Ti5Ga4 Structure : A4B5_hP18_193_bg_dg

Picture of Structure; Click for Big Picture
Prototype : Ga4Ti5
AFLOW prototype label : A4B5_hP18_193_bg_dg
Strukturbericht designation : None
Pearson symbol : hP18
Space group number : 193
Space group symbol : $P6_{3}/mcm$
AFLOW prototype command : aflow --proto=A4B5_hP18_193_bg_dg
--params=
$a$,$c/a$,$x_{3}$,$x_{4}$


Other compounds with this structure

  • Zr5Ga4, Hf5Sn4, Ba3TlTe5, and NbIrO


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} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Ga I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Ga I} \\ \mathbf{B}_{3} & = & \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(4d\right) & \mbox{Ti I} \\ \mathbf{B}_{4} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Ti I} \\ \mathbf{B}_{5} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(4d\right) & \mbox{Ti I} \\ \mathbf{B}_{6} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Ti I} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{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(6g\right) & \mbox{Ga II} \\ \mathbf{B}_{8} & = & x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{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(6g\right) & \mbox{Ga II} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Ga II} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{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(6g\right) & \mbox{Ga II} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{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(6g\right) & \mbox{Ga II} \\ \mathbf{B}_{12} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Ga II} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Ti II} \\ \mathbf{B}_{14} & = & x_{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Ti II} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Ti II} \\ \mathbf{B}_{16} & = & -x_{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Ti II} \\ \mathbf{B}_{17} & = & -x_{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Ti II} \\ \mathbf{B}_{18} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Ti II} \\ \end{array} \]

References

  • K. Schubert, H. G. Meissner, M. Pötzschke, W. Rossteutscher, and E. Stolz, Einige Strukturdaten metallischer Phasen (7), Naturwissenschaften 49, 57 (1962), doi:10.1007/BF00595382.

Found in

Geometry files


Prototype Generator

aflow --proto=A4B5_hP18_193_bg_dg --params=

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