data_LuSc2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.36
_cell_length_b   6.36
_cell_length_c   6.36
_cell_angle_alpha   60.0
_cell_angle_beta   60.0
_cell_angle_gamma   60.0
_symmetry_Int_Tables_number   1
_chemical_formula_structural   LuSc2O4
_chemical_formula_sum   'Lu2 Sc4 O8'
_cell_volume   181.53
_cell_formula_units_Z   2
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  0.0  0.0  0.0  1.0
  Lu  Lu1  1  0.25  0.25  0.25  1.0
  Sc  Sc10  1  0.37  0.37  0.62  1.0
  Sc  Sc11  1  0.37  0.62  0.37  1.0
  Sc  Sc12  1  0.62  0.62  0.62  1.0
  Sc  Sc13  1  0.62  0.37  0.37  1.0
  O  O2  1  0.46  0.53  0.53  1.0
  O  O3  1  0.46  0.46  0.46  1.0
  O  O4  1  0.53  0.46  0.53  1.0
  O  O5  1  0.7  0.7  0.78  1.0
  O  O6  1  0.53  0.53  0.46  1.0
  O  O7  1  0.7  0.78  0.7  1.0
  O  O8  1  0.78  0.78  0.78  1.0
  O  O9  1  0.78  0.7  0.7  1.0

data_LuSc2O4
_symmetry_space_group_name_H-M   R3m
_cell_length_a   6.36
_cell_length_b   6.36
_cell_length_c   15.57
_cell_angle_alpha   90.0
_cell_angle_beta   90.0
_cell_angle_gamma   120.0
_symmetry_Int_Tables_number   160
_chemical_formula_structural   LuSc2O4
_chemical_formula_sum   'Lu6 Sc12 O24'
_cell_volume   544.59
_cell_formula_units_Z   6
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
  2  '-y, x-y, z'
  3  '-x+y, -x, z'
  4  '-y, -x, z'
  5  '-x+y, y, z'
  6  'x, x-y, z'
  7  'x+1/3, y+2/3, z+2/3'
  8  '-y+1/3, x-y+2/3, z+2/3'
  9  '-x+y+1/3, -x+2/3, z+2/3'
  10  '-y+1/3, -x+2/3, z+2/3'
  11  '-x+y+1/3, y+2/3, z+2/3'
  12  'x+1/3, x-y+2/3, z+2/3'
  13  'x+2/3, y+1/3, z+1/3'
  14  '-y+2/3, x-y+1/3, z+1/3'
  15  '-x+y+2/3, -x+1/3, z+1/3'
  16  '-y+2/3, -x+1/3, z+1/3'
  17  '-x+y+2/3, y+1/3, z+1/3'
  18  'x+2/3, x-y+1/3, z+1/3'
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  3  0.0  0.0  0.0  1.0
  Lu  Lu1  3  0.0  0.0  0.75  1.0
  Sc  Sc2  9  0.08  0.16  0.55  1.0
  Sc  Sc3  3  0.0  0.0  0.38  1.0
  O  O4  9  0.03  0.05  0.27  1.0
  O  O5  9  0.05  0.03  0.49  1.0
  O  O6  3  0.0  0.0  0.22  1.0
  O  O7  3  0.0  0.0  0.54  1.0

Lu Lu Sc Sc Sc Sc O O O O O O O O
LuSc2O4 crystallizes in the trigonal R3m space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 3-coordinate geometry to four equivalent Lu(2) atoms. There is one shorter (3.85 Å) and three longer (3.91 Å) Lu(1)-Lu(2) bond lengths. In the second Lu site, Lu(2) is bonded in a 14-coordinate geometry to four equivalent Lu(1), three equivalent Sc(2), six equivalent Sc(1), and one O(2) atom. All Lu(2)-Sc(2) bond lengths are 3.71 Å. There are three shorter (3.33 Å) and three longer (3.40 Å) Lu(2)-Sc(1) bond lengths. The Lu(2)-O(2) bond length is 3.25 Å. There are two inequivalent Sc sites. In the first Sc site, Sc(1) is bonded in a single-bond geometry to two equivalent Lu(2), one O(2), and two equivalent O(1) atoms. The Sc(1)-O(2) bond length is 0.91 Å. Both Sc(1)-O(1) bond lengths are 1.16 Å. In the second Sc site, Sc(2) is bonded in a hexagonal planar geometry to three equivalent Lu(2), three equivalent O(1), and three equivalent O(3) atoms. All Sc(2)-O(1) bond lengths are 1.75 Å. All Sc(2)-O(3) bond lengths are 1.75 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Sc(2), two equivalent Sc(1), one O(2), and two equivalent O(1) atoms. The O(1)-O(2) bond length is 0.84 Å. Both O(1)-O(1) bond lengths are 0.49 Å. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Lu(2), three equivalent Sc(1), and three equivalent O(1) atoms. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Sc(2), one O(4), and two equivalent O(3) atoms. The O(3)-O(4) bond length is 0.84 Å. Both O(3)-O(3) bond lengths are 0.49 Å. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to three equivalent O(3) atoms.