The compound described by Mg14TiCuO16 is Molybdenum Carbide MAX Phase-derived structured and crystallizes in the tetragonal P4/mmm space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Cu(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Cu(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the third Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-6°. In the fourth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Cu(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. Ti(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. Cu(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form CuO6 octahedra that share corners with two equivalent Cu(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), and one Cu(1) atom to form OMg5Cu octahedra that share corners with two equivalent O(2)Mg5Ti octahedra, corners with four equivalent O(1)Mg5Cu octahedra, edges with two equivalent O(4)Mg4Cu2 octahedra, edges with two equivalent O(1)Mg5Cu octahedra, edges with two equivalent O(2)Mg5Ti octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Ti(1) atom to form OMg5Ti octahedra that share corners with two equivalent O(1)Mg5Cu octahedra, corners with four equivalent O(2)Mg5Ti octahedra, edges with two equivalent O(6)Mg4Ti2 octahedra, edges with two equivalent O(1)Mg5Cu octahedra, edges with two equivalent O(2)Mg5Ti octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the third O site, O(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)Mg4Cu2 octahedra,  an edgeedge with one O(6)Mg4Ti2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)Mg5Cu octahedra, and edges with four equivalent O(2)Mg5Ti octahedra. The corner-sharing octahedral tilt angles range from 2-5°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent Cu(1) atoms to form OMg4Cu2 octahedra that share corners with two equivalent O(4)Mg4Cu2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)Mg5Cu octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg4Cu2 octahedra, corners with two equivalent O(6)Mg4Ti2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)Mg5Cu octahedra, edges with four equivalent O(2)Mg5Ti octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to four equivalent Mg(3) and two equivalent Ti(1) atoms to form OMg4Ti2 octahedra that share corners with two equivalent O(6)Mg4Ti2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Ti octahedra. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_Mg14TiCuO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.567
_cell_length_b   8.567
_cell_length_c   4.238
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   311.031
_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  0.000  0.500  0.000  1.0
  Mg  Mg1  1  0.500  0.000  0.000  1.0
  Mg  Mg2  1  0.000  0.246  0.500  1.0
  Mg  Mg3  1  0.000  0.754  0.500  1.0
  Mg  Mg4  1  0.500  0.245  0.500  1.0
  Mg  Mg5  1  0.500  0.755  0.500  1.0
  Mg  Mg6  1  0.246  0.000  0.500  1.0
  Mg  Mg7  1  0.245  0.500  0.500  1.0
  Mg  Mg8  1  0.754  0.000  0.500  1.0
  Mg  Mg9  1  0.755  0.500  0.500  1.0
  Mg  Mg10  1  0.243  0.243  0.000  1.0
  Mg  Mg11  1  0.243  0.757  0.000  1.0
  Mg  Mg12  1  0.757  0.243  0.000  1.0
  Mg  Mg13  1  0.757  0.757  0.000  1.0
  Ti  Ti14  1  0.500  0.500  0.000  1.0
  Cu  Cu15  1  0.000  0.000  0.000  1.0
  O  O16  1  0.266  0.000  0.000  1.0
  O  O17  1  0.257  0.500  0.000  1.0
  O  O18  1  0.734  0.000  0.000  1.0
  O  O19  1  0.743  0.500  0.000  1.0
  O  O20  1  0.251  0.251  0.500  1.0
  O  O21  1  0.251  0.749  0.500  1.0
  O  O22  1  0.749  0.251  0.500  1.0
  O  O23  1  0.749  0.749  0.500  1.0
  O  O24  1  0.000  0.000  0.500  1.0
  O  O25  1  0.000  0.500  0.500  1.0
  O  O26  1  0.500  0.000  0.500  1.0
  O  O27  1  0.500  0.500  0.500  1.0
  O  O28  1  0.000  0.266  0.000  1.0
  O  O29  1  0.000  0.734  0.000  1.0
  O  O30  1  0.500  0.257  0.000  1.0
  O  O31  1  0.500  0.743  0.000  1.0
[/CIF]
.
The compound described by Mg14TiCuO16 is Molybdenum Carbide MAX Phase-derived structured and crystallizes in the tetragonal P4/mmm space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Cu(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Cu(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the third Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-6°. In the fourth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Cu(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. Ti(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. Cu(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form CuO6 octahedra that share corners with two equivalent Cu(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), and one Cu(1) atom to form OMg5Cu octahedra that share corners with two equivalent O(2)Mg5Ti octahedra, corners with four equivalent O(1)Mg5Cu octahedra, edges with two equivalent O(4)Mg4Cu2 octahedra, edges with two equivalent O(1)Mg5Cu octahedra, edges with two equivalent O(2)Mg5Ti octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Ti(1) atom to form OMg5Ti octahedra that share corners with two equivalent O(1)Mg5Cu octahedra, corners with four equivalent O(2)Mg5Ti octahedra, edges with two equivalent O(6)Mg4Ti2 octahedra, edges with two equivalent O(1)Mg5Cu octahedra, edges with two equivalent O(2)Mg5Ti octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the third O site, O(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)Mg4Cu2 octahedra,  an edgeedge with one O(6)Mg4Ti2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)Mg5Cu octahedra, and edges with four equivalent O(2)Mg5Ti octahedra. The corner-sharing octahedral tilt angles range from 2-5°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent Cu(1) atoms to form OMg4Cu2 octahedra that share corners with two equivalent O(4)Mg4Cu2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)Mg5Cu octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg4Cu2 octahedra, corners with two equivalent O(6)Mg4Ti2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)Mg5Cu octahedra, edges with four equivalent O(2)Mg5Ti octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to four equivalent Mg(3) and two equivalent Ti(1) atoms to form OMg4Ti2 octahedra that share corners with two equivalent O(6)Mg4Ti2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Ti octahedra. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_Mg14TiCuO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.567
_cell_length_b   8.567
_cell_length_c   4.238
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   311.031
_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  0.000  0.500  0.000  1.0
  Mg  Mg1  1  0.500  0.000  0.000  1.0
  Mg  Mg2  1  0.000  0.246  0.500  1.0
  Mg  Mg3  1  0.000  0.754  0.500  1.0
  Mg  Mg4  1  0.500  0.245  0.500  1.0
  Mg  Mg5  1  0.500  0.755  0.500  1.0
  Mg  Mg6  1  0.246  0.000  0.500  1.0
  Mg  Mg7  1  0.245  0.500  0.500  1.0
  Mg  Mg8  1  0.754  0.000  0.500  1.0
  Mg  Mg9  1  0.755  0.500  0.500  1.0
  Mg  Mg10  1  0.243  0.243  0.000  1.0
  Mg  Mg11  1  0.243  0.757  0.000  1.0
  Mg  Mg12  1  0.757  0.243  0.000  1.0
  Mg  Mg13  1  0.757  0.757  0.000  1.0
  Ti  Ti14  1  0.500  0.500  0.000  1.0
  Cu  Cu15  1  0.000  0.000  0.000  1.0
  O  O16  1  0.266  0.000  0.000  1.0
  O  O17  1  0.257  0.500  0.000  1.0
  O  O18  1  0.734  0.000  0.000  1.0
  O  O19  1  0.743  0.500  0.000  1.0
  O  O20  1  0.251  0.251  0.500  1.0
  O  O21  1  0.251  0.749  0.500  1.0
  O  O22  1  0.749  0.251  0.500  1.0
  O  O23  1  0.749  0.749  0.500  1.0
  O  O24  1  0.000  0.000  0.500  1.0
  O  O25  1  0.000  0.500  0.500  1.0
  O  O26  1  0.500  0.000  0.500  1.0
  O  O27  1  0.500  0.500  0.500  1.0
  O  O28  1  0.000  0.266  0.000  1.0
  O  O29  1  0.000  0.734  0.000  1.0
  O  O30  1  0.500  0.257  0.000  1.0
  O  O31  1  0.500  0.743  0.000  1.0
[/CIF]
.