The material described by MgLu4Ti2O10 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(3), one O(7), two equivalent O(10), and two equivalent O(2) atoms to form distorted MgO6 octahedra that share corners with two equivalent Ti(1)O5 trigonal bipyramids, corners with two equivalent Ti(2)O5 trigonal bipyramids, and edges with two equivalent Mg(1)O6 octahedra. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 5-coordinate geometry to one O(10), one O(5), one O(7), and two equivalent O(3) atoms. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to one O(1), one O(5), one O(8), one O(9), and two equivalent O(4) atoms. In the third Lu site, Lu(3) is bonded in a 5-coordinate geometry to one O(2), one O(3), one O(6), and two equivalent O(7) atoms. In the fourth Lu site, Lu(4) is bonded in a 6-coordinate geometry to one O(1), one O(4), one O(6), one O(9), and two equivalent O(8) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(2), one O(8), and two equivalent O(6) atoms to form TiO5 trigonal bipyramids that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Ti(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 60°. In the second Ti site, Ti(2) is bonded to one O(10), one O(4), one O(9), and two equivalent O(5) atoms to form TiO5 trigonal bipyramids that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Ti(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 59°. There are ten inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Lu(2), one Lu(4), and one Ti(1) atom. In the second O site, O(2) is bonded to two equivalent Mg(1), one Lu(3), and one Ti(1) atom to form distorted OLuMg2Ti trigonal pyramids that share  a cornercorner with one O(8)Lu3Ti tetrahedra, corners with three equivalent O(6)Lu2Ti2 tetrahedra, corners with three equivalent O(3)Lu3Mg tetrahedra, corners with two equivalent O(10)LuMg2Ti trigonal pyramids, corners with two equivalent O(2)LuMg2Ti trigonal pyramids, edges with two equivalent O(7)Lu3Mg tetrahedra, and  an edgeedge with one O(10)LuMg2Ti trigonal pyramid. In the third O site, O(3) is bonded to one Mg(1), one Lu(3), and two equivalent Lu(1) atoms to form OLu3Mg tetrahedra that share  a cornercorner with one O(6)Lu2Ti2 tetrahedra,  a cornercorner with one O(7)Lu3Mg tetrahedra, corners with two equivalent O(5)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Mg tetrahedra, corners with three equivalent O(2)LuMg2Ti trigonal pyramids, edges with two equivalent O(7)Lu3Mg tetrahedra, and edges with two equivalent O(10)LuMg2Ti trigonal pyramids. In the fourth O site, O(4) is bonded to one Lu(4), two equivalent Lu(2), and one Ti(2) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(6)Lu2Ti2 tetrahedra, corners with two equivalent O(4)Lu3Ti tetrahedra,  a cornercorner with one O(10)LuMg2Ti trigonal pyramid, edges with two equivalent O(5)Lu2Ti2 tetrahedra, and edges with two equivalent O(8)Lu3Ti tetrahedra. In the fifth O site, O(5) is bonded to one Lu(1), one Lu(2), and two equivalent Ti(2) atoms to form OLu2Ti2 tetrahedra that share  a cornercorner with one O(7)Lu3Mg tetrahedra,  a cornercorner with one O(8)Lu3Ti tetrahedra, corners with two equivalent O(5)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Mg tetrahedra, corners with three equivalent O(10)LuMg2Ti trigonal pyramids, and edges with two equivalent O(4)Lu3Ti tetrahedra. In the sixth O site, O(6) is bonded to one Lu(3), one Lu(4), and two equivalent Ti(1) atoms to form OLu2Ti2 tetrahedra that share  a cornercorner with one O(3)Lu3Mg tetrahedra,  a cornercorner with one O(4)Lu3Ti tetrahedra, corners with two equivalent O(6)Lu2Ti2 tetrahedra, corners with two equivalent O(7)Lu3Mg tetrahedra, corners with three equivalent O(2)LuMg2Ti trigonal pyramids, and edges with two equivalent O(8)Lu3Ti tetrahedra. In the seventh O site, O(7) is bonded to one Mg(1), one Lu(1), and two equivalent Lu(3) atoms to form OLu3Mg tetrahedra that share  a cornercorner with one O(5)Lu2Ti2 tetrahedra,  a cornercorner with one O(3)Lu3Mg tetrahedra, corners with two equivalent O(6)Lu2Ti2 tetrahedra, corners with two equivalent O(7)Lu3Mg tetrahedra, corners with three equivalent O(10)LuMg2Ti trigonal pyramids, edges with two equivalent O(3)Lu3Mg tetrahedra, and edges with two equivalent O(2)LuMg2Ti trigonal pyramids. In the eighth O site, O(8) is bonded to one Lu(2), two equivalent Lu(4), and one Ti(1) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(5)Lu2Ti2 tetrahedra, corners with two equivalent O(8)Lu3Ti tetrahedra,  a cornercorner with one O(2)LuMg2Ti trigonal pyramid, edges with two equivalent O(6)Lu2Ti2 tetrahedra, and edges with two equivalent O(4)Lu3Ti tetrahedra. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Lu(2), one Lu(4), and one Ti(2) atom. In the tenth O site, O(10) is bonded to two equivalent Mg(1), one Lu(1), and one Ti(2) atom to form distorted OLuMg2Ti trigonal pyramids that share  a cornercorner with one O(4)Lu3Ti tetrahedra, corners with three equivalent O(5)Lu2Ti2 tetrahedra, corners with three equivalent O(7)Lu3Mg tetrahedra, corners with two equivalent O(10)LuMg2Ti trigonal pyramids, corners with two equivalent O(2)LuMg2Ti trigonal pyramids, edges with two equivalent O(3)Lu3Mg tetrahedra, and  an edgeedge with one O(2)LuMg2Ti trigonal pyramid. is represented by the CIF file [CIF]
data_Lu4MgTi2O10
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.872
_cell_length_b   5.831
_cell_length_c   11.478
_cell_angle_alpha   79.452
_cell_angle_beta   90.000
_cell_angle_gamma   70.605
_symmetry_Int_Tables_number   1
_cell_volume   239.825
_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
  Lu  Lu0  1  0.178  0.644  0.885  1.0
  Lu  Lu1  1  0.149  0.701  0.558  1.0
  Lu  Lu2  1  0.822  0.357  0.115  1.0
  Lu  Lu3  1  0.851  0.298  0.442  1.0
  Mg  Mg4  1  0.501  0.999  0.002  1.0
  Ti  Ti5  1  0.137  0.727  0.268  1.0
  Ti  Ti6  1  0.864  0.272  0.732  1.0
  O  O7  1  0.024  0.952  0.379  1.0
  O  O8  1  0.024  0.953  0.121  1.0
  O  O9  1  0.667  0.666  0.963  1.0
  O  O10  1  0.725  0.550  0.577  1.0
  O  O11  1  0.291  0.419  0.747  1.0
  O  O12  1  0.709  0.582  0.253  1.0
  O  O13  1  0.333  0.335  0.037  1.0
  O  O14  1  0.275  0.449  0.424  1.0
  O  O15  1  0.976  0.048  0.620  1.0
  O  O16  1  0.975  0.049  0.878  1.0
[/CIF]
.
The material described by MgLu4Ti2O10 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(3), one O(7), two equivalent O(10), and two equivalent O(2) atoms to form distorted MgO6 octahedra that share corners with two equivalent Ti(1)O5 trigonal bipyramids, corners with two equivalent Ti(2)O5 trigonal bipyramids, and edges with two equivalent Mg(1)O6 octahedra. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 5-coordinate geometry to one O(10), one O(5), one O(7), and two equivalent O(3) atoms. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to one O(1), one O(5), one O(8), one O(9), and two equivalent O(4) atoms. In the third Lu site, Lu(3) is bonded in a 5-coordinate geometry to one O(2), one O(3), one O(6), and two equivalent O(7) atoms. In the fourth Lu site, Lu(4) is bonded in a 6-coordinate geometry to one O(1), one O(4), one O(6), one O(9), and two equivalent O(8) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(2), one O(8), and two equivalent O(6) atoms to form TiO5 trigonal bipyramids that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Ti(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 60°. In the second Ti site, Ti(2) is bonded to one O(10), one O(4), one O(9), and two equivalent O(5) atoms to form TiO5 trigonal bipyramids that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Ti(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 59°. There are ten inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Lu(2), one Lu(4), and one Ti(1) atom. In the second O site, O(2) is bonded to two equivalent Mg(1), one Lu(3), and one Ti(1) atom to form distorted OLuMg2Ti trigonal pyramids that share  a cornercorner with one O(8)Lu3Ti tetrahedra, corners with three equivalent O(6)Lu2Ti2 tetrahedra, corners with three equivalent O(3)Lu3Mg tetrahedra, corners with two equivalent O(10)LuMg2Ti trigonal pyramids, corners with two equivalent O(2)LuMg2Ti trigonal pyramids, edges with two equivalent O(7)Lu3Mg tetrahedra, and  an edgeedge with one O(10)LuMg2Ti trigonal pyramid. In the third O site, O(3) is bonded to one Mg(1), one Lu(3), and two equivalent Lu(1) atoms to form OLu3Mg tetrahedra that share  a cornercorner with one O(6)Lu2Ti2 tetrahedra,  a cornercorner with one O(7)Lu3Mg tetrahedra, corners with two equivalent O(5)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Mg tetrahedra, corners with three equivalent O(2)LuMg2Ti trigonal pyramids, edges with two equivalent O(7)Lu3Mg tetrahedra, and edges with two equivalent O(10)LuMg2Ti trigonal pyramids. In the fourth O site, O(4) is bonded to one Lu(4), two equivalent Lu(2), and one Ti(2) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(6)Lu2Ti2 tetrahedra, corners with two equivalent O(4)Lu3Ti tetrahedra,  a cornercorner with one O(10)LuMg2Ti trigonal pyramid, edges with two equivalent O(5)Lu2Ti2 tetrahedra, and edges with two equivalent O(8)Lu3Ti tetrahedra. In the fifth O site, O(5) is bonded to one Lu(1), one Lu(2), and two equivalent Ti(2) atoms to form OLu2Ti2 tetrahedra that share  a cornercorner with one O(7)Lu3Mg tetrahedra,  a cornercorner with one O(8)Lu3Ti tetrahedra, corners with two equivalent O(5)Lu2Ti2 tetrahedra, corners with two equivalent O(3)Lu3Mg tetrahedra, corners with three equivalent O(10)LuMg2Ti trigonal pyramids, and edges with two equivalent O(4)Lu3Ti tetrahedra. In the sixth O site, O(6) is bonded to one Lu(3), one Lu(4), and two equivalent Ti(1) atoms to form OLu2Ti2 tetrahedra that share  a cornercorner with one O(3)Lu3Mg tetrahedra,  a cornercorner with one O(4)Lu3Ti tetrahedra, corners with two equivalent O(6)Lu2Ti2 tetrahedra, corners with two equivalent O(7)Lu3Mg tetrahedra, corners with three equivalent O(2)LuMg2Ti trigonal pyramids, and edges with two equivalent O(8)Lu3Ti tetrahedra. In the seventh O site, O(7) is bonded to one Mg(1), one Lu(1), and two equivalent Lu(3) atoms to form OLu3Mg tetrahedra that share  a cornercorner with one O(5)Lu2Ti2 tetrahedra,  a cornercorner with one O(3)Lu3Mg tetrahedra, corners with two equivalent O(6)Lu2Ti2 tetrahedra, corners with two equivalent O(7)Lu3Mg tetrahedra, corners with three equivalent O(10)LuMg2Ti trigonal pyramids, edges with two equivalent O(3)Lu3Mg tetrahedra, and edges with two equivalent O(2)LuMg2Ti trigonal pyramids. In the eighth O site, O(8) is bonded to one Lu(2), two equivalent Lu(4), and one Ti(1) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(5)Lu2Ti2 tetrahedra, corners with two equivalent O(8)Lu3Ti tetrahedra,  a cornercorner with one O(2)LuMg2Ti trigonal pyramid, edges with two equivalent O(6)Lu2Ti2 tetrahedra, and edges with two equivalent O(4)Lu3Ti tetrahedra. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Lu(2), one Lu(4), and one Ti(2) atom. In the tenth O site, O(10) is bonded to two equivalent Mg(1), one Lu(1), and one Ti(2) atom to form distorted OLuMg2Ti trigonal pyramids that share  a cornercorner with one O(4)Lu3Ti tetrahedra, corners with three equivalent O(5)Lu2Ti2 tetrahedra, corners with three equivalent O(7)Lu3Mg tetrahedra, corners with two equivalent O(10)LuMg2Ti trigonal pyramids, corners with two equivalent O(2)LuMg2Ti trigonal pyramids, edges with two equivalent O(3)Lu3Mg tetrahedra, and  an edgeedge with one O(2)LuMg2Ti trigonal pyramid. is represented by the CIF file [CIF]
data_Lu4MgTi2O10
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.872
_cell_length_b   5.831
_cell_length_c   11.478
_cell_angle_alpha   79.452
_cell_angle_beta   90.000
_cell_angle_gamma   70.605
_symmetry_Int_Tables_number   1
_cell_volume   239.825
_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
  Lu  Lu0  1  0.178  0.644  0.885  1.0
  Lu  Lu1  1  0.149  0.701  0.558  1.0
  Lu  Lu2  1  0.822  0.357  0.115  1.0
  Lu  Lu3  1  0.851  0.298  0.442  1.0
  Mg  Mg4  1  0.501  0.999  0.002  1.0
  Ti  Ti5  1  0.137  0.727  0.268  1.0
  Ti  Ti6  1  0.864  0.272  0.732  1.0
  O  O7  1  0.024  0.952  0.379  1.0
  O  O8  1  0.024  0.953  0.121  1.0
  O  O9  1  0.667  0.666  0.963  1.0
  O  O10  1  0.725  0.550  0.577  1.0
  O  O11  1  0.291  0.419  0.747  1.0
  O  O12  1  0.709  0.582  0.253  1.0
  O  O13  1  0.333  0.335  0.037  1.0
  O  O14  1  0.275  0.449  0.424  1.0
  O  O15  1  0.976  0.048  0.620  1.0
  O  O16  1  0.975  0.049  0.878  1.0
[/CIF]
.