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 $A$2$B$2As3, where the ‘$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, Sci. Bull. 63, 952–956 (2018), doi:10.1016/j.scib.2018.06.011.

Geometry files


Prototype Generator

aflow --proto=A3B3C2_hP16_187_jk_jk_ck --params=

Species:

Running:

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