The structure described by LuGaO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to one O(3), three equivalent O(1), and three equivalent O(2) atoms. In the second Lu site, Lu(2) is bonded to one O(4), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent Ga(1)O5 trigonal bipyramids and edges with three equivalent Ga(1)O5 trigonal bipyramids. Ga(1) is bonded to one O(1), one O(2), one O(4), and two equivalent O(3) atoms to form GaO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with six equivalent Ga(1)O5 trigonal bipyramids, and  an edgeedge with one Lu(2)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(2), two equivalent Lu(1), and one Ga(1) atom to form OLu3Ga tetrahedra that share corners with four equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(1)Lu3Ga tetrahedra, corners with two equivalent O(4)LuGa3 trigonal pyramids, edges with three equivalent O(2)Lu3Ga tetrahedra, and edges with two equivalent O(3)LuGa3 trigonal pyramids. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Ga(1) atom to form distorted OLu3Ga tetrahedra that share corners with four equivalent O(1)Lu3Ga tetrahedra, corners with six equivalent O(2)Lu3Ga tetrahedra, corners with four equivalent O(3)LuGa3 trigonal pyramids, edges with three equivalent O(1)Lu3Ga tetrahedra, and  an edgeedge with one O(4)LuGa3 trigonal pyramid. In the third O site, O(3) is bonded to one Lu(1) and three equivalent Ga(1) atoms to form distorted OLuGa3 trigonal pyramids that share corners with six equivalent O(2)Lu3Ga tetrahedra, corners with three equivalent O(3)LuGa3 trigonal pyramids, corners with three equivalent O(4)LuGa3 trigonal pyramids, and edges with three equivalent O(1)Lu3Ga tetrahedra. In the fourth O site, O(4) is bonded to one Lu(2) and three equivalent Ga(1) atoms to form OLuGa3 trigonal pyramids that share corners with six equivalent O(1)Lu3Ga tetrahedra, corners with six equivalent O(3)LuGa3 trigonal pyramids, and edges with three equivalent O(2)Lu3Ga tetrahedra. is represented by the CIF card [CIF]
data_LuGaO3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.903
_cell_length_b   5.903
_cell_length_c   11.574
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.999
_symmetry_Int_Tables_number   1
_cell_volume   349.230
_cell_formula_units_Z   6
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  0.333  0.667  0.232  1.0
  Lu  Lu1  1  1.000  0.000  0.273  1.0
  Lu  Lu2  1  1.000  1.000  0.773  1.0
  Lu  Lu3  1  0.333  0.667  0.732  1.0
  Lu  Lu4  1  0.667  0.333  0.732  1.0
  Lu  Lu5  1  0.667  0.333  0.232  1.0
  Ga  Ga6  1  1.000  0.666  0.499  1.0
  Ga  Ga7  1  0.000  0.334  0.999  1.0
  Ga  Ga8  1  0.334  0.334  0.499  1.0
  Ga  Ga9  1  0.666  0.666  0.999  1.0
  Ga  Ga10  1  0.334  0.000  0.999  1.0
  Ga  Ga11  1  0.666  1.000  0.499  1.0
  O  O12  1  1.000  0.695  0.663  1.0
  O  O13  1  1.000  0.639  0.336  1.0
  O  O14  1  0.000  0.361  0.836  1.0
  O  O15  1  1.000  0.305  0.163  1.0
  O  O16  1  0.333  0.667  0.019  1.0
  O  O17  1  0.000  0.000  0.474  1.0
  O  O18  1  1.000  1.000  0.974  1.0
  O  O19  1  0.333  0.667  0.519  1.0
  O  O20  1  0.305  0.305  0.663  1.0
  O  O21  1  0.361  0.361  0.336  1.0
  O  O22  1  0.305  0.000  0.163  1.0
  O  O23  1  0.639  0.639  0.836  1.0
  O  O24  1  0.695  0.695  0.163  1.0
  O  O25  1  0.361  0.000  0.836  1.0
  O  O26  1  0.667  0.333  0.519  1.0
  O  O27  1  0.667  0.333  0.019  1.0
  O  O28  1  0.639  1.000  0.336  1.0
  O  O29  1  0.695  1.000  0.663  1.0
[/CIF]
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The structure described by LuGaO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to one O(3), three equivalent O(1), and three equivalent O(2) atoms. In the second Lu site, Lu(2) is bonded to one O(4), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent Ga(1)O5 trigonal bipyramids and edges with three equivalent Ga(1)O5 trigonal bipyramids. Ga(1) is bonded to one O(1), one O(2), one O(4), and two equivalent O(3) atoms to form GaO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with six equivalent Ga(1)O5 trigonal bipyramids, and  an edgeedge with one Lu(2)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(2), two equivalent Lu(1), and one Ga(1) atom to form OLu3Ga tetrahedra that share corners with four equivalent O(2)Lu3Ga tetrahedra, corners with six equivalent O(1)Lu3Ga tetrahedra, corners with two equivalent O(4)LuGa3 trigonal pyramids, edges with three equivalent O(2)Lu3Ga tetrahedra, and edges with two equivalent O(3)LuGa3 trigonal pyramids. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Ga(1) atom to form distorted OLu3Ga tetrahedra that share corners with four equivalent O(1)Lu3Ga tetrahedra, corners with six equivalent O(2)Lu3Ga tetrahedra, corners with four equivalent O(3)LuGa3 trigonal pyramids, edges with three equivalent O(1)Lu3Ga tetrahedra, and  an edgeedge with one O(4)LuGa3 trigonal pyramid. In the third O site, O(3) is bonded to one Lu(1) and three equivalent Ga(1) atoms to form distorted OLuGa3 trigonal pyramids that share corners with six equivalent O(2)Lu3Ga tetrahedra, corners with three equivalent O(3)LuGa3 trigonal pyramids, corners with three equivalent O(4)LuGa3 trigonal pyramids, and edges with three equivalent O(1)Lu3Ga tetrahedra. In the fourth O site, O(4) is bonded to one Lu(2) and three equivalent Ga(1) atoms to form OLuGa3 trigonal pyramids that share corners with six equivalent O(1)Lu3Ga tetrahedra, corners with six equivalent O(3)LuGa3 trigonal pyramids, and edges with three equivalent O(2)Lu3Ga tetrahedra. is represented by the CIF card [CIF]
data_LuGaO3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.903
_cell_length_b   5.903
_cell_length_c   11.574
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.999
_symmetry_Int_Tables_number   1
_cell_volume   349.230
_cell_formula_units_Z   6
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  0.333  0.667  0.232  1.0
  Lu  Lu1  1  1.000  0.000  0.273  1.0
  Lu  Lu2  1  1.000  1.000  0.773  1.0
  Lu  Lu3  1  0.333  0.667  0.732  1.0
  Lu  Lu4  1  0.667  0.333  0.732  1.0
  Lu  Lu5  1  0.667  0.333  0.232  1.0
  Ga  Ga6  1  1.000  0.666  0.499  1.0
  Ga  Ga7  1  0.000  0.334  0.999  1.0
  Ga  Ga8  1  0.334  0.334  0.499  1.0
  Ga  Ga9  1  0.666  0.666  0.999  1.0
  Ga  Ga10  1  0.334  0.000  0.999  1.0
  Ga  Ga11  1  0.666  1.000  0.499  1.0
  O  O12  1  1.000  0.695  0.663  1.0
  O  O13  1  1.000  0.639  0.336  1.0
  O  O14  1  0.000  0.361  0.836  1.0
  O  O15  1  1.000  0.305  0.163  1.0
  O  O16  1  0.333  0.667  0.019  1.0
  O  O17  1  0.000  0.000  0.474  1.0
  O  O18  1  1.000  1.000  0.974  1.0
  O  O19  1  0.333  0.667  0.519  1.0
  O  O20  1  0.305  0.305  0.663  1.0
  O  O21  1  0.361  0.361  0.336  1.0
  O  O22  1  0.305  0.000  0.163  1.0
  O  O23  1  0.639  0.639  0.836  1.0
  O  O24  1  0.695  0.695  0.163  1.0
  O  O25  1  0.361  0.000  0.836  1.0
  O  O26  1  0.667  0.333  0.519  1.0
  O  O27  1  0.667  0.333  0.019  1.0
  O  O28  1  0.639  1.000  0.336  1.0
  O  O29  1  0.695  1.000  0.663  1.0
[/CIF]
.