The material described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(13), one O(2), one O(4), and one O(8) atom to form MgO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one V(2)O6 octahedra, and edges with two equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-56°. 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)O6 octahedra,  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. The corner-sharing octahedral tilt angles range from 53-58°. 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)O6 octahedra, corners with three equivalent 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. The corner-sharing octahedral tilt angles range from 6-49°. 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 Mg(1)O6 octahedra, corners with two equivalent V(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-59°. 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 VO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent V(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one V(2)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-59°. 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)O6 octahedra,  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. The corner-sharing octahedral tilt angles range from 47-56°. 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, and  an edgeedge with one V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-58°. 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,  an edgeedge with one V(3)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-56°. In the fifth V site, V(5) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate 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 see-saw-like geometry to one Mg(1), 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 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 distorted trigonal non-coplanar geometry to one Ti(1), one V(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(2), one V(1), 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 to one Mg(1), one V(1), one V(4), and one V(5) atom to form a mixture of distorted corner and edge-sharing OMgV3 trigonal pyramids. 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 to one Mg(1), one Ti(3), one V(4), and one V(5) atom to form a mixture of corner and edge-sharing OMgTiV2 trigonal pyramids. In the fourteenth O site, O(14) is bonded in a 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 trigonal non-coplanar 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 Crystallographic Information File (CIF) [CIF]
data_MgTi3V5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.927
_cell_length_b   5.912
_cell_length_c   9.415
_cell_angle_alpha   91.083
_cell_angle_beta   89.576
_cell_angle_gamma   119.924
_symmetry_Int_Tables_number   1
_cell_volume   285.860
_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  0.824  0.636  0.449  1.0
  Ti  Ti1  1  0.164  0.821  0.184  1.0
  Ti  Ti2  1  0.176  0.325  0.219  1.0
  Ti  Ti3  1  0.321  0.123  0.708  1.0
  V  V4  1  0.345  0.676  0.487  1.0
  V  V5  1  0.668  0.856  0.210  1.0
  V  V6  1  0.674  0.325  0.988  1.0
  V  V7  1  0.859  0.195  0.703  1.0
  V  V8  1  0.778  0.656  0.746  1.0
  O  O9  1  0.148  0.826  0.593  1.0
  O  O10  1  0.053  0.536  0.337  1.0
  O  O11  1  0.335  0.658  0.102  1.0
  O  O12  1  0.005  0.992  0.317  1.0
  O  O13  1  0.003  0.013  0.812  1.0
  O  O14  1  0.160  0.341  0.605  1.0
  O  O15  1  0.499  0.961  0.330  1.0
  O  O16  1  0.493  0.526  0.339  1.0
  O  O17  1  0.338  0.163  0.106  1.0
  O  O18  1  0.678  0.834  0.600  1.0
  O  O19  1  0.502  0.475  0.849  1.0
  O  O20  1  0.523  0.041  0.821  1.0
  O  O21  1  0.665  0.357  0.606  1.0
  O  O22  1  0.831  0.668  0.106  1.0
  O  O23  1  0.942  0.483  0.840  1.0
  O  O24  1  0.851  0.180  0.109  1.0
[/CIF]
.
The material described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(13), one O(2), one O(4), and one O(8) atom to form MgO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one V(2)O6 octahedra, and edges with two equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-56°. 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)O6 octahedra,  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. The corner-sharing octahedral tilt angles range from 53-58°. 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)O6 octahedra, corners with three equivalent 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. The corner-sharing octahedral tilt angles range from 6-49°. 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 Mg(1)O6 octahedra, corners with two equivalent V(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-59°. 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 VO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent V(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one V(2)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-59°. 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)O6 octahedra,  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. The corner-sharing octahedral tilt angles range from 47-56°. 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, and  an edgeedge with one V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-58°. 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,  an edgeedge with one V(3)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-56°. In the fifth V site, V(5) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate 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 see-saw-like geometry to one Mg(1), 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 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 distorted trigonal non-coplanar geometry to one Ti(1), one V(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(2), one V(1), 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 to one Mg(1), one V(1), one V(4), and one V(5) atom to form a mixture of distorted corner and edge-sharing OMgV3 trigonal pyramids. 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 to one Mg(1), one Ti(3), one V(4), and one V(5) atom to form a mixture of corner and edge-sharing OMgTiV2 trigonal pyramids. In the fourteenth O site, O(14) is bonded in a 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 trigonal non-coplanar 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 Crystallographic Information File (CIF) [CIF]
data_MgTi3V5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.927
_cell_length_b   5.912
_cell_length_c   9.415
_cell_angle_alpha   91.083
_cell_angle_beta   89.576
_cell_angle_gamma   119.924
_symmetry_Int_Tables_number   1
_cell_volume   285.860
_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  0.824  0.636  0.449  1.0
  Ti  Ti1  1  0.164  0.821  0.184  1.0
  Ti  Ti2  1  0.176  0.325  0.219  1.0
  Ti  Ti3  1  0.321  0.123  0.708  1.0
  V  V4  1  0.345  0.676  0.487  1.0
  V  V5  1  0.668  0.856  0.210  1.0
  V  V6  1  0.674  0.325  0.988  1.0
  V  V7  1  0.859  0.195  0.703  1.0
  V  V8  1  0.778  0.656  0.746  1.0
  O  O9  1  0.148  0.826  0.593  1.0
  O  O10  1  0.053  0.536  0.337  1.0
  O  O11  1  0.335  0.658  0.102  1.0
  O  O12  1  0.005  0.992  0.317  1.0
  O  O13  1  0.003  0.013  0.812  1.0
  O  O14  1  0.160  0.341  0.605  1.0
  O  O15  1  0.499  0.961  0.330  1.0
  O  O16  1  0.493  0.526  0.339  1.0
  O  O17  1  0.338  0.163  0.106  1.0
  O  O18  1  0.678  0.834  0.600  1.0
  O  O19  1  0.502  0.475  0.849  1.0
  O  O20  1  0.523  0.041  0.821  1.0
  O  O21  1  0.665  0.357  0.606  1.0
  O  O22  1  0.831  0.668  0.106  1.0
  O  O23  1  0.942  0.483  0.840  1.0
  O  O24  1  0.851  0.180  0.109  1.0
[/CIF]
.