The crystal structure described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(11), one O(12), one O(14), one O(16), one O(5), and one O(9) atom to form MgO6 octahedra that share corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(5)O6 octahedra, corners with three equivalent V(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-48°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(14), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent V(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(16), one O(2), one O(3), one O(4), one O(8), and one O(9) atom to form TiO6 octahedra that share corners with two equivalent V(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. In the third Ti site, Ti(3) is bonded in a 6-coordinate geometry to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom. There are five inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(10), one O(2), one O(6), one O(7), and one O(8) atom to form distorted VO6 octahedra that share corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. In the second V site, V(2) is bonded to one O(14), one O(16), one O(3), one O(4), one O(7), and one O(8) atom to form VO6 octahedra that share corners with two equivalent V(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. In the third V site, V(3) is bonded to one O(14), one O(15), one O(16), and one O(9) atom to form VO4 tetrahedra that share  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(5)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent V(2)O6 octahedra, and corners with three equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-66°. In the fourth V site, V(4) is bonded to one O(10), one O(12), one O(13), one O(15), one O(5), and one O(6) atom to form VO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(1)O6 octahedra,  a cornercorner with one V(3)O4 tetrahedra, and edges with two equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-52°. In the fifth V site, V(5) is bonded to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom to form VO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(1)O6 octahedra,  a cornercorner with one V(3)O4 tetrahedra, and edges with two equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-52°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Ti(3), one V(1), and one V(5) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(1) atom. In the third O site, O(3) is bonded in a distorted T-shaped geometry to one Ti(1), one Ti(2), and one V(2) atom. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(2) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Ti(3), one V(4), and one V(5) atom to form corner-sharing OMgTiV2 trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Ti(3), one V(1), and one V(4) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Ti(1), one V(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Ti(2), one V(1), and one V(2) atom. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(1), one Ti(2), and one V(3) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one V(1), one V(4), and one V(5) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(3), and one V(5) atom. In the twelfth O site, O(12) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(3), and one V(4) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Ti(3), one V(4), and one V(5) atom. In the fourteenth O site, O(14) is bonded to one Mg(1), one Ti(1), one V(2), and one V(3) atom to form a mixture of distorted edge and corner-sharing OMgTiV2 trigonal pyramids. In the fifteenth O site, O(15) is bonded in a distorted trigonal planar geometry to one V(3), one V(4), and one V(5) atom. In the sixteenth O site, O(16) is bonded to one Mg(1), one Ti(2), one V(2), and one V(3) atom to form a mixture of distorted edge and corner-sharing OMgTiV2 trigonal pyramids. is represented by the CIF file [CIF]
data_MgTi3V5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.860
_cell_length_b   6.017
_cell_length_c   9.784
_cell_angle_alpha   90.390
_cell_angle_beta   81.685
_cell_angle_gamma   120.673
_symmetry_Int_Tables_number   1
_cell_volume   292.695
_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  0.187  0.094  0.949  1.0
  Ti  Ti1  1  0.230  0.843  0.222  1.0
  Ti  Ti2  1  0.297  0.389  0.221  1.0
  Ti  Ti3  1  0.269  0.132  0.655  1.0
  V  V4  1  0.337  0.665  0.491  1.0
  V  V5  1  0.752  0.908  0.220  1.0
  V  V6  1  0.836  0.416  0.011  1.0
  V  V7  1  0.739  0.117  0.712  1.0
  V  V8  1  0.736  0.618  0.713  1.0
  O  O9  1  0.120  0.807  0.587  1.0
  O  O10  1  0.093  0.542  0.328  1.0
  O  O11  1  0.459  0.735  0.109  1.0
  O  O12  1  0.075  0.040  0.309  1.0
  O  O13  1  0.922  0.960  0.801  1.0
  O  O14  1  0.119  0.306  0.588  1.0
  O  O15  1  0.543  0.992  0.331  1.0
  O  O16  1  0.551  0.562  0.331  1.0
  O  O17  1  0.457  0.231  0.095  1.0
  O  O18  1  0.625  0.810  0.601  1.0
  O  O19  1  0.414  0.424  0.811  1.0
  O  O20  1  0.415  0.991  0.810  1.0
  O  O21  1  0.641  0.319  0.594  1.0
  O  O22  1  0.973  0.757  0.093  1.0
  O  O23  1  0.883  0.441  0.819  1.0
  O  O24  1  0.982  0.225  0.091  1.0
[/CIF]
.
The crystal structure described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(11), one O(12), one O(14), one O(16), one O(5), and one O(9) atom to form MgO6 octahedra that share corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(5)O6 octahedra, corners with three equivalent V(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-48°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(14), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent V(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(16), one O(2), one O(3), one O(4), one O(8), and one O(9) atom to form TiO6 octahedra that share corners with two equivalent V(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. In the third Ti site, Ti(3) is bonded in a 6-coordinate geometry to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom. There are five inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(10), one O(2), one O(6), one O(7), and one O(8) atom to form distorted VO6 octahedra that share corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. In the second V site, V(2) is bonded to one O(14), one O(16), one O(3), one O(4), one O(7), and one O(8) atom to form VO6 octahedra that share corners with two equivalent V(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. In the third V site, V(3) is bonded to one O(14), one O(15), one O(16), and one O(9) atom to form VO4 tetrahedra that share  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(5)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent V(2)O6 octahedra, and corners with three equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-66°. In the fourth V site, V(4) is bonded to one O(10), one O(12), one O(13), one O(15), one O(5), and one O(6) atom to form VO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(1)O6 octahedra,  a cornercorner with one V(3)O4 tetrahedra, and edges with two equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-52°. In the fifth V site, V(5) is bonded to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom to form VO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(1)O6 octahedra,  a cornercorner with one V(3)O4 tetrahedra, and edges with two equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-52°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Ti(3), one V(1), and one V(5) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(1) atom. In the third O site, O(3) is bonded in a distorted T-shaped geometry to one Ti(1), one Ti(2), and one V(2) atom. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(2) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Ti(3), one V(4), and one V(5) atom to form corner-sharing OMgTiV2 trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Ti(3), one V(1), and one V(4) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Ti(1), one V(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Ti(2), one V(1), and one V(2) atom. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(1), one Ti(2), and one V(3) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one V(1), one V(4), and one V(5) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(3), and one V(5) atom. In the twelfth O site, O(12) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(3), and one V(4) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Ti(3), one V(4), and one V(5) atom. In the fourteenth O site, O(14) is bonded to one Mg(1), one Ti(1), one V(2), and one V(3) atom to form a mixture of distorted edge and corner-sharing OMgTiV2 trigonal pyramids. In the fifteenth O site, O(15) is bonded in a distorted trigonal planar geometry to one V(3), one V(4), and one V(5) atom. In the sixteenth O site, O(16) is bonded to one Mg(1), one Ti(2), one V(2), and one V(3) atom to form a mixture of distorted edge and corner-sharing OMgTiV2 trigonal pyramids. is represented by the CIF file [CIF]
data_MgTi3V5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.860
_cell_length_b   6.017
_cell_length_c   9.784
_cell_angle_alpha   90.390
_cell_angle_beta   81.685
_cell_angle_gamma   120.673
_symmetry_Int_Tables_number   1
_cell_volume   292.695
_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  0.187  0.094  0.949  1.0
  Ti  Ti1  1  0.230  0.843  0.222  1.0
  Ti  Ti2  1  0.297  0.389  0.221  1.0
  Ti  Ti3  1  0.269  0.132  0.655  1.0
  V  V4  1  0.337  0.665  0.491  1.0
  V  V5  1  0.752  0.908  0.220  1.0
  V  V6  1  0.836  0.416  0.011  1.0
  V  V7  1  0.739  0.117  0.712  1.0
  V  V8  1  0.736  0.618  0.713  1.0
  O  O9  1  0.120  0.807  0.587  1.0
  O  O10  1  0.093  0.542  0.328  1.0
  O  O11  1  0.459  0.735  0.109  1.0
  O  O12  1  0.075  0.040  0.309  1.0
  O  O13  1  0.922  0.960  0.801  1.0
  O  O14  1  0.119  0.306  0.588  1.0
  O  O15  1  0.543  0.992  0.331  1.0
  O  O16  1  0.551  0.562  0.331  1.0
  O  O17  1  0.457  0.231  0.095  1.0
  O  O18  1  0.625  0.810  0.601  1.0
  O  O19  1  0.414  0.424  0.811  1.0
  O  O20  1  0.415  0.991  0.810  1.0
  O  O21  1  0.641  0.319  0.594  1.0
  O  O22  1  0.973  0.757  0.093  1.0
  O  O23  1  0.883  0.441  0.819  1.0
  O  O24  1  0.982  0.225  0.091  1.0
[/CIF]
.