The material described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(11), one O(12), one O(15), and one O(3) atom to form MgO4 trigonal pyramids that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one V(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 V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-67°. 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,  a cornercorner with one Mg(1)O4 trigonal pyramid,  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 48-54°. 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,  a cornercorner with one Mg(1)O4 trigonal pyramid,  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 44-51°. 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 TiO6 octahedra that share corners with two equivalent V(1)O6 octahedra, corners with two equivalent Mg(1)O4 trigonal pyramids,  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. The corner-sharing octahedral tilt angles are 49°. 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, and  an edgeedge with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-50°. 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,  a cornercorner with one Mg(1)O4 trigonal pyramid,  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 46-52°. 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, corners with three equivalent Mg(1)O4 trigonal pyramids,  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 44-54°. 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)O6 octahedra, corners with two equivalent Mg(1)O4 trigonal pyramids,  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 47-49°. 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)O6 octahedra, corners with two equivalent Mg(1)O4 trigonal pyramids,  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 are 50°. 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 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 to one Mg(1), one Ti(1), one Ti(2), and one V(2) atom to form distorted corner-sharing OMgTi2V trigonal pyramids. 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 in a distorted 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 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 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 to one Mg(1), one Ti(3), one V(3), and one V(5) atom to form distorted OMgTiV2 tetrahedra that share  a cornercorner with one O(12)MgTiV2 tetrahedra,  a cornercorner with one O(3)MgTi2V trigonal pyramid, and  an edgeedge with one O(12)MgTiV2 tetrahedra. In the twelfth O site, O(12) is bonded to one Mg(1), one Ti(3), one V(3), and one V(4) atom to form distorted OMgTiV2 tetrahedra that share  a cornercorner with one O(11)MgTiV2 tetrahedra,  a cornercorner with one O(3)MgTi2V trigonal pyramid, and  an edgeedge with one O(11)MgTiV2 tetrahedra. In the thirteenth O site, O(13) is bonded in a 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 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 distorted rectangular see-saw-like geometry to one Mg(1), 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 file [CIF]
data_MgTi3V5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.957
_cell_length_b   5.961
_cell_length_c   9.236
_cell_angle_alpha   89.518
_cell_angle_beta   91.059
_cell_angle_gamma   119.449
_symmetry_Int_Tables_number   1
_cell_volume   285.557
_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  0.332  0.662  0.878  1.0
  Ti  Ti1  1  0.133  0.811  0.206  1.0
  Ti  Ti2  1  0.200  0.339  0.214  1.0
  Ti  Ti3  1  0.321  0.152  0.690  1.0
  V  V4  1  0.348  0.670  0.487  1.0
  V  V5  1  0.664  0.859  0.212  1.0
  V  V6  1  0.660  0.323  0.984  1.0
  V  V7  1  0.832  0.168  0.705  1.0
  V  V8  1  0.830  0.660  0.705  1.0
  O  O9  1  0.179  0.830  0.596  1.0
  O  O10  1  0.063  0.538  0.333  1.0
  O  O11  1  0.330  0.668  0.093  1.0
  O  O12  1  0.006  0.008  0.306  1.0
  O  O13  1  0.008  0.001  0.803  1.0
  O  O14  1  0.181  0.348  0.598  1.0
  O  O15  1  0.491  0.955  0.329  1.0
  O  O16  1  0.483  0.525  0.334  1.0
  O  O17  1  0.338  0.168  0.102  1.0
  O  O18  1  0.641  0.821  0.596  1.0
  O  O19  1  0.519  0.470  0.845  1.0
  O  O20  1  0.517  0.037  0.840  1.0
  O  O21  1  0.655  0.328  0.601  1.0
  O  O22  1  0.819  0.665  0.103  1.0
  O  O23  1  0.957  0.476  0.843  1.0
  O  O24  1  0.826  0.185  0.100  1.0
[/CIF]
.
The material described by MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(11), one O(12), one O(15), and one O(3) atom to form MgO4 trigonal pyramids that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one V(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 V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-67°. 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,  a cornercorner with one Mg(1)O4 trigonal pyramid,  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 48-54°. 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,  a cornercorner with one Mg(1)O4 trigonal pyramid,  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 44-51°. 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 TiO6 octahedra that share corners with two equivalent V(1)O6 octahedra, corners with two equivalent Mg(1)O4 trigonal pyramids,  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. The corner-sharing octahedral tilt angles are 49°. 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, and  an edgeedge with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-50°. 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,  a cornercorner with one Mg(1)O4 trigonal pyramid,  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 46-52°. 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, corners with three equivalent Mg(1)O4 trigonal pyramids,  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 44-54°. 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)O6 octahedra, corners with two equivalent Mg(1)O4 trigonal pyramids,  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 47-49°. 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)O6 octahedra, corners with two equivalent Mg(1)O4 trigonal pyramids,  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 are 50°. 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 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 to one Mg(1), one Ti(1), one Ti(2), and one V(2) atom to form distorted corner-sharing OMgTi2V trigonal pyramids. 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 in a distorted 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 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 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 to one Mg(1), one Ti(3), one V(3), and one V(5) atom to form distorted OMgTiV2 tetrahedra that share  a cornercorner with one O(12)MgTiV2 tetrahedra,  a cornercorner with one O(3)MgTi2V trigonal pyramid, and  an edgeedge with one O(12)MgTiV2 tetrahedra. In the twelfth O site, O(12) is bonded to one Mg(1), one Ti(3), one V(3), and one V(4) atom to form distorted OMgTiV2 tetrahedra that share  a cornercorner with one O(11)MgTiV2 tetrahedra,  a cornercorner with one O(3)MgTi2V trigonal pyramid, and  an edgeedge with one O(11)MgTiV2 tetrahedra. In the thirteenth O site, O(13) is bonded in a 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 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 distorted rectangular see-saw-like geometry to one Mg(1), 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 file [CIF]
data_MgTi3V5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.957
_cell_length_b   5.961
_cell_length_c   9.236
_cell_angle_alpha   89.518
_cell_angle_beta   91.059
_cell_angle_gamma   119.449
_symmetry_Int_Tables_number   1
_cell_volume   285.557
_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  0.332  0.662  0.878  1.0
  Ti  Ti1  1  0.133  0.811  0.206  1.0
  Ti  Ti2  1  0.200  0.339  0.214  1.0
  Ti  Ti3  1  0.321  0.152  0.690  1.0
  V  V4  1  0.348  0.670  0.487  1.0
  V  V5  1  0.664  0.859  0.212  1.0
  V  V6  1  0.660  0.323  0.984  1.0
  V  V7  1  0.832  0.168  0.705  1.0
  V  V8  1  0.830  0.660  0.705  1.0
  O  O9  1  0.179  0.830  0.596  1.0
  O  O10  1  0.063  0.538  0.333  1.0
  O  O11  1  0.330  0.668  0.093  1.0
  O  O12  1  0.006  0.008  0.306  1.0
  O  O13  1  0.008  0.001  0.803  1.0
  O  O14  1  0.181  0.348  0.598  1.0
  O  O15  1  0.491  0.955  0.329  1.0
  O  O16  1  0.483  0.525  0.334  1.0
  O  O17  1  0.338  0.168  0.102  1.0
  O  O18  1  0.641  0.821  0.596  1.0
  O  O19  1  0.519  0.470  0.845  1.0
  O  O20  1  0.517  0.037  0.840  1.0
  O  O21  1  0.655  0.328  0.601  1.0
  O  O22  1  0.819  0.665  0.103  1.0
  O  O23  1  0.957  0.476  0.843  1.0
  O  O24  1  0.826  0.185  0.100  1.0
[/CIF]
.