AlPO4 Structure: AB2_hP72_192_m_j2kl

Picture of Structure; Click for Big Picture
Prototype : AlPO4
AFLOW prototype label : AB2_hP72_192_m_j2kl
Strukturbericht designation : None
Pearson symbol : hP72
Space group number : 192
Space group symbol : $P6/mcc$
AFLOW prototype command : aflow --proto=AB2_hP72_192_m_j2kl
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$y_{4}$,$x_{5}$,$y_{5}$,$z_{5}$



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}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & x_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & -x_{1} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & -x_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & -x_{1} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & -x_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & x_{1} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & x_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{12} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12j\right) & \mbox{O I} \\ \mathbf{B}_{13} & = & 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(12k\right) & \mbox{O II} \\ \mathbf{B}_{14} & = & -2x_{2} \, \mathbf{a}_{1}-x_{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(12k\right) & \mbox{O II} \\ \mathbf{B}_{15} & = & x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{2}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O II} \\ \mathbf{B}_{16} & = & -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(12k\right) & \mbox{O II} \\ \mathbf{B}_{17} & = & 2x_{2} \, \mathbf{a}_{1} + x_{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(12k\right) & \mbox{O II} \\ \mathbf{B}_{18} & = & -x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \sqrt{3}x_{2}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O II} \\ \mathbf{B}_{19} & = & -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(12k\right) & \mbox{O II} \\ \mathbf{B}_{20} & = & 2x_{2} \, \mathbf{a}_{1} + x_{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(12k\right) & \mbox{O II} \\ \mathbf{B}_{21} & = & -x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \sqrt{3}x_{2}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O II} \\ \mathbf{B}_{22} & = & 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(12k\right) & \mbox{O II} \\ \mathbf{B}_{23} & = & -2x_{2} \, \mathbf{a}_{1}-x_{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(12k\right) & \mbox{O II} \\ \mathbf{B}_{24} & = & x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{2}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O II} \\ \mathbf{B}_{25} & = & x_{3} \, \mathbf{a}_{1} + 2x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{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(12k\right) & \mbox{O III} \\ \mathbf{B}_{26} & = & -2x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\frac{3}{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(12k\right) & \mbox{O III} \\ \mathbf{B}_{27} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O III} \\ \mathbf{B}_{28} & = & -x_{3} \, \mathbf{a}_{1}-2x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -\frac{3}{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(12k\right) & \mbox{O III} \\ \mathbf{B}_{29} & = & 2x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{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(12k\right) & \mbox{O III} \\ \mathbf{B}_{30} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \sqrt{3}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O III} \\ \mathbf{B}_{31} & = & -x_{3} \, \mathbf{a}_{1}-2x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{3}{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(12k\right) & \mbox{O III} \\ \mathbf{B}_{32} & = & 2x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{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(12k\right) & \mbox{O III} \\ \mathbf{B}_{33} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \sqrt{3}x_{3}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O III} \\ \mathbf{B}_{34} & = & x_{3} \, \mathbf{a}_{1} + 2x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{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(12k\right) & \mbox{O III} \\ \mathbf{B}_{35} & = & -2x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{3}{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(12k\right) & \mbox{O III} \\ \mathbf{B}_{36} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{3}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(12k\right) & \mbox{O III} \\ \mathbf{B}_{37} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} & = & \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}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{38} & = & -y_{4} \, \mathbf{a}_{1} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2}x_{4}-y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{39} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} & = & \left(-x_{4}+\frac{1}{2}y_{4}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{4}a \, \mathbf{\hat{y}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{40} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} & = & -\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}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{41} & = & y_{4} \, \mathbf{a}_{1} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{2} & = & \left(-\frac{1}{2}x_{4}+y_{4}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{42} & = & \left(x_{4}-y_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} & = & \left(x_{4}-\frac{1}{2}y_{4}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{4}a \, \mathbf{\hat{y}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{43} & = & y_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \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}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{44} & = & \left(x_{4}-y_{4}\right) \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \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}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{45} & = & -x_{4} \, \mathbf{a}_{1} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \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}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{46} & = & -y_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \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}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{47} & = & \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \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}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{48} & = & x_{4} \, \mathbf{a}_{1} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \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}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(12l\right) & \mbox{O IV} \\ \mathbf{B}_{49} & = & 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(24m\right) & \mbox{M} \\ \mathbf{B}_{50} & = & -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(24m\right) & \mbox{M} \\ \mathbf{B}_{51} & = & \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(24m\right) & \mbox{M} \\ \mathbf{B}_{52} & = & -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(24m\right) & \mbox{M} \\ \mathbf{B}_{53} & = & 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(24m\right) & \mbox{M} \\ \mathbf{B}_{54} & = & \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(24m\right) & \mbox{M} \\ \mathbf{B}_{55} & = & y_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \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}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{56} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \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}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{57} & = & -x_{5} \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \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}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{58} & = & -y_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \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}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{59} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \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}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{60} & = & x_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \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}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{61} & = & -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(24m\right) & \mbox{M} \\ \mathbf{B}_{62} & = & 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(24m\right) & \mbox{M} \\ \mathbf{B}_{63} & = & \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(24m\right) & \mbox{M} \\ \mathbf{B}_{64} & = & 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(24m\right) & \mbox{M} \\ \mathbf{B}_{65} & = & -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(24m\right) & \mbox{M} \\ \mathbf{B}_{66} & = & \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(24m\right) & \mbox{M} \\ \mathbf{B}_{67} & = & -y_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \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}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{68} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \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}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{69} & = & x_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \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}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{70} & = & y_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \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}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{71} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \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}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \mathbf{B}_{72} & = & -x_{5} \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \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}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(24m\right) & \mbox{M} \\ \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=AB2_hP72_192_m_j2kl --params=

Species:

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