The crystal structure described by MgCe2Ti4O12 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(3), one O(5), one O(6), one O(7), and one O(8) atom to form distorted MgO5 trigonal bipyramids that share corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and  a faceface with one Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 20-63°. There are two inequivalent Ce sites. In the first Ce site, Ce(1) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(11), one O(12), one O(2), one O(8), and one O(9) atom. In the second Ce site, Ce(2) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(4), and one O(6) atom. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(12), one O(2), one O(4), one O(5), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent Mg(1)O5 trigonal bipyramids,  an edgeedge with one Ti(3)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(1), one O(10), one O(11), one O(3), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with three equivalent Mg(1)O5 trigonal bipyramids,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(10), one O(11), one O(2), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share  an edgeedge with one Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(12), one O(3), one O(5), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share  an edgeedge with one Ti(2)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and  a faceface with one Mg(1)O5 trigonal bipyramid. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Ce(1), one Ti(2), and one Ti(4) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Ce(1), one Ti(1), and one Ti(3) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ce(2), one Ti(2), and one Ti(4) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Ce(2), one Ti(1), and one Ti(3) atom. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(1), and one Ti(4) atom. In the sixth O site, O(6) is bonded to one Mg(1), one Ce(2), one Ti(2), and one Ti(3) atom to form distorted corner-sharing OCeMgTi2 trigonal pyramids. In the seventh O site, O(7) is bonded in a T-shaped geometry to one Mg(1), one Ti(2), and one Ti(3) atom. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one Mg(1), one Ce(1), one Ti(1), and one Ti(4) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one Ce(1), one Ti(1), and one Ti(4) atom. In the tenth O site, O(10) is bonded to one Ce(1), one Ce(2), one Ti(2), and one Ti(3) atom to form distorted corner-sharing OCe2Ti2 tetrahedra. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one Ce(1), one Ce(2), one Ti(2), and one Ti(3) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to one Ce(1), one Ce(2), one Ti(1), and one Ti(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ce2MgTi4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.136
_cell_length_b   6.804
_cell_length_c   7.602
_cell_angle_alpha   78.023
_cell_angle_beta   75.184
_cell_angle_gamma   70.755
_symmetry_Int_Tables_number   1
_cell_volume   240.271
_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
  Ce  Ce0  1  0.807  0.827  0.140  1.0
  Ce  Ce1  1  0.222  0.201  0.826  1.0
  Mg  Mg2  1  0.787  0.466  0.524  1.0
  Ti  Ti3  1  0.457  0.365  0.190  1.0
  Ti  Ti4  1  0.035  0.839  0.646  1.0
  Ti  Ti5  1  0.527  0.666  0.841  1.0
  Ti  Ti6  1  0.002  0.142  0.322  1.0
  O  O7  1  0.948  0.873  0.403  1.0
  O  O8  1  0.540  0.629  0.101  1.0
  O  O9  1  0.033  0.141  0.582  1.0
  O  O10  1  0.446  0.401  0.912  1.0
  O  O11  1  0.600  0.317  0.404  1.0
  O  O12  1  0.923  0.552  0.717  1.0
  O  O13  1  0.425  0.694  0.596  1.0
  O  O14  1  0.061  0.463  0.277  1.0
  O  O15  1  0.383  0.086  0.200  1.0
  O  O16  1  0.144  0.854  0.884  1.0
  O  O17  1  0.647  0.925  0.810  1.0
  O  O18  1  0.876  0.178  0.096  1.0
[/CIF]
.
The crystal structure described by MgCe2Ti4O12 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(3), one O(5), one O(6), one O(7), and one O(8) atom to form distorted MgO5 trigonal bipyramids that share corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and  a faceface with one Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 20-63°. There are two inequivalent Ce sites. In the first Ce site, Ce(1) is bonded in a 7-coordinate geometry to one O(1), one O(10), one O(11), one O(12), one O(2), one O(8), and one O(9) atom. In the second Ce site, Ce(2) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(12), one O(3), one O(4), and one O(6) atom. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(12), one O(2), one O(4), one O(5), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent Mg(1)O5 trigonal bipyramids,  an edgeedge with one Ti(3)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(1), one O(10), one O(11), one O(3), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with three equivalent Mg(1)O5 trigonal bipyramids,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(10), one O(11), one O(2), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share  an edgeedge with one Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(12), one O(3), one O(5), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share  an edgeedge with one Ti(2)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and  a faceface with one Mg(1)O5 trigonal bipyramid. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Ce(1), one Ti(2), and one Ti(4) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Ce(1), one Ti(1), and one Ti(3) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ce(2), one Ti(2), and one Ti(4) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Ce(2), one Ti(1), and one Ti(3) atom. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(1), and one Ti(4) atom. In the sixth O site, O(6) is bonded to one Mg(1), one Ce(2), one Ti(2), and one Ti(3) atom to form distorted corner-sharing OCeMgTi2 trigonal pyramids. In the seventh O site, O(7) is bonded in a T-shaped geometry to one Mg(1), one Ti(2), and one Ti(3) atom. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one Mg(1), one Ce(1), one Ti(1), and one Ti(4) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one Ce(1), one Ti(1), and one Ti(4) atom. In the tenth O site, O(10) is bonded to one Ce(1), one Ce(2), one Ti(2), and one Ti(3) atom to form distorted corner-sharing OCe2Ti2 tetrahedra. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one Ce(1), one Ce(2), one Ti(2), and one Ti(3) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to one Ce(1), one Ce(2), one Ti(1), and one Ti(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ce2MgTi4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.136
_cell_length_b   6.804
_cell_length_c   7.602
_cell_angle_alpha   78.023
_cell_angle_beta   75.184
_cell_angle_gamma   70.755
_symmetry_Int_Tables_number   1
_cell_volume   240.271
_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
  Ce  Ce0  1  0.807  0.827  0.140  1.0
  Ce  Ce1  1  0.222  0.201  0.826  1.0
  Mg  Mg2  1  0.787  0.466  0.524  1.0
  Ti  Ti3  1  0.457  0.365  0.190  1.0
  Ti  Ti4  1  0.035  0.839  0.646  1.0
  Ti  Ti5  1  0.527  0.666  0.841  1.0
  Ti  Ti6  1  0.002  0.142  0.322  1.0
  O  O7  1  0.948  0.873  0.403  1.0
  O  O8  1  0.540  0.629  0.101  1.0
  O  O9  1  0.033  0.141  0.582  1.0
  O  O10  1  0.446  0.401  0.912  1.0
  O  O11  1  0.600  0.317  0.404  1.0
  O  O12  1  0.923  0.552  0.717  1.0
  O  O13  1  0.425  0.694  0.596  1.0
  O  O14  1  0.061  0.463  0.277  1.0
  O  O15  1  0.383  0.086  0.200  1.0
  O  O16  1  0.144  0.854  0.884  1.0
  O  O17  1  0.647  0.925  0.810  1.0
  O  O18  1  0.876  0.178  0.096  1.0
[/CIF]
.