H3Ho Structure: A3B_hP24_165_adg_f

Picture of Structure; Click for Big Picture
Prototype : H3Ho
AFLOW prototype label : A3B_hP24_165_adg_f
Strukturbericht designation : None
Pearson symbol : hP24
Space group number : 165
Space group symbol : $\mbox{P}\bar{3}\mbox{c1}$
AFLOW prototype command : aflow --proto=A3B_hP24_165_adg_f
--params=
$a$,$c/a$,$z_{2}$,$x_{3}$,$x_{4}$,$y_{4}$,$z_{4}$


Other compounds with this structure

  • H3Dy, H3Er, H3Gd, H3Lu, H3Sm, H3Tb, H3Tm, H3Y

  • The original prototype for this structure is LaF$_{3}$. We retain this structure as the prototype for the subclass of this prototype containing hydrogen. The data was taken for the deuteried, D$_{3}$Ho.

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} & =&\frac14 \, \mathbf{a}_{3}& =&\frac14 \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{H I} \\ \mathbf{B}_{2} & =&\frac34 \, \mathbf{a}_{3}& =&\frac34 \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{H I} \\ \mathbf{B}_{3} & =&\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{H II} \\ \mathbf{B}_{4} & =&\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{H II} \\ \mathbf{B}_{5} & =&\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{H II} \\ \mathbf{B}_{6} & =&\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{H II} \\ \mathbf{B}_{7} & =&x_{3} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, x_{3} \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}2 \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{Ho} \\ \mathbf{B}_{8} & =&x_{3} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, x_{3} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}2 \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{Ho} \\ \mathbf{B}_{9} & =&- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{Ho} \\ \mathbf{B}_{10} & =&- x_{3} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{3}& =&- \frac12 \, x_{3} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}2 \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{Ho} \\ \mathbf{B}_{11} & =&- x_{3} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&- \frac12 \, x_{3} \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}2 \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{Ho} \\ \mathbf{B}_{12} & =&x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{Ho} \\ \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{\sqrt3}2 \left(y_{4} - x_{4}\right) \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{14} & =&- y_{4} \, \mathbf{a}_{1}+ \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&\frac12 \left(x_{4} - 2 y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 x_{4} \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{15} & =&\left(y_{4} - x_{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& =&\frac12 \left(y_{4} - 2 x_{4}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 y_{4} \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{16} & =&y_{4} \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \left(x_{4} + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \left(x_{4} - y_{4}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{17} & =&\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \left(x_{4} - 2 y_{4}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{18} & =&- x_{4} \, \mathbf{a}_{1}+ \left(y_{4} - x_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \left(y_{4} - 2 x_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 y_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{19} & =&- 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{\sqrt3}2 \left(x_{4} - y_{4}\right) \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{20} & =&y_{4} \, \mathbf{a}_{1}+ \left(y_{4} - x_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&\frac12 \left(2 y_{4} - x_{4}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 x_{4} \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{21} & =&\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& =&\frac12 \left(2 x_{4} - y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 y_{4} \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{22} & =&- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&- \frac12 \left(x_{4} + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \left(y_{4} - x_{4}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{23} & =&\left(y_{4} - x_{4}\right) \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \left(2 y_{4} - x_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 x_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \mathbf{B}_{24} & =&x_{4} \, \mathbf{a}_{1}+ \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =&\frac12 \left(2 x_{4} - y_{4}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 y_{4} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(12g\right) & \mbox{H III} \\ \end{array} \]

References

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 3829.

Geometry files


Prototype Generator

aflow --proto=A3B_hP24_165_adg_f --params=

Species:

Running:

Output: