The material described by LiMg14BiO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. Li(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form LiO6 octahedra that share corners with two equivalent Li(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 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 Li(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Bi(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 Li(1)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, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. 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 Bi(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. 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 Li(1)O6 octahedra,  an edgeedge with one Bi(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 1-10°. Bi(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form BiO6 octahedra that share corners with two equivalent Bi(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. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OLiMg5 octahedra that share corners with two equivalent O(2)Mg5Bi octahedra, corners with four equivalent O(1)LiMg5 octahedra, edges with two equivalent O(4)Li2Mg4 octahedra, edges with two equivalent O(1)LiMg5 octahedra, edges with two equivalent O(2)Mg5Bi 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 0-7°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Bi(1) atom to form OMg5Bi octahedra that share corners with two equivalent O(1)LiMg5 octahedra, corners with four equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(1)LiMg5 octahedra, edges with two equivalent O(6)Mg4Bi2 octahedra, edges with two equivalent O(2)Mg5Bi 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 0-4°. 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)Li2Mg4 octahedra,  an edgeedge with one O(6)Mg4Bi2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)LiMg5 octahedra, and edges with four equivalent O(2)Mg5Bi octahedra. The corner-sharing octahedral tilt angles range from 5-10°. In the fourth O site, O(4) is bonded to two equivalent Li(1) and four equivalent Mg(2) atoms to form OLi2Mg4 octahedra that share corners with two equivalent O(4)Li2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)LiMg5 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)Li2Mg4 octahedra, corners with two equivalent O(6)Mg4Bi2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)LiMg5 octahedra, edges with four equivalent O(2)Mg5Bi 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 Bi(1) atoms to form OMg4Bi2 octahedra that share corners with two equivalent O(6)Mg4Bi2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Bi octahedra. The corner-sharing octahedra are not tilted. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiMg14BiO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.677
_cell_length_b   8.677
_cell_length_c   4.370
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   329.068
_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
  Li  Li0  1  0.000  0.000  0.000  1.0
  Mg  Mg1  1  0.000  0.500  0.000  1.0
  Mg  Mg2  1  0.500  0.000  0.000  1.0
  Mg  Mg3  1  0.000  0.241  0.500  1.0
  Mg  Mg4  1  0.000  0.759  0.500  1.0
  Mg  Mg5  1  0.500  0.233  0.500  1.0
  Mg  Mg6  1  0.500  0.767  0.500  1.0
  Mg  Mg7  1  0.241  0.000  0.500  1.0
  Mg  Mg8  1  0.233  0.500  0.500  1.0
  Mg  Mg9  1  0.759  0.000  0.500  1.0
  Mg  Mg10  1  0.767  0.500  0.500  1.0
  Mg  Mg11  1  0.237  0.237  0.000  1.0
  Mg  Mg12  1  0.237  0.763  0.000  1.0
  Mg  Mg13  1  0.763  0.237  0.000  1.0
  Mg  Mg14  1  0.763  0.763  0.000  1.0
  Bi  Bi15  1  0.500  0.500  0.000  1.0
  O  O16  1  0.256  0.000  0.000  1.0
  O  O17  1  0.234  0.500  0.000  1.0
  O  O18  1  0.744  0.000  0.000  1.0
  O  O19  1  0.766  0.500  0.000  1.0
  O  O20  1  0.252  0.252  0.500  1.0
  O  O21  1  0.252  0.748  0.500  1.0
  O  O22  1  0.748  0.252  0.500  1.0
  O  O23  1  0.748  0.748  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  0.256  0.000  1.0
  O  O29  1  0.000  0.744  0.000  1.0
  O  O30  1  0.500  0.234  0.000  1.0
  O  O31  1  0.500  0.766  0.000  1.0
[/CIF]
.
The material described by LiMg14BiO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. Li(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form LiO6 octahedra that share corners with two equivalent Li(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 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 Li(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Bi(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 Li(1)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, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. 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 Bi(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. 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 Li(1)O6 octahedra,  an edgeedge with one Bi(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 1-10°. Bi(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form BiO6 octahedra that share corners with two equivalent Bi(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. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OLiMg5 octahedra that share corners with two equivalent O(2)Mg5Bi octahedra, corners with four equivalent O(1)LiMg5 octahedra, edges with two equivalent O(4)Li2Mg4 octahedra, edges with two equivalent O(1)LiMg5 octahedra, edges with two equivalent O(2)Mg5Bi 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 0-7°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Bi(1) atom to form OMg5Bi octahedra that share corners with two equivalent O(1)LiMg5 octahedra, corners with four equivalent O(2)Mg5Bi octahedra, edges with two equivalent O(1)LiMg5 octahedra, edges with two equivalent O(6)Mg4Bi2 octahedra, edges with two equivalent O(2)Mg5Bi 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 0-4°. 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)Li2Mg4 octahedra,  an edgeedge with one O(6)Mg4Bi2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)LiMg5 octahedra, and edges with four equivalent O(2)Mg5Bi octahedra. The corner-sharing octahedral tilt angles range from 5-10°. In the fourth O site, O(4) is bonded to two equivalent Li(1) and four equivalent Mg(2) atoms to form OLi2Mg4 octahedra that share corners with two equivalent O(4)Li2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)LiMg5 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)Li2Mg4 octahedra, corners with two equivalent O(6)Mg4Bi2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)LiMg5 octahedra, edges with four equivalent O(2)Mg5Bi 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 Bi(1) atoms to form OMg4Bi2 octahedra that share corners with two equivalent O(6)Mg4Bi2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Bi octahedra. The corner-sharing octahedra are not tilted. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiMg14BiO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.677
_cell_length_b   8.677
_cell_length_c   4.370
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   329.068
_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
  Li  Li0  1  0.000  0.000  0.000  1.0
  Mg  Mg1  1  0.000  0.500  0.000  1.0
  Mg  Mg2  1  0.500  0.000  0.000  1.0
  Mg  Mg3  1  0.000  0.241  0.500  1.0
  Mg  Mg4  1  0.000  0.759  0.500  1.0
  Mg  Mg5  1  0.500  0.233  0.500  1.0
  Mg  Mg6  1  0.500  0.767  0.500  1.0
  Mg  Mg7  1  0.241  0.000  0.500  1.0
  Mg  Mg8  1  0.233  0.500  0.500  1.0
  Mg  Mg9  1  0.759  0.000  0.500  1.0
  Mg  Mg10  1  0.767  0.500  0.500  1.0
  Mg  Mg11  1  0.237  0.237  0.000  1.0
  Mg  Mg12  1  0.237  0.763  0.000  1.0
  Mg  Mg13  1  0.763  0.237  0.000  1.0
  Mg  Mg14  1  0.763  0.763  0.000  1.0
  Bi  Bi15  1  0.500  0.500  0.000  1.0
  O  O16  1  0.256  0.000  0.000  1.0
  O  O17  1  0.234  0.500  0.000  1.0
  O  O18  1  0.744  0.000  0.000  1.0
  O  O19  1  0.766  0.500  0.000  1.0
  O  O20  1  0.252  0.252  0.500  1.0
  O  O21  1  0.252  0.748  0.500  1.0
  O  O22  1  0.748  0.252  0.500  1.0
  O  O23  1  0.748  0.748  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  0.256  0.000  1.0
  O  O29  1  0.000  0.744  0.000  1.0
  O  O30  1  0.500  0.234  0.000  1.0
  O  O31  1  0.500  0.766  0.000  1.0
[/CIF]
.