The crystal structure described by KMg6HfO7 crystallizes in the tetragonal P4mm space group. K(1) is bonded in a 5-coordinate geometry to one O(1) and 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(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles are 1°. 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 Hf(1)O5 square pyramid, corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. In the third Mg site, Mg(3) is bonded in a T-shaped geometry to 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 Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Hf(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-12°. Hf(1) is bonded to one O(3) and four equivalent O(4) atoms to form HfO5 square pyramids that share  a cornercorner with one Mg(2)O5 square pyramid, corners with four equivalent Hf(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded to one K(1), one Mg(1), and four equivalent Mg(3) atoms to form distorted OKMg5 octahedra that share corners with four equivalent O(1)KMg5 octahedra,  a cornercorner with one O(2)Mg5 square pyramid, corners with four equivalent O(4)K2Hf2Mg trigonal bipyramids, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 2°. In the second O site, O(2) is bonded to one Mg(1) and four equivalent Mg(4) atoms to form OMg5 square pyramids that share  a cornercorner with one O(1)KMg5 octahedra, corners with four equivalent O(2)Mg5 square pyramids, corners with four equivalent O(4)K2Hf2Mg trigonal bipyramids, edges with four equivalent O(3)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to one Mg(2), four equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5 square pyramids, and edges with four equivalent O(4)K2Hf2Mg trigonal bipyramids. The corner-sharing octahedral tilt angles are 4°. In the fourth O site, O(4) is bonded to two equivalent K(1), one Mg(4), and two equivalent Hf(1) atoms to form distorted OK2Hf2Mg trigonal bipyramids that share  a cornercorner with one O(5)Mg6 octahedra, corners with two equivalent O(1)KMg5 octahedra, corners with two equivalent O(2)Mg5 square pyramids, corners with four equivalent O(4)K2Hf2Mg trigonal bipyramids, edges with two equivalent O(3)HfMg5 octahedra, and edges with four equivalent O(4)K2Hf2Mg trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-46°. 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,  a cornercorner with one O(4)K2Hf2Mg trigonal bipyramid, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with two equivalent O(2)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 1-3°. is represented by the Crystallographic Information File (CIF) [CIF]
data_KHfMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   11.802
_cell_length_b   4.178
_cell_length_c   4.178
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   206.050
_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  0.073  0.000  0.000  1.0
  Hf  Hf1  1  0.909  0.500  0.500  1.0
  Mg  Mg2  1  0.525  0.000  0.000  1.0
  Mg  Mg3  1  0.528  0.500  0.500  1.0
  Mg  Mg4  1  0.339  0.000  0.500  1.0
  Mg  Mg5  1  0.716  0.000  0.500  1.0
  Mg  Mg6  1  0.339  0.500  0.000  1.0
  Mg  Mg7  1  0.716  0.500  0.000  1.0
  O  O8  1  0.336  0.000  0.000  1.0
  O  O9  1  0.697  0.000  0.000  1.0
  O  O10  1  0.723  0.500  0.500  1.0
  O  O11  1  0.901  0.000  0.500  1.0
  O  O12  1  0.523  0.000  0.500  1.0
  O  O13  1  0.901  0.500  0.000  1.0
  O  O14  1  0.523  0.500  0.000  1.0
[/CIF]
.
The crystal structure described by KMg6HfO7 crystallizes in the tetragonal P4mm space group. K(1) is bonded in a 5-coordinate geometry to one O(1) and 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(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles are 1°. 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 Hf(1)O5 square pyramid, corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. In the third Mg site, Mg(3) is bonded in a T-shaped geometry to 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 Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Hf(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-12°. Hf(1) is bonded to one O(3) and four equivalent O(4) atoms to form HfO5 square pyramids that share  a cornercorner with one Mg(2)O5 square pyramid, corners with four equivalent Hf(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded to one K(1), one Mg(1), and four equivalent Mg(3) atoms to form distorted OKMg5 octahedra that share corners with four equivalent O(1)KMg5 octahedra,  a cornercorner with one O(2)Mg5 square pyramid, corners with four equivalent O(4)K2Hf2Mg trigonal bipyramids, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 2°. In the second O site, O(2) is bonded to one Mg(1) and four equivalent Mg(4) atoms to form OMg5 square pyramids that share  a cornercorner with one O(1)KMg5 octahedra, corners with four equivalent O(2)Mg5 square pyramids, corners with four equivalent O(4)K2Hf2Mg trigonal bipyramids, edges with four equivalent O(3)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to one Mg(2), four equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5 square pyramids, and edges with four equivalent O(4)K2Hf2Mg trigonal bipyramids. The corner-sharing octahedral tilt angles are 4°. In the fourth O site, O(4) is bonded to two equivalent K(1), one Mg(4), and two equivalent Hf(1) atoms to form distorted OK2Hf2Mg trigonal bipyramids that share  a cornercorner with one O(5)Mg6 octahedra, corners with two equivalent O(1)KMg5 octahedra, corners with two equivalent O(2)Mg5 square pyramids, corners with four equivalent O(4)K2Hf2Mg trigonal bipyramids, edges with two equivalent O(3)HfMg5 octahedra, and edges with four equivalent O(4)K2Hf2Mg trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-46°. 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,  a cornercorner with one O(4)K2Hf2Mg trigonal bipyramid, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with two equivalent O(2)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 1-3°. is represented by the Crystallographic Information File (CIF) [CIF]
data_KHfMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   11.802
_cell_length_b   4.178
_cell_length_c   4.178
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   206.050
_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  0.073  0.000  0.000  1.0
  Hf  Hf1  1  0.909  0.500  0.500  1.0
  Mg  Mg2  1  0.525  0.000  0.000  1.0
  Mg  Mg3  1  0.528  0.500  0.500  1.0
  Mg  Mg4  1  0.339  0.000  0.500  1.0
  Mg  Mg5  1  0.716  0.000  0.500  1.0
  Mg  Mg6  1  0.339  0.500  0.000  1.0
  Mg  Mg7  1  0.716  0.500  0.000  1.0
  O  O8  1  0.336  0.000  0.000  1.0
  O  O9  1  0.697  0.000  0.000  1.0
  O  O10  1  0.723  0.500  0.500  1.0
  O  O11  1  0.901  0.000  0.500  1.0
  O  O12  1  0.523  0.000  0.500  1.0
  O  O13  1  0.901  0.500  0.000  1.0
  O  O14  1  0.523  0.500  0.000  1.0
[/CIF]
.