The crystal structure described by MgTi8O16 crystallizes in the triclinic P-1 space group. Mg(1) is bonded to two equivalent O(1), two equivalent O(6), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and faces with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-60°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(2), one O(3), one O(6), and two equivalent O(8) atoms to form distorted TiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. In the second Ti site, Ti(2) is bonded to one O(1), one O(2), one O(4), one O(5), and two equivalent O(7) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 18-60°. In the third Ti site, Ti(3) is bonded in a 6-coordinate geometry to one O(1), one O(3), one O(4), one O(8), and two equivalent O(6) atoms. In the fourth Ti site, Ti(4) is bonded to one O(2), one O(3), one O(4), one O(7), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 18-53°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Ti(1), one Ti(2), and one Ti(3) atom to form a mixture of distorted face and corner-sharing OMgTi3 trigonal pyramids. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(2), and one Ti(4) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Ti(1), one Ti(3), and one Ti(4) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(3), and one Ti(4) atom. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Ti(2) and two equivalent Ti(4) atoms. In the sixth O site, O(6) is bonded to one Mg(1), one Ti(1), and two equivalent Ti(3) atoms to form a mixture of distorted face, corner, and edge-sharing OMgTi3 trigonal pyramids. In the seventh O site, O(7) is bonded in a T-shaped geometry to one Ti(4) and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded in a distorted see-saw-like geometry to one Mg(1), one Ti(3), and two equivalent Ti(1) atoms. is represented by the CIF file [CIF]
data_MgTi8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.333
_cell_length_b   5.603
_cell_length_c   9.299
_cell_angle_alpha   91.845
_cell_angle_beta   92.011
_cell_angle_gamma   89.995
_symmetry_Int_Tables_number   1
_cell_volume   277.554
_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
  Mg  Mg0  1  0.500  0.500  0.500  1.0
  Ti  Ti1  1  0.085  0.378  0.647  1.0
  Ti  Ti2  1  0.617  0.609  0.878  1.0
  Ti  Ti3  1  0.378  0.926  0.358  1.0
  Ti  Ti4  1  0.866  0.120  0.120  1.0
  Ti  Ti5  1  0.915  0.622  0.353  1.0
  Ti  Ti6  1  0.383  0.391  0.122  1.0
  Ti  Ti7  1  0.622  0.074  0.642  1.0
  Ti  Ti8  1  0.134  0.880  0.880  1.0
  O  O9  1  0.457  0.409  0.718  1.0
  O  O10  1  0.949  0.604  0.773  1.0
  O  O11  1  0.047  0.898  0.268  1.0
  O  O12  1  0.555  0.100  0.229  1.0
  O  O13  1  0.543  0.591  0.282  1.0
  O  O14  1  0.051  0.396  0.227  1.0
  O  O15  1  0.953  0.102  0.732  1.0
  O  O16  1  0.445  0.900  0.771  1.0
  O  O17  1  0.814  0.855  0.988  1.0
  O  O18  1  0.333  0.167  0.502  1.0
  O  O19  1  0.688  0.351  0.006  1.0
  O  O20  1  0.175  0.658  0.492  1.0
  O  O21  1  0.186  0.145  0.012  1.0
  O  O22  1  0.667  0.833  0.498  1.0
  O  O23  1  0.312  0.649  0.994  1.0
  O  O24  1  0.825  0.342  0.508  1.0
[/CIF]
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The crystal structure described by MgTi8O16 crystallizes in the triclinic P-1 space group. Mg(1) is bonded to two equivalent O(1), two equivalent O(6), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and faces with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-60°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(2), one O(3), one O(6), and two equivalent O(8) atoms to form distorted TiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. In the second Ti site, Ti(2) is bonded to one O(1), one O(2), one O(4), one O(5), and two equivalent O(7) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 18-60°. In the third Ti site, Ti(3) is bonded in a 6-coordinate geometry to one O(1), one O(3), one O(4), one O(8), and two equivalent O(6) atoms. In the fourth Ti site, Ti(4) is bonded to one O(2), one O(3), one O(4), one O(7), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 18-53°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Ti(1), one Ti(2), and one Ti(3) atom to form a mixture of distorted face and corner-sharing OMgTi3 trigonal pyramids. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(2), and one Ti(4) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Ti(1), one Ti(3), and one Ti(4) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(3), and one Ti(4) atom. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Ti(2) and two equivalent Ti(4) atoms. In the sixth O site, O(6) is bonded to one Mg(1), one Ti(1), and two equivalent Ti(3) atoms to form a mixture of distorted face, corner, and edge-sharing OMgTi3 trigonal pyramids. In the seventh O site, O(7) is bonded in a T-shaped geometry to one Ti(4) and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded in a distorted see-saw-like geometry to one Mg(1), one Ti(3), and two equivalent Ti(1) atoms. is represented by the CIF file [CIF]
data_MgTi8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.333
_cell_length_b   5.603
_cell_length_c   9.299
_cell_angle_alpha   91.845
_cell_angle_beta   92.011
_cell_angle_gamma   89.995
_symmetry_Int_Tables_number   1
_cell_volume   277.554
_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
  Mg  Mg0  1  0.500  0.500  0.500  1.0
  Ti  Ti1  1  0.085  0.378  0.647  1.0
  Ti  Ti2  1  0.617  0.609  0.878  1.0
  Ti  Ti3  1  0.378  0.926  0.358  1.0
  Ti  Ti4  1  0.866  0.120  0.120  1.0
  Ti  Ti5  1  0.915  0.622  0.353  1.0
  Ti  Ti6  1  0.383  0.391  0.122  1.0
  Ti  Ti7  1  0.622  0.074  0.642  1.0
  Ti  Ti8  1  0.134  0.880  0.880  1.0
  O  O9  1  0.457  0.409  0.718  1.0
  O  O10  1  0.949  0.604  0.773  1.0
  O  O11  1  0.047  0.898  0.268  1.0
  O  O12  1  0.555  0.100  0.229  1.0
  O  O13  1  0.543  0.591  0.282  1.0
  O  O14  1  0.051  0.396  0.227  1.0
  O  O15  1  0.953  0.102  0.732  1.0
  O  O16  1  0.445  0.900  0.771  1.0
  O  O17  1  0.814  0.855  0.988  1.0
  O  O18  1  0.333  0.167  0.502  1.0
  O  O19  1  0.688  0.351  0.006  1.0
  O  O20  1  0.175  0.658  0.492  1.0
  O  O21  1  0.186  0.145  0.012  1.0
  O  O22  1  0.667  0.833  0.498  1.0
  O  O23  1  0.312  0.649  0.994  1.0
  O  O24  1  0.825  0.342  0.508  1.0
[/CIF]
.