Al[PO4] Structure: AB4C_hP72_168_2d_8d_2d

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Prototype : Al[PO4]
AFLOW prototype label : AB4C_hP72_168_2d_8d_2d
Strukturbericht designation : None
Pearson symbol : hP72
Space group number : 168
Space group symbol : $P6$
AFLOW prototype command : aflow --proto=AB4C_hP72_168_2d_8d_2d
--params=
$a$,$c/a$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$ y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$



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} + y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{1}+y_{1}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{1}+y_{1}\right)a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al I} \\ \mathbf{B}_{2} & = & -y_{1} \, \mathbf{a}_{1} + \left(x_{1}-y_{1}\right) \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{1}-y_{1}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al I} \\ \mathbf{B}_{3} & = & \left(-x_{1}+y_{1}\right) \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(-x_{1}+\frac{1}{2}y_{1}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al I} \\ \mathbf{B}_{4} & = & -x_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{1}+y_{1}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{1}-y_{1}\right)a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al I} \\ \mathbf{B}_{5} & = & y_{1} \, \mathbf{a}_{1} + \left(-x_{1}+y_{1}\right) \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{1}+y_{1}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al I} \\ \mathbf{B}_{6} & = & \left(x_{1}-y_{1}\right) \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}-\frac{1}{2}y_{1}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al I} \\ \mathbf{B}_{7} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{2}+y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{2}+y_{2}\right)a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al II} \\ \mathbf{B}_{8} & = & -y_{2} \, \mathbf{a}_{1} + \left(x_{2}-y_{2}\right) \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{2}-y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al II} \\ \mathbf{B}_{9} & = & \left(-x_{2}+y_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(-x_{2}+\frac{1}{2}y_{2}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al II} \\ \mathbf{B}_{10} & = & -x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{2}+y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{2}-y_{2}\right)a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al II} \\ \mathbf{B}_{11} & = & y_{2} \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}\right) \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{2}+y_{2}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al II} \\ \mathbf{B}_{12} & = & \left(x_{2}-y_{2}\right) \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}-\frac{1}{2}y_{2}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{Al II} \\ \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(6d\right) & \mbox{O I} \\ \mathbf{B}_{14} & = & -y_{3} \, \mathbf{a}_{1} + \left(x_{3}-y_{3}\right) \, \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(6d\right) & \mbox{O I} \\ \mathbf{B}_{15} & = & \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + z_{3} \, \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}} + z_{3}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O I} \\ \mathbf{B}_{16} & = & -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(6d\right) & \mbox{O I} \\ \mathbf{B}_{17} & = & y_{3} \, \mathbf{a}_{1} + \left(-x_{3}+y_{3}\right) \, \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(6d\right) & \mbox{O I} \\ \mathbf{B}_{18} & = & \left(x_{3}-y_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \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}} + z_{3}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O I} \\ \mathbf{B}_{19} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{4}+y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{4}+y_{4}\right)a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O II} \\ \mathbf{B}_{20} & = & -y_{4} \, \mathbf{a}_{1} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{4}-y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O II} \\ \mathbf{B}_{21} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(-x_{4}+\frac{1}{2}y_{4}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O II} \\ \mathbf{B}_{22} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{4}+y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{4}-y_{4}\right)a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O II} \\ \mathbf{B}_{23} & = & y_{4} \, \mathbf{a}_{1} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{4}+y_{4}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O II} \\ \mathbf{B}_{24} & = & \left(x_{4}-y_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}-\frac{1}{2}y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O II} \\ \mathbf{B}_{25} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O III} \\ \mathbf{B}_{26} & = & -y_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O III} \\ \mathbf{B}_{27} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O III} \\ \mathbf{B}_{28} & = & -x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{5}-y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O III} \\ \mathbf{B}_{29} & = & y_{5} \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{5}+y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O III} \\ \mathbf{B}_{30} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}-\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O III} \\ \mathbf{B}_{31} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{6}+y_{6}\right)a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O IV} \\ \mathbf{B}_{32} & = & -y_{6} \, \mathbf{a}_{1} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{6}-y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O IV} \\ \mathbf{B}_{33} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(-x_{6}+\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O IV} \\ \mathbf{B}_{34} & = & -x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{6}-y_{6}\right)a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O IV} \\ \mathbf{B}_{35} & = & y_{6} \, \mathbf{a}_{1} + \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{6}+y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O IV} \\ \mathbf{B}_{36} & = & \left(x_{6}-y_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}-\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O IV} \\ \mathbf{B}_{37} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{7}+y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{7}+y_{7}\right)a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O V} \\ \mathbf{B}_{38} & = & -y_{7} \, \mathbf{a}_{1} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{7}-y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O V} \\ \mathbf{B}_{39} & = & \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(-x_{7}+\frac{1}{2}y_{7}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O V} \\ \mathbf{B}_{40} & = & -x_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{7}+y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{7}-y_{7}\right)a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O V} \\ \mathbf{B}_{41} & = & y_{7} \, \mathbf{a}_{1} + \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{7}+y_{7}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O V} \\ \mathbf{B}_{42} & = & \left(x_{7}-y_{7}\right) \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}-\frac{1}{2}y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O V} \\ \mathbf{B}_{43} & = & x_{8} \, \mathbf{a}_{1} + y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{8}+y_{8}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{8}+y_{8}\right)a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VI} \\ \mathbf{B}_{44} & = & -y_{8} \, \mathbf{a}_{1} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{8}-y_{8}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{8}a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VI} \\ \mathbf{B}_{45} & = & \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(-x_{8}+\frac{1}{2}y_{8}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{8}a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VI} \\ \mathbf{B}_{46} & = & -x_{8} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{8}+y_{8}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{8}-y_{8}\right)a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VI} \\ \mathbf{B}_{47} & = & y_{8} \, \mathbf{a}_{1} + \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{8}+y_{8}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{8}a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VI} \\ \mathbf{B}_{48} & = & \left(x_{8}-y_{8}\right) \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}-\frac{1}{2}y_{8}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{8}a \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VI} \\ \mathbf{B}_{49} & = & x_{9} \, \mathbf{a}_{1} + y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{9}+y_{9}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{9}+y_{9}\right)a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VII} \\ \mathbf{B}_{50} & = & -y_{9} \, \mathbf{a}_{1} + \left(x_{9}-y_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{9}-y_{9}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VII} \\ \mathbf{B}_{51} & = & \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(-x_{9}+\frac{1}{2}y_{9}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VII} \\ \mathbf{B}_{52} & = & -x_{9} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{9}+y_{9}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{9}-y_{9}\right)a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VII} \\ \mathbf{B}_{53} & = & y_{9} \, \mathbf{a}_{1} + \left(-x_{9}+y_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{9}+y_{9}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VII} \\ \mathbf{B}_{54} & = & \left(x_{9}-y_{9}\right) \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}-\frac{1}{2}y_{9}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{9}a \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VII} \\ \mathbf{B}_{55} & = & x_{10} \, \mathbf{a}_{1} + y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{10}+y_{10}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{10}+y_{10}\right)a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VIII} \\ \mathbf{B}_{56} & = & -y_{10} \, \mathbf{a}_{1} + \left(x_{10}-y_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{10}-y_{10}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VIII} \\ \mathbf{B}_{57} & = & \left(-x_{10}+y_{10}\right) \, \mathbf{a}_{1}-x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(-x_{10}+\frac{1}{2}y_{10}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{10}a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VIII} \\ \mathbf{B}_{58} & = & -x_{10} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{10}+y_{10}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{10}-y_{10}\right)a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VIII} \\ \mathbf{B}_{59} & = & y_{10} \, \mathbf{a}_{1} + \left(-x_{10}+y_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{10}+y_{10}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{10}a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VIII} \\ \mathbf{B}_{60} & = & \left(x_{10}-y_{10}\right) \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}-\frac{1}{2}y_{10}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{10}a \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{O VIII} \\ \mathbf{B}_{61} & = & x_{11} \, \mathbf{a}_{1} + y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{11}+y_{11}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{11}+y_{11}\right)a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P I} \\ \mathbf{B}_{62} & = & -y_{11} \, \mathbf{a}_{1} + \left(x_{11}-y_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{11}-y_{11}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P I} \\ \mathbf{B}_{63} & = & \left(-x_{11}+y_{11}\right) \, \mathbf{a}_{1}-x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(-x_{11}+\frac{1}{2}y_{11}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{11}a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P I} \\ \mathbf{B}_{64} & = & -x_{11} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{11}+y_{11}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{11}-y_{11}\right)a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P I} \\ \mathbf{B}_{65} & = & y_{11} \, \mathbf{a}_{1} + \left(-x_{11}+y_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{11}+y_{11}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{11}a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P I} \\ \mathbf{B}_{66} & = & \left(x_{11}-y_{11}\right) \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}-\frac{1}{2}y_{11}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{11}a \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P I} \\ \mathbf{B}_{67} & = & x_{12} \, \mathbf{a}_{1} + y_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{12}+y_{12}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{12}+y_{12}\right)a \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P II} \\ \mathbf{B}_{68} & = & -y_{12} \, \mathbf{a}_{1} + \left(x_{12}-y_{12}\right) \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{12}-y_{12}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{12}a \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P II} \\ \mathbf{B}_{69} & = & \left(-x_{12}+y_{12}\right) \, \mathbf{a}_{1}-x_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(-x_{12}+\frac{1}{2}y_{12}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{12}a \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P II} \\ \mathbf{B}_{70} & = & -x_{12} \, \mathbf{a}_{1}-y_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{12}+y_{12}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{12}-y_{12}\right)a \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P II} \\ \mathbf{B}_{71} & = & y_{12} \, \mathbf{a}_{1} + \left(-x_{12}+y_{12}\right) \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{12}+y_{12}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{12}a \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P II} \\ \mathbf{B}_{72} & = & \left(x_{12}-y_{12}\right) \, \mathbf{a}_{1} + x_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}-\frac{1}{2}y_{12}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{12}a \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(6d\right) & \mbox{P II} \\ \end{array} \]

References

  • J. W. Richardson Jr., J. J. Pluth, and J. V. Smith, Aluminophosphate number 5: time–of–flight neutron powder diffraction study of calcined powder at 295 K, Acta Crystallogr. C 43, 1469–1472 (1987), doi:10.1107/S0108270187091418.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=AB4C_hP72_168_2d_8d_2d --params=

Species:

Running:

Output: