The compound described by HoGaO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Ho sites. In the first Ho site, Ho(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 Ho site, Ho(2) is bonded to one O(4), three equivalent O(1), and three equivalent O(2) atoms to form distorted HoO7 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 Ho(2)O7 pentagonal bipyramid, corners with six equivalent Ga(1)O5 trigonal bipyramids, and  an edgeedge with one Ho(2)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Ho(2), two equivalent Ho(1), and one Ga(1) atom to form OHo3Ga tetrahedra that share corners with four equivalent O(2)Ho3Ga tetrahedra, corners with six equivalent O(1)Ho3Ga tetrahedra, corners with two equivalent O(4)HoGa3 trigonal pyramids, edges with three equivalent O(2)Ho3Ga tetrahedra, and edges with two equivalent O(3)HoGa3 trigonal pyramids. In the second O site, O(2) is bonded to one Ho(2), two equivalent Ho(1), and one Ga(1) atom to form distorted OHo3Ga tetrahedra that share corners with four equivalent O(1)Ho3Ga tetrahedra, corners with six equivalent O(2)Ho3Ga tetrahedra, corners with four equivalent O(3)HoGa3 trigonal pyramids, edges with three equivalent O(1)Ho3Ga tetrahedra, and  an edgeedge with one O(4)HoGa3 trigonal pyramid. In the third O site, O(3) is bonded to one Ho(1) and three equivalent Ga(1) atoms to form distorted OHoGa3 trigonal pyramids that share corners with six equivalent O(2)Ho3Ga tetrahedra, corners with three equivalent O(3)HoGa3 trigonal pyramids, corners with three equivalent O(4)HoGa3 trigonal pyramids, and edges with three equivalent O(1)Ho3Ga tetrahedra. In the fourth O site, O(4) is bonded to one Ho(2) and three equivalent Ga(1) atoms to form OHoGa3 trigonal pyramids that share corners with six equivalent O(1)Ho3Ga tetrahedra, corners with six equivalent O(3)HoGa3 trigonal pyramids, and edges with three equivalent O(2)Ho3Ga tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HoGaO3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.013
_cell_length_b   6.013
_cell_length_c   11.636
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   364.402
_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
  Ho  Ho0  1  0.333  0.667  0.230  1.0
  Ho  Ho1  1  0.000  0.000  0.272  1.0
  Ho  Ho2  1  1.000  1.000  0.772  1.0
  Ho  Ho3  1  0.333  0.667  0.730  1.0
  Ho  Ho4  1  0.667  0.333  0.730  1.0
  Ho  Ho5  1  0.667  0.333  0.230  1.0
  Ga  Ga6  1  1.000  0.666  0.497  1.0
  Ga  Ga7  1  0.000  0.334  0.997  1.0
  Ga  Ga8  1  0.334  0.334  0.497  1.0
  Ga  Ga9  1  0.666  0.666  0.997  1.0
  Ga  Ga10  1  0.334  0.000  0.997  1.0
  Ga  Ga11  1  0.666  1.000  0.497  1.0
  O  O12  1  1.000  0.694  0.659  1.0
  O  O13  1  1.000  0.640  0.335  1.0
  O  O14  1  0.000  0.360  0.835  1.0
  O  O15  1  0.000  0.306  0.159  1.0
  O  O16  1  0.333  0.667  0.016  1.0
  O  O17  1  0.333  0.667  0.516  1.0
  O  O18  1  1.000  1.000  0.474  1.0
  O  O19  1  0.000  0.000  0.974  1.0
  O  O20  1  0.306  0.306  0.659  1.0
  O  O21  1  0.360  0.360  0.335  1.0
  O  O22  1  0.306  0.000  0.159  1.0
  O  O23  1  0.640  0.640  0.835  1.0
  O  O24  1  0.694  0.694  0.159  1.0
  O  O25  1  0.360  0.000  0.835  1.0
  O  O26  1  0.667  0.333  0.516  1.0
  O  O27  1  0.667  0.333  0.016  1.0
  O  O28  1  0.640  1.000  0.335  1.0
  O  O29  1  0.694  1.000  0.659  1.0
[/CIF]
.
The compound described by HoGaO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Ho sites. In the first Ho site, Ho(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 Ho site, Ho(2) is bonded to one O(4), three equivalent O(1), and three equivalent O(2) atoms to form distorted HoO7 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 Ho(2)O7 pentagonal bipyramid, corners with six equivalent Ga(1)O5 trigonal bipyramids, and  an edgeedge with one Ho(2)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Ho(2), two equivalent Ho(1), and one Ga(1) atom to form OHo3Ga tetrahedra that share corners with four equivalent O(2)Ho3Ga tetrahedra, corners with six equivalent O(1)Ho3Ga tetrahedra, corners with two equivalent O(4)HoGa3 trigonal pyramids, edges with three equivalent O(2)Ho3Ga tetrahedra, and edges with two equivalent O(3)HoGa3 trigonal pyramids. In the second O site, O(2) is bonded to one Ho(2), two equivalent Ho(1), and one Ga(1) atom to form distorted OHo3Ga tetrahedra that share corners with four equivalent O(1)Ho3Ga tetrahedra, corners with six equivalent O(2)Ho3Ga tetrahedra, corners with four equivalent O(3)HoGa3 trigonal pyramids, edges with three equivalent O(1)Ho3Ga tetrahedra, and  an edgeedge with one O(4)HoGa3 trigonal pyramid. In the third O site, O(3) is bonded to one Ho(1) and three equivalent Ga(1) atoms to form distorted OHoGa3 trigonal pyramids that share corners with six equivalent O(2)Ho3Ga tetrahedra, corners with three equivalent O(3)HoGa3 trigonal pyramids, corners with three equivalent O(4)HoGa3 trigonal pyramids, and edges with three equivalent O(1)Ho3Ga tetrahedra. In the fourth O site, O(4) is bonded to one Ho(2) and three equivalent Ga(1) atoms to form OHoGa3 trigonal pyramids that share corners with six equivalent O(1)Ho3Ga tetrahedra, corners with six equivalent O(3)HoGa3 trigonal pyramids, and edges with three equivalent O(2)Ho3Ga tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HoGaO3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.013
_cell_length_b   6.013
_cell_length_c   11.636
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   364.402
_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
  Ho  Ho0  1  0.333  0.667  0.230  1.0
  Ho  Ho1  1  0.000  0.000  0.272  1.0
  Ho  Ho2  1  1.000  1.000  0.772  1.0
  Ho  Ho3  1  0.333  0.667  0.730  1.0
  Ho  Ho4  1  0.667  0.333  0.730  1.0
  Ho  Ho5  1  0.667  0.333  0.230  1.0
  Ga  Ga6  1  1.000  0.666  0.497  1.0
  Ga  Ga7  1  0.000  0.334  0.997  1.0
  Ga  Ga8  1  0.334  0.334  0.497  1.0
  Ga  Ga9  1  0.666  0.666  0.997  1.0
  Ga  Ga10  1  0.334  0.000  0.997  1.0
  Ga  Ga11  1  0.666  1.000  0.497  1.0
  O  O12  1  1.000  0.694  0.659  1.0
  O  O13  1  1.000  0.640  0.335  1.0
  O  O14  1  0.000  0.360  0.835  1.0
  O  O15  1  0.000  0.306  0.159  1.0
  O  O16  1  0.333  0.667  0.016  1.0
  O  O17  1  0.333  0.667  0.516  1.0
  O  O18  1  1.000  1.000  0.474  1.0
  O  O19  1  0.000  0.000  0.974  1.0
  O  O20  1  0.306  0.306  0.659  1.0
  O  O21  1  0.360  0.360  0.335  1.0
  O  O22  1  0.306  0.000  0.159  1.0
  O  O23  1  0.640  0.640  0.835  1.0
  O  O24  1  0.694  0.694  0.159  1.0
  O  O25  1  0.360  0.000  0.835  1.0
  O  O26  1  0.667  0.333  0.516  1.0
  O  O27  1  0.667  0.333  0.016  1.0
  O  O28  1  0.640  1.000  0.335  1.0
  O  O29  1  0.694  1.000  0.659  1.0
[/CIF]
.