The material structure described by K2Ti4O9 crystallizes in the monoclinic C2/m space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 8-coordinate geometry to two equivalent O(8), two equivalent O(9), and four equivalent O(6) atoms. In the second K site, K(2) is bonded in a 6-coordinate geometry to two equivalent O(5), two equivalent O(6), and two equivalent O(7) atoms. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(8), one O(9), and two equivalent O(1) atoms. In the second Ti site, Ti(2) is bonded to one O(1), one O(4), one O(5), one O(7), and two equivalent O(2) atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 32°. In the third Ti site, Ti(3) is bonded in a 6-coordinate geometry to one O(1), one O(5), one O(6), one O(9), and two equivalent O(3) atoms. In the fourth Ti site, Ti(4) is bonded to one O(2), one O(7), one O(8), and three equivalent O(4) atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 30°. There are nine inequivalent O sites. In the first O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to two equivalent K(2), one Ti(2), and one Ti(3) atom. In the second O site, O(6) is bonded in a distorted single-bond geometry to two equivalent K(2), four equivalent K(1), and one Ti(3) atom. In the third O site, O(7) is bonded to two equivalent K(2), one Ti(2), and one Ti(4) atom to form distorted OK2Ti2 tetrahedra that share corners with two equivalent O(7)K2Ti2 tetrahedra,  a cornercorner with one O(1)Ti4 trigonal pyramid, corners with two equivalent O(4)Ti4 trigonal pyramids, corners with three equivalent O(2)Ti4 trigonal pyramids, and  an edgeedge with one O(4)Ti4 trigonal pyramid. In the fourth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to two equivalent K(1), one Ti(1), and one Ti(4) atom. In the fifth O site, O(9) is bonded in a distorted linear geometry to two equivalent K(1), one Ti(1), and one Ti(3) atom. In the sixth O site, O(1) is bonded to one Ti(2), one Ti(3), and two equivalent Ti(1) atoms to form distorted OTi4 trigonal pyramids that share  a cornercorner with one O(7)K2Ti2 tetrahedra,  a cornercorner with one O(4)Ti4 trigonal pyramid, corners with two equivalent O(1)Ti4 trigonal pyramids, and edges with two equivalent O(2)Ti4 trigonal pyramids. In the seventh O site, O(2) is bonded to one Ti(1), one Ti(4), and two equivalent Ti(2) atoms to form distorted OTi4 trigonal pyramids that share corners with three equivalent O(7)K2Ti2 tetrahedra,  a cornercorner with one O(4)Ti4 trigonal pyramid, corners with two equivalent O(2)Ti4 trigonal pyramids, edges with two equivalent O(1)Ti4 trigonal pyramids, and edges with two equivalent O(4)Ti4 trigonal pyramids. In the eighth O site, O(3) is bonded in a 3-coordinate geometry to one Ti(1) and two equivalent Ti(3) atoms. In the ninth O site, O(4) is bonded to one Ti(2) and three equivalent Ti(4) atoms to form distorted OTi4 trigonal pyramids that share corners with two equivalent O(7)K2Ti2 tetrahedra,  a cornercorner with one O(1)Ti4 trigonal pyramid,  a cornercorner with one O(2)Ti4 trigonal pyramid, corners with two equivalent O(4)Ti4 trigonal pyramids,  an edgeedge with one O(7)K2Ti2 tetrahedra, edges with two equivalent O(2)Ti4 trigonal pyramids, and edges with two equivalent O(4)Ti4 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_K2Ti4O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.780
_cell_length_b   9.365
_cell_length_c   12.051
_cell_angle_alpha   106.336
_cell_angle_beta   89.997
_cell_angle_gamma   101.639
_symmetry_Int_Tables_number   1
_cell_volume   400.178
_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
  K  K0  1  0.583  0.165  0.083  1.0
  K  K1  1  0.417  0.835  0.917  1.0
  K  K2  1  0.523  0.045  0.329  1.0
  K  K3  1  0.477  0.955  0.671  1.0
  Ti  Ti4  1  0.246  0.492  0.167  1.0
  Ti  Ti5  1  0.754  0.508  0.834  1.0
  Ti  Ti6  1  0.839  0.678  0.376  1.0
  Ti  Ti7  1  0.161  0.322  0.624  1.0
  Ti  Ti8  1  0.878  0.757  0.139  1.0
  Ti  Ti9  1  0.122  0.243  0.861  1.0
  Ti  Ti10  1  0.203  0.406  0.396  1.0
  Ti  Ti11  1  0.797  0.594  0.604  1.0
  O  O12  1  0.768  0.536  0.201  1.0
  O  O13  1  0.232  0.464  0.799  1.0
  O  O14  1  0.308  0.617  0.359  1.0
  O  O15  1  0.692  0.383  0.641  1.0
  O  O16  1  0.350  0.700  0.144  1.0
  O  O17  1  0.650  0.300  0.856  1.0
  O  O18  1  0.730  0.460  0.422  1.0
  O  O19  1  0.270  0.540  0.578  1.0
  O  O20  1  0.917  0.834  0.318  1.0
  O  O21  1  0.083  0.166  0.682  1.0
  O  O22  1  0.968  0.937  0.120  1.0
  O  O23  1  0.032  0.063  0.880  1.0
  O  O24  1  0.121  0.243  0.461  1.0
  O  O25  1  0.879  0.757  0.539  1.0
  O  O26  1  0.161  0.322  0.242  1.0
  O  O27  1  0.839  0.678  0.758  1.0
  O  O28  1  0.182  0.365  0.026  1.0
  O  O29  1  0.818  0.635  0.974  1.0
[/CIF]
.
The material structure described by K2Ti4O9 crystallizes in the monoclinic C2/m space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 8-coordinate geometry to two equivalent O(8), two equivalent O(9), and four equivalent O(6) atoms. In the second K site, K(2) is bonded in a 6-coordinate geometry to two equivalent O(5), two equivalent O(6), and two equivalent O(7) atoms. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 6-coordinate geometry to one O(2), one O(3), one O(8), one O(9), and two equivalent O(1) atoms. In the second Ti site, Ti(2) is bonded to one O(1), one O(4), one O(5), one O(7), and two equivalent O(2) atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 32°. In the third Ti site, Ti(3) is bonded in a 6-coordinate geometry to one O(1), one O(5), one O(6), one O(9), and two equivalent O(3) atoms. In the fourth Ti site, Ti(4) is bonded to one O(2), one O(7), one O(8), and three equivalent O(4) atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 30°. There are nine inequivalent O sites. In the first O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to two equivalent K(2), one Ti(2), and one Ti(3) atom. In the second O site, O(6) is bonded in a distorted single-bond geometry to two equivalent K(2), four equivalent K(1), and one Ti(3) atom. In the third O site, O(7) is bonded to two equivalent K(2), one Ti(2), and one Ti(4) atom to form distorted OK2Ti2 tetrahedra that share corners with two equivalent O(7)K2Ti2 tetrahedra,  a cornercorner with one O(1)Ti4 trigonal pyramid, corners with two equivalent O(4)Ti4 trigonal pyramids, corners with three equivalent O(2)Ti4 trigonal pyramids, and  an edgeedge with one O(4)Ti4 trigonal pyramid. In the fourth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to two equivalent K(1), one Ti(1), and one Ti(4) atom. In the fifth O site, O(9) is bonded in a distorted linear geometry to two equivalent K(1), one Ti(1), and one Ti(3) atom. In the sixth O site, O(1) is bonded to one Ti(2), one Ti(3), and two equivalent Ti(1) atoms to form distorted OTi4 trigonal pyramids that share  a cornercorner with one O(7)K2Ti2 tetrahedra,  a cornercorner with one O(4)Ti4 trigonal pyramid, corners with two equivalent O(1)Ti4 trigonal pyramids, and edges with two equivalent O(2)Ti4 trigonal pyramids. In the seventh O site, O(2) is bonded to one Ti(1), one Ti(4), and two equivalent Ti(2) atoms to form distorted OTi4 trigonal pyramids that share corners with three equivalent O(7)K2Ti2 tetrahedra,  a cornercorner with one O(4)Ti4 trigonal pyramid, corners with two equivalent O(2)Ti4 trigonal pyramids, edges with two equivalent O(1)Ti4 trigonal pyramids, and edges with two equivalent O(4)Ti4 trigonal pyramids. In the eighth O site, O(3) is bonded in a 3-coordinate geometry to one Ti(1) and two equivalent Ti(3) atoms. In the ninth O site, O(4) is bonded to one Ti(2) and three equivalent Ti(4) atoms to form distorted OTi4 trigonal pyramids that share corners with two equivalent O(7)K2Ti2 tetrahedra,  a cornercorner with one O(1)Ti4 trigonal pyramid,  a cornercorner with one O(2)Ti4 trigonal pyramid, corners with two equivalent O(4)Ti4 trigonal pyramids,  an edgeedge with one O(7)K2Ti2 tetrahedra, edges with two equivalent O(2)Ti4 trigonal pyramids, and edges with two equivalent O(4)Ti4 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_K2Ti4O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.780
_cell_length_b   9.365
_cell_length_c   12.051
_cell_angle_alpha   106.336
_cell_angle_beta   89.997
_cell_angle_gamma   101.639
_symmetry_Int_Tables_number   1
_cell_volume   400.178
_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
  K  K0  1  0.583  0.165  0.083  1.0
  K  K1  1  0.417  0.835  0.917  1.0
  K  K2  1  0.523  0.045  0.329  1.0
  K  K3  1  0.477  0.955  0.671  1.0
  Ti  Ti4  1  0.246  0.492  0.167  1.0
  Ti  Ti5  1  0.754  0.508  0.834  1.0
  Ti  Ti6  1  0.839  0.678  0.376  1.0
  Ti  Ti7  1  0.161  0.322  0.624  1.0
  Ti  Ti8  1  0.878  0.757  0.139  1.0
  Ti  Ti9  1  0.122  0.243  0.861  1.0
  Ti  Ti10  1  0.203  0.406  0.396  1.0
  Ti  Ti11  1  0.797  0.594  0.604  1.0
  O  O12  1  0.768  0.536  0.201  1.0
  O  O13  1  0.232  0.464  0.799  1.0
  O  O14  1  0.308  0.617  0.359  1.0
  O  O15  1  0.692  0.383  0.641  1.0
  O  O16  1  0.350  0.700  0.144  1.0
  O  O17  1  0.650  0.300  0.856  1.0
  O  O18  1  0.730  0.460  0.422  1.0
  O  O19  1  0.270  0.540  0.578  1.0
  O  O20  1  0.917  0.834  0.318  1.0
  O  O21  1  0.083  0.166  0.682  1.0
  O  O22  1  0.968  0.937  0.120  1.0
  O  O23  1  0.032  0.063  0.880  1.0
  O  O24  1  0.121  0.243  0.461  1.0
  O  O25  1  0.879  0.757  0.539  1.0
  O  O26  1  0.161  0.322  0.242  1.0
  O  O27  1  0.839  0.678  0.758  1.0
  O  O28  1  0.182  0.365  0.026  1.0
  O  O29  1  0.818  0.635  0.974  1.0
[/CIF]
.