The crystal structure described by KMg6HfO7 crystallizes in the tetragonal P4mm space group. K(1) is bonded to one O(1), one O(2), and four equivalent O(4) atoms to form KO6 octahedra that share corners with two equivalent Hf(1)O6 octahedra, corners with four equivalent K(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-11°. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3) and four equivalent O(4) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(2)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, edges with four equivalent K(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. 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  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Hf(1)O6 octahedra. In the third Mg site, Mg(3) is bonded in a 3-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(4), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 6-16°. Hf(1) is bonded to one O(1), one O(2), and four equivalent O(5) atoms to form HfO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with four equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. There are five inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one K(1), four equivalent Mg(3), and one Hf(1) atom. In the second O site, O(2) is bonded to one K(1), four equivalent Mg(4), and one Hf(1) atom to form distorted OKHfMg4 octahedra that share corners with four equivalent O(2)KHfMg4 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles are 16°. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(4) atoms to form OMg6 octahedra that share corners with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, and edges with four equivalent O(2)KHfMg4 octahedra. The corner-sharing octahedral tilt angles are 6°. In the fourth O site, O(4) is bonded to two equivalent K(1), one Mg(3), one Mg(4), and two equivalent Mg(1) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(5)Hf2Mg4 octahedra, corners with four equivalent O(4)K2Mg4 octahedra, edges with two equivalent O(2)KHfMg4 octahedra, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)K2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted OHf2Mg4 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with four equivalent O(5)Hf2Mg4 octahedra, edges with two equivalent O(2)KHfMg4 octahedra, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(5)Hf2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. is represented by the CIF file [CIF]
data_KHfMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.127
_cell_length_b   4.539
_cell_length_c   4.539
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   187.991
_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  0.009  0.000  0.000  1.0
  Hf  Hf1  1  0.504  0.000  0.000  1.0
  Mg  Mg2  1  0.980  0.500  0.500  1.0
  Mg  Mg3  1  0.518  0.500  0.500  1.0
  Mg  Mg4  1  0.223  0.000  0.500  1.0
  Mg  Mg5  1  0.762  0.000  0.500  1.0
  Mg  Mg6  1  0.223  0.500  0.000  1.0
  Mg  Mg7  1  0.762  0.500  0.000  1.0
  O  O8  1  0.281  0.000  0.000  1.0
  O  O9  1  0.727  0.000  0.000  1.0
  O  O10  1  0.749  0.500  0.500  1.0
  O  O11  1  0.984  0.000  0.500  1.0
  O  O12  1  0.521  0.000  0.500  1.0
  O  O13  1  0.984  0.500  0.000  1.0
  O  O14  1  0.521  0.500  0.000  1.0
[/CIF]
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The crystal structure described by KMg6HfO7 crystallizes in the tetragonal P4mm space group. K(1) is bonded to one O(1), one O(2), and four equivalent O(4) atoms to form KO6 octahedra that share corners with two equivalent Hf(1)O6 octahedra, corners with four equivalent K(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-11°. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3) and four equivalent O(4) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(2)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, edges with four equivalent K(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. 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  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Hf(1)O6 octahedra. In the third Mg site, Mg(3) is bonded in a 3-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(4), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 6-16°. Hf(1) is bonded to one O(1), one O(2), and four equivalent O(5) atoms to form HfO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with four equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. There are five inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one K(1), four equivalent Mg(3), and one Hf(1) atom. In the second O site, O(2) is bonded to one K(1), four equivalent Mg(4), and one Hf(1) atom to form distorted OKHfMg4 octahedra that share corners with four equivalent O(2)KHfMg4 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles are 16°. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(4) atoms to form OMg6 octahedra that share corners with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, and edges with four equivalent O(2)KHfMg4 octahedra. The corner-sharing octahedral tilt angles are 6°. In the fourth O site, O(4) is bonded to two equivalent K(1), one Mg(3), one Mg(4), and two equivalent Mg(1) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(5)Hf2Mg4 octahedra, corners with four equivalent O(4)K2Mg4 octahedra, edges with two equivalent O(2)KHfMg4 octahedra, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)K2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted OHf2Mg4 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with four equivalent O(5)Hf2Mg4 octahedra, edges with two equivalent O(2)KHfMg4 octahedra, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(5)Hf2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. is represented by the CIF file [CIF]
data_KHfMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.127
_cell_length_b   4.539
_cell_length_c   4.539
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   187.991
_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  0.009  0.000  0.000  1.0
  Hf  Hf1  1  0.504  0.000  0.000  1.0
  Mg  Mg2  1  0.980  0.500  0.500  1.0
  Mg  Mg3  1  0.518  0.500  0.500  1.0
  Mg  Mg4  1  0.223  0.000  0.500  1.0
  Mg  Mg5  1  0.762  0.000  0.500  1.0
  Mg  Mg6  1  0.223  0.500  0.000  1.0
  Mg  Mg7  1  0.762  0.500  0.000  1.0
  O  O8  1  0.281  0.000  0.000  1.0
  O  O9  1  0.727  0.000  0.000  1.0
  O  O10  1  0.749  0.500  0.500  1.0
  O  O11  1  0.984  0.000  0.500  1.0
  O  O12  1  0.521  0.000  0.500  1.0
  O  O13  1  0.984  0.500  0.000  1.0
  O  O14  1  0.521  0.500  0.000  1.0
[/CIF]
.