The compound described by MgTiBi(PO4)3 crystallizes in the trigonal R3c space group. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form distorted MgO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra and  a faceface with one Ti(1)O6 octahedra. Ti(1) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form distorted TiO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra and  a faceface with one Mg(1)O6 octahedra. Bi(1) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(3) atoms. P(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form PO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-57°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted bent 120 degrees geometry to one Bi(1) and one P(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Mg(1), one Ti(1), and one P(1) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Mg(1), one Bi(1), and one P(1) atom. In the fourth O site, O(4) is bonded in a linear geometry to one Ti(1) and one P(1) atom. is represented by the CIF file [CIF]
data_MgTiBi(PO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.400
_cell_length_b   8.400
_cell_length_c   8.400
_cell_angle_alpha   64.631
_cell_angle_beta   64.631
_cell_angle_gamma   64.631
_symmetry_Int_Tables_number   1
_cell_volume   461.666
_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
  Mg  Mg0  1  0.993  0.993  0.993  1.0
  Mg  Mg1  1  0.493  0.493  0.493  1.0
  Ti  Ti2  1  0.149  0.149  0.149  1.0
  Ti  Ti3  1  0.649  0.649  0.649  1.0
  Bi  Bi4  1  0.332  0.332  0.332  1.0
  Bi  Bi5  1  0.832  0.832  0.832  1.0
  P  P6  1  0.065  0.429  0.760  1.0
  P  P7  1  0.429  0.760  0.065  1.0
  P  P8  1  0.760  0.065  0.429  1.0
  P  P9  1  0.260  0.929  0.565  1.0
  P  P10  1  0.565  0.260  0.929  1.0
  P  P11  1  0.929  0.565  0.260  1.0
  O  O12  1  0.058  0.563  0.343  1.0
  O  O13  1  0.343  0.058  0.563  1.0
  O  O14  1  0.069  0.235  0.906  1.0
  O  O15  1  0.563  0.343  0.058  1.0
  O  O16  1  0.063  0.558  0.843  1.0
  O  O17  1  0.243  0.418  0.593  1.0
  O  O18  1  0.235  0.906  0.069  1.0
  O  O19  1  0.418  0.593  0.243  1.0
  O  O20  1  0.207  0.007  0.379  1.0
  O  O21  1  0.593  0.243  0.418  1.0
  O  O22  1  0.093  0.918  0.743  1.0
  O  O23  1  0.379  0.207  0.007  1.0
  O  O24  1  0.558  0.843  0.063  1.0
  O  O25  1  0.906  0.069  0.235  1.0
  O  O26  1  0.406  0.735  0.569  1.0
  O  O27  1  0.843  0.063  0.558  1.0
  O  O28  1  0.569  0.406  0.735  1.0
  O  O29  1  0.743  0.093  0.918  1.0
  O  O30  1  0.735  0.569  0.406  1.0
  O  O31  1  0.007  0.379  0.207  1.0
  O  O32  1  0.507  0.707  0.879  1.0
  O  O33  1  0.918  0.743  0.093  1.0
  O  O34  1  0.707  0.879  0.507  1.0
  O  O35  1  0.879  0.507  0.707  1.0
[/CIF]
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The compound described by MgTiBi(PO4)3 crystallizes in the trigonal R3c space group. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form distorted MgO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra and  a faceface with one Ti(1)O6 octahedra. Ti(1) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form distorted TiO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra and  a faceface with one Mg(1)O6 octahedra. Bi(1) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(3) atoms. P(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form PO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-57°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted bent 120 degrees geometry to one Bi(1) and one P(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Mg(1), one Ti(1), and one P(1) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Mg(1), one Bi(1), and one P(1) atom. In the fourth O site, O(4) is bonded in a linear geometry to one Ti(1) and one P(1) atom. is represented by the CIF file [CIF]
data_MgTiBi(PO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.400
_cell_length_b   8.400
_cell_length_c   8.400
_cell_angle_alpha   64.631
_cell_angle_beta   64.631
_cell_angle_gamma   64.631
_symmetry_Int_Tables_number   1
_cell_volume   461.666
_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
  Mg  Mg0  1  0.993  0.993  0.993  1.0
  Mg  Mg1  1  0.493  0.493  0.493  1.0
  Ti  Ti2  1  0.149  0.149  0.149  1.0
  Ti  Ti3  1  0.649  0.649  0.649  1.0
  Bi  Bi4  1  0.332  0.332  0.332  1.0
  Bi  Bi5  1  0.832  0.832  0.832  1.0
  P  P6  1  0.065  0.429  0.760  1.0
  P  P7  1  0.429  0.760  0.065  1.0
  P  P8  1  0.760  0.065  0.429  1.0
  P  P9  1  0.260  0.929  0.565  1.0
  P  P10  1  0.565  0.260  0.929  1.0
  P  P11  1  0.929  0.565  0.260  1.0
  O  O12  1  0.058  0.563  0.343  1.0
  O  O13  1  0.343  0.058  0.563  1.0
  O  O14  1  0.069  0.235  0.906  1.0
  O  O15  1  0.563  0.343  0.058  1.0
  O  O16  1  0.063  0.558  0.843  1.0
  O  O17  1  0.243  0.418  0.593  1.0
  O  O18  1  0.235  0.906  0.069  1.0
  O  O19  1  0.418  0.593  0.243  1.0
  O  O20  1  0.207  0.007  0.379  1.0
  O  O21  1  0.593  0.243  0.418  1.0
  O  O22  1  0.093  0.918  0.743  1.0
  O  O23  1  0.379  0.207  0.007  1.0
  O  O24  1  0.558  0.843  0.063  1.0
  O  O25  1  0.906  0.069  0.235  1.0
  O  O26  1  0.406  0.735  0.569  1.0
  O  O27  1  0.843  0.063  0.558  1.0
  O  O28  1  0.569  0.406  0.735  1.0
  O  O29  1  0.743  0.093  0.918  1.0
  O  O30  1  0.735  0.569  0.406  1.0
  O  O31  1  0.007  0.379  0.207  1.0
  O  O32  1  0.507  0.707  0.879  1.0
  O  O33  1  0.918  0.743  0.093  1.0
  O  O34  1  0.707  0.879  0.507  1.0
  O  O35  1  0.879  0.507  0.707  1.0
[/CIF]
.