The crystal structure described by Hf3Sc4O12 crystallizes in the triclinic P-1 space group. There are four inequivalent Sc sites. In the first Sc site, Sc(1) is bonded in a 7-coordinate geometry to one O(12), one O(2), one O(3), one O(4), one O(6), and two equivalent O(7) atoms. In the second Sc site, Sc(2) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(5), one O(8), and one O(9) atom. In the third Sc site, Sc(3) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(4), one O(6), one O(7), and one O(9) atom. In the fourth Sc site, Sc(4) is bonded in a 7-coordinate geometry to one O(11), one O(8), one O(9), two equivalent O(1), and two equivalent O(5) atoms. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 7-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(5), and two equivalent O(8) atoms. In the second Hf site, Hf(2) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(7), two equivalent O(2), and two equivalent O(6) atoms. In the third Hf site, Hf(3) is bonded in an octahedral geometry to one O(1), one O(10), one O(2), one O(3), one O(4), and one O(9) atom. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Sc(4), one Hf(1), and one Hf(3) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Sc(1), one Hf(3), and two equivalent Hf(2) atoms. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Sc(1), one Sc(2), one Hf(1), and one Hf(3) atom. In the fourth O site, O(4) is bonded to one Sc(1), one Sc(3), one Hf(1), and one Hf(3) atom to form distorted OHf2Sc2 tetrahedra that share  a cornercorner with one O(5)HfSc3 tetrahedra,  a cornercorner with one O(7)HfSc3 tetrahedra, corners with two equivalent O(6)Hf2Sc2 tetrahedra, corners with two equivalent O(8)Hf2Sc2 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the fifth O site, O(5) is bonded to one Sc(2), two equivalent Sc(4), and one Hf(1) atom to form OHfSc3 tetrahedra that share  a cornercorner with one O(4)Hf2Sc2 tetrahedra,  a cornercorner with one O(12)HfSc3 tetrahedra, corners with two equivalent O(11)HfSc3 tetrahedra, corners with three equivalent O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the sixth O site, O(6) is bonded to one Sc(1), one Sc(3), and two equivalent Hf(2) atoms to form OHf2Sc2 tetrahedra that share  a cornercorner with one O(11)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra, corners with three equivalent O(7)HfSc3 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the seventh O site, O(7) is bonded to one Sc(3), two equivalent Sc(1), and one Hf(2) atom to form distorted OHfSc3 tetrahedra that share  a cornercorner with one O(4)Hf2Sc2 tetrahedra,  a cornercorner with one O(11)HfSc3 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra, corners with three equivalent O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(4)Hf2Sc2 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the eighth O site, O(8) is bonded to one Sc(2), one Sc(4), and two equivalent Hf(1) atoms to form OHf2Sc2 tetrahedra that share  a cornercorner with one O(12)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(11)HfSc3 tetrahedra, corners with three equivalent O(5)HfSc3 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Sc(2), one Sc(3), one Sc(4), and one Hf(3) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Sc(2), one Sc(3), one Hf(2), and one Hf(3) atom. In the eleventh O site, O(11) is bonded to one Sc(2), one Sc(3), one Sc(4), and one Hf(1) atom to form distorted OHfSc3 tetrahedra that share  a cornercorner with one O(6)Hf2Sc2 tetrahedra,  a cornercorner with one O(7)HfSc3 tetrahedra, corners with two equivalent O(8)Hf2Sc2 tetrahedra, corners with two equivalent O(5)HfSc3 tetrahedra,  an edgeedge with one O(4)Hf2Sc2 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the twelfth O site, O(12) is bonded to one Sc(1), one Sc(2), one Sc(3), and one Hf(2) atom to form OHfSc3 tetrahedra that share  a cornercorner with one O(8)Hf2Sc2 tetrahedra,  a cornercorner with one O(5)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(6)Hf2Sc2 tetrahedra, corners with two equivalent O(7)HfSc3 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. is represented by the CIF card [CIF]
data_Hf3Sc4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.145
_cell_length_b   6.142
_cell_length_c   12.213
_cell_angle_alpha   99.340
_cell_angle_beta   99.381
_cell_angle_gamma   99.635
_symmetry_Int_Tables_number   1
_cell_volume   439.824
_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
  Hf  Hf0  1  0.141  0.611  0.406  1.0
  Hf  Hf1  1  0.682  0.858  0.945  1.0
  Hf  Hf2  1  0.995  0.996  0.251  1.0
  Hf  Hf3  1  0.005  0.004  0.749  1.0
  Hf  Hf4  1  0.318  0.142  0.055  1.0
  Hf  Hf5  1  0.859  0.389  0.594  1.0
  Sc  Sc6  1  0.136  0.605  0.905  1.0
  Sc  Sc7  1  0.392  0.690  0.680  1.0
  Sc  Sc8  1  0.394  0.680  0.181  1.0
  Sc  Sc9  1  0.681  0.859  0.445  1.0
  Sc  Sc10  1  0.319  0.141  0.555  1.0
  Sc  Sc11  1  0.608  0.310  0.320  1.0
  Sc  Sc12  1  0.606  0.320  0.819  1.0
  Sc  Sc13  1  0.864  0.395  0.095  1.0
  O  O14  1  0.093  0.938  0.410  1.0
  O  O15  1  0.093  0.947  0.912  1.0
  O  O16  1  0.052  0.682  0.701  1.0
  O  O17  1  0.061  0.676  0.212  1.0
  O  O18  1  0.414  0.817  0.537  1.0
  O  O19  1  0.427  0.825  0.040  1.0
  O  O20  1  0.179  0.415  0.037  1.0
  O  O21  1  0.174  0.420  0.536  1.0
  O  O22  1  0.677  0.906  0.278  1.0
  O  O23  1  0.685  0.908  0.783  1.0
  O  O24  1  0.419  0.571  0.341  1.0
  O  O25  1  0.423  0.586  0.842  1.0
  O  O26  1  0.581  0.429  0.659  1.0
  O  O27  1  0.577  0.414  0.158  1.0
  O  O28  1  0.323  0.094  0.722  1.0
  O  O29  1  0.315  0.092  0.217  1.0
  O  O30  1  0.826  0.580  0.464  1.0
  O  O31  1  0.821  0.585  0.963  1.0
  O  O32  1  0.573  0.175  0.960  1.0
  O  O33  1  0.586  0.183  0.463  1.0
  O  O34  1  0.948  0.318  0.299  1.0
  O  O35  1  0.939  0.324  0.788  1.0
  O  O36  1  0.907  0.062  0.590  1.0
  O  O37  1  0.907  0.053  0.088  1.0
[/CIF]
.
The crystal structure described by Hf3Sc4O12 crystallizes in the triclinic P-1 space group. There are four inequivalent Sc sites. In the first Sc site, Sc(1) is bonded in a 7-coordinate geometry to one O(12), one O(2), one O(3), one O(4), one O(6), and two equivalent O(7) atoms. In the second Sc site, Sc(2) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(5), one O(8), and one O(9) atom. In the third Sc site, Sc(3) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(12), one O(4), one O(6), one O(7), and one O(9) atom. In the fourth Sc site, Sc(4) is bonded in a 7-coordinate geometry to one O(11), one O(8), one O(9), two equivalent O(1), and two equivalent O(5) atoms. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 7-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(5), and two equivalent O(8) atoms. In the second Hf site, Hf(2) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(7), two equivalent O(2), and two equivalent O(6) atoms. In the third Hf site, Hf(3) is bonded in an octahedral geometry to one O(1), one O(10), one O(2), one O(3), one O(4), and one O(9) atom. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Sc(4), one Hf(1), and one Hf(3) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Sc(1), one Hf(3), and two equivalent Hf(2) atoms. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Sc(1), one Sc(2), one Hf(1), and one Hf(3) atom. In the fourth O site, O(4) is bonded to one Sc(1), one Sc(3), one Hf(1), and one Hf(3) atom to form distorted OHf2Sc2 tetrahedra that share  a cornercorner with one O(5)HfSc3 tetrahedra,  a cornercorner with one O(7)HfSc3 tetrahedra, corners with two equivalent O(6)Hf2Sc2 tetrahedra, corners with two equivalent O(8)Hf2Sc2 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the fifth O site, O(5) is bonded to one Sc(2), two equivalent Sc(4), and one Hf(1) atom to form OHfSc3 tetrahedra that share  a cornercorner with one O(4)Hf2Sc2 tetrahedra,  a cornercorner with one O(12)HfSc3 tetrahedra, corners with two equivalent O(11)HfSc3 tetrahedra, corners with three equivalent O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the sixth O site, O(6) is bonded to one Sc(1), one Sc(3), and two equivalent Hf(2) atoms to form OHf2Sc2 tetrahedra that share  a cornercorner with one O(11)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra, corners with three equivalent O(7)HfSc3 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the seventh O site, O(7) is bonded to one Sc(3), two equivalent Sc(1), and one Hf(2) atom to form distorted OHfSc3 tetrahedra that share  a cornercorner with one O(4)Hf2Sc2 tetrahedra,  a cornercorner with one O(11)HfSc3 tetrahedra, corners with two equivalent O(12)HfSc3 tetrahedra, corners with three equivalent O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(4)Hf2Sc2 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. In the eighth O site, O(8) is bonded to one Sc(2), one Sc(4), and two equivalent Hf(1) atoms to form OHf2Sc2 tetrahedra that share  a cornercorner with one O(12)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(11)HfSc3 tetrahedra, corners with three equivalent O(5)HfSc3 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Sc(2), one Sc(3), one Sc(4), and one Hf(3) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Sc(2), one Sc(3), one Hf(2), and one Hf(3) atom. In the eleventh O site, O(11) is bonded to one Sc(2), one Sc(3), one Sc(4), and one Hf(1) atom to form distorted OHfSc3 tetrahedra that share  a cornercorner with one O(6)Hf2Sc2 tetrahedra,  a cornercorner with one O(7)HfSc3 tetrahedra, corners with two equivalent O(8)Hf2Sc2 tetrahedra, corners with two equivalent O(5)HfSc3 tetrahedra,  an edgeedge with one O(4)Hf2Sc2 tetrahedra,  an edgeedge with one O(8)Hf2Sc2 tetrahedra,  an edgeedge with one O(12)HfSc3 tetrahedra, and  an edgeedge with one O(5)HfSc3 tetrahedra. In the twelfth O site, O(12) is bonded to one Sc(1), one Sc(2), one Sc(3), and one Hf(2) atom to form OHfSc3 tetrahedra that share  a cornercorner with one O(8)Hf2Sc2 tetrahedra,  a cornercorner with one O(5)HfSc3 tetrahedra, corners with two equivalent O(4)Hf2Sc2 tetrahedra, corners with two equivalent O(6)Hf2Sc2 tetrahedra, corners with two equivalent O(7)HfSc3 tetrahedra,  an edgeedge with one O(6)Hf2Sc2 tetrahedra,  an edgeedge with one O(11)HfSc3 tetrahedra, and  an edgeedge with one O(7)HfSc3 tetrahedra. is represented by the CIF card [CIF]
data_Hf3Sc4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.145
_cell_length_b   6.142
_cell_length_c   12.213
_cell_angle_alpha   99.340
_cell_angle_beta   99.381
_cell_angle_gamma   99.635
_symmetry_Int_Tables_number   1
_cell_volume   439.824
_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
  Hf  Hf0  1  0.141  0.611  0.406  1.0
  Hf  Hf1  1  0.682  0.858  0.945  1.0
  Hf  Hf2  1  0.995  0.996  0.251  1.0
  Hf  Hf3  1  0.005  0.004  0.749  1.0
  Hf  Hf4  1  0.318  0.142  0.055  1.0
  Hf  Hf5  1  0.859  0.389  0.594  1.0
  Sc  Sc6  1  0.136  0.605  0.905  1.0
  Sc  Sc7  1  0.392  0.690  0.680  1.0
  Sc  Sc8  1  0.394  0.680  0.181  1.0
  Sc  Sc9  1  0.681  0.859  0.445  1.0
  Sc  Sc10  1  0.319  0.141  0.555  1.0
  Sc  Sc11  1  0.608  0.310  0.320  1.0
  Sc  Sc12  1  0.606  0.320  0.819  1.0
  Sc  Sc13  1  0.864  0.395  0.095  1.0
  O  O14  1  0.093  0.938  0.410  1.0
  O  O15  1  0.093  0.947  0.912  1.0
  O  O16  1  0.052  0.682  0.701  1.0
  O  O17  1  0.061  0.676  0.212  1.0
  O  O18  1  0.414  0.817  0.537  1.0
  O  O19  1  0.427  0.825  0.040  1.0
  O  O20  1  0.179  0.415  0.037  1.0
  O  O21  1  0.174  0.420  0.536  1.0
  O  O22  1  0.677  0.906  0.278  1.0
  O  O23  1  0.685  0.908  0.783  1.0
  O  O24  1  0.419  0.571  0.341  1.0
  O  O25  1  0.423  0.586  0.842  1.0
  O  O26  1  0.581  0.429  0.659  1.0
  O  O27  1  0.577  0.414  0.158  1.0
  O  O28  1  0.323  0.094  0.722  1.0
  O  O29  1  0.315  0.092  0.217  1.0
  O  O30  1  0.826  0.580  0.464  1.0
  O  O31  1  0.821  0.585  0.963  1.0
  O  O32  1  0.573  0.175  0.960  1.0
  O  O33  1  0.586  0.183  0.463  1.0
  O  O34  1  0.948  0.318  0.299  1.0
  O  O35  1  0.939  0.324  0.788  1.0
  O  O36  1  0.907  0.062  0.590  1.0
  O  O37  1  0.907  0.053  0.088  1.0
[/CIF]
.