The structure described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(13), one O(4), one O(6), one O(7), and one O(8) 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(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and  a faceface with one Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-49°. 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 52-57°. 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 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(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-52°. 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)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent V(4)O6 octahedra, edges with two equivalent V(5)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. 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, corners with two equivalent V(5)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 48-55°. 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, 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 Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-50°. 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 45-57°. 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, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 43-55°. 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,  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. The corner-sharing octahedral tilt angles range from 42-55°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 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 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 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 rectangular see-saw-like geometry to one Mg(1), one Ti(1), one V(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a 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 distorted 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 distorted 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 trigonal non-coplanar 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 trigonal pyramidal geometry to one Mg(1), 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 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   5.922
_cell_length_b   5.998
_cell_length_c   9.279
_cell_angle_alpha   89.764
_cell_angle_beta   88.658
_cell_angle_gamma   120.647
_symmetry_Int_Tables_number   1
_cell_volume   283.446
_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  0.361  0.182  0.449  1.0
  Ti  Ti1  1  0.147  0.798  0.209  1.0
  Ti  Ti2  1  0.202  0.340  0.186  1.0
  Ti  Ti3  1  0.327  0.159  0.760  1.0
  V  V4  1  0.320  0.661  0.485  1.0
  V  V5  1  0.677  0.846  0.214  1.0
  V  V6  1  0.705  0.344  0.988  1.0
  V  V7  1  0.831  0.164  0.699  1.0
  V  V8  1  0.825  0.668  0.702  1.0
  O  O9  1  0.148  0.842  0.603  1.0
  O  O10  1  0.039  0.522  0.334  1.0
  O  O11  1  0.348  0.679  0.100  1.0
  O  O12  1  0.033  0.018  0.311  1.0
  O  O13  1  0.969  0.987  0.818  1.0
  O  O14  1  0.152  0.314  0.599  1.0
  O  O15  1  0.473  0.961  0.344  1.0
  O  O16  1  0.469  0.508  0.335  1.0
  O  O17  1  0.358  0.180  0.092  1.0
  O  O18  1  0.640  0.823  0.610  1.0
  O  O19  1  0.523  0.476  0.846  1.0
  O  O20  1  0.525  0.044  0.847  1.0
  O  O21  1  0.630  0.316  0.607  1.0
  O  O22  1  0.843  0.665  0.097  1.0
  O  O23  1  0.947  0.474  0.824  1.0
  O  O24  1  0.853  0.195  0.098  1.0
[/CIF]
.
The structure described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(13), one O(4), one O(6), one O(7), and one O(8) 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(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and  a faceface with one Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-49°. 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 52-57°. 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 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(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-52°. 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)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent V(4)O6 octahedra, edges with two equivalent V(5)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. 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, corners with two equivalent V(5)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 48-55°. 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, 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 Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-50°. 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 45-57°. 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, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 43-55°. 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,  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. The corner-sharing octahedral tilt angles range from 42-55°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 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 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 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 rectangular see-saw-like geometry to one Mg(1), one Ti(1), one V(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a 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 distorted 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 distorted 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 trigonal non-coplanar 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 trigonal pyramidal geometry to one Mg(1), 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 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   5.922
_cell_length_b   5.998
_cell_length_c   9.279
_cell_angle_alpha   89.764
_cell_angle_beta   88.658
_cell_angle_gamma   120.647
_symmetry_Int_Tables_number   1
_cell_volume   283.446
_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  0.361  0.182  0.449  1.0
  Ti  Ti1  1  0.147  0.798  0.209  1.0
  Ti  Ti2  1  0.202  0.340  0.186  1.0
  Ti  Ti3  1  0.327  0.159  0.760  1.0
  V  V4  1  0.320  0.661  0.485  1.0
  V  V5  1  0.677  0.846  0.214  1.0
  V  V6  1  0.705  0.344  0.988  1.0
  V  V7  1  0.831  0.164  0.699  1.0
  V  V8  1  0.825  0.668  0.702  1.0
  O  O9  1  0.148  0.842  0.603  1.0
  O  O10  1  0.039  0.522  0.334  1.0
  O  O11  1  0.348  0.679  0.100  1.0
  O  O12  1  0.033  0.018  0.311  1.0
  O  O13  1  0.969  0.987  0.818  1.0
  O  O14  1  0.152  0.314  0.599  1.0
  O  O15  1  0.473  0.961  0.344  1.0
  O  O16  1  0.469  0.508  0.335  1.0
  O  O17  1  0.358  0.180  0.092  1.0
  O  O18  1  0.640  0.823  0.610  1.0
  O  O19  1  0.523  0.476  0.846  1.0
  O  O20  1  0.525  0.044  0.847  1.0
  O  O21  1  0.630  0.316  0.607  1.0
  O  O22  1  0.843  0.665  0.097  1.0
  O  O23  1  0.947  0.474  0.824  1.0
  O  O24  1  0.853  0.195  0.098  1.0
[/CIF]
.