The structure described by MgLu4Ti2O10 crystallizes in the monoclinic Pm space group. Mg(1) is bonded to one O(4) and four equivalent O(1) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Lu(1)O6 pentagonal pyramids, edges with two equivalent Mg(1)O5 square pyramids, and faces with two equivalent Ti(1)O6 pentagonal pyramids. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(3), one O(5), one O(6), and two equivalent O(2) atoms to form distorted LuO6 pentagonal pyramids that share  a cornercorner with one Ti(2)O6 octahedra, corners with three equivalent Lu(1)O6 pentagonal pyramids, corners with two equivalent Mg(1)O5 square pyramids, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Ti(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 30°. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(4), one O(6), and two equivalent O(5) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms to form TiO6 pentagonal pyramids that share corners with two equivalent Ti(1)O6 pentagonal pyramids, edges with two equivalent Lu(1)O6 pentagonal pyramids, and faces with two equivalent Mg(1)O5 square pyramids. In the second Ti site, Ti(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Lu(1)O6 pentagonal pyramids, and edges with four equivalent Lu(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 34°. There are six inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Lu(1), one Lu(2), and one Ti(1) atom to form OLu2Mg2Ti trigonal bipyramids that share  a cornercorner with one O(3)Lu2Ti2 tetrahedra, corners with three equivalent O(5)Lu3Ti tetrahedra,  a cornercorner with one O(4)Lu2MgTi2 trigonal bipyramid, corners with four equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with three equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(5)Lu3Ti tetrahedra, edges with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, and  a faceface with one O(1)Lu2Mg2Ti trigonal bipyramid. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Ti(2) atom to form OLu3Ti trigonal pyramids that share  a cornercorner with one O(4)Lu2MgTi2 trigonal bipyramid, corners with three equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with three equivalent O(2)Lu3Ti trigonal pyramids, edges with two equivalent O(3)Lu2Ti2 tetrahedra, and edges with two equivalent O(5)Lu3Ti tetrahedra. In the third O site, O(3) is bonded to two equivalent Lu(1) and two equivalent Ti(2) atoms to form distorted OLu2Ti2 tetrahedra that share corners with two equivalent O(3)Lu2Ti2 tetrahedra, corners with two equivalent O(5)Lu3Ti tetrahedra, corners with two equivalent O(1)Lu2Mg2Ti trigonal bipyramids, and edges with four equivalent O(2)Lu3Ti trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), two equivalent Lu(2), and two equivalent Ti(1) atoms to form OLu2MgTi2 trigonal bipyramids that share corners with two equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, corners with two equivalent O(2)Lu3Ti trigonal pyramids, edges with four equivalent O(5)Lu3Ti tetrahedra, and edges with four equivalent O(1)Lu2Mg2Ti trigonal bipyramids. In the fifth O site, O(5) is bonded to one Lu(1), two equivalent Lu(2), and one Ti(1) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(3)Lu2Ti2 tetrahedra, corners with three equivalent O(5)Lu3Ti tetrahedra, corners with three equivalent O(1)Lu2Mg2Ti trigonal bipyramids,  an edgeedge with one O(1)Lu2Mg2Ti trigonal bipyramid, edges with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, and edges with two equivalent O(2)Lu3Ti trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(2), and one Ti(2) atom. is represented by the CIF file [CIF]
data_Lu4MgTi2O10
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.048
_cell_length_b   5.782
_cell_length_c   10.536
_cell_angle_alpha   89.998
_cell_angle_beta   89.999
_cell_angle_gamma   69.478
_symmetry_Int_Tables_number   1
_cell_volume   230.961
_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  0.137  0.726  0.928  1.0
  Lu  Lu1  1  0.137  0.726  0.572  1.0
  Lu  Lu2  1  0.856  0.290  0.058  1.0
  Lu  Lu3  1  0.856  0.290  0.442  1.0
  Mg  Mg4  1  0.533  0.947  0.250  1.0
  Ti  Ti5  1  0.212  0.577  0.250  1.0
  Ti  Ti6  1  0.818  0.364  0.750  1.0
  O  O7  1  0.042  0.909  0.375  1.0
  O  O8  1  0.042  0.909  0.125  1.0
  O  O9  1  0.700  0.600  0.910  1.0
  O  O10  1  0.700  0.600  0.590  1.0
  O  O11  1  0.261  0.478  0.750  1.0
  O  O12  1  0.716  0.568  0.250  1.0
  O  O13  1  0.292  0.418  0.073  1.0
  O  O14  1  0.292  0.418  0.427  1.0
  O  O15  1  0.946  0.110  0.623  1.0
  O  O16  1  0.945  0.110  0.877  1.0
[/CIF]
.
The structure described by MgLu4Ti2O10 crystallizes in the monoclinic Pm space group. Mg(1) is bonded to one O(4) and four equivalent O(1) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Lu(1)O6 pentagonal pyramids, edges with two equivalent Mg(1)O5 square pyramids, and faces with two equivalent Ti(1)O6 pentagonal pyramids. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(3), one O(5), one O(6), and two equivalent O(2) atoms to form distorted LuO6 pentagonal pyramids that share  a cornercorner with one Ti(2)O6 octahedra, corners with three equivalent Lu(1)O6 pentagonal pyramids, corners with two equivalent Mg(1)O5 square pyramids, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Ti(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 30°. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(4), one O(6), and two equivalent O(5) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms to form TiO6 pentagonal pyramids that share corners with two equivalent Ti(1)O6 pentagonal pyramids, edges with two equivalent Lu(1)O6 pentagonal pyramids, and faces with two equivalent Mg(1)O5 square pyramids. In the second Ti site, Ti(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Lu(1)O6 pentagonal pyramids, and edges with four equivalent Lu(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 34°. There are six inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Lu(1), one Lu(2), and one Ti(1) atom to form OLu2Mg2Ti trigonal bipyramids that share  a cornercorner with one O(3)Lu2Ti2 tetrahedra, corners with three equivalent O(5)Lu3Ti tetrahedra,  a cornercorner with one O(4)Lu2MgTi2 trigonal bipyramid, corners with four equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with three equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(5)Lu3Ti tetrahedra, edges with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, and  a faceface with one O(1)Lu2Mg2Ti trigonal bipyramid. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Ti(2) atom to form OLu3Ti trigonal pyramids that share  a cornercorner with one O(4)Lu2MgTi2 trigonal bipyramid, corners with three equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with three equivalent O(2)Lu3Ti trigonal pyramids, edges with two equivalent O(3)Lu2Ti2 tetrahedra, and edges with two equivalent O(5)Lu3Ti tetrahedra. In the third O site, O(3) is bonded to two equivalent Lu(1) and two equivalent Ti(2) atoms to form distorted OLu2Ti2 tetrahedra that share corners with two equivalent O(3)Lu2Ti2 tetrahedra, corners with two equivalent O(5)Lu3Ti tetrahedra, corners with two equivalent O(1)Lu2Mg2Ti trigonal bipyramids, and edges with four equivalent O(2)Lu3Ti trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), two equivalent Lu(2), and two equivalent Ti(1) atoms to form OLu2MgTi2 trigonal bipyramids that share corners with two equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, corners with two equivalent O(2)Lu3Ti trigonal pyramids, edges with four equivalent O(5)Lu3Ti tetrahedra, and edges with four equivalent O(1)Lu2Mg2Ti trigonal bipyramids. In the fifth O site, O(5) is bonded to one Lu(1), two equivalent Lu(2), and one Ti(1) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(3)Lu2Ti2 tetrahedra, corners with three equivalent O(5)Lu3Ti tetrahedra, corners with three equivalent O(1)Lu2Mg2Ti trigonal bipyramids,  an edgeedge with one O(1)Lu2Mg2Ti trigonal bipyramid, edges with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, and edges with two equivalent O(2)Lu3Ti trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(2), and one Ti(2) atom. is represented by the CIF file [CIF]
data_Lu4MgTi2O10
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.048
_cell_length_b   5.782
_cell_length_c   10.536
_cell_angle_alpha   89.998
_cell_angle_beta   89.999
_cell_angle_gamma   69.478
_symmetry_Int_Tables_number   1
_cell_volume   230.961
_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  0.137  0.726  0.928  1.0
  Lu  Lu1  1  0.137  0.726  0.572  1.0
  Lu  Lu2  1  0.856  0.290  0.058  1.0
  Lu  Lu3  1  0.856  0.290  0.442  1.0
  Mg  Mg4  1  0.533  0.947  0.250  1.0
  Ti  Ti5  1  0.212  0.577  0.250  1.0
  Ti  Ti6  1  0.818  0.364  0.750  1.0
  O  O7  1  0.042  0.909  0.375  1.0
  O  O8  1  0.042  0.909  0.125  1.0
  O  O9  1  0.700  0.600  0.910  1.0
  O  O10  1  0.700  0.600  0.590  1.0
  O  O11  1  0.261  0.478  0.750  1.0
  O  O12  1  0.716  0.568  0.250  1.0
  O  O13  1  0.292  0.418  0.073  1.0
  O  O14  1  0.292  0.418  0.427  1.0
  O  O15  1  0.946  0.110  0.623  1.0
  O  O16  1  0.945  0.110  0.877  1.0
[/CIF]
.