The compound described by RbMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. Rb(1) is bonded in a 4-coordinate geometry to two equivalent O(10) and two equivalent O(6) atoms. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(2), two equivalent O(11), and two equivalent O(8) atoms to form a mixture of distorted corner and edge-sharing MgO5 trigonal bipyramids. In the second Mg site, Mg(2) is bonded to one O(3), two equivalent O(11), and two equivalent O(9) atoms to form a mixture of corner and edge-sharing MgO5 trigonal bipyramids. In the third Mg site, Mg(3) is bonded in a 5-coordinate geometry to one O(5), one O(6), one O(7), and two equivalent O(10) atoms. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(8), one O(9), and two equivalent O(11) atoms to form a mixture of corner and edge-sharing MgO5 trigonal bipyramids. In the fifth Mg site, Mg(5) is bonded in a T-shaped geometry to one O(8) and two equivalent O(4) atoms. In the sixth Mg site, Mg(6) is bonded to one O(7), two equivalent O(1), and two equivalent O(4) atoms to form MgO5 trigonal bipyramids that share corners with two equivalent Mg(4)O5 trigonal bipyramids, corners with two equivalent Mg(6)O5 trigonal bipyramids, and edges with two equivalent Hf(1)O5 trigonal bipyramids. In the seventh Mg site, Mg(7) is bonded to one O(6), two equivalent O(2), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing MgO5 trigonal bipyramids. In the eighth Mg site, Mg(8) is bonded to one O(9), two equivalent O(3), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing MgO5 trigonal bipyramids. In the ninth Mg site, Mg(9) is bonded in a see-saw-like geometry to one O(1), one O(11), and two equivalent O(4) atoms. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(2), one O(3), and two equivalent O(5) atoms to form MgO5 trigonal bipyramids that share  a cornercorner with one Mg(1)O5 trigonal bipyramid,  a cornercorner with one Mg(2)O5 trigonal bipyramid,  a cornercorner with one Hf(1)O5 trigonal bipyramid, corners with four equivalent Mg(10)O5 trigonal bipyramids, edges with two equivalent Mg(7)O5 trigonal bipyramids, and edges with two equivalent Mg(8)O5 trigonal bipyramids. Hf(1) is bonded to one O(1), two equivalent O(10), and two equivalent O(7) atoms to form HfO5 trigonal bipyramids that share corners with two equivalent Mg(10)O5 trigonal bipyramids, corners with two equivalent Hf(1)O5 trigonal bipyramids, and edges with two equivalent Mg(6)O5 trigonal bipyramids. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(6), two equivalent Mg(9), and one Hf(1) atom to form OHfMg4 trigonal bipyramids that share corners with two equivalent O(1)HfMg4 trigonal bipyramids, corners with two equivalent O(11)Mg5 trigonal bipyramids, edges with two equivalent O(7)Hf2Mg3 trigonal bipyramids, and edges with four equivalent O(4)Mg5 trigonal bipyramids. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(10), and two equivalent Mg(7) atoms to form distorted OMg5 trigonal bipyramids that share corners with two equivalent O(11)Mg5 trigonal bipyramids, corners with two equivalent O(2)Mg5 trigonal bipyramids, corners with two equivalent O(3)Mg5 trigonal bipyramids, corners with two equivalent O(8)Mg5 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, and edges with four equivalent O(5)Mg5 trigonal bipyramids. In the third O site, O(3) is bonded to one Mg(2), two equivalent Mg(10), and two equivalent Mg(8) atoms to form a mixture of corner and edge-sharing OMg5 trigonal bipyramids. In the fourth O site, O(4) is bonded to one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg5 trigonal bipyramids that share  a cornercorner with one O(7)Hf2Mg3 trigonal bipyramid,  a cornercorner with one O(9)Mg5 trigonal bipyramid, corners with four equivalent O(4)Mg5 trigonal bipyramids,  an edgeedge with one O(8)Mg5 trigonal bipyramid, edges with two equivalent O(1)HfMg4 trigonal bipyramids, and edges with two equivalent O(11)Mg5 trigonal bipyramids. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg5 trigonal bipyramids that share  a cornercorner with one O(7)Hf2Mg3 trigonal bipyramid,  a cornercorner with one O(9)Mg5 trigonal bipyramid, corners with four equivalent O(5)Mg5 trigonal bipyramids,  an edgeedge with one O(6)Rb2Mg3 trigonal bipyramid, edges with two equivalent O(2)Mg5 trigonal bipyramids, and edges with two equivalent O(3)Mg5 trigonal bipyramids. In the sixth O site, O(6) is bonded to two equivalent Rb(1), one Mg(7), and two equivalent Mg(3) atoms to form distorted ORb2Mg3 trigonal bipyramids that share corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(2)Mg5 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, and edges with two equivalent O(5)Mg5 trigonal bipyramids. In the seventh O site, O(7) is bonded to one Mg(6), two equivalent Mg(3), and two equivalent Hf(1) atoms to form OHf2Mg3 trigonal bipyramids that share corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(4)Mg5 trigonal bipyramids, corners with two equivalent O(5)Mg5 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, and edges with two equivalent O(1)HfMg4 trigonal bipyramids. In the eighth O site, O(8) is bonded to one Mg(5), two equivalent Mg(1), and two equivalent Mg(4) atoms to form a mixture of corner and edge-sharing OMg5 trigonal bipyramids. In the ninth O site, O(9) is bonded to one Mg(8), two equivalent Mg(2), and two equivalent Mg(4) atoms to form a mixture of corner and edge-sharing OMg5 trigonal bipyramids. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to one Rb(1), one Mg(10), two equivalent Mg(3), and one Hf(1) atom. In the eleventh O site, O(11) is bonded to one Mg(1), one Mg(2), one Mg(9), and two equivalent Mg(4) atoms to form OMg5 trigonal bipyramids that share  a cornercorner with one O(1)HfMg4 trigonal bipyramid,  a cornercorner with one O(2)Mg5 trigonal bipyramid,  a cornercorner with one O(3)Mg5 trigonal bipyramid, corners with four equivalent O(11)Mg5 trigonal bipyramids, edges with two equivalent O(4)Mg5 trigonal bipyramids, edges with two equivalent O(8)Mg5 trigonal bipyramids, and edges with two equivalent O(9)Mg5 trigonal bipyramids. is represented by the CIF card [CIF]
data_RbHfMg14O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.451
_cell_length_b   7.835
_cell_length_c   4.173
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   407.097
_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
  Rb  Rb0  1  0.064  0.000  0.000  1.0
  Hf  Hf1  1  0.039  0.500  0.000  1.0
  Mg  Mg2  1  0.534  0.000  0.000  1.0
  Mg  Mg3  1  0.543  0.500  0.000  1.0
  Mg  Mg4  1  0.924  0.247  0.500  1.0
  Mg  Mg5  1  0.924  0.753  0.500  1.0
  Mg  Mg6  1  0.481  0.262  0.500  1.0
  Mg  Mg7  1  0.481  0.738  0.500  1.0
  Mg  Mg8  1  0.322  0.000  0.500  1.0
  Mg  Mg9  1  0.230  0.500  0.500  1.0
  Mg  Mg10  1  0.752  0.000  0.500  1.0
  Mg  Mg11  1  0.702  0.500  0.500  1.0
  Mg  Mg12  1  0.314  0.262  0.000  1.0
  Mg  Mg13  1  0.314  0.738  0.000  1.0
  Mg  Mg14  1  0.760  0.258  0.000  1.0
  Mg  Mg15  1  0.760  0.742  0.000  1.0
  O  O16  1  0.210  0.500  0.000  1.0
  O  O17  1  0.703  0.000  0.000  1.0
  O  O18  1  0.703  0.500  0.000  1.0
  O  O19  1  0.315  0.276  0.500  1.0
  O  O20  1  0.315  0.724  0.500  1.0
  O  O21  1  0.762  0.261  0.500  1.0
  O  O22  1  0.762  0.739  0.500  1.0
  O  O23  1  0.920  0.000  0.500  1.0
  O  O24  1  0.048  0.500  0.500  1.0
  O  O25  1  0.496  0.000  0.500  1.0
  O  O26  1  0.542  0.500  0.500  1.0
  O  O27  1  0.933  0.308  0.000  1.0
  O  O28  1  0.933  0.692  0.000  1.0
  O  O29  1  0.482  0.260  0.000  1.0
  O  O30  1  0.482  0.740  0.000  1.0
[/CIF]
.
The compound described by RbMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. Rb(1) is bonded in a 4-coordinate geometry to two equivalent O(10) and two equivalent O(6) atoms. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(2), two equivalent O(11), and two equivalent O(8) atoms to form a mixture of distorted corner and edge-sharing MgO5 trigonal bipyramids. In the second Mg site, Mg(2) is bonded to one O(3), two equivalent O(11), and two equivalent O(9) atoms to form a mixture of corner and edge-sharing MgO5 trigonal bipyramids. In the third Mg site, Mg(3) is bonded in a 5-coordinate geometry to one O(5), one O(6), one O(7), and two equivalent O(10) atoms. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(8), one O(9), and two equivalent O(11) atoms to form a mixture of corner and edge-sharing MgO5 trigonal bipyramids. In the fifth Mg site, Mg(5) is bonded in a T-shaped geometry to one O(8) and two equivalent O(4) atoms. In the sixth Mg site, Mg(6) is bonded to one O(7), two equivalent O(1), and two equivalent O(4) atoms to form MgO5 trigonal bipyramids that share corners with two equivalent Mg(4)O5 trigonal bipyramids, corners with two equivalent Mg(6)O5 trigonal bipyramids, and edges with two equivalent Hf(1)O5 trigonal bipyramids. In the seventh Mg site, Mg(7) is bonded to one O(6), two equivalent O(2), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing MgO5 trigonal bipyramids. In the eighth Mg site, Mg(8) is bonded to one O(9), two equivalent O(3), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing MgO5 trigonal bipyramids. In the ninth Mg site, Mg(9) is bonded in a see-saw-like geometry to one O(1), one O(11), and two equivalent O(4) atoms. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(2), one O(3), and two equivalent O(5) atoms to form MgO5 trigonal bipyramids that share  a cornercorner with one Mg(1)O5 trigonal bipyramid,  a cornercorner with one Mg(2)O5 trigonal bipyramid,  a cornercorner with one Hf(1)O5 trigonal bipyramid, corners with four equivalent Mg(10)O5 trigonal bipyramids, edges with two equivalent Mg(7)O5 trigonal bipyramids, and edges with two equivalent Mg(8)O5 trigonal bipyramids. Hf(1) is bonded to one O(1), two equivalent O(10), and two equivalent O(7) atoms to form HfO5 trigonal bipyramids that share corners with two equivalent Mg(10)O5 trigonal bipyramids, corners with two equivalent Hf(1)O5 trigonal bipyramids, and edges with two equivalent Mg(6)O5 trigonal bipyramids. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(6), two equivalent Mg(9), and one Hf(1) atom to form OHfMg4 trigonal bipyramids that share corners with two equivalent O(1)HfMg4 trigonal bipyramids, corners with two equivalent O(11)Mg5 trigonal bipyramids, edges with two equivalent O(7)Hf2Mg3 trigonal bipyramids, and edges with four equivalent O(4)Mg5 trigonal bipyramids. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(10), and two equivalent Mg(7) atoms to form distorted OMg5 trigonal bipyramids that share corners with two equivalent O(11)Mg5 trigonal bipyramids, corners with two equivalent O(2)Mg5 trigonal bipyramids, corners with two equivalent O(3)Mg5 trigonal bipyramids, corners with two equivalent O(8)Mg5 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, and edges with four equivalent O(5)Mg5 trigonal bipyramids. In the third O site, O(3) is bonded to one Mg(2), two equivalent Mg(10), and two equivalent Mg(8) atoms to form a mixture of corner and edge-sharing OMg5 trigonal bipyramids. In the fourth O site, O(4) is bonded to one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg5 trigonal bipyramids that share  a cornercorner with one O(7)Hf2Mg3 trigonal bipyramid,  a cornercorner with one O(9)Mg5 trigonal bipyramid, corners with four equivalent O(4)Mg5 trigonal bipyramids,  an edgeedge with one O(8)Mg5 trigonal bipyramid, edges with two equivalent O(1)HfMg4 trigonal bipyramids, and edges with two equivalent O(11)Mg5 trigonal bipyramids. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg5 trigonal bipyramids that share  a cornercorner with one O(7)Hf2Mg3 trigonal bipyramid,  a cornercorner with one O(9)Mg5 trigonal bipyramid, corners with four equivalent O(5)Mg5 trigonal bipyramids,  an edgeedge with one O(6)Rb2Mg3 trigonal bipyramid, edges with two equivalent O(2)Mg5 trigonal bipyramids, and edges with two equivalent O(3)Mg5 trigonal bipyramids. In the sixth O site, O(6) is bonded to two equivalent Rb(1), one Mg(7), and two equivalent Mg(3) atoms to form distorted ORb2Mg3 trigonal bipyramids that share corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(2)Mg5 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, and edges with two equivalent O(5)Mg5 trigonal bipyramids. In the seventh O site, O(7) is bonded to one Mg(6), two equivalent Mg(3), and two equivalent Hf(1) atoms to form OHf2Mg3 trigonal bipyramids that share corners with two equivalent O(7)Hf2Mg3 trigonal bipyramids, corners with two equivalent O(4)Mg5 trigonal bipyramids, corners with two equivalent O(5)Mg5 trigonal bipyramids, corners with two equivalent O(6)Rb2Mg3 trigonal bipyramids, and edges with two equivalent O(1)HfMg4 trigonal bipyramids. In the eighth O site, O(8) is bonded to one Mg(5), two equivalent Mg(1), and two equivalent Mg(4) atoms to form a mixture of corner and edge-sharing OMg5 trigonal bipyramids. In the ninth O site, O(9) is bonded to one Mg(8), two equivalent Mg(2), and two equivalent Mg(4) atoms to form a mixture of corner and edge-sharing OMg5 trigonal bipyramids. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to one Rb(1), one Mg(10), two equivalent Mg(3), and one Hf(1) atom. In the eleventh O site, O(11) is bonded to one Mg(1), one Mg(2), one Mg(9), and two equivalent Mg(4) atoms to form OMg5 trigonal bipyramids that share  a cornercorner with one O(1)HfMg4 trigonal bipyramid,  a cornercorner with one O(2)Mg5 trigonal bipyramid,  a cornercorner with one O(3)Mg5 trigonal bipyramid, corners with four equivalent O(11)Mg5 trigonal bipyramids, edges with two equivalent O(4)Mg5 trigonal bipyramids, edges with two equivalent O(8)Mg5 trigonal bipyramids, and edges with two equivalent O(9)Mg5 trigonal bipyramids. is represented by the CIF card [CIF]
data_RbHfMg14O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.451
_cell_length_b   7.835
_cell_length_c   4.173
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   407.097
_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
  Rb  Rb0  1  0.064  0.000  0.000  1.0
  Hf  Hf1  1  0.039  0.500  0.000  1.0
  Mg  Mg2  1  0.534  0.000  0.000  1.0
  Mg  Mg3  1  0.543  0.500  0.000  1.0
  Mg  Mg4  1  0.924  0.247  0.500  1.0
  Mg  Mg5  1  0.924  0.753  0.500  1.0
  Mg  Mg6  1  0.481  0.262  0.500  1.0
  Mg  Mg7  1  0.481  0.738  0.500  1.0
  Mg  Mg8  1  0.322  0.000  0.500  1.0
  Mg  Mg9  1  0.230  0.500  0.500  1.0
  Mg  Mg10  1  0.752  0.000  0.500  1.0
  Mg  Mg11  1  0.702  0.500  0.500  1.0
  Mg  Mg12  1  0.314  0.262  0.000  1.0
  Mg  Mg13  1  0.314  0.738  0.000  1.0
  Mg  Mg14  1  0.760  0.258  0.000  1.0
  Mg  Mg15  1  0.760  0.742  0.000  1.0
  O  O16  1  0.210  0.500  0.000  1.0
  O  O17  1  0.703  0.000  0.000  1.0
  O  O18  1  0.703  0.500  0.000  1.0
  O  O19  1  0.315  0.276  0.500  1.0
  O  O20  1  0.315  0.724  0.500  1.0
  O  O21  1  0.762  0.261  0.500  1.0
  O  O22  1  0.762  0.739  0.500  1.0
  O  O23  1  0.920  0.000  0.500  1.0
  O  O24  1  0.048  0.500  0.500  1.0
  O  O25  1  0.496  0.000  0.500  1.0
  O  O26  1  0.542  0.500  0.500  1.0
  O  O27  1  0.933  0.308  0.000  1.0
  O  O28  1  0.933  0.692  0.000  1.0
  O  O29  1  0.482  0.260  0.000  1.0
  O  O30  1  0.482  0.740  0.000  1.0
[/CIF]
.