AuF3 Structure: AB3_hP24_179_b_ac

Picture of Structure; Click for Big Picture
Prototype : AuF3
AFLOW prototype label : AB3_hP24_179_b_ac
Strukturbericht designation : None
Pearson symbol : hP24
Space group number : 179
Space group symbol : $P6_{5}22$
AFLOW prototype command : aflow --proto=AB3_hP24_179_b_ac
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$



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

References

  • L. B. Asprey, F. H. Kruse, K. H. Jack, and R. Maitland, Preparation and properties of crystalline gold trifluoride, Inorg. Chem. 3, 602–604 (1964), doi:10.1021/ic50014a037.

Geometry files


Prototype Generator

aflow --proto=AB3_hP24_179_b_ac --params=

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