CrCl3 ($D0_{4}$) Crystal Structure: A3B_hP24_151_3c_2a

Picture of Structure; Click for Big Picture
Prototype : CrCl3
AFLOW prototype label : A3B_hP24_151_3c_2a
Strukturbericht designation : $D0_{4}$
Pearson symbol : hP24
Space group number : 151
Space group symbol : $\mbox{P3}_{1}\mbox{12}$
AFLOW prototype command : aflow --proto=A3B_hP24_151_3c_2a
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$


Trigonal Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

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}- x_{1} \, \mathbf{a}_{2}+ \frac13 \, \mathbf{a}_{3}& =&- \sqrt{3} \, x_{1} \, a \, \mathbf{\hat{y}}+ \frac13 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \mbox{Cr I} \\ \mathbf{B}_{2} & = &x_{1} \, \mathbf{a}_{1}+ 2 x_{1} \, \mathbf{a}_{2}+ \frac23 \, \mathbf{a}_{3}& =&\frac32 \, x_{1} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{1} \, a \, \mathbf{\hat{y}}+ \frac23 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \mbox{Cr I} \\ \mathbf{B}_{3} & = &- 2 x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}& =&- \frac32 \, x_{1} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{1} \, a \, \mathbf{\hat{y}}& \left(3a\right) & \mbox{Cr I} \\ \mathbf{B}_{4} & = &x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac13 \, \mathbf{a}_{3}& =&- \sqrt{3} \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac13 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \mbox{Cr II} \\ \mathbf{B}_{5} & = &x_{2} \, \mathbf{a}_{1}+ 2 x_{2} \, \mathbf{a}_{2}+ \frac23 \, \mathbf{a}_{3}& =&\frac32 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac23 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \mbox{Cr II} \\ \mathbf{B}_{6} & = &- 2 x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}& =&- \frac32 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{2} \, a \, \mathbf{\hat{y}}& \left(3a\right) & \mbox{Cr II} \\ \mathbf{B}_{7} & = &x_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{3} + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{3} - x_{3}\right) \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl I} \\ \mathbf{B}_{8} & = &- y_{3} \, \mathbf{a}_{1}+ \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+ \left(\frac13 + z_{3}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{3} - 2 y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac13 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl I} \\ \mathbf{B}_{9} & = &\left(y_{3} - x_{3}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \left(\frac23 + z_{3}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{3} - 2 x_{3}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac23 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl I} \\ \mathbf{B}_{10} & = &- y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \left(\frac23 - z_{3}\right) \, \mathbf{a}_{3}& =&- \frac12 \, \left(x_{3} + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{3} - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac23 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl I} \\ \mathbf{B}_{11} & = &\left(y_{3} - x_{3}\right) \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}+ \left(\frac13 - z_{3}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(2 y_{3} - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{3} \, a \, \mathbf{\hat{y}}+ \left(\frac13 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl I} \\ \mathbf{B}_{12} & = &x_{3} \, \mathbf{a}_{1}+ \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&\frac12 \, \left(2 x_{3} - y_{3}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{3} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl I} \\ \mathbf{B}_{13} & = &x_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{4} + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{4} - x_{4}\right) \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl II} \\ \mathbf{B}_{14} & = &- y_{4} \, \mathbf{a}_{1}+ \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac13 + z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{4} - 2 y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac13 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl II} \\ \mathbf{B}_{15} & = &\left(y_{4} - x_{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left(\frac23 + z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{4} - 2 x_{4}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac23 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl II} \\ \mathbf{B}_{16} & = &- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left(\frac23 - z_{4}\right) \, \mathbf{a}_{3}& =&- \frac12 \, \left(x_{4} + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{4} - x_{4}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac23 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl II} \\ \mathbf{B}_{17} & = &\left(y_{4} - x_{4}\right) \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ \left(\frac13 - z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(2 y_{4} - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac13 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl II} \\ \mathbf{B}_{18} & = &x_{4} \, \mathbf{a}_{1}+ \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&\frac12 \, \left(2 x_{4} - y_{4}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{4} \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl II} \\ \mathbf{B}_{19} & = &x_{5} \, \mathbf{a}_{1}+ y_{5} \, \mathbf{a}_{2}+ z_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{5} + y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl III} \\ \mathbf{B}_{20} & = &- y_{5} \, \mathbf{a}_{1}+ \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+ \left(\frac13 + z_{5}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{5} - 2 y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{5} \, a \, \mathbf{\hat{y}}+ \left(\frac13 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl III} \\ \mathbf{B}_{21} & = &\left(y_{5} - x_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+ \left(\frac23 + z_{5}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{5} - 2 x_{5}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{5} \, a \, \mathbf{\hat{y}}+ \left(\frac23 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl III} \\ \mathbf{B}_{22} & = &- y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+ \left(\frac23 - z_{5}\right) \, \mathbf{a}_{3}& =&- \frac12 \, \left(x_{5} + y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, \left(y_{5} - x_{5}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac23 - z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl III} \\ \mathbf{B}_{23} & = &\left(y_{5} - x_{5}\right) \, \mathbf{a}_{1}+ y_{5} \, \mathbf{a}_{2}+ \left(\frac13 - z_{5}\right) \, \mathbf{a}_{3}& =&\frac12 \, \left(2 y_{5} - x_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}{2} \, x_{5} \, a \, \mathbf{\hat{y}}+ \left(\frac13 - z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl III} \\ \mathbf{B}_{24} & = &x_{5} \, \mathbf{a}_{1}+ \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}& =&\frac12 \, \left(2 x_{5} - y_{5}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{2} \, y_{5} \, a \, \mathbf{\hat{y}}- z_{5} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cl III} \\ \end{array} \]

References

  • N. Wooster, The Structure of Chromium Trichloride CrCl3, Zeitschrift für Kristallographie – Crystalline Materials 74, 363–374 (1930), doi:10.1524/zkri.1930.74.1.363.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A3B_hP24_151_3c_2a --params=

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