The compound described by Lu4V4O13 crystallizes in the cubic F-43m space group. Lu(1) is bonded to one O(3), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 hexagonal pyramids that share corners with three equivalent Lu(1)O7 hexagonal pyramids, edges with three equivalent Lu(1)O7 hexagonal pyramids, and edges with six equivalent V(1)O6 octahedra. V(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form VO6 octahedra that share corners with six equivalent V(1)O6 octahedra and edges with six equivalent Lu(1)O7 hexagonal pyramids. The corner-sharing octahedral tilt angles range from 53-55°. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Lu(1) and two equivalent V(1) atoms to form distorted OLu2V2 tetrahedra that share corners with four equivalent O(2)Lu2V2 tetrahedra, corners with eight equivalent O(1)Lu2V2 tetrahedra,  an edgeedge with one O(3)Lu4 tetrahedra, and edges with four equivalent O(2)Lu2V2 tetrahedra. In the second O site, O(2) is bonded to two equivalent Lu(1) and two equivalent V(1) atoms to form OLu2V2 tetrahedra that share corners with two equivalent O(3)Lu4 tetrahedra, corners with four equivalent O(1)Lu2V2 tetrahedra, corners with eight equivalent O(2)Lu2V2 tetrahedra, and edges with four equivalent O(1)Lu2V2 tetrahedra. In the third O site, O(3) is bonded to four equivalent Lu(1) atoms to form a mixture of edge and corner-sharing OLu4 tetrahedra. is represented by the CIF file [CIF]
data_Lu4V4O13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.056
_cell_length_b   7.056
_cell_length_c   7.056
_cell_angle_alpha   60.000
_cell_angle_beta   60.000
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   248.405
_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  0.877  0.370  0.877  1.0
  Lu  Lu1  1  0.370  0.877  0.877  1.0
  Lu  Lu2  1  0.877  0.877  0.370  1.0
  Lu  Lu3  1  0.877  0.877  0.877  1.0
  V  V4  1  0.376  0.376  0.376  1.0
  V  V5  1  0.376  0.376  0.871  1.0
  V  V6  1  0.376  0.871  0.376  1.0
  V  V7  1  0.871  0.376  0.376  1.0
  O  O8  1  0.714  0.286  0.714  1.0
  O  O9  1  0.714  0.286  0.286  1.0
  O  O10  1  0.286  0.286  0.714  1.0
  O  O11  1  0.714  0.714  0.286  1.0
  O  O12  1  0.286  0.714  0.714  1.0
  O  O13  1  0.286  0.714  0.286  1.0
  O  O14  1  0.466  0.034  0.466  1.0
  O  O15  1  0.466  0.034  0.034  1.0
  O  O16  1  0.034  0.034  0.466  1.0
  O  O17  1  0.466  0.466  0.034  1.0
  O  O18  1  0.034  0.466  0.466  1.0
  O  O19  1  0.034  0.466  0.034  1.0
  O  O20  1  0.000  0.000  0.000  1.0
[/CIF]
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The compound described by Lu4V4O13 crystallizes in the cubic F-43m space group. Lu(1) is bonded to one O(3), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 hexagonal pyramids that share corners with three equivalent Lu(1)O7 hexagonal pyramids, edges with three equivalent Lu(1)O7 hexagonal pyramids, and edges with six equivalent V(1)O6 octahedra. V(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form VO6 octahedra that share corners with six equivalent V(1)O6 octahedra and edges with six equivalent Lu(1)O7 hexagonal pyramids. The corner-sharing octahedral tilt angles range from 53-55°. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Lu(1) and two equivalent V(1) atoms to form distorted OLu2V2 tetrahedra that share corners with four equivalent O(2)Lu2V2 tetrahedra, corners with eight equivalent O(1)Lu2V2 tetrahedra,  an edgeedge with one O(3)Lu4 tetrahedra, and edges with four equivalent O(2)Lu2V2 tetrahedra. In the second O site, O(2) is bonded to two equivalent Lu(1) and two equivalent V(1) atoms to form OLu2V2 tetrahedra that share corners with two equivalent O(3)Lu4 tetrahedra, corners with four equivalent O(1)Lu2V2 tetrahedra, corners with eight equivalent O(2)Lu2V2 tetrahedra, and edges with four equivalent O(1)Lu2V2 tetrahedra. In the third O site, O(3) is bonded to four equivalent Lu(1) atoms to form a mixture of edge and corner-sharing OLu4 tetrahedra. is represented by the CIF file [CIF]
data_Lu4V4O13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.056
_cell_length_b   7.056
_cell_length_c   7.056
_cell_angle_alpha   60.000
_cell_angle_beta   60.000
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   248.405
_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  0.877  0.370  0.877  1.0
  Lu  Lu1  1  0.370  0.877  0.877  1.0
  Lu  Lu2  1  0.877  0.877  0.370  1.0
  Lu  Lu3  1  0.877  0.877  0.877  1.0
  V  V4  1  0.376  0.376  0.376  1.0
  V  V5  1  0.376  0.376  0.871  1.0
  V  V6  1  0.376  0.871  0.376  1.0
  V  V7  1  0.871  0.376  0.376  1.0
  O  O8  1  0.714  0.286  0.714  1.0
  O  O9  1  0.714  0.286  0.286  1.0
  O  O10  1  0.286  0.286  0.714  1.0
  O  O11  1  0.714  0.714  0.286  1.0
  O  O12  1  0.286  0.714  0.714  1.0
  O  O13  1  0.286  0.714  0.286  1.0
  O  O14  1  0.466  0.034  0.466  1.0
  O  O15  1  0.466  0.034  0.034  1.0
  O  O16  1  0.034  0.034  0.466  1.0
  O  O17  1  0.466  0.466  0.034  1.0
  O  O18  1  0.034  0.466  0.466  1.0
  O  O19  1  0.034  0.466  0.034  1.0
  O  O20  1  0.000  0.000  0.000  1.0
[/CIF]
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