The material described by Na4MgTi3O8 is Caswellsilverite-derived structured and crystallizes in the triclinic P1 space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form NaO6 octahedra that share corners with six equivalent Na(4)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-17°. In the second Na site, Na(2) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form NaO6 octahedra that share corners with six equivalent Ti(3)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-12°. In the third Na site, Na(3) is bonded to one O(1), one O(2), one O(4), one O(6), one O(7), and one O(8) atom to form NaO6 octahedra that share corners with six equivalent Ti(1)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the fourth Na site, Na(4) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form NaO6 octahedra that share corners with six equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-17°. Mg(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(7), and one O(8) atom to form MgO6 octahedra that share corners with six equivalent Ti(2)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(2), one O(4), one O(6), one O(7), and one O(8) atom to form TiO6 octahedra that share corners with six equivalent Na(3)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the second Ti site, Ti(2) is bonded to one O(1), one O(2), one O(3), one O(5), one O(7), and one O(8) atom to form TiO6 octahedra that share corners with six equivalent Mg(1)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. In the third Ti site, Ti(3) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form TiO6 octahedra that share corners with six equivalent Na(2)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-12°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Na(2), one Na(3), one Mg(1), one Ti(1), one Ti(2), and one Ti(3) atom to form ONa2MgTi3 octahedra that share corners with six equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 1-5°. In the second O site, O(2) is bonded to one Na(1), one Na(3), one Na(4), one Mg(1), one Ti(1), and one Ti(2) atom to form ONa3MgTi2 octahedra that share corners with six equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the third O site, O(3) is bonded to one Na(1), one Na(2), one Na(4), one Mg(1), one Ti(2), and one Ti(3) atom to form ONa3MgTi2 octahedra that share corners with six equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the fourth O site, O(4) is bonded to one Na(1), one Na(2), one Na(3), one Na(4), one Ti(1), and one Ti(3) atom to form ONa4Ti2 octahedra that share corners with six equivalent O(6)Na4Ti2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, and edges with two equivalent O(7)Na3MgTi2 octahedra. The corner-sharing octahedral tilt angles range from 1-2°. In the fifth O site, O(5) is bonded to one Na(1), one Na(2), one Na(4), one Mg(1), one Ti(2), and one Ti(3) atom to form ONa3MgTi2 octahedra that share corners with six equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the sixth O site, O(6) is bonded to one Na(1), one Na(2), one Na(3), one Na(4), one Ti(1), and one Ti(3) atom to form ONa4Ti2 octahedra that share corners with six equivalent O(4)Na4Ti2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, and edges with two equivalent O(7)Na3MgTi2 octahedra. The corner-sharing octahedral tilt angles range from 1-2°. In the seventh O site, O(7) is bonded to one Na(1), one Na(3), one Na(4), one Mg(1), one Ti(1), and one Ti(2) atom to form ONa3MgTi2 octahedra that share corners with six equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the eighth O site, O(8) is bonded to one Na(2), one Na(3), one Mg(1), one Ti(1), one Ti(2), and one Ti(3) atom to form ONa2MgTi3 octahedra that share corners with six equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 1-5°. is represented by the CIF card [CIF]
data_Na4MgTi3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.329
_cell_length_b   6.179
_cell_length_c   6.192
_cell_angle_alpha   59.207
_cell_angle_beta   118.917
_cell_angle_gamma   90.044
_symmetry_Int_Tables_number   1
_cell_volume   171.982
_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
  Na  Na0  1  0.108  0.597  0.740  1.0
  Na  Na1  1  0.117  0.592  0.242  1.0
  Na  Na2  1  0.109  0.097  0.739  1.0
  Na  Na3  1  0.606  0.102  0.734  1.0
  Mg  Mg4  1  0.097  0.090  0.232  1.0
  Ti  Ti5  1  0.611  0.599  0.747  1.0
  Ti  Ti6  1  0.615  0.597  0.235  1.0
  Ti  Ti7  1  0.606  0.097  0.239  1.0
  O  O8  1  0.381  0.851  0.263  1.0
  O  O9  1  0.381  0.827  0.744  1.0
  O  O10  1  0.831  0.856  0.237  1.0
  O  O11  1  0.811  0.847  0.693  1.0
  O  O12  1  0.397  0.344  0.237  1.0
  O  O13  1  0.408  0.347  0.790  1.0
  O  O14  1  0.830  0.376  0.724  1.0
  O  O15  1  0.843  0.342  0.218  1.0
[/CIF]
.
The material described by Na4MgTi3O8 is Caswellsilverite-derived structured and crystallizes in the triclinic P1 space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form NaO6 octahedra that share corners with six equivalent Na(4)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-17°. In the second Na site, Na(2) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form NaO6 octahedra that share corners with six equivalent Ti(3)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-12°. In the third Na site, Na(3) is bonded to one O(1), one O(2), one O(4), one O(6), one O(7), and one O(8) atom to form NaO6 octahedra that share corners with six equivalent Ti(1)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the fourth Na site, Na(4) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form NaO6 octahedra that share corners with six equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-17°. Mg(1) is bonded to one O(1), one O(2), one O(3), one O(5), one O(7), and one O(8) atom to form MgO6 octahedra that share corners with six equivalent Ti(2)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(2), one O(4), one O(6), one O(7), and one O(8) atom to form TiO6 octahedra that share corners with six equivalent Na(3)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the second Ti site, Ti(2) is bonded to one O(1), one O(2), one O(3), one O(5), one O(7), and one O(8) atom to form TiO6 octahedra that share corners with six equivalent Mg(1)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(2)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. In the third Ti site, Ti(3) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form TiO6 octahedra that share corners with six equivalent Na(2)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Na(3)O6 octahedra, edges with two equivalent Na(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-12°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Na(2), one Na(3), one Mg(1), one Ti(1), one Ti(2), and one Ti(3) atom to form ONa2MgTi3 octahedra that share corners with six equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 1-5°. In the second O site, O(2) is bonded to one Na(1), one Na(3), one Na(4), one Mg(1), one Ti(1), and one Ti(2) atom to form ONa3MgTi2 octahedra that share corners with six equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the third O site, O(3) is bonded to one Na(1), one Na(2), one Na(4), one Mg(1), one Ti(2), and one Ti(3) atom to form ONa3MgTi2 octahedra that share corners with six equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the fourth O site, O(4) is bonded to one Na(1), one Na(2), one Na(3), one Na(4), one Ti(1), and one Ti(3) atom to form ONa4Ti2 octahedra that share corners with six equivalent O(6)Na4Ti2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, and edges with two equivalent O(7)Na3MgTi2 octahedra. The corner-sharing octahedral tilt angles range from 1-2°. In the fifth O site, O(5) is bonded to one Na(1), one Na(2), one Na(4), one Mg(1), one Ti(2), and one Ti(3) atom to form ONa3MgTi2 octahedra that share corners with six equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the sixth O site, O(6) is bonded to one Na(1), one Na(2), one Na(3), one Na(4), one Ti(1), and one Ti(3) atom to form ONa4Ti2 octahedra that share corners with six equivalent O(4)Na4Ti2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, and edges with two equivalent O(7)Na3MgTi2 octahedra. The corner-sharing octahedral tilt angles range from 1-2°. In the seventh O site, O(7) is bonded to one Na(1), one Na(3), one Na(4), one Mg(1), one Ti(1), and one Ti(2) atom to form ONa3MgTi2 octahedra that share corners with six equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(8)Na2MgTi3 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the eighth O site, O(8) is bonded to one Na(2), one Na(3), one Mg(1), one Ti(1), one Ti(2), and one Ti(3) atom to form ONa2MgTi3 octahedra that share corners with six equivalent O(1)Na2MgTi3 octahedra, edges with two equivalent O(2)Na3MgTi2 octahedra, edges with two equivalent O(3)Na3MgTi2 octahedra, edges with two equivalent O(5)Na3MgTi2 octahedra, edges with two equivalent O(7)Na3MgTi2 octahedra, edges with two equivalent O(4)Na4Ti2 octahedra, and edges with two equivalent O(6)Na4Ti2 octahedra. The corner-sharing octahedral tilt angles range from 1-5°. is represented by the CIF card [CIF]
data_Na4MgTi3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.329
_cell_length_b   6.179
_cell_length_c   6.192
_cell_angle_alpha   59.207
_cell_angle_beta   118.917
_cell_angle_gamma   90.044
_symmetry_Int_Tables_number   1
_cell_volume   171.982
_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
  Na  Na0  1  0.108  0.597  0.740  1.0
  Na  Na1  1  0.117  0.592  0.242  1.0
  Na  Na2  1  0.109  0.097  0.739  1.0
  Na  Na3  1  0.606  0.102  0.734  1.0
  Mg  Mg4  1  0.097  0.090  0.232  1.0
  Ti  Ti5  1  0.611  0.599  0.747  1.0
  Ti  Ti6  1  0.615  0.597  0.235  1.0
  Ti  Ti7  1  0.606  0.097  0.239  1.0
  O  O8  1  0.381  0.851  0.263  1.0
  O  O9  1  0.381  0.827  0.744  1.0
  O  O10  1  0.831  0.856  0.237  1.0
  O  O11  1  0.811  0.847  0.693  1.0
  O  O12  1  0.397  0.344  0.237  1.0
  O  O13  1  0.408  0.347  0.790  1.0
  O  O14  1  0.830  0.376  0.724  1.0
  O  O15  1  0.843  0.342  0.218  1.0
[/CIF]
.