The compound described by LuCuGaO4 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 Cu(1)O5 trigonal bipyramids, corners with three equivalent Ga(1)O5 trigonal bipyramids, and edges with six equivalent Lu(1)O6 octahedra. Cu(1) is bonded to one O(1), one O(3), and three equivalent O(4) atoms to form CuO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Cu(1)O5 trigonal bipyramids, and edges with three equivalent Ga(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 66°. 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 Cu(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 Cu(1) atom to form OLu3Cu tetrahedra that share corners with three equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(1)Lu3Cu tetrahedra,  a cornercorner with one O(3)Ga3Cu trigonal pyramid, corners with three equivalent O(4)GaCu3 trigonal pyramids, 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 distorted OLu3Ga tetrahedra that share corners with three equivalent O(1)Lu3Cu tetrahedra, corners with six equivalent O(2)Lu3Ga tetrahedra,  a cornercorner with one O(4)GaCu3 trigonal pyramid, corners with three equivalent O(3)Ga3Cu trigonal pyramids, and edges with three equivalent O(1)Lu3Cu tetrahedra. In the third O site, O(3) is bonded to one Cu(1) and three equivalent Ga(1) atoms to form OGa3Cu trigonal pyramids that share  a cornercorner with one O(1)Lu3Cu tetrahedra, corners with three equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(3)Ga3Cu trigonal pyramids, and edges with three equivalent O(4)GaCu3 trigonal pyramids. In the fourth O site, O(4) is bonded to three equivalent Cu(1) and one Ga(1) atom to form OGaCu3 trigonal pyramids that share  a cornercorner with one O(2)Lu3Ga tetrahedra, corners with three equivalent O(1)Lu3Cu tetrahedra, corners with six equivalent O(4)GaCu3 trigonal pyramids, and edges with three equivalent O(3)Ga3Cu trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_LuGaCuO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.276
_cell_length_b   8.276
_cell_length_c   8.276
_cell_angle_alpha   24.335
_cell_angle_beta   24.335
_cell_angle_gamma   24.335
_symmetry_Int_Tables_number   1
_cell_volume   84.620
_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  0.997  0.997  0.997  1.0
  Ga  Ga1  1  0.787  0.787  0.787  1.0
  Cu  Cu2  1  0.212  0.212  0.212  1.0
  O  O3  1  0.293  0.293  0.293  1.0
  O  O4  1  0.709  0.709  0.709  1.0
  O  O5  1  0.125  0.125  0.125  1.0
  O  O6  1  0.867  0.867  0.867  1.0
[/CIF]
.
The compound described by LuCuGaO4 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 Cu(1)O5 trigonal bipyramids, corners with three equivalent Ga(1)O5 trigonal bipyramids, and edges with six equivalent Lu(1)O6 octahedra. Cu(1) is bonded to one O(1), one O(3), and three equivalent O(4) atoms to form CuO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Cu(1)O5 trigonal bipyramids, and edges with three equivalent Ga(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 66°. 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 Cu(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 Cu(1) atom to form OLu3Cu tetrahedra that share corners with three equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(1)Lu3Cu tetrahedra,  a cornercorner with one O(3)Ga3Cu trigonal pyramid, corners with three equivalent O(4)GaCu3 trigonal pyramids, 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 distorted OLu3Ga tetrahedra that share corners with three equivalent O(1)Lu3Cu tetrahedra, corners with six equivalent O(2)Lu3Ga tetrahedra,  a cornercorner with one O(4)GaCu3 trigonal pyramid, corners with three equivalent O(3)Ga3Cu trigonal pyramids, and edges with three equivalent O(1)Lu3Cu tetrahedra. In the third O site, O(3) is bonded to one Cu(1) and three equivalent Ga(1) atoms to form OGa3Cu trigonal pyramids that share  a cornercorner with one O(1)Lu3Cu tetrahedra, corners with three equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(3)Ga3Cu trigonal pyramids, and edges with three equivalent O(4)GaCu3 trigonal pyramids. In the fourth O site, O(4) is bonded to three equivalent Cu(1) and one Ga(1) atom to form OGaCu3 trigonal pyramids that share  a cornercorner with one O(2)Lu3Ga tetrahedra, corners with three equivalent O(1)Lu3Cu tetrahedra, corners with six equivalent O(4)GaCu3 trigonal pyramids, and edges with three equivalent O(3)Ga3Cu trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_LuGaCuO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.276
_cell_length_b   8.276
_cell_length_c   8.276
_cell_angle_alpha   24.335
_cell_angle_beta   24.335
_cell_angle_gamma   24.335
_symmetry_Int_Tables_number   1
_cell_volume   84.620
_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  0.997  0.997  0.997  1.0
  Ga  Ga1  1  0.787  0.787  0.787  1.0
  Cu  Cu2  1  0.212  0.212  0.212  1.0
  O  O3  1  0.293  0.293  0.293  1.0
  O  O4  1  0.709  0.709  0.709  1.0
  O  O5  1  0.125  0.125  0.125  1.0
  O  O6  1  0.867  0.867  0.867  1.0
[/CIF]
.