The crystal structure described by MgLa8Hf4O20 crystallizes in the monoclinic Pm space group. Mg(1) is bonded to one O(14), one O(16), one O(20), and two equivalent O(13) atoms to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Hf(3)O5 trigonal bipyramid and corners with two equivalent Mg(1)O5 trigonal bipyramids. There are eight inequivalent La sites. In the first La site, La(1) is bonded in a 7-coordinate geometry to one O(20), one O(4), one O(6), two equivalent O(19), and two equivalent O(3) atoms. In the second La site, La(2) is bonded in a 7-coordinate geometry to one O(20), one O(6), one O(8), two equivalent O(1), and two equivalent O(7) atoms. In the third La site, La(3) is bonded to one O(11), one O(3), one O(5), two equivalent O(10), and two equivalent O(4) atoms to form distorted LaO7 hexagonal pyramids that share  a cornercorner with one Hf(2)O5 trigonal bipyramid,  an edgeedge with one La(4)O7 hexagonal pyramid, edges with two equivalent La(3)O7 hexagonal pyramids, and edges with two equivalent Hf(1)O5 trigonal bipyramids. In the fourth La site, La(4) is bonded to one O(11), one O(5), one O(7), two equivalent O(12), and two equivalent O(8) atoms to form distorted LaO7 hexagonal pyramids that share  a cornercorner with one Hf(2)O5 trigonal bipyramid, corners with two equivalent Hf(3)O5 trigonal bipyramids,  an edgeedge with one La(3)O7 hexagonal pyramid, edges with two equivalent La(4)O7 hexagonal pyramids, and edges with two equivalent Hf(1)O5 trigonal bipyramids. In the fifth La site, La(5) is bonded in a 5-coordinate geometry to one O(10), one O(14), one O(16), two equivalent O(13), and two equivalent O(9) atoms. In the sixth La site, La(6) is bonded in a 7-coordinate geometry to one O(10), one O(16), one O(18), two equivalent O(11), and two equivalent O(17) atoms. In the seventh La site, La(7) is bonded in a 7-coordinate geometry to one O(1), one O(13), one O(15), two equivalent O(14), and two equivalent O(20) atoms. In the eighth La site, La(8) is bonded to one O(1), one O(15), one O(17), two equivalent O(18), and two equivalent O(2) atoms to form distorted LaO7 hexagonal pyramids that share corners with two equivalent Hf(1)O5 trigonal bipyramids, edges with two equivalent La(8)O7 hexagonal pyramids, and edges with two equivalent Hf(3)O5 trigonal bipyramids. There are four inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one O(2), one O(4), one O(8), and two equivalent O(5) atoms to form distorted HfO5 trigonal bipyramids that share corners with two equivalent La(8)O7 hexagonal pyramids, corners with two equivalent Hf(1)O5 trigonal bipyramids, edges with two equivalent La(3)O7 hexagonal pyramids, and edges with two equivalent La(4)O7 hexagonal pyramids. In the second Hf site, Hf(2) is bonded to one O(3), one O(7), one O(9), and two equivalent O(6) atoms to form distorted HfO5 trigonal bipyramids that share  a cornercorner with one La(3)O7 hexagonal pyramid,  a cornercorner with one La(4)O7 hexagonal pyramid, and corners with two equivalent Hf(2)O5 trigonal bipyramids. In the third Hf site, Hf(3) is bonded to one O(12), one O(14), one O(18), and two equivalent O(15) atoms to form distorted HfO5 trigonal bipyramids that share corners with two equivalent La(4)O7 hexagonal pyramids,  a cornercorner with one Mg(1)O5 trigonal bipyramid, corners with two equivalent Hf(3)O5 trigonal bipyramids, and edges with two equivalent La(8)O7 hexagonal pyramids. In the fourth Hf site, Hf(4) is bonded in a 5-coordinate geometry to one O(13), one O(17), one O(19), and two equivalent O(16) atoms. There are twenty inequivalent O sites. In the first O site, O(1) is bonded to one La(7), one La(8), and two equivalent La(2) atoms to form OLa4 tetrahedra that share  a cornercorner with one O(17)La3Hf tetrahedra, corners with two equivalent O(18)La3Hf tetrahedra, corners with two equivalent O(7)La3Hf tetrahedra, corners with two equivalent O(8)La3Hf tetrahedra, corners with two equivalent O(1)La4 tetrahedra,  an edgeedge with one O(7)La3Hf tetrahedra, edges with two equivalent O(20)La4Mg trigonal bipyramids, and  an edgeedge with one O(15)La2Hf2 trigonal pyramid. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to two equivalent La(8) and one Hf(1) atom. In the third O site, O(3) is bonded to one La(3), two equivalent La(1), and one Hf(2) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(5)La2Hf2 tetrahedra,  a cornercorner with one O(7)La3Hf tetrahedra,  a cornercorner with one O(11)La4 tetrahedra, corners with two equivalent O(3)La3Hf tetrahedra, corners with two equivalent O(10)La4 tetrahedra, corners with two equivalent O(20)La4Mg trigonal bipyramids, and edges with two equivalent O(4)La3Hf tetrahedra. In the fourth O site, O(4) is bonded to one La(1), two equivalent La(3), and one Hf(1) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(8)La3Hf tetrahedra, corners with two equivalent O(4)La3Hf tetrahedra, corners with two equivalent O(10)La4 tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(20)La4Mg trigonal bipyramid,  an edgeedge with one O(10)La4 tetrahedra, edges with two equivalent O(5)La2Hf2 tetrahedra, and edges with two equivalent O(3)La3Hf tetrahedra. In the fifth O site, O(5) is bonded to one La(3), one La(4), and two equivalent Hf(1) atoms to form distorted OLa2Hf2 tetrahedra that share  a cornercorner with one O(3)La3Hf tetrahedra,  a cornercorner with one O(7)La3Hf tetrahedra, corners with two equivalent O(5)La2Hf2 tetrahedra, corners with two equivalent O(10)La4 tetrahedra,  an edgeedge with one O(11)La4 tetrahedra, edges with two equivalent O(4)La3Hf tetrahedra, and edges with two equivalent O(8)La3Hf tetrahedra. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one La(1), one La(2), and two equivalent Hf(2) atoms. In the seventh O site, O(7) is bonded to one La(4), two equivalent La(2), and one Hf(2) atom to form distorted OLa3Hf tetrahedra that share  a cornercorner with one O(5)La2Hf2 tetrahedra,  a cornercorner with one O(3)La3Hf tetrahedra,  a cornercorner with one O(11)La4 tetrahedra, corners with two equivalent O(7)La3Hf tetrahedra, corners with two equivalent O(1)La4 tetrahedra, corners with two equivalent O(20)La4Mg trigonal bipyramids,  an edgeedge with one O(1)La4 tetrahedra, and edges with two equivalent O(8)La3Hf tetrahedra. In the eighth O site, O(8) is bonded to one La(2), two equivalent La(4), and one Hf(1) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(4)La3Hf tetrahedra, corners with two equivalent O(8)La3Hf tetrahedra, corners with two equivalent O(1)La4 tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(20)La4Mg trigonal bipyramid, edges with two equivalent O(5)La2Hf2 tetrahedra, and edges with two equivalent O(7)La3Hf tetrahedra. In the ninth O site, O(9) is bonded in a trigonal planar geometry to two equivalent La(5) and one Hf(2) atom. In the tenth O site, O(10) is bonded to one La(5), one La(6), and two equivalent La(3) atoms to form distorted OLa4 tetrahedra that share  a cornercorner with one O(18)La3Hf tetrahedra, corners with two equivalent O(5)La2Hf2 tetrahedra, corners with two equivalent O(17)La3Hf tetrahedra, corners with two equivalent O(3)La3Hf tetrahedra, corners with two equivalent O(4)La3Hf tetrahedra, corners with two equivalent O(10)La4 tetrahedra,  an edgeedge with one O(4)La3Hf tetrahedra, edges with two equivalent O(11)La4 tetrahedra, and  an edgeedge with one O(16)La2Hf2Mg trigonal bipyramid. In the eleventh O site, O(11) is bonded to one La(3), one La(4), and two equivalent La(6) atoms to form OLa4 tetrahedra that share  a cornercorner with one O(3)La3Hf tetrahedra,  a cornercorner with one O(7)La3Hf tetrahedra, corners with two equivalent O(17)La3Hf tetrahedra, corners with two equivalent O(18)La3Hf tetrahedra, corners with two equivalent O(4)La3Hf tetrahedra, corners with two equivalent O(8)La3Hf tetrahedra, corners with two equivalent O(11)La4 tetrahedra, corners with two equivalent O(16)La2Hf2Mg trigonal bipyramids,  an edgeedge with one O(5)La2Hf2 tetrahedra,  an edgeedge with one O(17)La3Hf tetrahedra, and edges with two equivalent O(10)La4 tetrahedra. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to two equivalent La(4) and one Hf(3) atom. In the thirteenth O site, O(13) is bonded in a 6-coordinate geometry to two equivalent Mg(1), one La(7), two equivalent La(5), and one Hf(4) atom. In the fourteenth O site, O(14) is bonded in a 5-coordinate geometry to one Mg(1), one La(5), two equivalent La(7), and one Hf(3) atom. In the fifteenth O site, O(15) is bonded to one La(7), one La(8), and two equivalent Hf(3) atoms to form distorted OLa2Hf2 trigonal pyramids that share  a cornercorner with one O(17)La3Hf tetrahedra, corners with two equivalent O(20)La4Mg trigonal bipyramids, corners with two equivalent O(15)La2Hf2 trigonal pyramids,  an edgeedge with one O(1)La4 tetrahedra, and edges with two equivalent O(18)La3Hf tetrahedra. In the sixteenth O site, O(16) is bonded to one Mg(1), one La(5), one La(6), and two equivalent Hf(4) atoms to form distorted OLa2Hf2Mg trigonal bipyramids that share  a cornercorner with one O(18)La3Hf tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(20)La4Mg trigonal bipyramid, corners with two equivalent O(16)La2Hf2Mg trigonal bipyramids,  an edgeedge with one O(10)La4 tetrahedra, and edges with two equivalent O(17)La3Hf tetrahedra. In the seventeenth O site, O(17) is bonded to one La(8), two equivalent La(6), and one Hf(4) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(1)La4 tetrahedra, corners with two equivalent O(17)La3Hf tetrahedra, corners with two equivalent O(10)La4 tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(15)La2Hf2 trigonal pyramid,  an edgeedge with one O(11)La4 tetrahedra, edges with two equivalent O(18)La3Hf tetrahedra, and edges with two equivalent O(16)La2Hf2Mg trigonal bipyramids. In the eighteenth O site, O(18) is bonded to one La(6), two equivalent La(8), and one Hf(3) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(10)La4 tetrahedra, corners with two equivalent O(18)La3Hf tetrahedra, corners with two equivalent O(1)La4 tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(16)La2Hf2Mg trigonal bipyramid, edges with two equivalent O(17)La3Hf tetrahedra, and edges with two equivalent O(15)La2Hf2 trigonal pyramids. In the nineteenth O site, O(19) is bonded in a distorted trigonal non-coplanar geometry to two equivalent La(1) and one Hf(4) atom. In the twentieth O site, O(20) is bonded to one Mg(1), one La(1), one La(2), and two equivalent La(7) atoms to form distorted OLa4Mg trigonal bipyramids that share  a cornercorner with one O(4)La3Hf tetrahedra,  a cornercorner with one O(8)La3Hf tetrahedra, corners with two equivalent O(3)La3Hf tetrahedra, corners with two equivalent O(7)La3Hf tetrahedra,  a cornercorner with one O(16)La2Hf2Mg trigonal bipyramid, corners with two equivalent O(20)La4Mg trigonal bipyramids, corners with two equivalent O(15)La2Hf2 trigonal pyramids, and edges with two equivalent O(1)La4 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_La8Hf4MgO20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   11.362
_cell_length_b   12.045
_cell_length_c   3.949
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.066
_symmetry_Int_Tables_number   1
_cell_volume   540.428
_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
  La  La0  1  0.107  0.703  0.250  1.0
  La  La1  1  0.141  0.067  0.250  1.0
  La  La2  1  0.361  0.556  0.750  1.0
  La  La3  1  0.394  0.220  0.750  1.0
  La  La4  1  0.584  0.774  0.250  1.0
  La  La5  1  0.632  0.441  0.250  1.0
  La  La6  1  0.878  0.979  0.750  1.0
  La  La7  1  0.888  0.282  0.750  1.0
  Hf  Hf8  1  0.177  0.377  0.250  1.0
  Hf  Hf9  1  0.314  0.876  0.750  1.0
  Hf  Hf10  1  0.681  0.120  0.250  1.0
  Hf  Hf11  1  0.835  0.614  0.750  1.0
  Mg  Mg12  1  0.839  0.799  0.250  1.0
  O  O13  1  0.029  0.113  0.750  1.0
  O  O14  1  0.010  0.339  0.250  1.0
  O  O15  1  0.232  0.727  0.750  1.0
  O  O16  1  0.233  0.538  0.250  1.0
  O  O17  1  0.236  0.381  0.750  1.0
  O  O18  1  0.260  0.881  0.250  1.0
  O  O19  1  0.281  0.042  0.750  1.0
  O  O20  1  0.266  0.231  0.250  1.0
  O  O21  1  0.481  0.830  0.750  1.0
  O  O22  1  0.487  0.608  0.250  1.0
  O  O23  1  0.503  0.401  0.750  1.0
  O  O24  1  0.513  0.159  0.250  1.0
  O  O25  1  0.778  0.779  0.750  1.0
  O  O26  1  0.725  0.949  0.250  1.0
  O  O27  1  0.730  0.122  0.750  1.0
  O  O28  1  0.747  0.627  0.250  1.0
  O  O29  1  0.771  0.458  0.750  1.0
  O  O30  1  0.750  0.277  0.250  1.0
  O  O31  1  0.006  0.613  0.750  1.0
  O  O32  1  0.984  0.896  0.250  1.0
[/CIF]
.
The crystal structure described by MgLa8Hf4O20 crystallizes in the monoclinic Pm space group. Mg(1) is bonded to one O(14), one O(16), one O(20), and two equivalent O(13) atoms to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Hf(3)O5 trigonal bipyramid and corners with two equivalent Mg(1)O5 trigonal bipyramids. There are eight inequivalent La sites. In the first La site, La(1) is bonded in a 7-coordinate geometry to one O(20), one O(4), one O(6), two equivalent O(19), and two equivalent O(3) atoms. In the second La site, La(2) is bonded in a 7-coordinate geometry to one O(20), one O(6), one O(8), two equivalent O(1), and two equivalent O(7) atoms. In the third La site, La(3) is bonded to one O(11), one O(3), one O(5), two equivalent O(10), and two equivalent O(4) atoms to form distorted LaO7 hexagonal pyramids that share  a cornercorner with one Hf(2)O5 trigonal bipyramid,  an edgeedge with one La(4)O7 hexagonal pyramid, edges with two equivalent La(3)O7 hexagonal pyramids, and edges with two equivalent Hf(1)O5 trigonal bipyramids. In the fourth La site, La(4) is bonded to one O(11), one O(5), one O(7), two equivalent O(12), and two equivalent O(8) atoms to form distorted LaO7 hexagonal pyramids that share  a cornercorner with one Hf(2)O5 trigonal bipyramid, corners with two equivalent Hf(3)O5 trigonal bipyramids,  an edgeedge with one La(3)O7 hexagonal pyramid, edges with two equivalent La(4)O7 hexagonal pyramids, and edges with two equivalent Hf(1)O5 trigonal bipyramids. In the fifth La site, La(5) is bonded in a 5-coordinate geometry to one O(10), one O(14), one O(16), two equivalent O(13), and two equivalent O(9) atoms. In the sixth La site, La(6) is bonded in a 7-coordinate geometry to one O(10), one O(16), one O(18), two equivalent O(11), and two equivalent O(17) atoms. In the seventh La site, La(7) is bonded in a 7-coordinate geometry to one O(1), one O(13), one O(15), two equivalent O(14), and two equivalent O(20) atoms. In the eighth La site, La(8) is bonded to one O(1), one O(15), one O(17), two equivalent O(18), and two equivalent O(2) atoms to form distorted LaO7 hexagonal pyramids that share corners with two equivalent Hf(1)O5 trigonal bipyramids, edges with two equivalent La(8)O7 hexagonal pyramids, and edges with two equivalent Hf(3)O5 trigonal bipyramids. There are four inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one O(2), one O(4), one O(8), and two equivalent O(5) atoms to form distorted HfO5 trigonal bipyramids that share corners with two equivalent La(8)O7 hexagonal pyramids, corners with two equivalent Hf(1)O5 trigonal bipyramids, edges with two equivalent La(3)O7 hexagonal pyramids, and edges with two equivalent La(4)O7 hexagonal pyramids. In the second Hf site, Hf(2) is bonded to one O(3), one O(7), one O(9), and two equivalent O(6) atoms to form distorted HfO5 trigonal bipyramids that share  a cornercorner with one La(3)O7 hexagonal pyramid,  a cornercorner with one La(4)O7 hexagonal pyramid, and corners with two equivalent Hf(2)O5 trigonal bipyramids. In the third Hf site, Hf(3) is bonded to one O(12), one O(14), one O(18), and two equivalent O(15) atoms to form distorted HfO5 trigonal bipyramids that share corners with two equivalent La(4)O7 hexagonal pyramids,  a cornercorner with one Mg(1)O5 trigonal bipyramid, corners with two equivalent Hf(3)O5 trigonal bipyramids, and edges with two equivalent La(8)O7 hexagonal pyramids. In the fourth Hf site, Hf(4) is bonded in a 5-coordinate geometry to one O(13), one O(17), one O(19), and two equivalent O(16) atoms. There are twenty inequivalent O sites. In the first O site, O(1) is bonded to one La(7), one La(8), and two equivalent La(2) atoms to form OLa4 tetrahedra that share  a cornercorner with one O(17)La3Hf tetrahedra, corners with two equivalent O(18)La3Hf tetrahedra, corners with two equivalent O(7)La3Hf tetrahedra, corners with two equivalent O(8)La3Hf tetrahedra, corners with two equivalent O(1)La4 tetrahedra,  an edgeedge with one O(7)La3Hf tetrahedra, edges with two equivalent O(20)La4Mg trigonal bipyramids, and  an edgeedge with one O(15)La2Hf2 trigonal pyramid. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to two equivalent La(8) and one Hf(1) atom. In the third O site, O(3) is bonded to one La(3), two equivalent La(1), and one Hf(2) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(5)La2Hf2 tetrahedra,  a cornercorner with one O(7)La3Hf tetrahedra,  a cornercorner with one O(11)La4 tetrahedra, corners with two equivalent O(3)La3Hf tetrahedra, corners with two equivalent O(10)La4 tetrahedra, corners with two equivalent O(20)La4Mg trigonal bipyramids, and edges with two equivalent O(4)La3Hf tetrahedra. In the fourth O site, O(4) is bonded to one La(1), two equivalent La(3), and one Hf(1) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(8)La3Hf tetrahedra, corners with two equivalent O(4)La3Hf tetrahedra, corners with two equivalent O(10)La4 tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(20)La4Mg trigonal bipyramid,  an edgeedge with one O(10)La4 tetrahedra, edges with two equivalent O(5)La2Hf2 tetrahedra, and edges with two equivalent O(3)La3Hf tetrahedra. In the fifth O site, O(5) is bonded to one La(3), one La(4), and two equivalent Hf(1) atoms to form distorted OLa2Hf2 tetrahedra that share  a cornercorner with one O(3)La3Hf tetrahedra,  a cornercorner with one O(7)La3Hf tetrahedra, corners with two equivalent O(5)La2Hf2 tetrahedra, corners with two equivalent O(10)La4 tetrahedra,  an edgeedge with one O(11)La4 tetrahedra, edges with two equivalent O(4)La3Hf tetrahedra, and edges with two equivalent O(8)La3Hf tetrahedra. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one La(1), one La(2), and two equivalent Hf(2) atoms. In the seventh O site, O(7) is bonded to one La(4), two equivalent La(2), and one Hf(2) atom to form distorted OLa3Hf tetrahedra that share  a cornercorner with one O(5)La2Hf2 tetrahedra,  a cornercorner with one O(3)La3Hf tetrahedra,  a cornercorner with one O(11)La4 tetrahedra, corners with two equivalent O(7)La3Hf tetrahedra, corners with two equivalent O(1)La4 tetrahedra, corners with two equivalent O(20)La4Mg trigonal bipyramids,  an edgeedge with one O(1)La4 tetrahedra, and edges with two equivalent O(8)La3Hf tetrahedra. In the eighth O site, O(8) is bonded to one La(2), two equivalent La(4), and one Hf(1) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(4)La3Hf tetrahedra, corners with two equivalent O(8)La3Hf tetrahedra, corners with two equivalent O(1)La4 tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(20)La4Mg trigonal bipyramid, edges with two equivalent O(5)La2Hf2 tetrahedra, and edges with two equivalent O(7)La3Hf tetrahedra. In the ninth O site, O(9) is bonded in a trigonal planar geometry to two equivalent La(5) and one Hf(2) atom. In the tenth O site, O(10) is bonded to one La(5), one La(6), and two equivalent La(3) atoms to form distorted OLa4 tetrahedra that share  a cornercorner with one O(18)La3Hf tetrahedra, corners with two equivalent O(5)La2Hf2 tetrahedra, corners with two equivalent O(17)La3Hf tetrahedra, corners with two equivalent O(3)La3Hf tetrahedra, corners with two equivalent O(4)La3Hf tetrahedra, corners with two equivalent O(10)La4 tetrahedra,  an edgeedge with one O(4)La3Hf tetrahedra, edges with two equivalent O(11)La4 tetrahedra, and  an edgeedge with one O(16)La2Hf2Mg trigonal bipyramid. In the eleventh O site, O(11) is bonded to one La(3), one La(4), and two equivalent La(6) atoms to form OLa4 tetrahedra that share  a cornercorner with one O(3)La3Hf tetrahedra,  a cornercorner with one O(7)La3Hf tetrahedra, corners with two equivalent O(17)La3Hf tetrahedra, corners with two equivalent O(18)La3Hf tetrahedra, corners with two equivalent O(4)La3Hf tetrahedra, corners with two equivalent O(8)La3Hf tetrahedra, corners with two equivalent O(11)La4 tetrahedra, corners with two equivalent O(16)La2Hf2Mg trigonal bipyramids,  an edgeedge with one O(5)La2Hf2 tetrahedra,  an edgeedge with one O(17)La3Hf tetrahedra, and edges with two equivalent O(10)La4 tetrahedra. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to two equivalent La(4) and one Hf(3) atom. In the thirteenth O site, O(13) is bonded in a 6-coordinate geometry to two equivalent Mg(1), one La(7), two equivalent La(5), and one Hf(4) atom. In the fourteenth O site, O(14) is bonded in a 5-coordinate geometry to one Mg(1), one La(5), two equivalent La(7), and one Hf(3) atom. In the fifteenth O site, O(15) is bonded to one La(7), one La(8), and two equivalent Hf(3) atoms to form distorted OLa2Hf2 trigonal pyramids that share  a cornercorner with one O(17)La3Hf tetrahedra, corners with two equivalent O(20)La4Mg trigonal bipyramids, corners with two equivalent O(15)La2Hf2 trigonal pyramids,  an edgeedge with one O(1)La4 tetrahedra, and edges with two equivalent O(18)La3Hf tetrahedra. In the sixteenth O site, O(16) is bonded to one Mg(1), one La(5), one La(6), and two equivalent Hf(4) atoms to form distorted OLa2Hf2Mg trigonal bipyramids that share  a cornercorner with one O(18)La3Hf tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(20)La4Mg trigonal bipyramid, corners with two equivalent O(16)La2Hf2Mg trigonal bipyramids,  an edgeedge with one O(10)La4 tetrahedra, and edges with two equivalent O(17)La3Hf tetrahedra. In the seventeenth O site, O(17) is bonded to one La(8), two equivalent La(6), and one Hf(4) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(1)La4 tetrahedra, corners with two equivalent O(17)La3Hf tetrahedra, corners with two equivalent O(10)La4 tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(15)La2Hf2 trigonal pyramid,  an edgeedge with one O(11)La4 tetrahedra, edges with two equivalent O(18)La3Hf tetrahedra, and edges with two equivalent O(16)La2Hf2Mg trigonal bipyramids. In the eighteenth O site, O(18) is bonded to one La(6), two equivalent La(8), and one Hf(3) atom to form OLa3Hf tetrahedra that share  a cornercorner with one O(10)La4 tetrahedra, corners with two equivalent O(18)La3Hf tetrahedra, corners with two equivalent O(1)La4 tetrahedra, corners with two equivalent O(11)La4 tetrahedra,  a cornercorner with one O(16)La2Hf2Mg trigonal bipyramid, edges with two equivalent O(17)La3Hf tetrahedra, and edges with two equivalent O(15)La2Hf2 trigonal pyramids. In the nineteenth O site, O(19) is bonded in a distorted trigonal non-coplanar geometry to two equivalent La(1) and one Hf(4) atom. In the twentieth O site, O(20) is bonded to one Mg(1), one La(1), one La(2), and two equivalent La(7) atoms to form distorted OLa4Mg trigonal bipyramids that share  a cornercorner with one O(4)La3Hf tetrahedra,  a cornercorner with one O(8)La3Hf tetrahedra, corners with two equivalent O(3)La3Hf tetrahedra, corners with two equivalent O(7)La3Hf tetrahedra,  a cornercorner with one O(16)La2Hf2Mg trigonal bipyramid, corners with two equivalent O(20)La4Mg trigonal bipyramids, corners with two equivalent O(15)La2Hf2 trigonal pyramids, and edges with two equivalent O(1)La4 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_La8Hf4MgO20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   11.362
_cell_length_b   12.045
_cell_length_c   3.949
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.066
_symmetry_Int_Tables_number   1
_cell_volume   540.428
_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
  La  La0  1  0.107  0.703  0.250  1.0
  La  La1  1  0.141  0.067  0.250  1.0
  La  La2  1  0.361  0.556  0.750  1.0
  La  La3  1  0.394  0.220  0.750  1.0
  La  La4  1  0.584  0.774  0.250  1.0
  La  La5  1  0.632  0.441  0.250  1.0
  La  La6  1  0.878  0.979  0.750  1.0
  La  La7  1  0.888  0.282  0.750  1.0
  Hf  Hf8  1  0.177  0.377  0.250  1.0
  Hf  Hf9  1  0.314  0.876  0.750  1.0
  Hf  Hf10  1  0.681  0.120  0.250  1.0
  Hf  Hf11  1  0.835  0.614  0.750  1.0
  Mg  Mg12  1  0.839  0.799  0.250  1.0
  O  O13  1  0.029  0.113  0.750  1.0
  O  O14  1  0.010  0.339  0.250  1.0
  O  O15  1  0.232  0.727  0.750  1.0
  O  O16  1  0.233  0.538  0.250  1.0
  O  O17  1  0.236  0.381  0.750  1.0
  O  O18  1  0.260  0.881  0.250  1.0
  O  O19  1  0.281  0.042  0.750  1.0
  O  O20  1  0.266  0.231  0.250  1.0
  O  O21  1  0.481  0.830  0.750  1.0
  O  O22  1  0.487  0.608  0.250  1.0
  O  O23  1  0.503  0.401  0.750  1.0
  O  O24  1  0.513  0.159  0.250  1.0
  O  O25  1  0.778  0.779  0.750  1.0
  O  O26  1  0.725  0.949  0.250  1.0
  O  O27  1  0.730  0.122  0.750  1.0
  O  O28  1  0.747  0.627  0.250  1.0
  O  O29  1  0.771  0.458  0.750  1.0
  O  O30  1  0.750  0.277  0.250  1.0
  O  O31  1  0.006  0.613  0.750  1.0
  O  O32  1  0.984  0.896  0.250  1.0
[/CIF]
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