The material structure described by K3Lu(PO4)2 crystallizes in the trigonal P-3 space group. There are three inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to two equivalent O(2), two equivalent O(3), two equivalent O(4), and three equivalent O(1) atoms. In the second K site, K(2) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(4) atoms. In the third K site, K(3) is bonded to six equivalent O(3) and six equivalent O(4) atoms to form KO12 cuboctahedra that share edges with six equivalent P(1)O4 tetrahedra and faces with two equivalent Lu(2)O6 octahedra. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form LuO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra. In the second Lu site, Lu(2) is bonded to six equivalent O(3) atoms to form LuO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra and faces with two equivalent K(3)O12 cuboctahedra. P(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form PO4 tetrahedra that share  a cornercorner with one Lu(2)O6 octahedra, corners with two equivalent Lu(1)O6 octahedra, and  an edgeedge with one K(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 5-31°. There are four inequivalent O sites. In the first O site, O(4) is bonded in a distorted single-bond geometry to one K(2), one K(3), two equivalent K(1), and one P(1) atom. In the second O site, O(1) is bonded in a distorted linear geometry to three equivalent K(1), one Lu(1), and one P(1) atom. In the third O site, O(2) is bonded in a 5-coordinate geometry to one K(2), two equivalent K(1), one Lu(1), and one P(1) atom. In the fourth O site, O(3) is bonded in a 2-coordinate geometry to one K(3), two equivalent K(1), one Lu(2), and one P(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K3Lu(PO4)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.554
_cell_length_b   9.554
_cell_length_c   7.608
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   601.446
_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  0.335  0.333  0.248  1.0
  K  K1  1  0.998  0.665  0.248  1.0
  K  K2  1  0.667  0.002  0.248  1.0
  K  K3  1  0.665  0.667  0.752  1.0
  K  K4  1  0.002  0.335  0.752  1.0
  K  K5  1  0.333  0.998  0.752  1.0
  K  K6  1  0.333  0.667  0.508  1.0
  K  K7  1  0.667  0.333  0.492  1.0
  K  K8  1  0.000  0.000  0.500  1.0
  Lu  Lu9  1  0.333  0.667  0.034  1.0
  Lu  Lu10  1  0.667  0.333  0.966  1.0
  Lu  Lu11  1  0.000  0.000  0.000  1.0
  P  P12  1  0.328  0.340  0.768  1.0
  P  P13  1  0.013  0.672  0.768  1.0
  P  P14  1  0.660  0.987  0.768  1.0
  P  P15  1  0.672  0.660  0.232  1.0
  P  P16  1  0.987  0.328  0.232  1.0
  P  P17  1  0.340  0.013  0.232  1.0
  O  O18  1  0.338  0.478  0.885  1.0
  O  O19  1  0.141  0.662  0.885  1.0
  O  O20  1  0.522  0.859  0.885  1.0
  O  O21  1  0.662  0.522  0.115  1.0
  O  O22  1  0.859  0.338  0.115  1.0
  O  O23  1  0.478  0.141  0.115  1.0
  O  O24  1  0.486  0.335  0.790  1.0
  O  O25  1  0.849  0.514  0.790  1.0
  O  O26  1  0.665  0.151  0.790  1.0
  O  O27  1  0.514  0.665  0.210  1.0
  O  O28  1  0.151  0.486  0.210  1.0
  O  O29  1  0.335  0.849  0.210  1.0
  O  O30  1  0.186  0.178  0.833  1.0
  O  O31  1  0.992  0.814  0.833  1.0
  O  O32  1  0.822  0.008  0.833  1.0
  O  O33  1  0.814  0.822  0.167  1.0
  O  O34  1  0.008  0.186  0.167  1.0
  O  O35  1  0.178  0.992  0.167  1.0
  O  O36  1  0.369  0.071  0.420  1.0
  O  O37  1  0.929  0.298  0.420  1.0
  O  O38  1  0.702  0.631  0.420  1.0
  O  O39  1  0.631  0.929  0.580  1.0
  O  O40  1  0.071  0.702  0.580  1.0
  O  O41  1  0.298  0.369  0.580  1.0
[/CIF]
.
The material structure described by K3Lu(PO4)2 crystallizes in the trigonal P-3 space group. There are three inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to two equivalent O(2), two equivalent O(3), two equivalent O(4), and three equivalent O(1) atoms. In the second K site, K(2) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(4) atoms. In the third K site, K(3) is bonded to six equivalent O(3) and six equivalent O(4) atoms to form KO12 cuboctahedra that share edges with six equivalent P(1)O4 tetrahedra and faces with two equivalent Lu(2)O6 octahedra. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form LuO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra. In the second Lu site, Lu(2) is bonded to six equivalent O(3) atoms to form LuO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra and faces with two equivalent K(3)O12 cuboctahedra. P(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form PO4 tetrahedra that share  a cornercorner with one Lu(2)O6 octahedra, corners with two equivalent Lu(1)O6 octahedra, and  an edgeedge with one K(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 5-31°. There are four inequivalent O sites. In the first O site, O(4) is bonded in a distorted single-bond geometry to one K(2), one K(3), two equivalent K(1), and one P(1) atom. In the second O site, O(1) is bonded in a distorted linear geometry to three equivalent K(1), one Lu(1), and one P(1) atom. In the third O site, O(2) is bonded in a 5-coordinate geometry to one K(2), two equivalent K(1), one Lu(1), and one P(1) atom. In the fourth O site, O(3) is bonded in a 2-coordinate geometry to one K(3), two equivalent K(1), one Lu(2), and one P(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K3Lu(PO4)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.554
_cell_length_b   9.554
_cell_length_c   7.608
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   601.446
_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  0.335  0.333  0.248  1.0
  K  K1  1  0.998  0.665  0.248  1.0
  K  K2  1  0.667  0.002  0.248  1.0
  K  K3  1  0.665  0.667  0.752  1.0
  K  K4  1  0.002  0.335  0.752  1.0
  K  K5  1  0.333  0.998  0.752  1.0
  K  K6  1  0.333  0.667  0.508  1.0
  K  K7  1  0.667  0.333  0.492  1.0
  K  K8  1  0.000  0.000  0.500  1.0
  Lu  Lu9  1  0.333  0.667  0.034  1.0
  Lu  Lu10  1  0.667  0.333  0.966  1.0
  Lu  Lu11  1  0.000  0.000  0.000  1.0
  P  P12  1  0.328  0.340  0.768  1.0
  P  P13  1  0.013  0.672  0.768  1.0
  P  P14  1  0.660  0.987  0.768  1.0
  P  P15  1  0.672  0.660  0.232  1.0
  P  P16  1  0.987  0.328  0.232  1.0
  P  P17  1  0.340  0.013  0.232  1.0
  O  O18  1  0.338  0.478  0.885  1.0
  O  O19  1  0.141  0.662  0.885  1.0
  O  O20  1  0.522  0.859  0.885  1.0
  O  O21  1  0.662  0.522  0.115  1.0
  O  O22  1  0.859  0.338  0.115  1.0
  O  O23  1  0.478  0.141  0.115  1.0
  O  O24  1  0.486  0.335  0.790  1.0
  O  O25  1  0.849  0.514  0.790  1.0
  O  O26  1  0.665  0.151  0.790  1.0
  O  O27  1  0.514  0.665  0.210  1.0
  O  O28  1  0.151  0.486  0.210  1.0
  O  O29  1  0.335  0.849  0.210  1.0
  O  O30  1  0.186  0.178  0.833  1.0
  O  O31  1  0.992  0.814  0.833  1.0
  O  O32  1  0.822  0.008  0.833  1.0
  O  O33  1  0.814  0.822  0.167  1.0
  O  O34  1  0.008  0.186  0.167  1.0
  O  O35  1  0.178  0.992  0.167  1.0
  O  O36  1  0.369  0.071  0.420  1.0
  O  O37  1  0.929  0.298  0.420  1.0
  O  O38  1  0.702  0.631  0.420  1.0
  O  O39  1  0.631  0.929  0.580  1.0
  O  O40  1  0.071  0.702  0.580  1.0
  O  O41  1  0.298  0.369  0.580  1.0
[/CIF]
.