The material described by LuCoGaO4 is Aluminum carbonitride-derived structured and crystallizes in the trigonal R3m space group. Lu(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted LuO6 octahedra that share corners with three equivalent Co(1)O5 trigonal bipyramids, corners with three equivalent Ga(1)O5 trigonal bipyramids, and edges with six equivalent Lu(1)O6 octahedra. Co(1) is bonded to one O(1), one O(3), and three equivalent O(4) atoms to form distorted CoO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Co(1)O5 trigonal bipyramids, and edges with three equivalent Ga(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 63°. Ga(1) is bonded to one O(2), one O(4), and three equivalent O(3) atoms to form GaO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Ga(1)O5 trigonal bipyramids, and edges with three equivalent Co(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 62°. There are four inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(1) and one Co(1) atom to form OLu3Co tetrahedra that share corners with three equivalent O(4)GaCo3 tetrahedra, corners with three equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(1)Lu3Co tetrahedra,  a cornercorner with one O(3)Ga3Co trigonal pyramid, and edges with three equivalent O(2)Lu3Ga tetrahedra. In the second O site, O(2) is bonded to three equivalent Lu(1) and one Ga(1) atom to form OLu3Ga tetrahedra that share  a cornercorner with one O(4)GaCo3 tetrahedra, corners with three equivalent O(1)Lu3Co tetrahedra, corners with six equivalent O(2)Lu3Ga tetrahedra, corners with three equivalent O(3)Ga3Co trigonal pyramids, and edges with three equivalent O(1)Lu3Co tetrahedra. In the third O site, O(3) is bonded to one Co(1) and three equivalent Ga(1) atoms to form distorted OGa3Co trigonal pyramids that share  a cornercorner with one O(1)Lu3Co tetrahedra, corners with three equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(3)Ga3Co trigonal pyramids, and edges with three equivalent O(4)GaCo3 tetrahedra. In the fourth O site, O(4) is bonded to three equivalent Co(1) and one Ga(1) atom to form OGaCo3 tetrahedra that share  a cornercorner with one O(2)Lu3Ga tetrahedra, corners with three equivalent O(1)Lu3Co tetrahedra, corners with six equivalent O(4)GaCo3 tetrahedra, and edges with three equivalent O(3)Ga3Co trigonal pyramids. is represented by the CIF file [CIF]
data_LuGaCoO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.667
_cell_length_b   8.667
_cell_length_c   8.667
_cell_angle_alpha   22.787
_cell_angle_beta   22.787
_cell_angle_gamma   22.787
_symmetry_Int_Tables_number   1
_cell_volume   85.701
_cell_formula_units_Z   1
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
  Lu  Lu0  1  0.999  0.999  0.999  1.0
  Ga  Ga1  1  0.214  0.214  0.214  1.0
  Co  Co2  1  0.784  0.784  0.784  1.0
  O  O3  1  0.705  0.705  0.705  1.0
  O  O4  1  0.290  0.290  0.290  1.0
  O  O5  1  0.878  0.878  0.878  1.0
  O  O6  1  0.136  0.136  0.136  1.0
[/CIF]
.
The material described by LuCoGaO4 is Aluminum carbonitride-derived structured and crystallizes in the trigonal R3m space group. Lu(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted LuO6 octahedra that share corners with three equivalent Co(1)O5 trigonal bipyramids, corners with three equivalent Ga(1)O5 trigonal bipyramids, and edges with six equivalent Lu(1)O6 octahedra. Co(1) is bonded to one O(1), one O(3), and three equivalent O(4) atoms to form distorted CoO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Co(1)O5 trigonal bipyramids, and edges with three equivalent Ga(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 63°. Ga(1) is bonded to one O(2), one O(4), and three equivalent O(3) atoms to form GaO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Ga(1)O5 trigonal bipyramids, and edges with three equivalent Co(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 62°. There are four inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(1) and one Co(1) atom to form OLu3Co tetrahedra that share corners with three equivalent O(4)GaCo3 tetrahedra, corners with three equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(1)Lu3Co tetrahedra,  a cornercorner with one O(3)Ga3Co trigonal pyramid, and edges with three equivalent O(2)Lu3Ga tetrahedra. In the second O site, O(2) is bonded to three equivalent Lu(1) and one Ga(1) atom to form OLu3Ga tetrahedra that share  a cornercorner with one O(4)GaCo3 tetrahedra, corners with three equivalent O(1)Lu3Co tetrahedra, corners with six equivalent O(2)Lu3Ga tetrahedra, corners with three equivalent O(3)Ga3Co trigonal pyramids, and edges with three equivalent O(1)Lu3Co tetrahedra. In the third O site, O(3) is bonded to one Co(1) and three equivalent Ga(1) atoms to form distorted OGa3Co trigonal pyramids that share  a cornercorner with one O(1)Lu3Co tetrahedra, corners with three equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(3)Ga3Co trigonal pyramids, and edges with three equivalent O(4)GaCo3 tetrahedra. In the fourth O site, O(4) is bonded to three equivalent Co(1) and one Ga(1) atom to form OGaCo3 tetrahedra that share  a cornercorner with one O(2)Lu3Ga tetrahedra, corners with three equivalent O(1)Lu3Co tetrahedra, corners with six equivalent O(4)GaCo3 tetrahedra, and edges with three equivalent O(3)Ga3Co trigonal pyramids. is represented by the CIF file [CIF]
data_LuGaCoO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.667
_cell_length_b   8.667
_cell_length_c   8.667
_cell_angle_alpha   22.787
_cell_angle_beta   22.787
_cell_angle_gamma   22.787
_symmetry_Int_Tables_number   1
_cell_volume   85.701
_cell_formula_units_Z   1
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
  Lu  Lu0  1  0.999  0.999  0.999  1.0
  Ga  Ga1  1  0.214  0.214  0.214  1.0
  Co  Co2  1  0.784  0.784  0.784  1.0
  O  O3  1  0.705  0.705  0.705  1.0
  O  O4  1  0.290  0.290  0.290  1.0
  O  O5  1  0.878  0.878  0.878  1.0
  O  O6  1  0.136  0.136  0.136  1.0
[/CIF]
.