Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B2CD10E22F8_tP90_75_d_d_ab_5d_11d_4d-001

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Li$_{3}$[AlP$_{2}$O$_{7}$F(OH)](H$_{2}$O)$_{0.5}$ Structure: A2B2CD10E22F8_tP90_75_d_d_ab_5d_11d_4d-001

Picture of Structure; Click for Big Picture
Prototype Al$_{2}$F$_{2}$(H$_{2}$O)Li$_{6}$O$_{16}$P$_{4}$
AFLOW prototype label A2B2CD10E22F8_tP90_75_d_d_ab_5d_11d_4d-001
CCDC 2386067
Pearson symbol tP90
Space group number 75
Space group symbol $P4$
AFLOW prototype command aflow --proto=A2B2CD10E22F8_tP90_75_d_d_ab_5d_11d_4d-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak y_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak y_{24}, \allowbreak z_{24}$

  • This structure should be named Li$_{6}$[AlP$_{2}$O$_{7}$F(OH)]$_{2}$(H$_{2}$O), but we respect the labeling used by (Hao, 2024).
  • The positions of the hydrogen atoms in the water molecules are not located. Since fixing those positions necessarily destroys the $P4$ symmetry it is likely that the molecules are freely rotating. We have labeled these sites as H2O in the aflow.cif file, and they are represented by hydrogen atoms on this page.
  • The OH radicals are not labeled. It is possible that the hydrogens attach to random oxygen atoms. In any case we follow (Hao, 2024) and ignore these hydrogen atoms.
  • The O VIII through O XI sites are partially occupied, at 37.5% for the first two and 12.5% for the second pair. Similarly, the P I and P III sites are 60% occupied and the P II and P IV sites are 40% filled. The P I/P II and P III/P IV distances are very small, so only one of each pair is filled in any unit cell.
  • Finally, space group $P4$ #75 is polar and allows an arbitary placement of the origin of the z-axis. We used this to move the first water molecule on the (1a) site to the origin to provide structural clarity.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $z_{1} \, \mathbf{a}_{3}$ = $c z_{1} \,\mathbf{\hat{z}}$ (1a) H I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (1b) H II
$\mathbf{B_{3}}$ = $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (4d) Al I
$\mathbf{B_{4}}$ = $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (4d) Al I
$\mathbf{B_{5}}$ = $- y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $- a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (4d) Al I
$\mathbf{B_{6}}$ = $y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (4d) Al I
$\mathbf{B_{7}}$ = $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (4d) F I
$\mathbf{B_{8}}$ = $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (4d) F I
$\mathbf{B_{9}}$ = $- y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (4d) F I
$\mathbf{B_{10}}$ = $y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (4d) F I
$\mathbf{B_{11}}$ = $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4d) Li I
$\mathbf{B_{12}}$ = $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4d) Li I
$\mathbf{B_{13}}$ = $- y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4d) Li I
$\mathbf{B_{14}}$ = $y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4d) Li I
$\mathbf{B_{15}}$ = $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4d) Li II
$\mathbf{B_{16}}$ = $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4d) Li II
$\mathbf{B_{17}}$ = $- y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4d) Li II
$\mathbf{B_{18}}$ = $y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4d) Li II
$\mathbf{B_{19}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4d) Li III
$\mathbf{B_{20}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4d) Li III
$\mathbf{B_{21}}$ = $- y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4d) Li III
$\mathbf{B_{22}}$ = $y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4d) Li III
$\mathbf{B_{23}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4d) Li IV
$\mathbf{B_{24}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4d) Li IV
$\mathbf{B_{25}}$ = $- y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $- a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4d) Li IV
$\mathbf{B_{26}}$ = $y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4d) Li IV
$\mathbf{B_{27}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4d) Li V
$\mathbf{B_{28}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4d) Li V
$\mathbf{B_{29}}$ = $- y_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $- a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4d) Li V
$\mathbf{B_{30}}$ = $y_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4d) Li V
$\mathbf{B_{31}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4d) O I
$\mathbf{B_{32}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4d) O I
$\mathbf{B_{33}}$ = $- y_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $- a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4d) O I
$\mathbf{B_{34}}$ = $y_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4d) O I
$\mathbf{B_{35}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4d) O II
$\mathbf{B_{36}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4d) O II
$\mathbf{B_{37}}$ = $- y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $- a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4d) O II
$\mathbf{B_{38}}$ = $y_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4d) O II
$\mathbf{B_{39}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4d) O III
$\mathbf{B_{40}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4d) O III
$\mathbf{B_{41}}$ = $- y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $- a y_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4d) O III
$\mathbf{B_{42}}$ = $y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $a y_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4d) O III
$\mathbf{B_{43}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4d) O IV
$\mathbf{B_{44}}$ = $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4d) O IV
$\mathbf{B_{45}}$ = $- y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $- a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4d) O IV
$\mathbf{B_{46}}$ = $y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4d) O IV
$\mathbf{B_{47}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4d) O V
$\mathbf{B_{48}}$ = $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4d) O V
$\mathbf{B_{49}}$ = $- y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $- a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4d) O V
$\mathbf{B_{50}}$ = $y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4d) O V
$\mathbf{B_{51}}$ = $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4d) O VI
$\mathbf{B_{52}}$ = $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4d) O VI
$\mathbf{B_{53}}$ = $- y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $- a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4d) O VI
$\mathbf{B_{54}}$ = $y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4d) O VI
$\mathbf{B_{55}}$ = $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $a x_{16} \,\mathbf{\hat{x}}+a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4d) O VII
$\mathbf{B_{56}}$ = $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $- a x_{16} \,\mathbf{\hat{x}}- a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4d) O VII
$\mathbf{B_{57}}$ = $- y_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $- a y_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4d) O VII
$\mathbf{B_{58}}$ = $y_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $a y_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4d) O VII
$\mathbf{B_{59}}$ = $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4d) O VIII
$\mathbf{B_{60}}$ = $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $- a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4d) O VIII
$\mathbf{B_{61}}$ = $- y_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $- a y_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4d) O VIII
$\mathbf{B_{62}}$ = $y_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $a y_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4d) O VIII
$\mathbf{B_{63}}$ = $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4d) O IX
$\mathbf{B_{64}}$ = $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $- a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4d) O IX
$\mathbf{B_{65}}$ = $- y_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $- a y_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4d) O IX
$\mathbf{B_{66}}$ = $y_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $a y_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4d) O IX
$\mathbf{B_{67}}$ = $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $a x_{19} \,\mathbf{\hat{x}}+a y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4d) O X
$\mathbf{B_{68}}$ = $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $- a x_{19} \,\mathbf{\hat{x}}- a y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4d) O X
$\mathbf{B_{69}}$ = $- y_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $- a y_{19} \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4d) O X
$\mathbf{B_{70}}$ = $y_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $a y_{19} \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4d) O X
$\mathbf{B_{71}}$ = $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $a x_{20} \,\mathbf{\hat{x}}+a y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4d) O XI
$\mathbf{B_{72}}$ = $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $- a x_{20} \,\mathbf{\hat{x}}- a y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4d) O XI
$\mathbf{B_{73}}$ = $- y_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $- a y_{20} \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4d) O XI
$\mathbf{B_{74}}$ = $y_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $a y_{20} \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4d) O XI
$\mathbf{B_{75}}$ = $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $a x_{21} \,\mathbf{\hat{x}}+a y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4d) P I
$\mathbf{B_{76}}$ = $- x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $- a x_{21} \,\mathbf{\hat{x}}- a y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4d) P I
$\mathbf{B_{77}}$ = $- y_{21} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $- a y_{21} \,\mathbf{\hat{x}}+a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4d) P I
$\mathbf{B_{78}}$ = $y_{21} \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $a y_{21} \,\mathbf{\hat{x}}- a x_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4d) P I
$\mathbf{B_{79}}$ = $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $a x_{22} \,\mathbf{\hat{x}}+a y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4d) P II
$\mathbf{B_{80}}$ = $- x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $- a x_{22} \,\mathbf{\hat{x}}- a y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4d) P II
$\mathbf{B_{81}}$ = $- y_{22} \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $- a y_{22} \,\mathbf{\hat{x}}+a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4d) P II
$\mathbf{B_{82}}$ = $y_{22} \, \mathbf{a}_{1}- x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $a y_{22} \,\mathbf{\hat{x}}- a x_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4d) P II
$\mathbf{B_{83}}$ = $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ = $a x_{23} \,\mathbf{\hat{x}}+a y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ (4d) P III
$\mathbf{B_{84}}$ = $- x_{23} \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ = $- a x_{23} \,\mathbf{\hat{x}}- a y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ (4d) P III
$\mathbf{B_{85}}$ = $- y_{23} \, \mathbf{a}_{1}+x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ = $- a y_{23} \,\mathbf{\hat{x}}+a x_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ (4d) P III
$\mathbf{B_{86}}$ = $y_{23} \, \mathbf{a}_{1}- x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ = $a y_{23} \,\mathbf{\hat{x}}- a x_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ (4d) P III
$\mathbf{B_{87}}$ = $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ = $a x_{24} \,\mathbf{\hat{x}}+a y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ (4d) P IV
$\mathbf{B_{88}}$ = $- x_{24} \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ = $- a x_{24} \,\mathbf{\hat{x}}- a y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ (4d) P IV
$\mathbf{B_{89}}$ = $- y_{24} \, \mathbf{a}_{1}+x_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ = $- a y_{24} \,\mathbf{\hat{x}}+a x_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ (4d) P IV
$\mathbf{B_{90}}$ = $y_{24} \, \mathbf{a}_{1}- x_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ = $a y_{24} \,\mathbf{\hat{x}}- a x_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ (4d) P IV

References

  • Y. Hao, C. Chen, C. Hou, S. Liu, Z. Peng, Y. Lin, H. Li, X. Zhao, K. Koirala, H. Lu, C. Deng, and K. Hu, Li$_{3}$[AlP$_{2}$O$_{7}$F(OH)](H$_{2}$O)$_{0.5}$ and A[Al$_{2}$(PO$_{4}$)$_{2}$F(H$_{2}$O)] (A = K, Rb): Counter Cation Templates Derived Three Polar Alkaline Metal Fluoroaluminophosphates, Inorg. Chem. 63, 24885–24895 (2024), doi:10.1021/acs.inorgchem.4c04417.

First cited in

  • N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).

Geometry files


Prototype Generator

aflow --proto=A2B2CD10E22F8_tP90_75_d_d_ab_5d_11d_4d --params=$a,c/a,z_{1},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22},x_{23},y_{23},z_{23},x_{24},y_{24},z_{24}$

Species:

Running:

Output: