_{2}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{As I} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + 2x_{2} \, \mathbf{a}_{2} & = & \frac{3}{2}x_{2}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{As I} \\ \mathbf{B}_{4} & = & -2x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} & = & -\frac{3}{2}x_{2}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{As I} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -\sqrt{3}x_{3}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Cr I} \\ \mathbf{B}_{6} & = & x_{3} \, \mathbf{a}_{1} + 2x_{3} \, \mathbf{a}_{2} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Cr I} \\ \mathbf{B}_{7} & = & -2x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(3j\right) & \mbox{Cr I} \\ \mathbf{B}_{8} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{As II} \\ \mathbf{B}_{9} & = & x_{4} \, \mathbf{a}_{1} + 2x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{As II} \\ \mathbf{B}_{10} & = & -2x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{As II} \\ \mathbf{B}_{11} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{5}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Cr II} \\ \mathbf{B}_{12} & = & x_{5} \, \mathbf{a}_{1} + 2x_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{5}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Cr II} \\ \mathbf{B}_{13} & = & -2x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{5}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{Cr II} \\ \mathbf{B}_{14} & = & x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{K II} \\ \mathbf{B}_{15} & = & x_{6} \, \mathbf{a}_{1} + 2x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{6}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{K II} \\ \mathbf{B}_{16} & = & -2x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{6}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3k\right) & \mbox{K II} \\ \end{array} \]

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 K2Cr3As3 with Significant Electron Correlations, Phys. Rev. X 5, 011013 (2015), doi:10.1103/PhysRevX.5.011013.

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 K2Mo3As3, http://arxiv.org/abs/1805.05257 (2018). ArXiv:1805.05257 [cond–mat.supr–con].

Geometry files


Prototype Generator

aflow --proto=A3B3C2_hP16_187_jk_jk_ck --params=

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