The compound described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(4), one O(6), one O(7), and one O(8) atom to form MgO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent V(1)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, and  a faceface with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-46°. 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 TiO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  a cornercorner with one V(1)O4 tetrahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 41-56°. 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 Mg(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  a cornercorner with one V(1)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-52°. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom to form distorted TiO6 octahedra that share corners with two equivalent V(1)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent V(4)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. 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), and one O(6) atom to form VO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(5)O6 octahedra, and corners with three equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-61°. 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 distorted VO6 octahedra that share corners with two equivalent V(3)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. In the third V site, V(3) is bonded to one O(11), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form VO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra, and  an edgeedge with one V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-56°. 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 V(1)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. 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 V(1)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ti(3), one V(1), and one V(5) atom. In the second O site, O(2) is bonded in a 3-coordinate 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 trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(2) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(1), one Ti(2), and one V(2) atom. In the fifth O site, O(5) is bonded in a trigonal non-coplanar geometry to one Ti(3), one V(4), and one V(5) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(3), one V(1), and one V(4) atom. In the seventh O site, O(7) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(2), and one V(2) atom. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Ti(1), one Ti(2), and one V(3) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Mg(1), one V(1), one V(4), and one V(5) atom. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to one Ti(3), one V(3), and one V(5) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal non-coplanar geometry to one Ti(3), one V(3), and one V(4) atom. In the thirteenth O site, O(13) is bonded in a distorted T-shaped geometry to one Ti(3), one V(4), and one V(5) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal planar geometry to one Ti(1), one V(2), and one V(3) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one V(3), one V(4), and one V(5) atom. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to one Ti(2), one V(2), and one V(3) atom. is represented by the CIF card [CIF]
data_MgTi3V5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.908
_cell_length_b   6.007
_cell_length_c   9.872
_cell_angle_alpha   89.298
_cell_angle_beta   99.615
_cell_angle_gamma   120.476
_symmetry_Int_Tables_number   1
_cell_volume   296.632
_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  0.811  0.897  0.451  1.0
  Ti  Ti1  1  0.282  0.891  0.209  1.0
  Ti  Ti2  1  0.266  0.370  0.206  1.0
  Ti  Ti3  1  0.255  0.146  0.737  1.0
  V  V4  1  0.155  0.578  0.516  1.0
  V  V5  1  0.737  0.854  0.167  1.0
  V  V6  1  0.675  0.330  0.987  1.0
  V  V7  1  0.712  0.115  0.704  1.0
  V  V8  1  0.746  0.607  0.723  1.0
  O  O9  1  0.014  0.761  0.589  1.0
  O  O10  1  0.145  0.573  0.336  1.0
  O  O11  1  0.346  0.677  0.097  1.0
  O  O12  1  0.096  0.043  0.301  1.0
  O  O13  1  0.921  0.964  0.799  1.0
  O  O14  1  0.005  0.249  0.582  1.0
  O  O15  1  0.613  0.014  0.306  1.0
  O  O16  1  0.601  0.580  0.307  1.0
  O  O17  1  0.370  0.183  0.102  1.0
  O  O18  1  0.524  0.756  0.587  1.0
  O  O19  1  0.464  0.460  0.839  1.0
  O  O20  1  0.456  0.022  0.836  1.0
  O  O21  1  0.507  0.270  0.610  1.0
  O  O22  1  0.862  0.683  0.088  1.0
  O  O23  1  0.908  0.469  0.826  1.0
  O  O24  1  0.872  0.185  0.089  1.0
[/CIF]
.
The compound described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(4), one O(6), one O(7), and one O(8) atom to form MgO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent V(1)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, and  a faceface with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-46°. 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 TiO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  a cornercorner with one V(1)O4 tetrahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 41-56°. 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 Mg(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  a cornercorner with one V(1)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-52°. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom to form distorted TiO6 octahedra that share corners with two equivalent V(1)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent V(4)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. 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), and one O(6) atom to form VO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(5)O6 octahedra, and corners with three equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-61°. 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 distorted VO6 octahedra that share corners with two equivalent V(3)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. In the third V site, V(3) is bonded to one O(11), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form VO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra, and  an edgeedge with one V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-56°. 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 V(1)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. 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 V(1)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ti(3), one V(1), and one V(5) atom. In the second O site, O(2) is bonded in a 3-coordinate 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 trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(2) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(1), one Ti(2), and one V(2) atom. In the fifth O site, O(5) is bonded in a trigonal non-coplanar geometry to one Ti(3), one V(4), and one V(5) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(3), one V(1), and one V(4) atom. In the seventh O site, O(7) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(2), and one V(2) atom. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Ti(1), one Ti(2), and one V(3) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Mg(1), one V(1), one V(4), and one V(5) atom. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to one Ti(3), one V(3), and one V(5) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal non-coplanar geometry to one Ti(3), one V(3), and one V(4) atom. In the thirteenth O site, O(13) is bonded in a distorted T-shaped geometry to one Ti(3), one V(4), and one V(5) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal planar geometry to one Ti(1), one V(2), and one V(3) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one V(3), one V(4), and one V(5) atom. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to one Ti(2), one V(2), and one V(3) atom. is represented by the CIF card [CIF]
data_MgTi3V5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.908
_cell_length_b   6.007
_cell_length_c   9.872
_cell_angle_alpha   89.298
_cell_angle_beta   99.615
_cell_angle_gamma   120.476
_symmetry_Int_Tables_number   1
_cell_volume   296.632
_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  0.811  0.897  0.451  1.0
  Ti  Ti1  1  0.282  0.891  0.209  1.0
  Ti  Ti2  1  0.266  0.370  0.206  1.0
  Ti  Ti3  1  0.255  0.146  0.737  1.0
  V  V4  1  0.155  0.578  0.516  1.0
  V  V5  1  0.737  0.854  0.167  1.0
  V  V6  1  0.675  0.330  0.987  1.0
  V  V7  1  0.712  0.115  0.704  1.0
  V  V8  1  0.746  0.607  0.723  1.0
  O  O9  1  0.014  0.761  0.589  1.0
  O  O10  1  0.145  0.573  0.336  1.0
  O  O11  1  0.346  0.677  0.097  1.0
  O  O12  1  0.096  0.043  0.301  1.0
  O  O13  1  0.921  0.964  0.799  1.0
  O  O14  1  0.005  0.249  0.582  1.0
  O  O15  1  0.613  0.014  0.306  1.0
  O  O16  1  0.601  0.580  0.307  1.0
  O  O17  1  0.370  0.183  0.102  1.0
  O  O18  1  0.524  0.756  0.587  1.0
  O  O19  1  0.464  0.460  0.839  1.0
  O  O20  1  0.456  0.022  0.836  1.0
  O  O21  1  0.507  0.270  0.610  1.0
  O  O22  1  0.862  0.683  0.088  1.0
  O  O23  1  0.908  0.469  0.826  1.0
  O  O24  1  0.872  0.185  0.089  1.0
[/CIF]
.