The compound described by MgEr4Zr4O14 crystallizes in the orthorhombic Pmm2 space group. Mg(1) is bonded to two equivalent O(4), two equivalent O(6), and two equivalent O(8) atoms to form distorted MgO6 octahedra that share corners with two equivalent Zr(2)O6 octahedra, edges with four equivalent Zr(3)O7 hexagonal pyramids,  an edgeedge with one Zr(2)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are three inequivalent Er sites. In the first Er site, Er(1) is bonded to one O(1), one O(10), two equivalent O(2), and two equivalent O(9) atoms to form distorted ErO6 octahedra that share corners with two equivalent Er(1)O6 octahedra, edges with two equivalent Er(1)O6 octahedra, and edges with two equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 31-79°. In the second Er site, Er(2) is bonded in a 6-coordinate geometry to two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms. In the third Er site, Er(3) is bonded in a 4-coordinate geometry to two equivalent O(5) and two equivalent O(9) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a body-centered cubic geometry to two equivalent O(1), two equivalent O(5), two equivalent O(7), and two equivalent O(9) atoms. In the second Zr site, Zr(2) is bonded to two equivalent O(10), two equivalent O(2), and two equivalent O(4) atoms to form distorted ZrO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Zr(2)O6 octahedra, and edges with four equivalent Er(1)O6 octahedra. The corner-sharing octahedral tilt angles are 8°. In the third Zr site, Zr(3) is bonded to one O(3), one O(7), one O(8), two equivalent O(5), and two equivalent O(6) atoms to form distorted ZrO7 hexagonal pyramids that share  a cornercorner with one Zr(3)O7 hexagonal pyramid, edges with three equivalent Zr(3)O7 hexagonal pyramids, and edges with two equivalent Mg(1)O6 octahedra. There are ten inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Er(1) and two equivalent Zr(1) atoms to form OEr2Zr2 tetrahedra that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(2)Er3Zr tetrahedra, corners with four equivalent O(5)ErZr3 tetrahedra, corners with two equivalent O(10)Er2Zr2 trigonal pyramids,  an edgeedge with one O(7)Zr4 tetrahedra, and edges with four equivalent O(9)Er3Zr tetrahedra. In the second O site, O(2) is bonded to one Er(2), two equivalent Er(1), and one Zr(2) atom to form distorted OEr3Zr tetrahedra that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with two equivalent O(3)Er2Zr2 tetrahedra, corners with two equivalent O(9)Er3Zr tetrahedra, corners with four equivalent O(2)Er3Zr tetrahedra,  an edgeedge with one O(9)Er3Zr tetrahedra, and edges with two equivalent O(10)Er2Zr2 trigonal pyramids. In the third O site, O(3) is bonded to two equivalent Er(2) and two equivalent Zr(3) atoms to form OEr2Zr2 tetrahedra that share corners with two equivalent O(3)Er2Zr2 tetrahedra, corners with four equivalent O(2)Er3Zr tetrahedra, corners with four equivalent O(5)ErZr3 tetrahedra, and  an edgeedge with one O(7)Zr4 tetrahedra. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to two equivalent Mg(1) and two equivalent Zr(2) atoms. In the fifth O site, O(5) is bonded to one Er(3), one Zr(1), and two equivalent Zr(3) atoms to form OErZr3 tetrahedra that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with two equivalent O(3)Er2Zr2 tetrahedra, corners with two equivalent O(9)Er3Zr tetrahedra, corners with four equivalent O(5)ErZr3 tetrahedra,  an edgeedge with one O(9)Er3Zr tetrahedra, and edges with two equivalent O(7)Zr4 tetrahedra. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Mg(1), one Er(2), and two equivalent Zr(3) atoms. In the seventh O site, O(7) is bonded to two equivalent Zr(1) and two equivalent Zr(3) atoms to form OZr4 tetrahedra that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(9)Er3Zr tetrahedra,  an edgeedge with one O(1)Er2Zr2 tetrahedra,  an edgeedge with one O(3)Er2Zr2 tetrahedra, and edges with four equivalent O(5)ErZr3 tetrahedra. In the eighth O site, O(8) is bonded in a distorted see-saw-like geometry to two equivalent Mg(1) and two equivalent Zr(3) atoms. In the ninth O site, O(9) is bonded to one Er(3), two equivalent Er(1), and one Zr(1) atom to form distorted OEr3Zr tetrahedra that share corners with two equivalent O(2)Er3Zr tetrahedra, corners with two equivalent O(5)ErZr3 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(9)Er3Zr tetrahedra, corners with two equivalent O(10)Er2Zr2 trigonal pyramids,  an edgeedge with one O(2)Er3Zr tetrahedra,  an edgeedge with one O(5)ErZr3 tetrahedra, and edges with two equivalent O(1)Er2Zr2 tetrahedra. In the tenth O site, O(10) is bonded to two equivalent Er(1) and two equivalent Zr(2) atoms to form distorted OEr2Zr2 trigonal pyramids that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with four equivalent O(9)Er3Zr tetrahedra, corners with two equivalent O(10)Er2Zr2 trigonal pyramids, and edges with four equivalent O(2)Er3Zr tetrahedra. is represented by the CIF file [CIF]
data_Er4MgZr4O14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.475
_cell_length_b   15.364
_cell_length_c   13.261
_cell_angle_alpha   30.337
_cell_angle_beta   58.389
_cell_angle_gamma   63.104
_symmetry_Int_Tables_number   1
_cell_volume   304.568
_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
  Er  Er0  1  0.991  0.228  0.026  1.0
  Er  Er1  1  0.942  0.000  0.529  1.0
  Er  Er2  1  0.991  0.772  0.482  1.0
  Er  Er3  1  0.978  0.500  0.511  1.0
  Mg  Mg4  1  0.631  0.500  0.185  1.0
  Zr  Zr5  1  0.969  0.000  0.015  1.0
  Zr  Zr6  1  0.134  0.500  0.933  1.0
  Zr  Zr7  1  0.945  0.214  0.564  1.0
  Zr  Zr8  1  0.945  0.786  0.992  1.0
  O  O9  1  0.250  0.000  0.125  1.0
  O  O10  1  0.212  0.231  0.163  1.0
  O  O11  1  0.195  0.000  0.653  1.0
  O  O12  1  0.416  0.500  0.042  1.0
  O  O13  1  0.191  0.244  0.660  1.0
  O  O14  1  0.191  0.756  0.148  1.0
  O  O15  1  0.664  0.252  0.416  1.0
  O  O16  1  0.714  0.000  0.893  1.0
  O  O17  1  0.919  0.500  0.290  1.0
  O  O18  1  0.730  0.276  0.859  1.0
  O  O19  1  0.730  0.724  0.411  1.0
  O  O20  1  0.212  0.769  0.625  1.0
  O  O21  1  0.886  0.500  0.807  1.0
  O  O22  1  0.664  0.748  0.920  1.0
[/CIF]
.
The compound described by MgEr4Zr4O14 crystallizes in the orthorhombic Pmm2 space group. Mg(1) is bonded to two equivalent O(4), two equivalent O(6), and two equivalent O(8) atoms to form distorted MgO6 octahedra that share corners with two equivalent Zr(2)O6 octahedra, edges with four equivalent Zr(3)O7 hexagonal pyramids,  an edgeedge with one Zr(2)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 8°. There are three inequivalent Er sites. In the first Er site, Er(1) is bonded to one O(1), one O(10), two equivalent O(2), and two equivalent O(9) atoms to form distorted ErO6 octahedra that share corners with two equivalent Er(1)O6 octahedra, edges with two equivalent Er(1)O6 octahedra, and edges with two equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 31-79°. In the second Er site, Er(2) is bonded in a 6-coordinate geometry to two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms. In the third Er site, Er(3) is bonded in a 4-coordinate geometry to two equivalent O(5) and two equivalent O(9) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded in a body-centered cubic geometry to two equivalent O(1), two equivalent O(5), two equivalent O(7), and two equivalent O(9) atoms. In the second Zr site, Zr(2) is bonded to two equivalent O(10), two equivalent O(2), and two equivalent O(4) atoms to form distorted ZrO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Zr(2)O6 octahedra, and edges with four equivalent Er(1)O6 octahedra. The corner-sharing octahedral tilt angles are 8°. In the third Zr site, Zr(3) is bonded to one O(3), one O(7), one O(8), two equivalent O(5), and two equivalent O(6) atoms to form distorted ZrO7 hexagonal pyramids that share  a cornercorner with one Zr(3)O7 hexagonal pyramid, edges with three equivalent Zr(3)O7 hexagonal pyramids, and edges with two equivalent Mg(1)O6 octahedra. There are ten inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Er(1) and two equivalent Zr(1) atoms to form OEr2Zr2 tetrahedra that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(2)Er3Zr tetrahedra, corners with four equivalent O(5)ErZr3 tetrahedra, corners with two equivalent O(10)Er2Zr2 trigonal pyramids,  an edgeedge with one O(7)Zr4 tetrahedra, and edges with four equivalent O(9)Er3Zr tetrahedra. In the second O site, O(2) is bonded to one Er(2), two equivalent Er(1), and one Zr(2) atom to form distorted OEr3Zr tetrahedra that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with two equivalent O(3)Er2Zr2 tetrahedra, corners with two equivalent O(9)Er3Zr tetrahedra, corners with four equivalent O(2)Er3Zr tetrahedra,  an edgeedge with one O(9)Er3Zr tetrahedra, and edges with two equivalent O(10)Er2Zr2 trigonal pyramids. In the third O site, O(3) is bonded to two equivalent Er(2) and two equivalent Zr(3) atoms to form OEr2Zr2 tetrahedra that share corners with two equivalent O(3)Er2Zr2 tetrahedra, corners with four equivalent O(2)Er3Zr tetrahedra, corners with four equivalent O(5)ErZr3 tetrahedra, and  an edgeedge with one O(7)Zr4 tetrahedra. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to two equivalent Mg(1) and two equivalent Zr(2) atoms. In the fifth O site, O(5) is bonded to one Er(3), one Zr(1), and two equivalent Zr(3) atoms to form OErZr3 tetrahedra that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with two equivalent O(3)Er2Zr2 tetrahedra, corners with two equivalent O(9)Er3Zr tetrahedra, corners with four equivalent O(5)ErZr3 tetrahedra,  an edgeedge with one O(9)Er3Zr tetrahedra, and edges with two equivalent O(7)Zr4 tetrahedra. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Mg(1), one Er(2), and two equivalent Zr(3) atoms. In the seventh O site, O(7) is bonded to two equivalent Zr(1) and two equivalent Zr(3) atoms to form OZr4 tetrahedra that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(9)Er3Zr tetrahedra,  an edgeedge with one O(1)Er2Zr2 tetrahedra,  an edgeedge with one O(3)Er2Zr2 tetrahedra, and edges with four equivalent O(5)ErZr3 tetrahedra. In the eighth O site, O(8) is bonded in a distorted see-saw-like geometry to two equivalent Mg(1) and two equivalent Zr(3) atoms. In the ninth O site, O(9) is bonded to one Er(3), two equivalent Er(1), and one Zr(1) atom to form distorted OEr3Zr tetrahedra that share corners with two equivalent O(2)Er3Zr tetrahedra, corners with two equivalent O(5)ErZr3 tetrahedra, corners with two equivalent O(7)Zr4 tetrahedra, corners with four equivalent O(9)Er3Zr tetrahedra, corners with two equivalent O(10)Er2Zr2 trigonal pyramids,  an edgeedge with one O(2)Er3Zr tetrahedra,  an edgeedge with one O(5)ErZr3 tetrahedra, and edges with two equivalent O(1)Er2Zr2 tetrahedra. In the tenth O site, O(10) is bonded to two equivalent Er(1) and two equivalent Zr(2) atoms to form distorted OEr2Zr2 trigonal pyramids that share corners with two equivalent O(1)Er2Zr2 tetrahedra, corners with four equivalent O(9)Er3Zr tetrahedra, corners with two equivalent O(10)Er2Zr2 trigonal pyramids, and edges with four equivalent O(2)Er3Zr tetrahedra. is represented by the CIF file [CIF]
data_Er4MgZr4O14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.475
_cell_length_b   15.364
_cell_length_c   13.261
_cell_angle_alpha   30.337
_cell_angle_beta   58.389
_cell_angle_gamma   63.104
_symmetry_Int_Tables_number   1
_cell_volume   304.568
_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
  Er  Er0  1  0.991  0.228  0.026  1.0
  Er  Er1  1  0.942  0.000  0.529  1.0
  Er  Er2  1  0.991  0.772  0.482  1.0
  Er  Er3  1  0.978  0.500  0.511  1.0
  Mg  Mg4  1  0.631  0.500  0.185  1.0
  Zr  Zr5  1  0.969  0.000  0.015  1.0
  Zr  Zr6  1  0.134  0.500  0.933  1.0
  Zr  Zr7  1  0.945  0.214  0.564  1.0
  Zr  Zr8  1  0.945  0.786  0.992  1.0
  O  O9  1  0.250  0.000  0.125  1.0
  O  O10  1  0.212  0.231  0.163  1.0
  O  O11  1  0.195  0.000  0.653  1.0
  O  O12  1  0.416  0.500  0.042  1.0
  O  O13  1  0.191  0.244  0.660  1.0
  O  O14  1  0.191  0.756  0.148  1.0
  O  O15  1  0.664  0.252  0.416  1.0
  O  O16  1  0.714  0.000  0.893  1.0
  O  O17  1  0.919  0.500  0.290  1.0
  O  O18  1  0.730  0.276  0.859  1.0
  O  O19  1  0.730  0.724  0.411  1.0
  O  O20  1  0.212  0.769  0.625  1.0
  O  O21  1  0.886  0.500  0.807  1.0
  O  O22  1  0.664  0.748  0.920  1.0
[/CIF]
.