The compound described by Na4Zr2Si3O12 crystallizes in the trigonal R3c space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form ZrO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra. In the second Zr site, Zr(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form ZrO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra. Si(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form SiO4 tetrahedra that share corners with two equivalent Zr(1)O6 octahedra and corners with two equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 25-40°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Na(2), two equivalent Na(1), one Zr(1), and one Si(1) atom to form a mixture of distorted corner, edge, and face-sharing ONa3ZrSi trigonal bipyramids. In the second O site, O(2) is bonded to one Na(2), two equivalent Na(1), one Zr(2), and one Si(1) atom to form a mixture of distorted corner, edge, and face-sharing ONa3ZrSi trigonal bipyramids. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Na(1), one Zr(2), and one Si(1) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Na(1), one Zr(1), and one Si(1) atom. is represented by the CIF file [CIF]
data_Na4Zr2(SiO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.217
_cell_length_b   9.217
_cell_length_c   9.217
_cell_angle_alpha   60.741
_cell_angle_beta   60.741
_cell_angle_gamma   60.741
_symmetry_Int_Tables_number   1
_cell_volume   562.926
_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
  Na  Na0  1  0.749  0.388  0.119  1.0
  Na  Na1  1  0.249  0.619  0.888  1.0
  Na  Na2  1  0.388  0.119  0.749  1.0
  Na  Na3  1  0.619  0.888  0.249  1.0
  Na  Na4  1  0.119  0.749  0.388  1.0
  Na  Na5  1  0.499  0.499  0.499  1.0
  Na  Na6  1  0.888  0.249  0.619  1.0
  Na  Na7  1  0.999  0.999  0.999  1.0
  Zr  Zr8  1  0.645  0.645  0.645  1.0
  Zr  Zr9  1  0.851  0.851  0.851  1.0
  Zr  Zr10  1  0.145  0.145  0.145  1.0
  Zr  Zr11  1  0.351  0.351  0.351  1.0
  Si  Si12  1  0.950  0.544  0.248  1.0
  Si  Si13  1  0.450  0.748  0.044  1.0
  Si  Si14  1  0.748  0.044  0.450  1.0
  Si  Si15  1  0.044  0.450  0.748  1.0
  Si  Si16  1  0.544  0.248  0.950  1.0
  Si  Si17  1  0.248  0.950  0.544  1.0
  O  O18  1  0.267  0.916  0.062  1.0
  O  O19  1  0.432  0.581  0.228  1.0
  O  O20  1  0.006  0.622  0.791  1.0
  O  O21  1  0.767  0.562  0.416  1.0
  O  O22  1  0.062  0.267  0.916  1.0
  O  O23  1  0.416  0.767  0.562  1.0
  O  O24  1  0.204  0.986  0.375  1.0
  O  O25  1  0.704  0.875  0.486  1.0
  O  O26  1  0.622  0.791  0.006  1.0
  O  O27  1  0.562  0.416  0.767  1.0
  O  O28  1  0.986  0.375  0.204  1.0
  O  O29  1  0.932  0.728  0.081  1.0
  O  O30  1  0.291  0.122  0.506  1.0
  O  O31  1  0.728  0.081  0.932  1.0
  O  O32  1  0.875  0.486  0.704  1.0
  O  O33  1  0.122  0.506  0.291  1.0
  O  O34  1  0.081  0.932  0.728  1.0
  O  O35  1  0.486  0.704  0.875  1.0
  O  O36  1  0.375  0.204  0.986  1.0
  O  O37  1  0.581  0.228  0.432  1.0
  O  O38  1  0.506  0.291  0.122  1.0
  O  O39  1  0.228  0.432  0.581  1.0
  O  O40  1  0.916  0.062  0.267  1.0
  O  O41  1  0.791  0.006  0.622  1.0
[/CIF]
.
The compound described by Na4Zr2Si3O12 crystallizes in the trigonal R3c space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form ZrO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra. In the second Zr site, Zr(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form ZrO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra. Si(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form SiO4 tetrahedra that share corners with two equivalent Zr(1)O6 octahedra and corners with two equivalent Zr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 25-40°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Na(2), two equivalent Na(1), one Zr(1), and one Si(1) atom to form a mixture of distorted corner, edge, and face-sharing ONa3ZrSi trigonal bipyramids. In the second O site, O(2) is bonded to one Na(2), two equivalent Na(1), one Zr(2), and one Si(1) atom to form a mixture of distorted corner, edge, and face-sharing ONa3ZrSi trigonal bipyramids. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Na(1), one Zr(2), and one Si(1) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Na(1), one Zr(1), and one Si(1) atom. is represented by the CIF file [CIF]
data_Na4Zr2(SiO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.217
_cell_length_b   9.217
_cell_length_c   9.217
_cell_angle_alpha   60.741
_cell_angle_beta   60.741
_cell_angle_gamma   60.741
_symmetry_Int_Tables_number   1
_cell_volume   562.926
_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
  Na  Na0  1  0.749  0.388  0.119  1.0
  Na  Na1  1  0.249  0.619  0.888  1.0
  Na  Na2  1  0.388  0.119  0.749  1.0
  Na  Na3  1  0.619  0.888  0.249  1.0
  Na  Na4  1  0.119  0.749  0.388  1.0
  Na  Na5  1  0.499  0.499  0.499  1.0
  Na  Na6  1  0.888  0.249  0.619  1.0
  Na  Na7  1  0.999  0.999  0.999  1.0
  Zr  Zr8  1  0.645  0.645  0.645  1.0
  Zr  Zr9  1  0.851  0.851  0.851  1.0
  Zr  Zr10  1  0.145  0.145  0.145  1.0
  Zr  Zr11  1  0.351  0.351  0.351  1.0
  Si  Si12  1  0.950  0.544  0.248  1.0
  Si  Si13  1  0.450  0.748  0.044  1.0
  Si  Si14  1  0.748  0.044  0.450  1.0
  Si  Si15  1  0.044  0.450  0.748  1.0
  Si  Si16  1  0.544  0.248  0.950  1.0
  Si  Si17  1  0.248  0.950  0.544  1.0
  O  O18  1  0.267  0.916  0.062  1.0
  O  O19  1  0.432  0.581  0.228  1.0
  O  O20  1  0.006  0.622  0.791  1.0
  O  O21  1  0.767  0.562  0.416  1.0
  O  O22  1  0.062  0.267  0.916  1.0
  O  O23  1  0.416  0.767  0.562  1.0
  O  O24  1  0.204  0.986  0.375  1.0
  O  O25  1  0.704  0.875  0.486  1.0
  O  O26  1  0.622  0.791  0.006  1.0
  O  O27  1  0.562  0.416  0.767  1.0
  O  O28  1  0.986  0.375  0.204  1.0
  O  O29  1  0.932  0.728  0.081  1.0
  O  O30  1  0.291  0.122  0.506  1.0
  O  O31  1  0.728  0.081  0.932  1.0
  O  O32  1  0.875  0.486  0.704  1.0
  O  O33  1  0.122  0.506  0.291  1.0
  O  O34  1  0.081  0.932  0.728  1.0
  O  O35  1  0.486  0.704  0.875  1.0
  O  O36  1  0.375  0.204  0.986  1.0
  O  O37  1  0.581  0.228  0.432  1.0
  O  O38  1  0.506  0.291  0.122  1.0
  O  O39  1  0.228  0.432  0.581  1.0
  O  O40  1  0.916  0.062  0.267  1.0
  O  O41  1  0.791  0.006  0.622  1.0
[/CIF]
.