The crystal structure described by MgLu4(CoO3)4 is Orthorhombic Perovskite-derived structured and crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 4-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(5), and one O(6) atom. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 8-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(5), one O(6), one O(7), and one O(9) atom. In the second Lu site, Lu(2) is bonded in a 8-coordinate geometry to one O(11), one O(12), one O(3), one O(5), one O(6), one O(7), one O(8), and one O(9) atom. In the third Lu site, Lu(3) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(12), one O(2), one O(4), one O(7), one O(8), and one O(9) atom. In the fourth Lu site, Lu(4) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(12), one O(2), one O(3), one O(4), one O(5), and one O(8) atom. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(5), one O(6), one O(8), and one O(9) atom. In the second Co site, Co(2) is bonded in a 5-coordinate geometry to one O(12), one O(2), one O(3), one O(4), one O(6), and one O(7) atom. In the third Co site, Co(3) is bonded to one O(10), one O(11), one O(12), one O(3), one O(4), and one O(7) atom to form corner-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 42-45°. In the fourth Co site, Co(4) is bonded to one O(1), one O(10), one O(11), one O(5), one O(8), and one O(9) atom to form corner-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 42-45°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Mg(1), one Lu(1), one Lu(3), one Lu(4), one Co(1), and one Co(4) atom. In the second O site, O(2) is bonded to one Lu(3), one Lu(4), one Co(1), and one Co(2) atom to form distorted OLu2Co2 tetrahedra that share corners with two equivalent O(10)Lu2Co2 trigonal pyramids,  an edgeedge with one O(7)Lu3Co2 trigonal bipyramid, and  an edgeedge with one O(9)Lu3Co2 trigonal bipyramid. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), one Lu(4), one Co(2), and one Co(3) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Mg(1), one Lu(1), one Lu(3), one Lu(4), one Co(2), and one Co(3) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), one Lu(4), one Co(1), and one Co(4) atom. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), one Co(1), and one Co(2) atom. In the seventh O site, O(7) is bonded to one Lu(1), one Lu(2), one Lu(3), one Co(2), and one Co(3) atom to form distorted OLu3Co2 trigonal bipyramids that share  a cornercorner with one O(9)Lu3Co2 trigonal bipyramid,  an edgeedge with one O(2)Lu2Co2 tetrahedra,  an edgeedge with one O(9)Lu3Co2 trigonal bipyramid, and  an edgeedge with one O(10)Lu2Co2 trigonal pyramid. In the eighth O site, O(8) is bonded in a 5-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), one Co(1), and one Co(4) atom. In the ninth O site, O(9) is bonded to one Lu(1), one Lu(2), one Lu(3), one Co(1), and one Co(4) atom to form distorted OLu3Co2 trigonal bipyramids that share  a cornercorner with one O(7)Lu3Co2 trigonal bipyramid,  an edgeedge with one O(2)Lu2Co2 tetrahedra,  an edgeedge with one O(7)Lu3Co2 trigonal bipyramid, and  an edgeedge with one O(10)Lu2Co2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Lu(3), one Lu(4), one Co(3), and one Co(4) atom to form distorted OLu2Co2 trigonal pyramids that share corners with two equivalent O(2)Lu2Co2 tetrahedra,  an edgeedge with one O(7)Lu3Co2 trigonal bipyramid, and  an edgeedge with one O(9)Lu3Co2 trigonal bipyramid. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), one Co(3), and one Co(4) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), one Co(2), and one Co(3) atom. is represented by the CIF card [CIF]
data_Lu4Mg(CoO3)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.210
_cell_length_b   5.963
_cell_length_c   7.105
_cell_angle_alpha   90.020
_cell_angle_beta   89.844
_cell_angle_gamma   93.474
_symmetry_Int_Tables_number   1
_cell_volume   220.337
_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  0.538  0.580  0.251  1.0
  Lu  Lu1  1  0.913  0.139  0.251  1.0
  Lu  Lu2  1  0.461  0.397  0.750  1.0
  Lu  Lu3  1  1.000  0.904  0.750  1.0
  Mg  Mg4  1  0.069  0.750  0.244  1.0
  Co  Co5  1  0.001  0.474  0.518  1.0
  Co  Co6  1  1.000  0.470  0.981  1.0
  Co  Co7  1  0.485  0.997  0.998  1.0
  Co  Co8  1  0.485  0.996  0.502  1.0
  O  O9  1  0.318  0.678  0.547  1.0
  O  O10  1  0.860  0.542  0.750  1.0
  O  O11  1  0.801  0.831  0.063  1.0
  O  O12  1  0.315  0.677  0.955  1.0
  O  O13  1  0.804  0.829  0.435  1.0
  O  O14  1  0.133  0.444  0.251  1.0
  O  O15  1  0.665  0.308  0.053  1.0
  O  O16  1  0.186  0.161  0.559  1.0
  O  O17  1  0.665  0.309  0.447  1.0
  O  O18  1  0.618  0.046  0.750  1.0
  O  O19  1  0.361  0.953  0.251  1.0
  O  O20  1  0.186  0.160  0.942  1.0
[/CIF]
.
The crystal structure described by MgLu4(CoO3)4 is Orthorhombic Perovskite-derived structured and crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 4-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(5), and one O(6) atom. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 8-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(5), one O(6), one O(7), and one O(9) atom. In the second Lu site, Lu(2) is bonded in a 8-coordinate geometry to one O(11), one O(12), one O(3), one O(5), one O(6), one O(7), one O(8), and one O(9) atom. In the third Lu site, Lu(3) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(12), one O(2), one O(4), one O(7), one O(8), and one O(9) atom. In the fourth Lu site, Lu(4) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(12), one O(2), one O(3), one O(4), one O(5), and one O(8) atom. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(5), one O(6), one O(8), and one O(9) atom. In the second Co site, Co(2) is bonded in a 5-coordinate geometry to one O(12), one O(2), one O(3), one O(4), one O(6), and one O(7) atom. In the third Co site, Co(3) is bonded to one O(10), one O(11), one O(12), one O(3), one O(4), and one O(7) atom to form corner-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 42-45°. In the fourth Co site, Co(4) is bonded to one O(1), one O(10), one O(11), one O(5), one O(8), and one O(9) atom to form corner-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 42-45°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Mg(1), one Lu(1), one Lu(3), one Lu(4), one Co(1), and one Co(4) atom. In the second O site, O(2) is bonded to one Lu(3), one Lu(4), one Co(1), and one Co(2) atom to form distorted OLu2Co2 tetrahedra that share corners with two equivalent O(10)Lu2Co2 trigonal pyramids,  an edgeedge with one O(7)Lu3Co2 trigonal bipyramid, and  an edgeedge with one O(9)Lu3Co2 trigonal bipyramid. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), one Lu(4), one Co(2), and one Co(3) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Mg(1), one Lu(1), one Lu(3), one Lu(4), one Co(2), and one Co(3) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), one Lu(4), one Co(1), and one Co(4) atom. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), one Co(1), and one Co(2) atom. In the seventh O site, O(7) is bonded to one Lu(1), one Lu(2), one Lu(3), one Co(2), and one Co(3) atom to form distorted OLu3Co2 trigonal bipyramids that share  a cornercorner with one O(9)Lu3Co2 trigonal bipyramid,  an edgeedge with one O(2)Lu2Co2 tetrahedra,  an edgeedge with one O(9)Lu3Co2 trigonal bipyramid, and  an edgeedge with one O(10)Lu2Co2 trigonal pyramid. In the eighth O site, O(8) is bonded in a 5-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), one Co(1), and one Co(4) atom. In the ninth O site, O(9) is bonded to one Lu(1), one Lu(2), one Lu(3), one Co(1), and one Co(4) atom to form distorted OLu3Co2 trigonal bipyramids that share  a cornercorner with one O(7)Lu3Co2 trigonal bipyramid,  an edgeedge with one O(2)Lu2Co2 tetrahedra,  an edgeedge with one O(7)Lu3Co2 trigonal bipyramid, and  an edgeedge with one O(10)Lu2Co2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Lu(3), one Lu(4), one Co(3), and one Co(4) atom to form distorted OLu2Co2 trigonal pyramids that share corners with two equivalent O(2)Lu2Co2 tetrahedra,  an edgeedge with one O(7)Lu3Co2 trigonal bipyramid, and  an edgeedge with one O(9)Lu3Co2 trigonal bipyramid. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), one Co(3), and one Co(4) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), one Co(2), and one Co(3) atom. is represented by the CIF card [CIF]
data_Lu4Mg(CoO3)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.210
_cell_length_b   5.963
_cell_length_c   7.105
_cell_angle_alpha   90.020
_cell_angle_beta   89.844
_cell_angle_gamma   93.474
_symmetry_Int_Tables_number   1
_cell_volume   220.337
_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  0.538  0.580  0.251  1.0
  Lu  Lu1  1  0.913  0.139  0.251  1.0
  Lu  Lu2  1  0.461  0.397  0.750  1.0
  Lu  Lu3  1  1.000  0.904  0.750  1.0
  Mg  Mg4  1  0.069  0.750  0.244  1.0
  Co  Co5  1  0.001  0.474  0.518  1.0
  Co  Co6  1  1.000  0.470  0.981  1.0
  Co  Co7  1  0.485  0.997  0.998  1.0
  Co  Co8  1  0.485  0.996  0.502  1.0
  O  O9  1  0.318  0.678  0.547  1.0
  O  O10  1  0.860  0.542  0.750  1.0
  O  O11  1  0.801  0.831  0.063  1.0
  O  O12  1  0.315  0.677  0.955  1.0
  O  O13  1  0.804  0.829  0.435  1.0
  O  O14  1  0.133  0.444  0.251  1.0
  O  O15  1  0.665  0.308  0.053  1.0
  O  O16  1  0.186  0.161  0.559  1.0
  O  O17  1  0.665  0.309  0.447  1.0
  O  O18  1  0.618  0.046  0.750  1.0
  O  O19  1  0.361  0.953  0.251  1.0
  O  O20  1  0.186  0.160  0.942  1.0
[/CIF]
.