The compound described by K2TiSi3O9 crystallizes in the trigonal R3 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 6-coordinate geometry to one O(1), one O(4), one O(5), one O(6), and two equivalent O(3) atoms. In the second K site, K(2) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(4) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to three equivalent O(1) and three equivalent O(6) atoms to form TiO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra and corners with three equivalent Si(2)O4 tetrahedra. In the second Ti site, Ti(2) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form TiO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra and corners with three equivalent Si(2)O4 tetrahedra. There are two inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1), one O(2), one O(3), and one O(5) atom to form SiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, and corners with two equivalent Si(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 44-46°. In the second Si site, Si(2) is bonded to one O(2), one O(3), one O(4), and one O(6) atom to form SiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, and corners with two equivalent Si(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 48°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one K(1), one Ti(1), and one Si(1) atom. In the second O site, O(2) is bonded in a distorted bent 120 degrees geometry to one K(2), one Si(1), and one Si(2) atom. In the third O site, O(3) is bonded in a distorted bent 120 degrees geometry to two equivalent K(1), one Si(1), and one Si(2) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one K(1), one K(2), one Ti(2), and one Si(2) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one K(1), one Ti(2), and one Si(1) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one K(1), one Ti(1), and one Si(2) atom. is represented by the CIF file [CIF]
data_K2Ti(SiO3)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.716
_cell_length_b   7.716
_cell_length_c   7.716
_cell_angle_alpha   82.441
_cell_angle_beta   82.441
_cell_angle_gamma   82.441
_symmetry_Int_Tables_number   1
_cell_volume   448.332
_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  0.228  0.770  0.995  1.0
  K  K1  1  0.770  0.995  0.228  1.0
  K  K2  1  0.995  0.228  0.770  1.0
  K  K3  1  0.496  0.496  0.496  1.0
  Ti  Ti4  1  0.222  0.222  0.222  1.0
  Ti  Ti5  1  0.741  0.741  0.741  1.0
  Si  Si6  1  0.891  0.510  0.098  1.0
  Si  Si7  1  0.098  0.891  0.510  1.0
  Si  Si8  1  0.510  0.098  0.891  1.0
  Si  Si9  1  0.015  0.549  0.436  1.0
  Si  Si10  1  0.436  0.015  0.549  1.0
  Si  Si11  1  0.549  0.436  0.015  1.0
  O  O12  1  0.324  0.100  0.018  1.0
  O  O13  1  0.467  0.157  0.684  1.0
  O  O14  1  0.684  0.467  0.157  1.0
  O  O15  1  0.244  0.942  0.629  1.0
  O  O16  1  0.942  0.629  0.244  1.0
  O  O17  1  0.588  0.848  0.556  1.0
  O  O18  1  0.632  0.911  0.904  1.0
  O  O19  1  0.911  0.904  0.632  1.0
  O  O20  1  0.556  0.588  0.848  1.0
  O  O21  1  0.629  0.244  0.942  1.0
  O  O22  1  0.904  0.632  0.911  1.0
  O  O23  1  0.848  0.556  0.588  1.0
  O  O24  1  0.157  0.684  0.467  1.0
  O  O25  1  0.426  0.121  0.354  1.0
  O  O26  1  0.354  0.426  0.121  1.0
  O  O27  1  0.100  0.018  0.324  1.0
  O  O28  1  0.121  0.354  0.426  1.0
  O  O29  1  0.018  0.324  0.100  1.0
[/CIF]
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The compound described by K2TiSi3O9 crystallizes in the trigonal R3 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 6-coordinate geometry to one O(1), one O(4), one O(5), one O(6), and two equivalent O(3) atoms. In the second K site, K(2) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(4) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to three equivalent O(1) and three equivalent O(6) atoms to form TiO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra and corners with three equivalent Si(2)O4 tetrahedra. In the second Ti site, Ti(2) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form TiO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra and corners with three equivalent Si(2)O4 tetrahedra. There are two inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1), one O(2), one O(3), and one O(5) atom to form SiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, and corners with two equivalent Si(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 44-46°. In the second Si site, Si(2) is bonded to one O(2), one O(3), one O(4), and one O(6) atom to form SiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, and corners with two equivalent Si(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 48°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one K(1), one Ti(1), and one Si(1) atom. In the second O site, O(2) is bonded in a distorted bent 120 degrees geometry to one K(2), one Si(1), and one Si(2) atom. In the third O site, O(3) is bonded in a distorted bent 120 degrees geometry to two equivalent K(1), one Si(1), and one Si(2) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one K(1), one K(2), one Ti(2), and one Si(2) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one K(1), one Ti(2), and one Si(1) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one K(1), one Ti(1), and one Si(2) atom. is represented by the CIF file [CIF]
data_K2Ti(SiO3)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.716
_cell_length_b   7.716
_cell_length_c   7.716
_cell_angle_alpha   82.441
_cell_angle_beta   82.441
_cell_angle_gamma   82.441
_symmetry_Int_Tables_number   1
_cell_volume   448.332
_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  0.228  0.770  0.995  1.0
  K  K1  1  0.770  0.995  0.228  1.0
  K  K2  1  0.995  0.228  0.770  1.0
  K  K3  1  0.496  0.496  0.496  1.0
  Ti  Ti4  1  0.222  0.222  0.222  1.0
  Ti  Ti5  1  0.741  0.741  0.741  1.0
  Si  Si6  1  0.891  0.510  0.098  1.0
  Si  Si7  1  0.098  0.891  0.510  1.0
  Si  Si8  1  0.510  0.098  0.891  1.0
  Si  Si9  1  0.015  0.549  0.436  1.0
  Si  Si10  1  0.436  0.015  0.549  1.0
  Si  Si11  1  0.549  0.436  0.015  1.0
  O  O12  1  0.324  0.100  0.018  1.0
  O  O13  1  0.467  0.157  0.684  1.0
  O  O14  1  0.684  0.467  0.157  1.0
  O  O15  1  0.244  0.942  0.629  1.0
  O  O16  1  0.942  0.629  0.244  1.0
  O  O17  1  0.588  0.848  0.556  1.0
  O  O18  1  0.632  0.911  0.904  1.0
  O  O19  1  0.911  0.904  0.632  1.0
  O  O20  1  0.556  0.588  0.848  1.0
  O  O21  1  0.629  0.244  0.942  1.0
  O  O22  1  0.904  0.632  0.911  1.0
  O  O23  1  0.848  0.556  0.588  1.0
  O  O24  1  0.157  0.684  0.467  1.0
  O  O25  1  0.426  0.121  0.354  1.0
  O  O26  1  0.354  0.426  0.121  1.0
  O  O27  1  0.100  0.018  0.324  1.0
  O  O28  1  0.121  0.354  0.426  1.0
  O  O29  1  0.018  0.324  0.100  1.0
[/CIF]
.