The crystal structure described by KNaMg6O7 crystallizes in the tetragonal P4mm space group. K(1) is bonded in a 5-coordinate geometry to one O(2) and four equivalent O(4) atoms. Na(1) is bonded in a distorted square co-planar geometry to four equivalent O(4) atoms. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), and four equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(4)O5 square pyramids. The corner-sharing octahedral tilt angles are 6°. In the second Mg site, Mg(2) is bonded to one O(3) and four equivalent O(5) atoms to form MgO5 square pyramids that share corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O5 square pyramids. In the third Mg site, Mg(3) is bonded in a 4-coordinate geometry to one O(4), one O(5), and two equivalent O(1) atoms. In the fourth Mg site, Mg(4) is bonded to one O(5), two equivalent O(2), and two equivalent O(3) atoms to form MgO5 square pyramids that share corners with four equivalent Mg(4)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(4)O5 square pyramids. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1) and four equivalent Mg(3) atoms to form distorted OMg5 square pyramids that share  a cornercorner with one O(2)KMg5 octahedra, corners with four equivalent O(1)Mg5 square pyramids, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the second O site, O(2) is bonded to one K(1), one Mg(1), and four equivalent Mg(4) atoms to form OKMg5 octahedra that share corners with four equivalent O(2)KMg5 octahedra,  a cornercorner with one O(1)Mg5 square pyramid, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg5 square pyramids. The corner-sharing octahedral tilt angles are 6°. In the third O site, O(3) is bonded to one Mg(2) and four equivalent Mg(4) atoms to form OMg5 square pyramids that share corners with four equivalent O(3)Mg5 square pyramids, edges with four equivalent O(2)KMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent K(1), two equivalent Na(1), and one Mg(3) atom. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(1), and two equivalent Mg(2) atoms to form OMg6 octahedra that share corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(2)KMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)Mg5 square pyramids, and edges with two equivalent O(3)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 4-6°. is represented by the Crystallographic Information File (CIF) [CIF]
data_KNaMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.254
_cell_length_b   4.254
_cell_length_c   10.898
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   197.231
_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
  K  K0  1  0.000  0.000  0.965  1.0
  Na  Na1  1  0.500  0.500  0.035  1.0
  Mg  Mg2  1  0.000  0.000  0.486  1.0
  Mg  Mg3  1  0.500  0.500  0.503  1.0
  Mg  Mg4  1  0.000  0.500  0.260  1.0
  Mg  Mg5  1  0.000  0.500  0.688  1.0
  Mg  Mg6  1  0.500  0.000  0.260  1.0
  Mg  Mg7  1  0.500  0.000  0.688  1.0
  O  O8  1  0.000  0.000  0.302  1.0
  O  O9  1  0.000  0.000  0.698  1.0
  O  O10  1  0.500  0.500  0.699  1.0
  O  O11  1  0.000  0.500  0.087  1.0
  O  O12  1  0.000  0.500  0.496  1.0
  O  O13  1  0.500  0.000  0.087  1.0
  O  O14  1  0.500  0.000  0.496  1.0
[/CIF]
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The crystal structure described by KNaMg6O7 crystallizes in the tetragonal P4mm space group. K(1) is bonded in a 5-coordinate geometry to one O(2) and four equivalent O(4) atoms. Na(1) is bonded in a distorted square co-planar geometry to four equivalent O(4) atoms. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), and four equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(4)O5 square pyramids. The corner-sharing octahedral tilt angles are 6°. In the second Mg site, Mg(2) is bonded to one O(3) and four equivalent O(5) atoms to form MgO5 square pyramids that share corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O5 square pyramids. In the third Mg site, Mg(3) is bonded in a 4-coordinate geometry to one O(4), one O(5), and two equivalent O(1) atoms. In the fourth Mg site, Mg(4) is bonded to one O(5), two equivalent O(2), and two equivalent O(3) atoms to form MgO5 square pyramids that share corners with four equivalent Mg(4)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(4)O5 square pyramids. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1) and four equivalent Mg(3) atoms to form distorted OMg5 square pyramids that share  a cornercorner with one O(2)KMg5 octahedra, corners with four equivalent O(1)Mg5 square pyramids, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the second O site, O(2) is bonded to one K(1), one Mg(1), and four equivalent Mg(4) atoms to form OKMg5 octahedra that share corners with four equivalent O(2)KMg5 octahedra,  a cornercorner with one O(1)Mg5 square pyramid, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg5 square pyramids. The corner-sharing octahedral tilt angles are 6°. In the third O site, O(3) is bonded to one Mg(2) and four equivalent Mg(4) atoms to form OMg5 square pyramids that share corners with four equivalent O(3)Mg5 square pyramids, edges with four equivalent O(2)KMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent K(1), two equivalent Na(1), and one Mg(3) atom. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(1), and two equivalent Mg(2) atoms to form OMg6 octahedra that share corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(2)KMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)Mg5 square pyramids, and edges with two equivalent O(3)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 4-6°. is represented by the Crystallographic Information File (CIF) [CIF]
data_KNaMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.254
_cell_length_b   4.254
_cell_length_c   10.898
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   197.231
_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
  K  K0  1  0.000  0.000  0.965  1.0
  Na  Na1  1  0.500  0.500  0.035  1.0
  Mg  Mg2  1  0.000  0.000  0.486  1.0
  Mg  Mg3  1  0.500  0.500  0.503  1.0
  Mg  Mg4  1  0.000  0.500  0.260  1.0
  Mg  Mg5  1  0.000  0.500  0.688  1.0
  Mg  Mg6  1  0.500  0.000  0.260  1.0
  Mg  Mg7  1  0.500  0.000  0.688  1.0
  O  O8  1  0.000  0.000  0.302  1.0
  O  O9  1  0.000  0.000  0.698  1.0
  O  O10  1  0.500  0.500  0.699  1.0
  O  O11  1  0.000  0.500  0.087  1.0
  O  O12  1  0.000  0.500  0.496  1.0
  O  O13  1  0.500  0.000  0.087  1.0
  O  O14  1  0.500  0.000  0.496  1.0
[/CIF]
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