The material described by K3NaTi2(SiO4)3 crystallizes in the trigonal R-3c space group. K(1) is bonded in a 8-coordinate geometry to four equivalent O(1) and four equivalent O(2) atoms. Na(1) is bonded in a distorted hexagonal planar geometry to six equivalent O(2) atoms. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra. Si(1) is bonded to two equivalent O(1) and two equivalent O(2) atoms to form SiO4 tetrahedra that share corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 23-35°. There are two inequivalent O sites. In the first O site, O(2) is bonded to two equivalent K(1), one Na(1), one Ti(1), and one Si(1) atom to form a mixture of distorted face, corner, and edge-sharing OK2NaTiSi trigonal bipyramids. In the second O site, O(1) is bonded in a distorted bent 150 degrees geometry to two equivalent K(1), one Ti(1), and one Si(1) atom. is represented by the CIF file [CIF]
data_K3NaTi2(SiO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.045
_cell_length_b   9.045
_cell_length_c   9.045
_cell_angle_alpha   61.491
_cell_angle_beta   61.491
_cell_angle_gamma   61.491
_symmetry_Int_Tables_number   1
_cell_volume   540.783
_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  0.900  0.600  0.250  1.0
  K  K1  1  0.600  0.250  0.900  1.0
  K  K2  1  0.250  0.900  0.600  1.0
  K  K3  1  0.400  0.750  0.100  1.0
  K  K4  1  0.750  0.100  0.400  1.0
  K  K5  1  0.100  0.400  0.750  1.0
  Na  Na6  1  0.500  0.500  0.500  1.0
  Na  Na7  1  0.000  0.000  0.000  1.0
  O  O8  1  0.499  0.138  0.288  1.0
  O  O9  1  0.138  0.288  0.499  1.0
  O  O10  1  0.288  0.499  0.138  1.0
  O  O11  1  0.999  0.788  0.638  1.0
  O  O12  1  0.788  0.638  0.999  1.0
  O  O13  1  0.638  0.999  0.788  1.0
  O  O14  1  0.501  0.862  0.712  1.0
  O  O15  1  0.862  0.712  0.501  1.0
  O  O16  1  0.712  0.501  0.862  1.0
  O  O17  1  0.001  0.212  0.362  1.0
  O  O18  1  0.212  0.362  0.001  1.0
  O  O19  1  0.362  0.001  0.212  1.0
  O  O20  1  0.429  0.227  0.579  1.0
  O  O21  1  0.227  0.579  0.429  1.0
  O  O22  1  0.579  0.429  0.227  1.0
  O  O23  1  0.929  0.079  0.727  1.0
  O  O24  1  0.079  0.727  0.929  1.0
  O  O25  1  0.727  0.929  0.079  1.0
  O  O26  1  0.571  0.773  0.421  1.0
  O  O27  1  0.773  0.421  0.571  1.0
  O  O28  1  0.421  0.571  0.773  1.0
  O  O29  1  0.071  0.921  0.273  1.0
  O  O30  1  0.921  0.273  0.071  1.0
  O  O31  1  0.273  0.071  0.921  1.0
  Si  Si32  1  0.545  0.955  0.250  1.0
  Si  Si33  1  0.955  0.250  0.545  1.0
  Si  Si34  1  0.250  0.545  0.955  1.0
  Si  Si35  1  0.045  0.750  0.455  1.0
  Si  Si36  1  0.750  0.455  0.045  1.0
  Si  Si37  1  0.455  0.045  0.750  1.0
  Ti  Ti38  1  0.351  0.351  0.351  1.0
  Ti  Ti39  1  0.851  0.851  0.851  1.0
  Ti  Ti40  1  0.649  0.649  0.649  1.0
  Ti  Ti41  1  0.149  0.149  0.149  1.0
[/CIF]
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The material described by K3NaTi2(SiO4)3 crystallizes in the trigonal R-3c space group. K(1) is bonded in a 8-coordinate geometry to four equivalent O(1) and four equivalent O(2) atoms. Na(1) is bonded in a distorted hexagonal planar geometry to six equivalent O(2) atoms. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with six equivalent Si(1)O4 tetrahedra. Si(1) is bonded to two equivalent O(1) and two equivalent O(2) atoms to form SiO4 tetrahedra that share corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 23-35°. There are two inequivalent O sites. In the first O site, O(2) is bonded to two equivalent K(1), one Na(1), one Ti(1), and one Si(1) atom to form a mixture of distorted face, corner, and edge-sharing OK2NaTiSi trigonal bipyramids. In the second O site, O(1) is bonded in a distorted bent 150 degrees geometry to two equivalent K(1), one Ti(1), and one Si(1) atom. is represented by the CIF file [CIF]
data_K3NaTi2(SiO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.045
_cell_length_b   9.045
_cell_length_c   9.045
_cell_angle_alpha   61.491
_cell_angle_beta   61.491
_cell_angle_gamma   61.491
_symmetry_Int_Tables_number   1
_cell_volume   540.783
_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  0.900  0.600  0.250  1.0
  K  K1  1  0.600  0.250  0.900  1.0
  K  K2  1  0.250  0.900  0.600  1.0
  K  K3  1  0.400  0.750  0.100  1.0
  K  K4  1  0.750  0.100  0.400  1.0
  K  K5  1  0.100  0.400  0.750  1.0
  Na  Na6  1  0.500  0.500  0.500  1.0
  Na  Na7  1  0.000  0.000  0.000  1.0
  O  O8  1  0.499  0.138  0.288  1.0
  O  O9  1  0.138  0.288  0.499  1.0
  O  O10  1  0.288  0.499  0.138  1.0
  O  O11  1  0.999  0.788  0.638  1.0
  O  O12  1  0.788  0.638  0.999  1.0
  O  O13  1  0.638  0.999  0.788  1.0
  O  O14  1  0.501  0.862  0.712  1.0
  O  O15  1  0.862  0.712  0.501  1.0
  O  O16  1  0.712  0.501  0.862  1.0
  O  O17  1  0.001  0.212  0.362  1.0
  O  O18  1  0.212  0.362  0.001  1.0
  O  O19  1  0.362  0.001  0.212  1.0
  O  O20  1  0.429  0.227  0.579  1.0
  O  O21  1  0.227  0.579  0.429  1.0
  O  O22  1  0.579  0.429  0.227  1.0
  O  O23  1  0.929  0.079  0.727  1.0
  O  O24  1  0.079  0.727  0.929  1.0
  O  O25  1  0.727  0.929  0.079  1.0
  O  O26  1  0.571  0.773  0.421  1.0
  O  O27  1  0.773  0.421  0.571  1.0
  O  O28  1  0.421  0.571  0.773  1.0
  O  O29  1  0.071  0.921  0.273  1.0
  O  O30  1  0.921  0.273  0.071  1.0
  O  O31  1  0.273  0.071  0.921  1.0
  Si  Si32  1  0.545  0.955  0.250  1.0
  Si  Si33  1  0.955  0.250  0.545  1.0
  Si  Si34  1  0.250  0.545  0.955  1.0
  Si  Si35  1  0.045  0.750  0.455  1.0
  Si  Si36  1  0.750  0.455  0.045  1.0
  Si  Si37  1  0.455  0.045  0.750  1.0
  Ti  Ti38  1  0.351  0.351  0.351  1.0
  Ti  Ti39  1  0.851  0.851  0.851  1.0
  Ti  Ti40  1  0.649  0.649  0.649  1.0
  Ti  Ti41  1  0.149  0.149  0.149  1.0
[/CIF]
.