The structure described by MgSm3Ti4O14 crystallizes in the trigonal R-3m space group. Mg(1) is bonded to two equivalent O(3) and six equivalent O(1) atoms to form distorted MgO8 hexagonal bipyramids that share edges with six equivalent Sm(1)O8 hexagonal bipyramids and edges with six equivalent Ti(2)O6 octahedra. Sm(1) is bonded to two equivalent O(1), two equivalent O(3), and four equivalent O(2) atoms to form SmO8 hexagonal bipyramids that share edges with two equivalent Mg(1)O8 hexagonal bipyramids, edges with four equivalent Sm(1)O8 hexagonal bipyramids, edges with two equivalent Ti(1)O6 octahedra, and edges with four equivalent Ti(2)O6 octahedra. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to six equivalent O(2) atoms to form TiO6 octahedra that share corners with six equivalent Ti(2)O6 octahedra and edges with six equivalent Sm(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles are 49°. In the second Ti site, Ti(2) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, edges with two equivalent Mg(1)O8 hexagonal bipyramids, and edges with four equivalent Sm(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles range from 44-49°. There are three inequivalent O sites. In the first O site, O(3) is bonded to one Mg(1) and three equivalent Sm(1) atoms to form OSm3Mg tetrahedra that share corners with four equivalent O(3)Sm3Mg tetrahedra, corners with six equivalent O(2)Sm2Ti2 tetrahedra, and edges with three equivalent O(2)Sm2Ti2 tetrahedra. In the second O site, O(1) is bonded in a 4-coordinate geometry to one Mg(1), one Sm(1), and two equivalent Ti(2) atoms. In the third O site, O(2) is bonded to two equivalent Sm(1), one Ti(1), and one Ti(2) atom to form distorted OSm2Ti2 tetrahedra that share corners with two equivalent O(3)Sm3Mg tetrahedra, corners with eight equivalent O(2)Sm2Ti2 tetrahedra,  an edgeedge with one O(3)Sm3Mg tetrahedra, and edges with two equivalent O(2)Sm2Ti2 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Sm3MgTi4O14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.172
_cell_length_b   7.172
_cell_length_c   7.172
_cell_angle_alpha   61.149
_cell_angle_beta   61.149
_cell_angle_gamma   61.149
_symmetry_Int_Tables_number   1
_cell_volume   267.551
_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
  Sm  Sm0  1  0.000  0.500  0.500  1.0
  Sm  Sm1  1  0.500  0.500  0.000  1.0
  Sm  Sm2  1  0.500  0.000  0.500  1.0
  Mg  Mg3  1  0.500  0.500  0.500  1.0
  Ti  Ti4  1  0.000  0.000  0.000  1.0
  Ti  Ti5  1  0.500  0.000  0.000  1.0
  Ti  Ti6  1  0.000  0.000  0.500  1.0
  Ti  Ti7  1  0.000  0.500  0.000  1.0
  O  O8  1  0.931  0.322  0.322  1.0
  O  O9  1  0.328  0.920  0.920  1.0
  O  O10  1  0.322  0.322  0.931  1.0
  O  O11  1  0.920  0.920  0.328  1.0
  O  O12  1  0.920  0.328  0.920  1.0
  O  O13  1  0.322  0.931  0.322  1.0
  O  O14  1  0.069  0.678  0.678  1.0
  O  O15  1  0.672  0.080  0.080  1.0
  O  O16  1  0.678  0.678  0.069  1.0
  O  O17  1  0.080  0.080  0.672  1.0
  O  O18  1  0.080  0.672  0.080  1.0
  O  O19  1  0.678  0.069  0.678  1.0
  O  O20  1  0.386  0.386  0.386  1.0
  O  O21  1  0.614  0.614  0.614  1.0
[/CIF]
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The structure described by MgSm3Ti4O14 crystallizes in the trigonal R-3m space group. Mg(1) is bonded to two equivalent O(3) and six equivalent O(1) atoms to form distorted MgO8 hexagonal bipyramids that share edges with six equivalent Sm(1)O8 hexagonal bipyramids and edges with six equivalent Ti(2)O6 octahedra. Sm(1) is bonded to two equivalent O(1), two equivalent O(3), and four equivalent O(2) atoms to form SmO8 hexagonal bipyramids that share edges with two equivalent Mg(1)O8 hexagonal bipyramids, edges with four equivalent Sm(1)O8 hexagonal bipyramids, edges with two equivalent Ti(1)O6 octahedra, and edges with four equivalent Ti(2)O6 octahedra. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to six equivalent O(2) atoms to form TiO6 octahedra that share corners with six equivalent Ti(2)O6 octahedra and edges with six equivalent Sm(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles are 49°. In the second Ti site, Ti(2) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, edges with two equivalent Mg(1)O8 hexagonal bipyramids, and edges with four equivalent Sm(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles range from 44-49°. There are three inequivalent O sites. In the first O site, O(3) is bonded to one Mg(1) and three equivalent Sm(1) atoms to form OSm3Mg tetrahedra that share corners with four equivalent O(3)Sm3Mg tetrahedra, corners with six equivalent O(2)Sm2Ti2 tetrahedra, and edges with three equivalent O(2)Sm2Ti2 tetrahedra. In the second O site, O(1) is bonded in a 4-coordinate geometry to one Mg(1), one Sm(1), and two equivalent Ti(2) atoms. In the third O site, O(2) is bonded to two equivalent Sm(1), one Ti(1), and one Ti(2) atom to form distorted OSm2Ti2 tetrahedra that share corners with two equivalent O(3)Sm3Mg tetrahedra, corners with eight equivalent O(2)Sm2Ti2 tetrahedra,  an edgeedge with one O(3)Sm3Mg tetrahedra, and edges with two equivalent O(2)Sm2Ti2 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Sm3MgTi4O14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.172
_cell_length_b   7.172
_cell_length_c   7.172
_cell_angle_alpha   61.149
_cell_angle_beta   61.149
_cell_angle_gamma   61.149
_symmetry_Int_Tables_number   1
_cell_volume   267.551
_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
  Sm  Sm0  1  0.000  0.500  0.500  1.0
  Sm  Sm1  1  0.500  0.500  0.000  1.0
  Sm  Sm2  1  0.500  0.000  0.500  1.0
  Mg  Mg3  1  0.500  0.500  0.500  1.0
  Ti  Ti4  1  0.000  0.000  0.000  1.0
  Ti  Ti5  1  0.500  0.000  0.000  1.0
  Ti  Ti6  1  0.000  0.000  0.500  1.0
  Ti  Ti7  1  0.000  0.500  0.000  1.0
  O  O8  1  0.931  0.322  0.322  1.0
  O  O9  1  0.328  0.920  0.920  1.0
  O  O10  1  0.322  0.322  0.931  1.0
  O  O11  1  0.920  0.920  0.328  1.0
  O  O12  1  0.920  0.328  0.920  1.0
  O  O13  1  0.322  0.931  0.322  1.0
  O  O14  1  0.069  0.678  0.678  1.0
  O  O15  1  0.672  0.080  0.080  1.0
  O  O16  1  0.678  0.678  0.069  1.0
  O  O17  1  0.080  0.080  0.672  1.0
  O  O18  1  0.080  0.672  0.080  1.0
  O  O19  1  0.678  0.069  0.678  1.0
  O  O20  1  0.386  0.386  0.386  1.0
  O  O21  1  0.614  0.614  0.614  1.0
[/CIF]
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