The material described by NaMg4(AsO4)3 crystallizes in the tetragonal I-42d space group. Na(1) is bonded in a distorted body-centered cubic geometry to four equivalent O(2) and four equivalent O(3) atoms. There are two 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(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent As(1)O4 tetrahedra, corners with two equivalent As(2)O4 tetrahedra, edges with two equivalent Mg(2)O6 octahedra, and  an edgeedge with one As(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 56°. In the second Mg site, Mg(2) 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 two equivalent Mg(1)O6 octahedra, corners with two equivalent As(2)O4 tetrahedra, corners with four equivalent As(1)O4 tetrahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 56°. There are two inequivalent As sites. In the first As site, As(1) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form AsO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, and  an edgeedge with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-49°. In the second As site, As(2) is bonded to four equivalent O(1) atoms to form AsO4 tetrahedra that share corners with four equivalent Mg(1)O6 octahedra and corners with four equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-50°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(2), and one As(2) atom. In the second O site, O(2) is bonded to one Na(1), one Mg(1), one Mg(2), and one As(1) atom to form a mixture of distorted edge and corner-sharing ONaMg2As trigonal pyramids. In the third O site, O(3) is bonded to one Na(1), one Mg(1), one Mg(2), and one As(1) atom to form a mixture of distorted edge and corner-sharing ONaMg2As tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaMg4(AsO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.908
_cell_length_b   10.908
_cell_length_c   10.908
_cell_angle_alpha   143.089
_cell_angle_beta   143.089
_cell_angle_gamma   53.192
_symmetry_Int_Tables_number   1
_cell_volume   465.173
_cell_formula_units_Z   2
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  0.250  0.750  0.500  1.0
  Na  Na1  1  0.500  0.500  0.000  1.0
  Mg  Mg2  1  0.375  0.882  0.007  1.0
  Mg  Mg3  1  0.118  0.125  0.493  1.0
  Mg  Mg4  1  0.632  0.625  0.507  1.0
  Mg  Mg5  1  0.875  0.368  0.993  1.0
  Mg  Mg6  1  0.770  0.770  0.000  1.0
  Mg  Mg7  1  0.230  0.230  0.000  1.0
  Mg  Mg8  1  0.980  0.480  0.500  1.0
  Mg  Mg9  1  0.520  0.020  0.500  1.0
  As  As10  1  0.375  0.469  0.594  1.0
  As  As11  1  0.531  0.125  0.906  1.0
  As  As12  1  0.219  0.625  0.094  1.0
  As  As13  1  0.875  0.781  0.406  1.0
  As  As14  1  0.750  0.250  0.500  1.0
  As  As15  1  0.000  0.000  0.000  1.0
  O  O16  1  0.735  0.502  0.648  1.0
  O  O17  1  0.853  0.086  0.352  1.0
  O  O18  1  0.252  0.985  0.148  1.0
  O  O19  1  0.914  0.265  0.767  1.0
  O  O20  1  0.498  0.147  0.233  1.0
  O  O21  1  0.015  0.164  0.267  1.0
  O  O22  1  0.897  0.748  0.733  1.0
  O  O23  1  0.836  0.103  0.852  1.0
  O  O24  1  0.071  0.803  0.177  1.0
  O  O25  1  0.626  0.894  0.823  1.0
  O  O26  1  0.553  0.321  0.677  1.0
  O  O27  1  0.106  0.929  0.732  1.0
  O  O28  1  0.197  0.374  0.268  1.0
  O  O29  1  0.679  0.356  0.232  1.0
  O  O30  1  0.124  0.447  0.768  1.0
  O  O31  1  0.644  0.876  0.323  1.0
  O  O32  1  0.856  0.551  0.289  1.0
  O  O33  1  0.449  0.737  0.305  1.0
  O  O34  1  0.432  0.144  0.695  1.0
  O  O35  1  0.487  0.699  0.805  1.0
  O  O36  1  0.894  0.682  0.195  1.0
  O  O37  1  0.263  0.568  0.711  1.0
  O  O38  1  0.301  0.106  0.789  1.0
  O  O39  1  0.318  0.513  0.211  1.0
[/CIF]
.
The material described by NaMg4(AsO4)3 crystallizes in the tetragonal I-42d space group. Na(1) is bonded in a distorted body-centered cubic geometry to four equivalent O(2) and four equivalent O(3) atoms. There are two 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(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent As(1)O4 tetrahedra, corners with two equivalent As(2)O4 tetrahedra, edges with two equivalent Mg(2)O6 octahedra, and  an edgeedge with one As(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 56°. In the second Mg site, Mg(2) 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 two equivalent Mg(1)O6 octahedra, corners with two equivalent As(2)O4 tetrahedra, corners with four equivalent As(1)O4 tetrahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 56°. There are two inequivalent As sites. In the first As site, As(1) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form AsO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, and  an edgeedge with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-49°. In the second As site, As(2) is bonded to four equivalent O(1) atoms to form AsO4 tetrahedra that share corners with four equivalent Mg(1)O6 octahedra and corners with four equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-50°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(2), and one As(2) atom. In the second O site, O(2) is bonded to one Na(1), one Mg(1), one Mg(2), and one As(1) atom to form a mixture of distorted edge and corner-sharing ONaMg2As trigonal pyramids. In the third O site, O(3) is bonded to one Na(1), one Mg(1), one Mg(2), and one As(1) atom to form a mixture of distorted edge and corner-sharing ONaMg2As tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaMg4(AsO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.908
_cell_length_b   10.908
_cell_length_c   10.908
_cell_angle_alpha   143.089
_cell_angle_beta   143.089
_cell_angle_gamma   53.192
_symmetry_Int_Tables_number   1
_cell_volume   465.173
_cell_formula_units_Z   2
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  0.250  0.750  0.500  1.0
  Na  Na1  1  0.500  0.500  0.000  1.0
  Mg  Mg2  1  0.375  0.882  0.007  1.0
  Mg  Mg3  1  0.118  0.125  0.493  1.0
  Mg  Mg4  1  0.632  0.625  0.507  1.0
  Mg  Mg5  1  0.875  0.368  0.993  1.0
  Mg  Mg6  1  0.770  0.770  0.000  1.0
  Mg  Mg7  1  0.230  0.230  0.000  1.0
  Mg  Mg8  1  0.980  0.480  0.500  1.0
  Mg  Mg9  1  0.520  0.020  0.500  1.0
  As  As10  1  0.375  0.469  0.594  1.0
  As  As11  1  0.531  0.125  0.906  1.0
  As  As12  1  0.219  0.625  0.094  1.0
  As  As13  1  0.875  0.781  0.406  1.0
  As  As14  1  0.750  0.250  0.500  1.0
  As  As15  1  0.000  0.000  0.000  1.0
  O  O16  1  0.735  0.502  0.648  1.0
  O  O17  1  0.853  0.086  0.352  1.0
  O  O18  1  0.252  0.985  0.148  1.0
  O  O19  1  0.914  0.265  0.767  1.0
  O  O20  1  0.498  0.147  0.233  1.0
  O  O21  1  0.015  0.164  0.267  1.0
  O  O22  1  0.897  0.748  0.733  1.0
  O  O23  1  0.836  0.103  0.852  1.0
  O  O24  1  0.071  0.803  0.177  1.0
  O  O25  1  0.626  0.894  0.823  1.0
  O  O26  1  0.553  0.321  0.677  1.0
  O  O27  1  0.106  0.929  0.732  1.0
  O  O28  1  0.197  0.374  0.268  1.0
  O  O29  1  0.679  0.356  0.232  1.0
  O  O30  1  0.124  0.447  0.768  1.0
  O  O31  1  0.644  0.876  0.323  1.0
  O  O32  1  0.856  0.551  0.289  1.0
  O  O33  1  0.449  0.737  0.305  1.0
  O  O34  1  0.432  0.144  0.695  1.0
  O  O35  1  0.487  0.699  0.805  1.0
  O  O36  1  0.894  0.682  0.195  1.0
  O  O37  1  0.263  0.568  0.711  1.0
  O  O38  1  0.301  0.106  0.789  1.0
  O  O39  1  0.318  0.513  0.211  1.0
[/CIF]
.