The material structure described by Zr5Sc2O13 crystallizes in the trigonal R3 space group. There are two inequivalent Sc sites. In the first Sc site, Sc(2) is bonded in a body-centered cubic geometry to one O(4), one O(9), three equivalent O(5), and three equivalent O(7) atoms. In the second Sc site, Sc(1) is bonded to one O(10), one O(2), one O(3), one O(5), one O(7), and two equivalent O(1) atoms to form distorted ScO7 pentagonal bipyramids that share  a cornercorner with one Zr(1)O6 octahedra, corners with two equivalent Sc(1)O7 pentagonal bipyramids, and edges with three equivalent Zr(3)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 51°. There are four inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to three equivalent O(3) and three equivalent O(6) atoms to form ZrO6 octahedra that share corners with three equivalent Sc(1)O7 pentagonal bipyramids and corners with three equivalent Zr(3)O7 pentagonal bipyramids. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(4), one O(5), one O(6), one O(8), and two equivalent O(2) atoms. In the third Zr site, Zr(3) is bonded to one O(1), one O(5), one O(6), one O(7), one O(8), and two equivalent O(10) atoms to form distorted ZrO7 pentagonal bipyramids that share  a cornercorner with one Zr(1)O6 octahedra, corners with two equivalent Zr(3)O7 pentagonal bipyramids, and edges with three equivalent Sc(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 46°. In the fourth Zr site, Zr(4) is bonded in a 7-coordinate geometry to one O(10), one O(2), one O(3), one O(7), one O(9), and two equivalent O(8) atoms. There are ten inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Sc(1), one Zr(2), and one Zr(3) atom to form OZr2Sc2 tetrahedra that share  a cornercorner with one O(4)Zr3Sc tetrahedra, corners with two equivalent O(1)Zr2Sc2 tetrahedra, corners with two equivalent O(5)Zr2Sc2 tetrahedra, corners with two equivalent O(10)Zr3Sc tetrahedra, corners with two equivalent O(8)Zr4 tetrahedra, corners with three equivalent O(7)Zr2Sc2 tetrahedra,  an edgeedge with one O(5)Zr2Sc2 tetrahedra,  an edgeedge with one O(10)Zr3Sc tetrahedra, and edges with two equivalent O(2)Zr3Sc tetrahedra. In the second O site, O(2) is bonded to one Sc(1), one Zr(4), and two equivalent Zr(2) atoms to form OZr3Sc tetrahedra that share  a cornercorner with one O(9)Zr3Sc tetrahedra, corners with two equivalent O(10)Zr3Sc tetrahedra, corners with two equivalent O(2)Zr3Sc tetrahedra, corners with two equivalent O(8)Zr4 tetrahedra, corners with three equivalent O(5)Zr2Sc2 tetrahedra,  an edgeedge with one O(7)Zr2Sc2 tetrahedra,  an edgeedge with one O(4)Zr3Sc tetrahedra,  an edgeedge with one O(8)Zr4 tetrahedra, and edges with two equivalent O(1)Zr2Sc2 tetrahedra. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Sc(1), one Zr(1), and one Zr(4) atom. In the fourth O site, O(4) is bonded to one Sc(2) and three equivalent Zr(2) atoms to form distorted OZr3Sc tetrahedra that share  a cornercorner with one O(9)Zr3Sc tetrahedra, corners with three equivalent O(1)Zr2Sc2 tetrahedra, corners with three equivalent O(7)Zr2Sc2 tetrahedra, corners with three equivalent O(8)Zr4 tetrahedra, edges with three equivalent O(5)Zr2Sc2 tetrahedra, and edges with three equivalent O(2)Zr3Sc tetrahedra. In the fifth O site, O(5) is bonded to one Sc(1), one Sc(2), one Zr(2), and one Zr(3) atom to form OZr2Sc2 tetrahedra that share  a cornercorner with one O(7)Zr2Sc2 tetrahedra,  a cornercorner with one O(9)Zr3Sc tetrahedra, corners with two equivalent O(1)Zr2Sc2 tetrahedra, corners with two equivalent O(5)Zr2Sc2 tetrahedra, corners with three equivalent O(10)Zr3Sc tetrahedra, corners with three equivalent O(2)Zr3Sc tetrahedra,  an edgeedge with one O(1)Zr2Sc2 tetrahedra,  an edgeedge with one O(4)Zr3Sc tetrahedra,  an edgeedge with one O(8)Zr4 tetrahedra, and edges with two equivalent O(7)Zr2Sc2 tetrahedra. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Zr(1), one Zr(2), and one Zr(3) atom. In the seventh O site, O(7) is bonded to one Sc(1), one Sc(2), one Zr(3), and one Zr(4) atom to form OZr2Sc2 tetrahedra that share  a cornercorner with one O(5)Zr2Sc2 tetrahedra,  a cornercorner with one O(4)Zr3Sc tetrahedra, corners with two equivalent O(7)Zr2Sc2 tetrahedra, corners with two equivalent O(10)Zr3Sc tetrahedra, corners with three equivalent O(1)Zr2Sc2 tetrahedra, corners with three equivalent O(8)Zr4 tetrahedra,  an edgeedge with one O(10)Zr3Sc tetrahedra,  an edgeedge with one O(2)Zr3Sc tetrahedra,  an edgeedge with one O(9)Zr3Sc tetrahedra, and edges with two equivalent O(5)Zr2Sc2 tetrahedra. In the eighth O site, O(8) is bonded to one Zr(2), one Zr(3), and two equivalent Zr(4) atoms to form OZr4 tetrahedra that share  a cornercorner with one O(4)Zr3Sc tetrahedra, corners with two equivalent O(1)Zr2Sc2 tetrahedra, corners with two equivalent O(2)Zr3Sc tetrahedra, corners with two equivalent O(8)Zr4 tetrahedra, corners with three equivalent O(7)Zr2Sc2 tetrahedra,  an edgeedge with one O(5)Zr2Sc2 tetrahedra,  an edgeedge with one O(2)Zr3Sc tetrahedra,  an edgeedge with one O(9)Zr3Sc tetrahedra, and edges with two equivalent O(10)Zr3Sc tetrahedra. In the ninth O site, O(9) is bonded to one Sc(2) and three equivalent Zr(4) atoms to form distorted OZr3Sc tetrahedra that share  a cornercorner with one O(4)Zr3Sc tetrahedra, corners with three equivalent O(5)Zr2Sc2 tetrahedra, corners with three equivalent O(10)Zr3Sc tetrahedra, corners with three equivalent O(2)Zr3Sc tetrahedra, edges with three equivalent O(7)Zr2Sc2 tetrahedra, and edges with three equivalent O(8)Zr4 tetrahedra. In the tenth O site, O(10) is bonded to one Sc(1), one Zr(4), and two equivalent Zr(3) atoms to form OZr3Sc tetrahedra that share  a cornercorner with one O(9)Zr3Sc tetrahedra, corners with two equivalent O(1)Zr2Sc2 tetrahedra, corners with two equivalent O(7)Zr2Sc2 tetrahedra, corners with two equivalent O(10)Zr3Sc tetrahedra, corners with two equivalent O(2)Zr3Sc tetrahedra, corners with three equivalent O(5)Zr2Sc2 tetrahedra,  an edgeedge with one O(1)Zr2Sc2 tetrahedra,  an edgeedge with one O(7)Zr2Sc2 tetrahedra, and edges with two equivalent O(8)Zr4 tetrahedra. is represented by the CIF card [CIF]
data_Zr5Sc2O13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.099
_cell_length_b   8.099
_cell_length_c   8.099
_cell_angle_alpha   73.394
_cell_angle_beta   73.394
_cell_angle_gamma   73.394
_symmetry_Int_Tables_number   1
_cell_volume   475.701
_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
  Zr  Zr0  1  0.004  0.004  0.004  1.0
  Zr  Zr1  1  0.286  0.135  0.548  1.0
  Zr  Zr2  1  0.548  0.286  0.135  1.0
  Zr  Zr3  1  0.602  0.098  0.789  1.0
  Zr  Zr4  1  0.135  0.548  0.286  1.0
  Zr  Zr5  1  0.789  0.602  0.098  1.0
  Zr  Zr6  1  0.867  0.450  0.711  1.0
  Zr  Zr7  1  0.098  0.789  0.602  1.0
  Zr  Zr8  1  0.450  0.711  0.867  1.0
  Zr  Zr9  1  0.711  0.867  0.450  1.0
  Sc  Sc10  1  0.904  0.211  0.395  1.0
  Sc  Sc11  1  0.211  0.395  0.904  1.0
  Sc  Sc12  1  0.500  0.500  0.500  1.0
  Sc  Sc13  1  0.395  0.904  0.211  1.0
  O  O14  1  0.173  0.022  0.402  1.0
  O  O15  1  0.508  0.047  0.334  1.0
  O  O16  1  0.402  0.173  0.022  1.0
  O  O17  1  0.869  0.048  0.258  1.0
  O  O18  1  0.022  0.402  0.173  1.0
  O  O19  1  0.047  0.334  0.508  1.0
  O  O20  1  0.048  0.258  0.869  1.0
  O  O21  1  0.357  0.357  0.357  1.0
  O  O22  1  0.387  0.282  0.683  1.0
  O  O23  1  0.334  0.508  0.047  1.0
  O  O24  1  0.746  0.128  0.952  1.0
  O  O25  1  0.683  0.387  0.282  1.0
  O  O26  1  0.717  0.314  0.618  1.0
  O  O27  1  0.282  0.683  0.387  1.0
  O  O28  1  0.314  0.618  0.717  1.0
  O  O29  1  0.258  0.869  0.048  1.0
  O  O30  1  0.668  0.489  0.953  1.0
  O  O31  1  0.618  0.717  0.314  1.0
  O  O32  1  0.644  0.644  0.644  1.0
  O  O33  1  0.952  0.746  0.128  1.0
  O  O34  1  0.953  0.668  0.489  1.0
  O  O35  1  0.972  0.604  0.826  1.0
  O  O36  1  0.128  0.952  0.746  1.0
  O  O37  1  0.604  0.826  0.972  1.0
  O  O38  1  0.489  0.953  0.668  1.0
  O  O39  1  0.826  0.972  0.604  1.0
[/CIF]
.
The material structure described by Zr5Sc2O13 crystallizes in the trigonal R3 space group. There are two inequivalent Sc sites. In the first Sc site, Sc(2) is bonded in a body-centered cubic geometry to one O(4), one O(9), three equivalent O(5), and three equivalent O(7) atoms. In the second Sc site, Sc(1) is bonded to one O(10), one O(2), one O(3), one O(5), one O(7), and two equivalent O(1) atoms to form distorted ScO7 pentagonal bipyramids that share  a cornercorner with one Zr(1)O6 octahedra, corners with two equivalent Sc(1)O7 pentagonal bipyramids, and edges with three equivalent Zr(3)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 51°. There are four inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to three equivalent O(3) and three equivalent O(6) atoms to form ZrO6 octahedra that share corners with three equivalent Sc(1)O7 pentagonal bipyramids and corners with three equivalent Zr(3)O7 pentagonal bipyramids. In the second Zr site, Zr(2) is bonded in a 7-coordinate geometry to one O(1), one O(4), one O(5), one O(6), one O(8), and two equivalent O(2) atoms. In the third Zr site, Zr(3) is bonded to one O(1), one O(5), one O(6), one O(7), one O(8), and two equivalent O(10) atoms to form distorted ZrO7 pentagonal bipyramids that share  a cornercorner with one Zr(1)O6 octahedra, corners with two equivalent Zr(3)O7 pentagonal bipyramids, and edges with three equivalent Sc(1)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 46°. In the fourth Zr site, Zr(4) is bonded in a 7-coordinate geometry to one O(10), one O(2), one O(3), one O(7), one O(9), and two equivalent O(8) atoms. There are ten inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Sc(1), one Zr(2), and one Zr(3) atom to form OZr2Sc2 tetrahedra that share  a cornercorner with one O(4)Zr3Sc tetrahedra, corners with two equivalent O(1)Zr2Sc2 tetrahedra, corners with two equivalent O(5)Zr2Sc2 tetrahedra, corners with two equivalent O(10)Zr3Sc tetrahedra, corners with two equivalent O(8)Zr4 tetrahedra, corners with three equivalent O(7)Zr2Sc2 tetrahedra,  an edgeedge with one O(5)Zr2Sc2 tetrahedra,  an edgeedge with one O(10)Zr3Sc tetrahedra, and edges with two equivalent O(2)Zr3Sc tetrahedra. In the second O site, O(2) is bonded to one Sc(1), one Zr(4), and two equivalent Zr(2) atoms to form OZr3Sc tetrahedra that share  a cornercorner with one O(9)Zr3Sc tetrahedra, corners with two equivalent O(10)Zr3Sc tetrahedra, corners with two equivalent O(2)Zr3Sc tetrahedra, corners with two equivalent O(8)Zr4 tetrahedra, corners with three equivalent O(5)Zr2Sc2 tetrahedra,  an edgeedge with one O(7)Zr2Sc2 tetrahedra,  an edgeedge with one O(4)Zr3Sc tetrahedra,  an edgeedge with one O(8)Zr4 tetrahedra, and edges with two equivalent O(1)Zr2Sc2 tetrahedra. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Sc(1), one Zr(1), and one Zr(4) atom. In the fourth O site, O(4) is bonded to one Sc(2) and three equivalent Zr(2) atoms to form distorted OZr3Sc tetrahedra that share  a cornercorner with one O(9)Zr3Sc tetrahedra, corners with three equivalent O(1)Zr2Sc2 tetrahedra, corners with three equivalent O(7)Zr2Sc2 tetrahedra, corners with three equivalent O(8)Zr4 tetrahedra, edges with three equivalent O(5)Zr2Sc2 tetrahedra, and edges with three equivalent O(2)Zr3Sc tetrahedra. In the fifth O site, O(5) is bonded to one Sc(1), one Sc(2), one Zr(2), and one Zr(3) atom to form OZr2Sc2 tetrahedra that share  a cornercorner with one O(7)Zr2Sc2 tetrahedra,  a cornercorner with one O(9)Zr3Sc tetrahedra, corners with two equivalent O(1)Zr2Sc2 tetrahedra, corners with two equivalent O(5)Zr2Sc2 tetrahedra, corners with three equivalent O(10)Zr3Sc tetrahedra, corners with three equivalent O(2)Zr3Sc tetrahedra,  an edgeedge with one O(1)Zr2Sc2 tetrahedra,  an edgeedge with one O(4)Zr3Sc tetrahedra,  an edgeedge with one O(8)Zr4 tetrahedra, and edges with two equivalent O(7)Zr2Sc2 tetrahedra. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Zr(1), one Zr(2), and one Zr(3) atom. In the seventh O site, O(7) is bonded to one Sc(1), one Sc(2), one Zr(3), and one Zr(4) atom to form OZr2Sc2 tetrahedra that share  a cornercorner with one O(5)Zr2Sc2 tetrahedra,  a cornercorner with one O(4)Zr3Sc tetrahedra, corners with two equivalent O(7)Zr2Sc2 tetrahedra, corners with two equivalent O(10)Zr3Sc tetrahedra, corners with three equivalent O(1)Zr2Sc2 tetrahedra, corners with three equivalent O(8)Zr4 tetrahedra,  an edgeedge with one O(10)Zr3Sc tetrahedra,  an edgeedge with one O(2)Zr3Sc tetrahedra,  an edgeedge with one O(9)Zr3Sc tetrahedra, and edges with two equivalent O(5)Zr2Sc2 tetrahedra. In the eighth O site, O(8) is bonded to one Zr(2), one Zr(3), and two equivalent Zr(4) atoms to form OZr4 tetrahedra that share  a cornercorner with one O(4)Zr3Sc tetrahedra, corners with two equivalent O(1)Zr2Sc2 tetrahedra, corners with two equivalent O(2)Zr3Sc tetrahedra, corners with two equivalent O(8)Zr4 tetrahedra, corners with three equivalent O(7)Zr2Sc2 tetrahedra,  an edgeedge with one O(5)Zr2Sc2 tetrahedra,  an edgeedge with one O(2)Zr3Sc tetrahedra,  an edgeedge with one O(9)Zr3Sc tetrahedra, and edges with two equivalent O(10)Zr3Sc tetrahedra. In the ninth O site, O(9) is bonded to one Sc(2) and three equivalent Zr(4) atoms to form distorted OZr3Sc tetrahedra that share  a cornercorner with one O(4)Zr3Sc tetrahedra, corners with three equivalent O(5)Zr2Sc2 tetrahedra, corners with three equivalent O(10)Zr3Sc tetrahedra, corners with three equivalent O(2)Zr3Sc tetrahedra, edges with three equivalent O(7)Zr2Sc2 tetrahedra, and edges with three equivalent O(8)Zr4 tetrahedra. In the tenth O site, O(10) is bonded to one Sc(1), one Zr(4), and two equivalent Zr(3) atoms to form OZr3Sc tetrahedra that share  a cornercorner with one O(9)Zr3Sc tetrahedra, corners with two equivalent O(1)Zr2Sc2 tetrahedra, corners with two equivalent O(7)Zr2Sc2 tetrahedra, corners with two equivalent O(10)Zr3Sc tetrahedra, corners with two equivalent O(2)Zr3Sc tetrahedra, corners with three equivalent O(5)Zr2Sc2 tetrahedra,  an edgeedge with one O(1)Zr2Sc2 tetrahedra,  an edgeedge with one O(7)Zr2Sc2 tetrahedra, and edges with two equivalent O(8)Zr4 tetrahedra. is represented by the CIF card [CIF]
data_Zr5Sc2O13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.099
_cell_length_b   8.099
_cell_length_c   8.099
_cell_angle_alpha   73.394
_cell_angle_beta   73.394
_cell_angle_gamma   73.394
_symmetry_Int_Tables_number   1
_cell_volume   475.701
_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
  Zr  Zr0  1  0.004  0.004  0.004  1.0
  Zr  Zr1  1  0.286  0.135  0.548  1.0
  Zr  Zr2  1  0.548  0.286  0.135  1.0
  Zr  Zr3  1  0.602  0.098  0.789  1.0
  Zr  Zr4  1  0.135  0.548  0.286  1.0
  Zr  Zr5  1  0.789  0.602  0.098  1.0
  Zr  Zr6  1  0.867  0.450  0.711  1.0
  Zr  Zr7  1  0.098  0.789  0.602  1.0
  Zr  Zr8  1  0.450  0.711  0.867  1.0
  Zr  Zr9  1  0.711  0.867  0.450  1.0
  Sc  Sc10  1  0.904  0.211  0.395  1.0
  Sc  Sc11  1  0.211  0.395  0.904  1.0
  Sc  Sc12  1  0.500  0.500  0.500  1.0
  Sc  Sc13  1  0.395  0.904  0.211  1.0
  O  O14  1  0.173  0.022  0.402  1.0
  O  O15  1  0.508  0.047  0.334  1.0
  O  O16  1  0.402  0.173  0.022  1.0
  O  O17  1  0.869  0.048  0.258  1.0
  O  O18  1  0.022  0.402  0.173  1.0
  O  O19  1  0.047  0.334  0.508  1.0
  O  O20  1  0.048  0.258  0.869  1.0
  O  O21  1  0.357  0.357  0.357  1.0
  O  O22  1  0.387  0.282  0.683  1.0
  O  O23  1  0.334  0.508  0.047  1.0
  O  O24  1  0.746  0.128  0.952  1.0
  O  O25  1  0.683  0.387  0.282  1.0
  O  O26  1  0.717  0.314  0.618  1.0
  O  O27  1  0.282  0.683  0.387  1.0
  O  O28  1  0.314  0.618  0.717  1.0
  O  O29  1  0.258  0.869  0.048  1.0
  O  O30  1  0.668  0.489  0.953  1.0
  O  O31  1  0.618  0.717  0.314  1.0
  O  O32  1  0.644  0.644  0.644  1.0
  O  O33  1  0.952  0.746  0.128  1.0
  O  O34  1  0.953  0.668  0.489  1.0
  O  O35  1  0.972  0.604  0.826  1.0
  O  O36  1  0.128  0.952  0.746  1.0
  O  O37  1  0.604  0.826  0.972  1.0
  O  O38  1  0.489  0.953  0.668  1.0
  O  O39  1  0.826  0.972  0.604  1.0
[/CIF]
.