The material structure described by NaNb13O33 crystallizes in the triclinic P1 space group. Na(1) is bonded in a square co-planar geometry to two equivalent O(21) and two equivalent O(7) atoms. There are thirteen inequivalent Nb sites. In the first Nb site, Nb(1) is bonded in a 6-coordinate geometry to one O(12), one O(18), one O(27), one O(7), and two equivalent O(24) atoms. In the second Nb site, Nb(2) is bonded to one O(12), one O(22), one O(28), one O(6), and two equivalent O(16) atoms to form distorted corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-16°. In the third Nb site, Nb(3) is bonded to one O(11), one O(17), one O(2), one O(23), and two equivalent O(32) atoms to form a mixture of distorted corner and edge-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 1-33°. In the fourth Nb site, Nb(4) is bonded to one O(14), one O(31), one O(33), one O(9), and two equivalent O(8) atoms to form corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 2-15°. In the fifth Nb site, Nb(5) is bonded in a 6-coordinate geometry to one O(10), one O(13), one O(24), one O(25), and two equivalent O(18) atoms. In the sixth Nb site, Nb(6) is bonded to one O(1), one O(22), one O(30), one O(32), and two equivalent O(17) atoms to form a mixture of distorted corner and edge-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-33°. In the seventh Nb site, Nb(7) is bonded in a 6-coordinate geometry to one O(18), one O(26), one O(7), one O(9), and two equivalent O(13) atoms. In the eighth Nb site, Nb(8) is bonded in a 6-coordinate geometry to one O(19), one O(27), one O(30), one O(5), and two equivalent O(4) atoms. In the ninth Nb site, Nb(9) is bonded in a 6-coordinate geometry to one O(21), one O(25), one O(31), one O(4), and two equivalent O(5) atoms. In the tenth Nb site, Nb(10) is bonded to one O(10), one O(14), one O(20), one O(23), and two equivalent O(3) atoms to form a mixture of distorted corner and edge-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-33°. In the eleventh Nb site, Nb(11) is bonded to one O(1), one O(15), one O(26), one O(3), and two equivalent O(20) atoms to form a mixture of distorted corner and edge-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-33°. In the twelfth Nb site, Nb(12) is bonded in a 6-coordinate geometry to one O(11), one O(21), one O(28), one O(4), and two equivalent O(19) atoms. In the thirteenth Nb site, Nb(13) is bonded to one O(15), one O(2), one O(33), one O(6), and two equivalent O(29) atoms to form corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. There are thirty-three inequivalent O sites. In the first O site, O(1) is bonded in a linear geometry to one Nb(11) and one Nb(6) atom. In the second O site, O(2) is bonded in a linear geometry to one Nb(13) and one Nb(3) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Nb(11) and two equivalent Nb(10) atoms. In the fourth O site, O(4) is bonded to one Nb(12), one Nb(9), and two equivalent Nb(8) atoms to form distorted ONb4 trigonal pyramids that share corners with two equivalent O(4)Nb4 trigonal pyramids and  an edgeedge with one O(21)Na2Nb2 tetrahedra. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Nb(8) and two equivalent Nb(9) atoms. In the sixth O site, O(6) is bonded in a linear geometry to one Nb(13) and one Nb(2) atom. In the seventh O site, O(7) is bonded to two equivalent Na(1), one Nb(1), and one Nb(7) atom to form ONa2Nb2 tetrahedra that share corners with two equivalent O(21)Na2Nb2 tetrahedra, corners with two equivalent O(7)Na2Nb2 tetrahedra,  an edgeedge with one O(21)Na2Nb2 tetrahedra, and  an edgeedge with one O(18)Nb4 trigonal pyramid. In the eighth O site, O(8) is bonded in a linear geometry to two equivalent Nb(4) atoms. In the ninth O site, O(9) is bonded in a linear geometry to one Nb(4) and one Nb(7) atom. In the tenth O site, O(10) is bonded in a linear geometry to one Nb(10) and one Nb(5) atom. In the eleventh O site, O(11) is bonded in a linear geometry to one Nb(12) and one Nb(3) atom. In the twelfth O site, O(12) is bonded in a linear geometry to one Nb(1) and one Nb(2) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one Nb(5) and two equivalent Nb(7) atoms. In the fourteenth O site, O(14) is bonded in a linear geometry to one Nb(10) and one Nb(4) atom. In the fifteenth O site, O(15) is bonded in a linear geometry to one Nb(11) and one Nb(13) atom. In the sixteenth O site, O(16) is bonded in a linear geometry to two equivalent Nb(2) atoms. In the seventeenth O site, O(17) is bonded in a 3-coordinate geometry to one Nb(3) and two equivalent Nb(6) atoms. In the eighteenth O site, O(18) is bonded to one Nb(1), one Nb(7), and two equivalent Nb(5) atoms to form distorted ONb4 trigonal pyramids that share corners with two equivalent O(18)Nb4 trigonal pyramids and  an edgeedge with one O(7)Na2Nb2 tetrahedra. In the nineteenth O site, O(19) is bonded in a 3-coordinate geometry to one Nb(8) and two equivalent Nb(12) atoms. In the twentieth O site, O(20) is bonded in a 3-coordinate geometry to one Nb(10) and two equivalent Nb(11) atoms. In the twenty-first O site, O(21) is bonded to two equivalent Na(1), one Nb(12), and one Nb(9) atom to form ONa2Nb2 tetrahedra that share corners with two equivalent O(21)Na2Nb2 tetrahedra, corners with two equivalent O(7)Na2Nb2 tetrahedra,  an edgeedge with one O(7)Na2Nb2 tetrahedra, and  an edgeedge with one O(4)Nb4 trigonal pyramid. In the twenty-second O site, O(22) is bonded in a linear geometry to one Nb(2) and one Nb(6) atom. In the twenty-third O site, O(23) is bonded in a linear geometry to one Nb(10) and one Nb(3) atom. In the twenty-fourth O site, O(24) is bonded in a 3-coordinate geometry to one Nb(5) and two equivalent Nb(1) atoms. In the twenty-fifth O site, O(25) is bonded in a linear geometry to one Nb(5) and one Nb(9) atom. In the twenty-sixth O site, O(26) is bonded in a linear geometry to one Nb(11) and one Nb(7) atom. In the twenty-seventh O site, O(27) is bonded in a linear geometry to one Nb(1) and one Nb(8) atom. In the twenty-eighth O site, O(28) is bonded in a linear geometry to one Nb(12) and one Nb(2) atom. In the twenty-ninth O site, O(29) is bonded in a linear geometry to two equivalent Nb(13) atoms. In the thirtieth O site, O(30) is bonded in a linear geometry to one Nb(6) and one Nb(8) atom. In the thirty-first O site, O(31) is bonded in a linear geometry to one Nb(4) and one Nb(9) atom. In the thirty-second O site, O(32) is bonded in a 3-coordinate geometry to one Nb(6) and two equivalent Nb(3) atoms. In the thirty-third O site, O(33) is bonded in a linear geometry to one Nb(13) and one Nb(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaNb13O33
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.878
_cell_length_b   11.609
_cell_length_c   15.664
_cell_angle_alpha   91.500
_cell_angle_beta   89.968
_cell_angle_gamma   99.603
_symmetry_Int_Tables_number   1
_cell_volume   695.020
_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
  Na  Na0  1  0.508  0.001  0.497  1.0
  Nb  Nb1  1  0.144  0.275  0.467  1.0
  Nb  Nb2  1  0.056  0.141  0.229  1.0
  Nb  Nb3  1  0.848  0.690  0.095  1.0
  Nb  Nb4  1  0.917  0.860  0.772  1.0
  Nb  Nb5  1  0.711  0.416  0.625  1.0
  Nb  Nb6  1  0.228  0.449  0.137  1.0
  Nb  Nb7  1  0.091  0.174  0.675  1.0
  Nb  Nb8  1  0.294  0.586  0.374  1.0
  Nb  Nb9  1  0.865  0.727  0.533  1.0
  Nb  Nb10  1  0.774  0.551  0.862  1.0
  Nb  Nb11  1  0.152  0.311  0.904  1.0
  Nb  Nb12  1  0.919  0.826  0.325  1.0
  Nb  Nb13  1  0.013  0.001  1.000  1.0
  O  O14  1  0.197  0.388  0.027  1.0
  O  O15  1  0.920  0.838  0.050  1.0
  O  O16  1  0.249  0.502  0.862  1.0
  O  O17  1  0.821  0.637  0.389  1.0
  O  O18  1  0.351  0.697  0.506  1.0
  O  O19  1  0.035  0.070  0.120  1.0
  O  O20  1  0.073  0.138  0.544  1.0
  O  O21  1  0.434  0.860  0.755  1.0
  O  O22  1  0.019  0.024  0.709  1.0
  O  O23  1  0.734  0.467  0.735  1.0
  O  O24  1  0.875  0.743  0.213  1.0
  O  O25  1  0.109  0.201  0.365  1.0
  O  O26  1  0.613  0.219  0.663  1.0
  O  O27  1  0.848  0.694  0.805  1.0
  O  O28  1  0.075  0.164  0.951  1.0
  O  O29  1  0.577  0.140  0.246  1.0
  O  O30  1  0.750  0.498  0.137  1.0
  O  O31  1  0.186  0.364  0.611  1.0
  O  O32  1  0.396  0.782  0.338  1.0
  O  O33  1  0.680  0.361  0.900  1.0
  O  O34  1  0.933  0.862  0.456  1.0
  O  O35  1  0.160  0.306  0.195  1.0
  O  O36  1  0.802  0.612  0.972  1.0
  O  O37  1  0.658  0.304  0.496  1.0
  O  O38  1  0.780  0.553  0.567  1.0
  O  O39  1  0.126  0.256  0.787  1.0
  O  O40  1  0.225  0.446  0.430  1.0
  O  O41  1  0.996  0.976  0.291  1.0
  O  O42  1  0.500  0.001  0.000  1.0
  O  O43  1  0.266  0.537  0.264  1.0
  O  O44  1  0.904  0.800  0.636  1.0
  O  O45  1  0.321  0.641  0.098  1.0
  O  O46  1  0.969  0.929  0.881  1.0
[/CIF]
.
The material structure described by NaNb13O33 crystallizes in the triclinic P1 space group. Na(1) is bonded in a square co-planar geometry to two equivalent O(21) and two equivalent O(7) atoms. There are thirteen inequivalent Nb sites. In the first Nb site, Nb(1) is bonded in a 6-coordinate geometry to one O(12), one O(18), one O(27), one O(7), and two equivalent O(24) atoms. In the second Nb site, Nb(2) is bonded to one O(12), one O(22), one O(28), one O(6), and two equivalent O(16) atoms to form distorted corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-16°. In the third Nb site, Nb(3) is bonded to one O(11), one O(17), one O(2), one O(23), and two equivalent O(32) atoms to form a mixture of distorted corner and edge-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 1-33°. In the fourth Nb site, Nb(4) is bonded to one O(14), one O(31), one O(33), one O(9), and two equivalent O(8) atoms to form corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 2-15°. In the fifth Nb site, Nb(5) is bonded in a 6-coordinate geometry to one O(10), one O(13), one O(24), one O(25), and two equivalent O(18) atoms. In the sixth Nb site, Nb(6) is bonded to one O(1), one O(22), one O(30), one O(32), and two equivalent O(17) atoms to form a mixture of distorted corner and edge-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-33°. In the seventh Nb site, Nb(7) is bonded in a 6-coordinate geometry to one O(18), one O(26), one O(7), one O(9), and two equivalent O(13) atoms. In the eighth Nb site, Nb(8) is bonded in a 6-coordinate geometry to one O(19), one O(27), one O(30), one O(5), and two equivalent O(4) atoms. In the ninth Nb site, Nb(9) is bonded in a 6-coordinate geometry to one O(21), one O(25), one O(31), one O(4), and two equivalent O(5) atoms. In the tenth Nb site, Nb(10) is bonded to one O(10), one O(14), one O(20), one O(23), and two equivalent O(3) atoms to form a mixture of distorted corner and edge-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-33°. In the eleventh Nb site, Nb(11) is bonded to one O(1), one O(15), one O(26), one O(3), and two equivalent O(20) atoms to form a mixture of distorted corner and edge-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-33°. In the twelfth Nb site, Nb(12) is bonded in a 6-coordinate geometry to one O(11), one O(21), one O(28), one O(4), and two equivalent O(19) atoms. In the thirteenth Nb site, Nb(13) is bonded to one O(15), one O(2), one O(33), one O(6), and two equivalent O(29) atoms to form corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. There are thirty-three inequivalent O sites. In the first O site, O(1) is bonded in a linear geometry to one Nb(11) and one Nb(6) atom. In the second O site, O(2) is bonded in a linear geometry to one Nb(13) and one Nb(3) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Nb(11) and two equivalent Nb(10) atoms. In the fourth O site, O(4) is bonded to one Nb(12), one Nb(9), and two equivalent Nb(8) atoms to form distorted ONb4 trigonal pyramids that share corners with two equivalent O(4)Nb4 trigonal pyramids and  an edgeedge with one O(21)Na2Nb2 tetrahedra. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Nb(8) and two equivalent Nb(9) atoms. In the sixth O site, O(6) is bonded in a linear geometry to one Nb(13) and one Nb(2) atom. In the seventh O site, O(7) is bonded to two equivalent Na(1), one Nb(1), and one Nb(7) atom to form ONa2Nb2 tetrahedra that share corners with two equivalent O(21)Na2Nb2 tetrahedra, corners with two equivalent O(7)Na2Nb2 tetrahedra,  an edgeedge with one O(21)Na2Nb2 tetrahedra, and  an edgeedge with one O(18)Nb4 trigonal pyramid. In the eighth O site, O(8) is bonded in a linear geometry to two equivalent Nb(4) atoms. In the ninth O site, O(9) is bonded in a linear geometry to one Nb(4) and one Nb(7) atom. In the tenth O site, O(10) is bonded in a linear geometry to one Nb(10) and one Nb(5) atom. In the eleventh O site, O(11) is bonded in a linear geometry to one Nb(12) and one Nb(3) atom. In the twelfth O site, O(12) is bonded in a linear geometry to one Nb(1) and one Nb(2) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one Nb(5) and two equivalent Nb(7) atoms. In the fourteenth O site, O(14) is bonded in a linear geometry to one Nb(10) and one Nb(4) atom. In the fifteenth O site, O(15) is bonded in a linear geometry to one Nb(11) and one Nb(13) atom. In the sixteenth O site, O(16) is bonded in a linear geometry to two equivalent Nb(2) atoms. In the seventeenth O site, O(17) is bonded in a 3-coordinate geometry to one Nb(3) and two equivalent Nb(6) atoms. In the eighteenth O site, O(18) is bonded to one Nb(1), one Nb(7), and two equivalent Nb(5) atoms to form distorted ONb4 trigonal pyramids that share corners with two equivalent O(18)Nb4 trigonal pyramids and  an edgeedge with one O(7)Na2Nb2 tetrahedra. In the nineteenth O site, O(19) is bonded in a 3-coordinate geometry to one Nb(8) and two equivalent Nb(12) atoms. In the twentieth O site, O(20) is bonded in a 3-coordinate geometry to one Nb(10) and two equivalent Nb(11) atoms. In the twenty-first O site, O(21) is bonded to two equivalent Na(1), one Nb(12), and one Nb(9) atom to form ONa2Nb2 tetrahedra that share corners with two equivalent O(21)Na2Nb2 tetrahedra, corners with two equivalent O(7)Na2Nb2 tetrahedra,  an edgeedge with one O(7)Na2Nb2 tetrahedra, and  an edgeedge with one O(4)Nb4 trigonal pyramid. In the twenty-second O site, O(22) is bonded in a linear geometry to one Nb(2) and one Nb(6) atom. In the twenty-third O site, O(23) is bonded in a linear geometry to one Nb(10) and one Nb(3) atom. In the twenty-fourth O site, O(24) is bonded in a 3-coordinate geometry to one Nb(5) and two equivalent Nb(1) atoms. In the twenty-fifth O site, O(25) is bonded in a linear geometry to one Nb(5) and one Nb(9) atom. In the twenty-sixth O site, O(26) is bonded in a linear geometry to one Nb(11) and one Nb(7) atom. In the twenty-seventh O site, O(27) is bonded in a linear geometry to one Nb(1) and one Nb(8) atom. In the twenty-eighth O site, O(28) is bonded in a linear geometry to one Nb(12) and one Nb(2) atom. In the twenty-ninth O site, O(29) is bonded in a linear geometry to two equivalent Nb(13) atoms. In the thirtieth O site, O(30) is bonded in a linear geometry to one Nb(6) and one Nb(8) atom. In the thirty-first O site, O(31) is bonded in a linear geometry to one Nb(4) and one Nb(9) atom. In the thirty-second O site, O(32) is bonded in a 3-coordinate geometry to one Nb(6) and two equivalent Nb(3) atoms. In the thirty-third O site, O(33) is bonded in a linear geometry to one Nb(13) and one Nb(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaNb13O33
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.878
_cell_length_b   11.609
_cell_length_c   15.664
_cell_angle_alpha   91.500
_cell_angle_beta   89.968
_cell_angle_gamma   99.603
_symmetry_Int_Tables_number   1
_cell_volume   695.020
_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
  Na  Na0  1  0.508  0.001  0.497  1.0
  Nb  Nb1  1  0.144  0.275  0.467  1.0
  Nb  Nb2  1  0.056  0.141  0.229  1.0
  Nb  Nb3  1  0.848  0.690  0.095  1.0
  Nb  Nb4  1  0.917  0.860  0.772  1.0
  Nb  Nb5  1  0.711  0.416  0.625  1.0
  Nb  Nb6  1  0.228  0.449  0.137  1.0
  Nb  Nb7  1  0.091  0.174  0.675  1.0
  Nb  Nb8  1  0.294  0.586  0.374  1.0
  Nb  Nb9  1  0.865  0.727  0.533  1.0
  Nb  Nb10  1  0.774  0.551  0.862  1.0
  Nb  Nb11  1  0.152  0.311  0.904  1.0
  Nb  Nb12  1  0.919  0.826  0.325  1.0
  Nb  Nb13  1  0.013  0.001  1.000  1.0
  O  O14  1  0.197  0.388  0.027  1.0
  O  O15  1  0.920  0.838  0.050  1.0
  O  O16  1  0.249  0.502  0.862  1.0
  O  O17  1  0.821  0.637  0.389  1.0
  O  O18  1  0.351  0.697  0.506  1.0
  O  O19  1  0.035  0.070  0.120  1.0
  O  O20  1  0.073  0.138  0.544  1.0
  O  O21  1  0.434  0.860  0.755  1.0
  O  O22  1  0.019  0.024  0.709  1.0
  O  O23  1  0.734  0.467  0.735  1.0
  O  O24  1  0.875  0.743  0.213  1.0
  O  O25  1  0.109  0.201  0.365  1.0
  O  O26  1  0.613  0.219  0.663  1.0
  O  O27  1  0.848  0.694  0.805  1.0
  O  O28  1  0.075  0.164  0.951  1.0
  O  O29  1  0.577  0.140  0.246  1.0
  O  O30  1  0.750  0.498  0.137  1.0
  O  O31  1  0.186  0.364  0.611  1.0
  O  O32  1  0.396  0.782  0.338  1.0
  O  O33  1  0.680  0.361  0.900  1.0
  O  O34  1  0.933  0.862  0.456  1.0
  O  O35  1  0.160  0.306  0.195  1.0
  O  O36  1  0.802  0.612  0.972  1.0
  O  O37  1  0.658  0.304  0.496  1.0
  O  O38  1  0.780  0.553  0.567  1.0
  O  O39  1  0.126  0.256  0.787  1.0
  O  O40  1  0.225  0.446  0.430  1.0
  O  O41  1  0.996  0.976  0.291  1.0
  O  O42  1  0.500  0.001  0.000  1.0
  O  O43  1  0.266  0.537  0.264  1.0
  O  O44  1  0.904  0.800  0.636  1.0
  O  O45  1  0.321  0.641  0.098  1.0
  O  O46  1  0.969  0.929  0.881  1.0
[/CIF]
.