Lu2CoGa3 Structure : AB3C2_hP24_194_f_k_bh

Picture of Structure; Click for Big Picture
Prototype : CoGa3Lu2
AFLOW prototype label : AB3C2_hP24_194_f_k_bh
Strukturbericht designation : None
Pearson symbol : hP24
Space group number : 194
Space group symbol : $P6_{3}/mmc$
AFLOW prototype command : aflow --proto=AB3C2_hP24_194_f_k_bh
--params=
$a$,$c/a$,$z_{2}$,$x_{3}$,$x_{4}$,$z_{4}$


Other compounds with this structure

  • Dy2CoGa3, Er2CoGa3, Er2RhSi3, Ho2CoGa3, Nd2PdSi3, Tb2CoGa3, Tm2CoGa3, Y2CoGa3, and Yb2CoGa3


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}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Lu I} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Lu I} \\ \mathbf{B}_{3} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Co} \\ \mathbf{B}_{4} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Co} \\ \mathbf{B}_{5} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Co} \\ \mathbf{B}_{6} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{2}\right)c \, \mathbf{\hat{z}} & \left(4f\right) & \mbox{Co} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + 2x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Lu II} \\ \mathbf{B}_{8} & = & -2x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Lu II} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Lu II} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1}-2x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Lu II} \\ \mathbf{B}_{11} & = & 2x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Lu II} \\ \mathbf{B}_{12} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \sqrt{3}x_{3}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Lu II} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + 2x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{14} & = & -2x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{15} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{16} & = & -x_{4} \, \mathbf{a}_{1}-2x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{17} & = & 2x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{18} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \sqrt{3}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{19} & = & 2x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{20} & = & -x_{4} \, \mathbf{a}_{1}-2x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{21} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \sqrt{3}x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{22} & = & -2x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{23} & = & x_{4} \, \mathbf{a}_{1} + 2x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \mathbf{B}_{24} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & -\sqrt{3}x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{Ga} \\ \end{array} \]

References

  • R. E. Gladyshevskii, K. Cenzual, and E. Parthé, Er2RhSi3 and $R$2CoGa3 ($R$ = Y, Tb, Dy, Ho, Er, Tm, Yb) with Lu2CoGa3 type structure: new members of the AlB2 structure family, J. Alloys\ Compd. 189, 221–228 (1992), doi:10.1016/0925-8388(92)90711-H.

Geometry files


Prototype Generator

aflow --proto=AB3C2_hP24_194_f_k_bh --params=

Species:

Running:

Output: