The crystal structure described by K2LiAlF6 is (Cubic) Perovskite-derived structured and crystallizes in the trigonal P-3m1 space group. There are three inequivalent K sites. In the first K site, K(1) is bonded to three equivalent F(2) and nine equivalent F(3) atoms to form KF12 cuboctahedra that share corners with three equivalent K(2)F12 cuboctahedra, corners with six equivalent K(1)F12 cuboctahedra, corners with three equivalent Li(1)F6 octahedra,  a faceface with one K(3)F12 cuboctahedra, faces with three equivalent K(1)F12 cuboctahedra, faces with three equivalent K(2)F12 cuboctahedra, faces with three equivalent Li(2)F6 octahedra, and faces with four equivalent Al(1)F6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the second K site, K(2) is bonded to three equivalent F(1), three equivalent F(3), and six equivalent F(2) atoms to form KF12 cuboctahedra that share corners with three equivalent K(1)F12 cuboctahedra, corners with three equivalent K(3)F12 cuboctahedra, corners with six equivalent K(2)F12 cuboctahedra, faces with three equivalent K(1)F12 cuboctahedra, faces with three equivalent K(3)F12 cuboctahedra,  a faceface with one Li(2)F6 octahedra,  a faceface with one Al(2)F6 octahedra, faces with three equivalent Li(1)F6 octahedra, and faces with three equivalent Al(1)F6 octahedra. In the third K site, K(3) is bonded to three equivalent F(2) and nine equivalent F(1) atoms to form distorted KF12 cuboctahedra that share corners with three equivalent K(2)F12 cuboctahedra, corners with six equivalent K(3)F12 cuboctahedra, corners with three equivalent Al(1)F6 octahedra,  a faceface with one K(1)F12 cuboctahedra, faces with three equivalent K(2)F12 cuboctahedra, faces with three equivalent K(3)F12 cuboctahedra, faces with three equivalent Al(2)F6 octahedra, and faces with four equivalent Li(1)F6 octahedra. The corner-sharing octahedral tilt angles are 12°. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to three equivalent F(1) and three equivalent F(2) atoms to form distorted LiF6 octahedra that share corners with three equivalent K(1)F12 cuboctahedra, corners with three equivalent Al(2)F6 octahedra, faces with three equivalent K(2)F12 cuboctahedra, faces with four equivalent K(3)F12 cuboctahedra, and  a faceface with one Al(1)F6 octahedra. The corner-sharing octahedral tilt angles are 7°. In the second Li site, Li(2) is bonded to six equivalent F(3) atoms to form LiF6 octahedra that share corners with six equivalent Al(1)F6 octahedra, faces with two equivalent K(2)F12 cuboctahedra, and faces with six equivalent K(1)F12 cuboctahedra. The corner-sharing octahedra are not tilted. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to three equivalent F(2) and three equivalent F(3) atoms to form AlF6 octahedra that share corners with three equivalent K(3)F12 cuboctahedra, corners with three equivalent Li(2)F6 octahedra, faces with three equivalent K(2)F12 cuboctahedra, faces with four equivalent K(1)F12 cuboctahedra, and  a faceface with one Li(1)F6 octahedra. The corner-sharing octahedra are not tilted. In the second Al site, Al(2) is bonded to six equivalent F(1) atoms to form AlF6 octahedra that share corners with six equivalent Li(1)F6 octahedra, faces with two equivalent K(2)F12 cuboctahedra, and faces with six equivalent K(3)F12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. There are three inequivalent F sites. In the first F site, F(1) is bonded in a distorted linear geometry to one K(2), three equivalent K(3), one Li(1), and one Al(2) atom. In the second F site, F(2) is bonded in a 6-coordinate geometry to one K(1), one K(3), two equivalent K(2), one Li(1), and one Al(1) atom. In the third F site, F(3) is bonded in a distorted linear geometry to one K(2), three equivalent K(1), one Li(2), and one Al(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K2LiAlF6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.533
_cell_length_b   5.533
_cell_length_c   13.547
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   359.214
_cell_formula_units_Z   3
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  K  K0  1  0.000  0.000  0.745  1.0
  K  K1  1  0.333  0.667  0.081  1.0
  K  K2  1  0.000  0.000  0.439  1.0
  K  K3  1  0.333  0.667  0.585  1.0
  K  K4  1  0.667  0.333  0.922  1.0
  K  K5  1  0.667  0.333  0.228  1.0
  Li  Li6  1  0.000  0.000  0.191  1.0
  Li  Li7  1  0.667  0.333  0.476  1.0
  Li  Li8  1  0.333  0.667  0.833  1.0
  Al  Al9  1  0.667  0.333  0.672  1.0
  Al  Al10  1  0.000  0.000  0.995  1.0
  Al  Al11  1  0.333  0.667  0.333  1.0
  F  F12  1  0.643  0.822  0.257  1.0
  F  F13  1  0.816  0.184  0.590  1.0
  F  F14  1  0.850  0.150  0.076  1.0
  F  F15  1  0.023  0.512  0.410  1.0
  F  F16  1  0.511  0.022  0.747  1.0
  F  F17  1  0.488  0.977  0.410  1.0
  F  F18  1  0.156  0.844  0.919  1.0
  F  F19  1  0.511  0.489  0.747  1.0
  F  F20  1  0.178  0.357  0.257  1.0
  F  F21  1  0.816  0.633  0.590  1.0
  F  F22  1  0.850  0.701  0.076  1.0
  F  F23  1  0.367  0.184  0.590  1.0
  F  F24  1  0.299  0.150  0.076  1.0
  F  F25  1  0.178  0.822  0.257  1.0
  F  F26  1  0.689  0.844  0.919  1.0
  F  F27  1  0.978  0.489  0.747  1.0
  F  F28  1  0.156  0.311  0.919  1.0
  F  F29  1  0.488  0.512  0.410  1.0
[/CIF]
.
The crystal structure described by K2LiAlF6 is (Cubic) Perovskite-derived structured and crystallizes in the trigonal P-3m1 space group. There are three inequivalent K sites. In the first K site, K(1) is bonded to three equivalent F(2) and nine equivalent F(3) atoms to form KF12 cuboctahedra that share corners with three equivalent K(2)F12 cuboctahedra, corners with six equivalent K(1)F12 cuboctahedra, corners with three equivalent Li(1)F6 octahedra,  a faceface with one K(3)F12 cuboctahedra, faces with three equivalent K(1)F12 cuboctahedra, faces with three equivalent K(2)F12 cuboctahedra, faces with three equivalent Li(2)F6 octahedra, and faces with four equivalent Al(1)F6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the second K site, K(2) is bonded to three equivalent F(1), three equivalent F(3), and six equivalent F(2) atoms to form KF12 cuboctahedra that share corners with three equivalent K(1)F12 cuboctahedra, corners with three equivalent K(3)F12 cuboctahedra, corners with six equivalent K(2)F12 cuboctahedra, faces with three equivalent K(1)F12 cuboctahedra, faces with three equivalent K(3)F12 cuboctahedra,  a faceface with one Li(2)F6 octahedra,  a faceface with one Al(2)F6 octahedra, faces with three equivalent Li(1)F6 octahedra, and faces with three equivalent Al(1)F6 octahedra. In the third K site, K(3) is bonded to three equivalent F(2) and nine equivalent F(1) atoms to form distorted KF12 cuboctahedra that share corners with three equivalent K(2)F12 cuboctahedra, corners with six equivalent K(3)F12 cuboctahedra, corners with three equivalent Al(1)F6 octahedra,  a faceface with one K(1)F12 cuboctahedra, faces with three equivalent K(2)F12 cuboctahedra, faces with three equivalent K(3)F12 cuboctahedra, faces with three equivalent Al(2)F6 octahedra, and faces with four equivalent Li(1)F6 octahedra. The corner-sharing octahedral tilt angles are 12°. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to three equivalent F(1) and three equivalent F(2) atoms to form distorted LiF6 octahedra that share corners with three equivalent K(1)F12 cuboctahedra, corners with three equivalent Al(2)F6 octahedra, faces with three equivalent K(2)F12 cuboctahedra, faces with four equivalent K(3)F12 cuboctahedra, and  a faceface with one Al(1)F6 octahedra. The corner-sharing octahedral tilt angles are 7°. In the second Li site, Li(2) is bonded to six equivalent F(3) atoms to form LiF6 octahedra that share corners with six equivalent Al(1)F6 octahedra, faces with two equivalent K(2)F12 cuboctahedra, and faces with six equivalent K(1)F12 cuboctahedra. The corner-sharing octahedra are not tilted. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to three equivalent F(2) and three equivalent F(3) atoms to form AlF6 octahedra that share corners with three equivalent K(3)F12 cuboctahedra, corners with three equivalent Li(2)F6 octahedra, faces with three equivalent K(2)F12 cuboctahedra, faces with four equivalent K(1)F12 cuboctahedra, and  a faceface with one Li(1)F6 octahedra. The corner-sharing octahedra are not tilted. In the second Al site, Al(2) is bonded to six equivalent F(1) atoms to form AlF6 octahedra that share corners with six equivalent Li(1)F6 octahedra, faces with two equivalent K(2)F12 cuboctahedra, and faces with six equivalent K(3)F12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. There are three inequivalent F sites. In the first F site, F(1) is bonded in a distorted linear geometry to one K(2), three equivalent K(3), one Li(1), and one Al(2) atom. In the second F site, F(2) is bonded in a 6-coordinate geometry to one K(1), one K(3), two equivalent K(2), one Li(1), and one Al(1) atom. In the third F site, F(3) is bonded in a distorted linear geometry to one K(2), three equivalent K(1), one Li(2), and one Al(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K2LiAlF6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.533
_cell_length_b   5.533
_cell_length_c   13.547
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   359.214
_cell_formula_units_Z   3
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  K  K0  1  0.000  0.000  0.745  1.0
  K  K1  1  0.333  0.667  0.081  1.0
  K  K2  1  0.000  0.000  0.439  1.0
  K  K3  1  0.333  0.667  0.585  1.0
  K  K4  1  0.667  0.333  0.922  1.0
  K  K5  1  0.667  0.333  0.228  1.0
  Li  Li6  1  0.000  0.000  0.191  1.0
  Li  Li7  1  0.667  0.333  0.476  1.0
  Li  Li8  1  0.333  0.667  0.833  1.0
  Al  Al9  1  0.667  0.333  0.672  1.0
  Al  Al10  1  0.000  0.000  0.995  1.0
  Al  Al11  1  0.333  0.667  0.333  1.0
  F  F12  1  0.643  0.822  0.257  1.0
  F  F13  1  0.816  0.184  0.590  1.0
  F  F14  1  0.850  0.150  0.076  1.0
  F  F15  1  0.023  0.512  0.410  1.0
  F  F16  1  0.511  0.022  0.747  1.0
  F  F17  1  0.488  0.977  0.410  1.0
  F  F18  1  0.156  0.844  0.919  1.0
  F  F19  1  0.511  0.489  0.747  1.0
  F  F20  1  0.178  0.357  0.257  1.0
  F  F21  1  0.816  0.633  0.590  1.0
  F  F22  1  0.850  0.701  0.076  1.0
  F  F23  1  0.367  0.184  0.590  1.0
  F  F24  1  0.299  0.150  0.076  1.0
  F  F25  1  0.178  0.822  0.257  1.0
  F  F26  1  0.689  0.844  0.919  1.0
  F  F27  1  0.978  0.489  0.747  1.0
  F  F28  1  0.156  0.311  0.919  1.0
  F  F29  1  0.488  0.512  0.410  1.0
[/CIF]
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