The compound 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 to one O(1), one O(2), and four equivalent O(5) atoms to form NaO6 octahedra that share corners with four equivalent Na(1)O6 octahedra, edges with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(4)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 6°. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a square co-planar geometry to four equivalent O(4) atoms. 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 Na(1)O6 octahedra, and edges with four equivalent Mg(4)O5 trigonal bipyramids. In the third Mg site, Mg(3) is bonded in a square co-planar 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 trigonal bipyramids that share corners with four equivalent Mg(4)O5 trigonal bipyramids, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(4)O5 trigonal bipyramids. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1) and four equivalent Mg(3) atoms to form ONaMg4 square pyramids that share  a cornercorner with one O(2)KNaMg4 octahedra, corners with four equivalent O(1)NaMg4 square pyramids, corners with four equivalent O(4)K2Mg3 trigonal bipyramids, and edges with four equivalent O(5)Na2Mg4 octahedra. The corner-sharing octahedra are not tilted. In the second O site, O(2) is bonded to one K(1), one Na(1), and four equivalent Mg(4) atoms to form distorted OKNaMg4 octahedra that share corners with four equivalent O(2)KNaMg4 octahedra,  a cornercorner with one O(1)NaMg4 square pyramid, corners with four equivalent O(4)K2Mg3 trigonal bipyramids, edges with four equivalent O(5)Na2Mg4 octahedra, and edges with four equivalent O(3)Mg5 square pyramids. The corner-sharing octahedral tilt angles are 20°. 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)KNaMg4 octahedra, and edges with four equivalent O(5)Na2Mg4 octahedra. In the fourth O site, O(4) is bonded to two equivalent K(1), one Mg(3), and two equivalent Mg(1) atoms to form OK2Mg3 trigonal bipyramids that share  a cornercorner with one O(5)Na2Mg4 octahedra, corners with two equivalent O(2)KNaMg4 octahedra, corners with two equivalent O(1)NaMg4 square pyramids, corners with four equivalent O(4)K2Mg3 trigonal bipyramids, and edges with four equivalent O(4)K2Mg3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-55°. In the fifth O site, O(5) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent Mg(2) atoms to form ONa2Mg4 octahedra that share corners with four equivalent O(5)Na2Mg4 octahedra,  a cornercorner with one O(4)K2Mg3 trigonal bipyramid, edges with two equivalent O(2)KNaMg4 octahedra, edges with four equivalent O(5)Na2Mg4 octahedra, edges with two equivalent O(3)Mg5 square pyramids, and edges with two equivalent O(1)NaMg4 square pyramids. The corner-sharing octahedral tilt angles range from 6-11°. is represented by the CIF file [CIF]
data_KNaMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.247
_cell_length_b   4.247
_cell_length_c   10.988
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   198.165
_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  0.964  1.0
  Na  Na1  1  0.000  0.000  0.485  1.0
  Mg  Mg2  1  0.500  0.500  0.082  1.0
  Mg  Mg3  1  0.500  0.500  0.494  1.0
  Mg  Mg4  1  0.000  0.500  0.281  1.0
  Mg  Mg5  1  0.000  0.500  0.673  1.0
  Mg  Mg6  1  0.500  0.000  0.281  1.0
  Mg  Mg7  1  0.500  0.000  0.673  1.0
  O  O8  1  0.000  0.000  0.284  1.0
  O  O9  1  0.000  0.000  0.707  1.0
  O  O10  1  0.500  0.500  0.680  1.0
  O  O11  1  0.000  0.500  0.098  1.0
  O  O12  1  0.000  0.500  0.475  1.0
  O  O13  1  0.500  0.000  0.098  1.0
  O  O14  1  0.500  0.000  0.475  1.0
[/CIF]
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The compound 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 to one O(1), one O(2), and four equivalent O(5) atoms to form NaO6 octahedra that share corners with four equivalent Na(1)O6 octahedra, edges with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(4)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 6°. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a square co-planar geometry to four equivalent O(4) atoms. 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 Na(1)O6 octahedra, and edges with four equivalent Mg(4)O5 trigonal bipyramids. In the third Mg site, Mg(3) is bonded in a square co-planar 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 trigonal bipyramids that share corners with four equivalent Mg(4)O5 trigonal bipyramids, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(4)O5 trigonal bipyramids. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1) and four equivalent Mg(3) atoms to form ONaMg4 square pyramids that share  a cornercorner with one O(2)KNaMg4 octahedra, corners with four equivalent O(1)NaMg4 square pyramids, corners with four equivalent O(4)K2Mg3 trigonal bipyramids, and edges with four equivalent O(5)Na2Mg4 octahedra. The corner-sharing octahedra are not tilted. In the second O site, O(2) is bonded to one K(1), one Na(1), and four equivalent Mg(4) atoms to form distorted OKNaMg4 octahedra that share corners with four equivalent O(2)KNaMg4 octahedra,  a cornercorner with one O(1)NaMg4 square pyramid, corners with four equivalent O(4)K2Mg3 trigonal bipyramids, edges with four equivalent O(5)Na2Mg4 octahedra, and edges with four equivalent O(3)Mg5 square pyramids. The corner-sharing octahedral tilt angles are 20°. 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)KNaMg4 octahedra, and edges with four equivalent O(5)Na2Mg4 octahedra. In the fourth O site, O(4) is bonded to two equivalent K(1), one Mg(3), and two equivalent Mg(1) atoms to form OK2Mg3 trigonal bipyramids that share  a cornercorner with one O(5)Na2Mg4 octahedra, corners with two equivalent O(2)KNaMg4 octahedra, corners with two equivalent O(1)NaMg4 square pyramids, corners with four equivalent O(4)K2Mg3 trigonal bipyramids, and edges with four equivalent O(4)K2Mg3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-55°. In the fifth O site, O(5) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent Mg(2) atoms to form ONa2Mg4 octahedra that share corners with four equivalent O(5)Na2Mg4 octahedra,  a cornercorner with one O(4)K2Mg3 trigonal bipyramid, edges with two equivalent O(2)KNaMg4 octahedra, edges with four equivalent O(5)Na2Mg4 octahedra, edges with two equivalent O(3)Mg5 square pyramids, and edges with two equivalent O(1)NaMg4 square pyramids. The corner-sharing octahedral tilt angles range from 6-11°. is represented by the CIF file [CIF]
data_KNaMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.247
_cell_length_b   4.247
_cell_length_c   10.988
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   198.165
_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  0.964  1.0
  Na  Na1  1  0.000  0.000  0.485  1.0
  Mg  Mg2  1  0.500  0.500  0.082  1.0
  Mg  Mg3  1  0.500  0.500  0.494  1.0
  Mg  Mg4  1  0.000  0.500  0.281  1.0
  Mg  Mg5  1  0.000  0.500  0.673  1.0
  Mg  Mg6  1  0.500  0.000  0.281  1.0
  Mg  Mg7  1  0.500  0.000  0.673  1.0
  O  O8  1  0.000  0.000  0.284  1.0
  O  O9  1  0.000  0.000  0.707  1.0
  O  O10  1  0.500  0.500  0.680  1.0
  O  O11  1  0.000  0.500  0.098  1.0
  O  O12  1  0.000  0.500  0.475  1.0
  O  O13  1  0.500  0.000  0.098  1.0
  O  O14  1  0.500  0.000  0.475  1.0
[/CIF]
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