The material described by MgDy4Ti2O10 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(10), one O(3), one O(4), and one O(8) atom to form MgO4 tetrahedra that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Dy(4)O6 octahedra, corners with two equivalent Ti(1)O4 tetrahedra, and  an edgeedge with one Dy(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 33-76°. There are four inequivalent Dy sites. In the first Dy site, Dy(1) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(9) atom to form DyO6 pentagonal pyramids that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra, corners with two equivalent Ti(1)O4 tetrahedra,  an edgeedge with one Dy(2)O6 octahedra,  an edgeedge with one Dy(4)O6 octahedra, edges with two equivalent Dy(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 11-28°. In the second Dy site, Dy(2) is bonded to one O(10), one O(2), one O(5), one O(6), one O(7), and one O(9) atom to form distorted DyO6 octahedra that share  a cornercorner with one Dy(4)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Dy(1)O6 pentagonal pyramid,  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra, edges with two equivalent Dy(3)O6 octahedra, edges with two equivalent Dy(4)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Dy(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 18-29°. In the third Dy site, Dy(3) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), and one O(9) atom to form distorted DyO6 octahedra that share  a cornercorner with one Dy(4)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Dy(1)O6 pentagonal pyramid,  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  an edgeedge with one Dy(4)O6 octahedra, edges with two equivalent Dy(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Dy(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 14-16°. In the fourth Dy site, Dy(4) is bonded to one O(10), one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form distorted DyO6 octahedra that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Ti(1)O4 tetrahedra,  an edgeedge with one Dy(3)O6 octahedra, edges with two equivalent Dy(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Dy(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 14-29°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(3), one O(7), and one O(8) atom to form TiO4 tetrahedra that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Dy(4)O6 octahedra, corners with two equivalent Dy(1)O6 pentagonal pyramids, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-72°. In the second Ti site, Ti(2) is bonded to one O(2), one O(4), one O(5), one O(6), one O(7), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra, edges with two equivalent Dy(2)O6 octahedra, edges with two equivalent Dy(3)O6 octahedra, edges with two equivalent Dy(4)O6 octahedra, and edges with two equivalent Dy(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 16-18°. There are ten inequivalent O sites. In the first O site, O(1) is bonded in a trigonal planar geometry to one Dy(1), one Dy(3), and one Ti(1) atom. In the second O site, O(2) is bonded to one Dy(2), one Dy(3), one Dy(4), and one Ti(2) atom to form distorted ODy3Ti trigonal pyramids that share corners with two equivalent O(6)Dy4Ti square pyramids, corners with three equivalent O(7)Dy2Ti2 tetrahedra,  a cornercorner with one O(9)Dy3Ti trigonal pyramid,  an edgeedge with one O(6)Dy4Ti square pyramid, edges with two equivalent O(5)Dy4Ti square pyramids, and  an edgeedge with one O(9)Dy3Ti trigonal pyramid. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Mg(1), one Dy(1), and one Ti(1) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Dy(1), one Dy(3), and one Ti(2) atom. In the fifth O site, O(5) is bonded to one Dy(1), one Dy(2), one Dy(3), one Dy(4), and one Ti(2) atom to form ODy4Ti square pyramids that share  a cornercorner with one O(6)Dy4Ti square pyramid,  a cornercorner with one O(7)Dy2Ti2 tetrahedra, corners with two equivalent O(9)Dy3Ti trigonal pyramids, edges with two equivalent O(6)Dy4Ti square pyramids,  an edgeedge with one O(7)Dy2Ti2 tetrahedra,  an edgeedge with one O(9)Dy3Ti trigonal pyramid, and edges with two equivalent O(2)Dy3Ti trigonal pyramids. In the sixth O site, O(6) is bonded to one Dy(1), one Dy(2), one Dy(3), one Dy(4), and one Ti(2) atom to form ODy4Ti square pyramids that share  a cornercorner with one O(5)Dy4Ti square pyramid,  a cornercorner with one O(7)Dy2Ti2 tetrahedra, corners with two equivalent O(2)Dy3Ti trigonal pyramids, edges with two equivalent O(5)Dy4Ti square pyramids,  an edgeedge with one O(7)Dy2Ti2 tetrahedra,  an edgeedge with one O(2)Dy3Ti trigonal pyramid, and edges with two equivalent O(9)Dy3Ti trigonal pyramids. In the seventh O site, O(7) is bonded to one Dy(2), one Dy(4), one Ti(1), and one Ti(2) atom to form distorted ODy2Ti2 tetrahedra that share  a cornercorner with one O(5)Dy4Ti square pyramid,  a cornercorner with one O(6)Dy4Ti square pyramid, corners with three equivalent O(2)Dy3Ti trigonal pyramids,  an edgeedge with one O(5)Dy4Ti square pyramid,  an edgeedge with one O(6)Dy4Ti square pyramid, and  an edgeedge with one O(9)Dy3Ti trigonal pyramid. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Mg(1), one Dy(4), and one Ti(1) atom. In the ninth O site, O(9) is bonded to one Dy(1), one Dy(2), one Dy(3), and one Ti(2) atom to form distorted ODy3Ti trigonal pyramids that share corners with two equivalent O(5)Dy4Ti square pyramids,  a cornercorner with one O(2)Dy3Ti trigonal pyramid,  an edgeedge with one O(5)Dy4Ti square pyramid, edges with two equivalent O(6)Dy4Ti square pyramids,  an edgeedge with one O(7)Dy2Ti2 tetrahedra, and  an edgeedge with one O(2)Dy3Ti trigonal pyramid. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Dy(2), and one Dy(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Dy4MgTi2O10
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.850
_cell_length_b   7.200
_cell_length_c   8.551
_cell_angle_alpha   65.931
_cell_angle_beta   108.816
_cell_angle_gamma   131.029
_symmetry_Int_Tables_number   1
_cell_volume   247.287
_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
  Dy  Dy0  1  0.453  0.674  0.781  1.0
  Dy  Dy1  1  0.312  0.724  0.130  1.0
  Dy  Dy2  1  0.716  0.339  0.871  1.0
  Dy  Dy3  1  0.592  0.382  0.236  1.0
  Mg  Mg4  1  0.221  0.347  0.532  1.0
  Ti  Ti5  1  0.941  0.825  0.469  1.0
  Ti  Ti6  1  0.019  0.033  0.001  1.0
  O  O7  1  0.019  0.606  0.652  1.0
  O  O8  1  0.426  0.089  0.114  1.0
  O  O9  1  0.601  0.715  0.548  1.0
  O  O10  1  0.247  0.257  0.785  1.0
  O  O11  1  0.852  0.659  0.976  1.0
  O  O12  1  0.183  0.407  0.021  1.0
  O  O13  1  0.781  0.791  0.235  1.0
  O  O14  1  0.295  0.162  0.455  1.0
  O  O15  1  0.610  0.974  0.893  1.0
  O  O16  1  0.012  0.443  0.335  1.0
[/CIF]
.
The material described by MgDy4Ti2O10 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(10), one O(3), one O(4), and one O(8) atom to form MgO4 tetrahedra that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Dy(4)O6 octahedra, corners with two equivalent Ti(1)O4 tetrahedra, and  an edgeedge with one Dy(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 33-76°. There are four inequivalent Dy sites. In the first Dy site, Dy(1) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(9) atom to form DyO6 pentagonal pyramids that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra, corners with two equivalent Ti(1)O4 tetrahedra,  an edgeedge with one Dy(2)O6 octahedra,  an edgeedge with one Dy(4)O6 octahedra, edges with two equivalent Dy(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 11-28°. In the second Dy site, Dy(2) is bonded to one O(10), one O(2), one O(5), one O(6), one O(7), and one O(9) atom to form distorted DyO6 octahedra that share  a cornercorner with one Dy(4)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Dy(1)O6 pentagonal pyramid,  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra, edges with two equivalent Dy(3)O6 octahedra, edges with two equivalent Dy(4)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Dy(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 18-29°. In the third Dy site, Dy(3) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), and one O(9) atom to form distorted DyO6 octahedra that share  a cornercorner with one Dy(4)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Dy(1)O6 pentagonal pyramid,  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  an edgeedge with one Dy(4)O6 octahedra, edges with two equivalent Dy(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Dy(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 14-16°. In the fourth Dy site, Dy(4) is bonded to one O(10), one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form distorted DyO6 octahedra that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Ti(1)O4 tetrahedra,  an edgeedge with one Dy(3)O6 octahedra, edges with two equivalent Dy(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Dy(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 14-29°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(3), one O(7), and one O(8) atom to form TiO4 tetrahedra that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Dy(4)O6 octahedra, corners with two equivalent Dy(1)O6 pentagonal pyramids, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-72°. In the second Ti site, Ti(2) is bonded to one O(2), one O(4), one O(5), one O(6), one O(7), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Dy(2)O6 octahedra,  a cornercorner with one Dy(3)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra, edges with two equivalent Dy(2)O6 octahedra, edges with two equivalent Dy(3)O6 octahedra, edges with two equivalent Dy(4)O6 octahedra, and edges with two equivalent Dy(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 16-18°. There are ten inequivalent O sites. In the first O site, O(1) is bonded in a trigonal planar geometry to one Dy(1), one Dy(3), and one Ti(1) atom. In the second O site, O(2) is bonded to one Dy(2), one Dy(3), one Dy(4), and one Ti(2) atom to form distorted ODy3Ti trigonal pyramids that share corners with two equivalent O(6)Dy4Ti square pyramids, corners with three equivalent O(7)Dy2Ti2 tetrahedra,  a cornercorner with one O(9)Dy3Ti trigonal pyramid,  an edgeedge with one O(6)Dy4Ti square pyramid, edges with two equivalent O(5)Dy4Ti square pyramids, and  an edgeedge with one O(9)Dy3Ti trigonal pyramid. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Mg(1), one Dy(1), and one Ti(1) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Dy(1), one Dy(3), and one Ti(2) atom. In the fifth O site, O(5) is bonded to one Dy(1), one Dy(2), one Dy(3), one Dy(4), and one Ti(2) atom to form ODy4Ti square pyramids that share  a cornercorner with one O(6)Dy4Ti square pyramid,  a cornercorner with one O(7)Dy2Ti2 tetrahedra, corners with two equivalent O(9)Dy3Ti trigonal pyramids, edges with two equivalent O(6)Dy4Ti square pyramids,  an edgeedge with one O(7)Dy2Ti2 tetrahedra,  an edgeedge with one O(9)Dy3Ti trigonal pyramid, and edges with two equivalent O(2)Dy3Ti trigonal pyramids. In the sixth O site, O(6) is bonded to one Dy(1), one Dy(2), one Dy(3), one Dy(4), and one Ti(2) atom to form ODy4Ti square pyramids that share  a cornercorner with one O(5)Dy4Ti square pyramid,  a cornercorner with one O(7)Dy2Ti2 tetrahedra, corners with two equivalent O(2)Dy3Ti trigonal pyramids, edges with two equivalent O(5)Dy4Ti square pyramids,  an edgeedge with one O(7)Dy2Ti2 tetrahedra,  an edgeedge with one O(2)Dy3Ti trigonal pyramid, and edges with two equivalent O(9)Dy3Ti trigonal pyramids. In the seventh O site, O(7) is bonded to one Dy(2), one Dy(4), one Ti(1), and one Ti(2) atom to form distorted ODy2Ti2 tetrahedra that share  a cornercorner with one O(5)Dy4Ti square pyramid,  a cornercorner with one O(6)Dy4Ti square pyramid, corners with three equivalent O(2)Dy3Ti trigonal pyramids,  an edgeedge with one O(5)Dy4Ti square pyramid,  an edgeedge with one O(6)Dy4Ti square pyramid, and  an edgeedge with one O(9)Dy3Ti trigonal pyramid. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Mg(1), one Dy(4), and one Ti(1) atom. In the ninth O site, O(9) is bonded to one Dy(1), one Dy(2), one Dy(3), and one Ti(2) atom to form distorted ODy3Ti trigonal pyramids that share corners with two equivalent O(5)Dy4Ti square pyramids,  a cornercorner with one O(2)Dy3Ti trigonal pyramid,  an edgeedge with one O(5)Dy4Ti square pyramid, edges with two equivalent O(6)Dy4Ti square pyramids,  an edgeedge with one O(7)Dy2Ti2 tetrahedra, and  an edgeedge with one O(2)Dy3Ti trigonal pyramid. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Dy(2), and one Dy(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Dy4MgTi2O10
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.850
_cell_length_b   7.200
_cell_length_c   8.551
_cell_angle_alpha   65.931
_cell_angle_beta   108.816
_cell_angle_gamma   131.029
_symmetry_Int_Tables_number   1
_cell_volume   247.287
_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
  Dy  Dy0  1  0.453  0.674  0.781  1.0
  Dy  Dy1  1  0.312  0.724  0.130  1.0
  Dy  Dy2  1  0.716  0.339  0.871  1.0
  Dy  Dy3  1  0.592  0.382  0.236  1.0
  Mg  Mg4  1  0.221  0.347  0.532  1.0
  Ti  Ti5  1  0.941  0.825  0.469  1.0
  Ti  Ti6  1  0.019  0.033  0.001  1.0
  O  O7  1  0.019  0.606  0.652  1.0
  O  O8  1  0.426  0.089  0.114  1.0
  O  O9  1  0.601  0.715  0.548  1.0
  O  O10  1  0.247  0.257  0.785  1.0
  O  O11  1  0.852  0.659  0.976  1.0
  O  O12  1  0.183  0.407  0.021  1.0
  O  O13  1  0.781  0.791  0.235  1.0
  O  O14  1  0.295  0.162  0.455  1.0
  O  O15  1  0.610  0.974  0.893  1.0
  O  O16  1  0.012  0.443  0.335  1.0
[/CIF]
.