The structure described by Li6Hf2O7 crystallizes in the monoclinic P2_1/c space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), one O(4), and two equivalent O(3) atoms to form LiO5 square pyramids that share corners with three equivalent Li(1)O5 square pyramids, corners with four equivalent Li(2)O5 square pyramids, edges with four equivalent Hf(1)O6 octahedra, and edges with two equivalent Li(2)O5 square pyramids. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(4), and two equivalent O(3) atoms to form LiO5 square pyramids that share corners with three equivalent Li(2)O5 square pyramids, corners with four equivalent Li(1)O5 square pyramids, edges with four equivalent Hf(1)O6 octahedra, and edges with two equivalent Li(1)O5 square pyramids. In the third Li site, Li(3) is bonded in a 4-coordinate geometry to one O(3), two equivalent O(2), and two equivalent O(4) atoms. Hf(1) is bonded to one O(1), one O(3), two equivalent O(2), and two equivalent O(4) atoms to form HfO6 octahedra that share corners with three equivalent Hf(1)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with four equivalent Li(1)O5 square pyramids, and edges with four equivalent Li(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-10°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), two equivalent Li(2), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with six equivalent O(3)Li5Hf octahedra, edges with two equivalent O(3)Li5Hf octahedra, edges with four equivalent O(2)Li4Hf2 octahedra, and edges with four equivalent O(4)Li4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 2-19°. In the second O site, O(2) is bonded to one Li(1), one Li(2), two equivalent Li(3), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with six equivalent O(4)Li4Hf2 octahedra, edges with two equivalent O(1)Li4Hf2 octahedra, edges with two equivalent O(2)Li4Hf2 octahedra, edges with two equivalent O(4)Li4Hf2 octahedra, and edges with four equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 3-27°. In the third O site, O(3) is bonded to one Li(3), two equivalent Li(1), two equivalent Li(2), and one Hf(1) atom to form OLi5Hf octahedra that share corners with three equivalent O(1)Li4Hf2 octahedra,  an edgeedge with one O(1)Li4Hf2 octahedra, edges with two equivalent O(3)Li5Hf octahedra, edges with four equivalent O(2)Li4Hf2 octahedra, and edges with four equivalent O(4)Li4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 2-19°. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), two equivalent Li(3), and two equivalent Hf(1) atoms to form distorted OLi4Hf2 octahedra that share corners with six equivalent O(2)Li4Hf2 octahedra, edges with two equivalent O(1)Li4Hf2 octahedra, edges with two equivalent O(2)Li4Hf2 octahedra, edges with two equivalent O(4)Li4Hf2 octahedra, and edges with four equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 3-27°. is represented by the CIF file [CIF]
data_Li6Hf2O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.968
_cell_length_b   5.277
_cell_length_c   10.236
_cell_angle_alpha   69.953
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   302.812
_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
  Li  Li0  1  0.780  0.207  0.143  1.0
  Li  Li1  1  0.235  0.215  0.138  1.0
  Li  Li2  1  0.495  0.840  0.124  1.0
  Li  Li3  1  0.995  0.160  0.376  1.0
  Li  Li4  1  0.735  0.785  0.362  1.0
  Li  Li5  1  0.280  0.793  0.357  1.0
  Li  Li6  1  0.720  0.207  0.643  1.0
  Li  Li7  1  0.265  0.215  0.638  1.0
  Li  Li8  1  0.005  0.840  0.624  1.0
  Li  Li9  1  0.505  0.160  0.876  1.0
  Li  Li10  1  0.765  0.785  0.862  1.0
  Li  Li11  1  0.220  0.793  0.857  1.0
  Hf  Hf12  1  0.006  0.729  0.133  1.0
  Hf  Hf13  1  0.506  0.271  0.367  1.0
  Hf  Hf14  1  0.494  0.729  0.633  1.0
  Hf  Hf15  1  0.994  0.271  0.867  1.0
  O  O16  1  0.000  0.500  0.000  1.0
  O  O17  1  0.766  0.990  0.003  1.0
  O  O18  1  0.508  0.040  0.245  1.0
  O  O19  1  0.278  0.519  0.237  1.0
  O  O20  1  0.778  0.481  0.263  1.0
  O  O21  1  0.008  0.960  0.255  1.0
  O  O22  1  0.266  0.010  0.497  1.0
  O  O23  1  0.500  0.500  0.500  1.0
  O  O24  1  0.734  0.990  0.503  1.0
  O  O25  1  0.992  0.040  0.745  1.0
  O  O26  1  0.222  0.519  0.737  1.0
  O  O27  1  0.722  0.481  0.763  1.0
  O  O28  1  0.492  0.960  0.755  1.0
  O  O29  1  0.234  0.010  0.997  1.0
[/CIF]
.
The structure described by Li6Hf2O7 crystallizes in the monoclinic P2_1/c space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), one O(4), and two equivalent O(3) atoms to form LiO5 square pyramids that share corners with three equivalent Li(1)O5 square pyramids, corners with four equivalent Li(2)O5 square pyramids, edges with four equivalent Hf(1)O6 octahedra, and edges with two equivalent Li(2)O5 square pyramids. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(4), and two equivalent O(3) atoms to form LiO5 square pyramids that share corners with three equivalent Li(2)O5 square pyramids, corners with four equivalent Li(1)O5 square pyramids, edges with four equivalent Hf(1)O6 octahedra, and edges with two equivalent Li(1)O5 square pyramids. In the third Li site, Li(3) is bonded in a 4-coordinate geometry to one O(3), two equivalent O(2), and two equivalent O(4) atoms. Hf(1) is bonded to one O(1), one O(3), two equivalent O(2), and two equivalent O(4) atoms to form HfO6 octahedra that share corners with three equivalent Hf(1)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with four equivalent Li(1)O5 square pyramids, and edges with four equivalent Li(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-10°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), two equivalent Li(2), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with six equivalent O(3)Li5Hf octahedra, edges with two equivalent O(3)Li5Hf octahedra, edges with four equivalent O(2)Li4Hf2 octahedra, and edges with four equivalent O(4)Li4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 2-19°. In the second O site, O(2) is bonded to one Li(1), one Li(2), two equivalent Li(3), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with six equivalent O(4)Li4Hf2 octahedra, edges with two equivalent O(1)Li4Hf2 octahedra, edges with two equivalent O(2)Li4Hf2 octahedra, edges with two equivalent O(4)Li4Hf2 octahedra, and edges with four equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 3-27°. In the third O site, O(3) is bonded to one Li(3), two equivalent Li(1), two equivalent Li(2), and one Hf(1) atom to form OLi5Hf octahedra that share corners with three equivalent O(1)Li4Hf2 octahedra,  an edgeedge with one O(1)Li4Hf2 octahedra, edges with two equivalent O(3)Li5Hf octahedra, edges with four equivalent O(2)Li4Hf2 octahedra, and edges with four equivalent O(4)Li4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 2-19°. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), two equivalent Li(3), and two equivalent Hf(1) atoms to form distorted OLi4Hf2 octahedra that share corners with six equivalent O(2)Li4Hf2 octahedra, edges with two equivalent O(1)Li4Hf2 octahedra, edges with two equivalent O(2)Li4Hf2 octahedra, edges with two equivalent O(4)Li4Hf2 octahedra, and edges with four equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 3-27°. is represented by the CIF file [CIF]
data_Li6Hf2O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.968
_cell_length_b   5.277
_cell_length_c   10.236
_cell_angle_alpha   69.953
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   302.812
_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
  Li  Li0  1  0.780  0.207  0.143  1.0
  Li  Li1  1  0.235  0.215  0.138  1.0
  Li  Li2  1  0.495  0.840  0.124  1.0
  Li  Li3  1  0.995  0.160  0.376  1.0
  Li  Li4  1  0.735  0.785  0.362  1.0
  Li  Li5  1  0.280  0.793  0.357  1.0
  Li  Li6  1  0.720  0.207  0.643  1.0
  Li  Li7  1  0.265  0.215  0.638  1.0
  Li  Li8  1  0.005  0.840  0.624  1.0
  Li  Li9  1  0.505  0.160  0.876  1.0
  Li  Li10  1  0.765  0.785  0.862  1.0
  Li  Li11  1  0.220  0.793  0.857  1.0
  Hf  Hf12  1  0.006  0.729  0.133  1.0
  Hf  Hf13  1  0.506  0.271  0.367  1.0
  Hf  Hf14  1  0.494  0.729  0.633  1.0
  Hf  Hf15  1  0.994  0.271  0.867  1.0
  O  O16  1  0.000  0.500  0.000  1.0
  O  O17  1  0.766  0.990  0.003  1.0
  O  O18  1  0.508  0.040  0.245  1.0
  O  O19  1  0.278  0.519  0.237  1.0
  O  O20  1  0.778  0.481  0.263  1.0
  O  O21  1  0.008  0.960  0.255  1.0
  O  O22  1  0.266  0.010  0.497  1.0
  O  O23  1  0.500  0.500  0.500  1.0
  O  O24  1  0.734  0.990  0.503  1.0
  O  O25  1  0.992  0.040  0.745  1.0
  O  O26  1  0.222  0.519  0.737  1.0
  O  O27  1  0.722  0.481  0.763  1.0
  O  O28  1  0.492  0.960  0.755  1.0
  O  O29  1  0.234  0.010  0.997  1.0
[/CIF]
.