The compound described by K4BaSi3O9 crystallizes in the orthorhombic Ama2 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. In the second K site, K(2) is bonded in a 9-coordinate geometry to one O(5), two equivalent O(1), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. In the third K site, K(3) is bonded in a 6-coordinate geometry to two equivalent O(1), two equivalent O(3), and two equivalent O(6) atoms. In the fourth K site, K(4) is bonded to one O(5), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form KO6 octahedra that share corners with two equivalent Si(1)O4 tetrahedra and corners with four equivalent Si(2)O4 tetrahedra. Ba(1) is bonded in a 8-coordinate geometry to one O(5), one O(6), two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms. There are two inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(5), one O(6), and two equivalent O(3) atoms to form SiO4 tetrahedra that share corners with two equivalent K(4)O6 octahedra and corners with two equivalent Si(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-60°. In the second Si site, Si(2) 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 K(4)O6 octahedra,  a cornercorner with one Si(1)O4 tetrahedra, and  a cornercorner with one Si(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 30-39°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 1-coordinate geometry to one K(1), one K(2), one K(3), one K(4), one Ba(1), and one Si(2) atom. In the second O site, O(2) is bonded in a distorted bent 150 degrees geometry to one K(1), two equivalent K(2), and two equivalent Si(2) atoms. In the third O site, O(3) is bonded in a distorted linear geometry to one K(1), one K(2), one K(3), one Ba(1), one Si(1), and one Si(2) atom. In the fourth O site, O(4) is bonded in a distorted single-bond geometry to one K(1), one K(2), one K(4), one Ba(1), and one Si(2) atom. In the fifth O site, O(5) is bonded in a distorted single-bond geometry to one K(2), one K(4), two equivalent K(1), one Ba(1), and one Si(1) atom. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one K(4), two equivalent K(3), one Ba(1), and one Si(1) atom. is represented by the CIF card [CIF]
data_K4Ba(SiO3)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.332
_cell_length_b   7.332
_cell_length_c   11.290
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   111.770
_symmetry_Int_Tables_number   1
_cell_volume   563.727
_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  0.490  0.510  0.000  1.0
  K  K1  1  0.327  0.774  0.750  1.0
  K  K2  1  0.960  0.040  0.000  1.0
  K  K3  1  0.226  0.673  0.250  1.0
  K  K4  1  0.960  0.040  0.500  1.0
  K  K5  1  0.490  0.510  0.500  1.0
  K  K6  1  0.752  0.765  0.250  1.0
  K  K7  1  0.235  0.248  0.750  1.0
  Ba  Ba8  1  0.740  0.266  0.750  1.0
  Ba  Ba9  1  0.734  0.260  0.250  1.0
  Si  Si10  1  0.808  0.737  0.750  1.0
  Si  Si11  1  0.019  0.587  0.527  1.0
  Si  Si12  1  0.263  0.192  0.250  1.0
  Si  Si13  1  0.413  0.981  0.473  1.0
  Si  Si14  1  0.413  0.981  0.027  1.0
  Si  Si15  1  0.019  0.587  0.973  1.0
  O  O16  1  0.051  0.400  0.914  1.0
  O  O17  1  0.245  0.755  0.000  1.0
  O  O18  1  0.310  0.076  0.368  1.0
  O  O19  1  0.600  0.949  0.414  1.0
  O  O20  1  0.924  0.690  0.868  1.0
  O  O21  1  0.444  0.113  0.591  1.0
  O  O22  1  0.421  0.417  0.250  1.0
  O  O23  1  0.887  0.556  0.409  1.0
  O  O24  1  0.887  0.556  0.091  1.0
  O  O25  1  0.600  0.949  0.086  1.0
  O  O26  1  0.033  0.155  0.250  1.0
  O  O27  1  0.245  0.755  0.500  1.0
  O  O28  1  0.583  0.579  0.750  1.0
  O  O29  1  0.310  0.076  0.132  1.0
  O  O30  1  0.444  0.113  0.909  1.0
  O  O31  1  0.924  0.690  0.632  1.0
  O  O32  1  0.051  0.400  0.586  1.0
  O  O33  1  0.845  0.967  0.750  1.0
[/CIF]
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The compound described by K4BaSi3O9 crystallizes in the orthorhombic Ama2 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. In the second K site, K(2) is bonded in a 9-coordinate geometry to one O(5), two equivalent O(1), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. In the third K site, K(3) is bonded in a 6-coordinate geometry to two equivalent O(1), two equivalent O(3), and two equivalent O(6) atoms. In the fourth K site, K(4) is bonded to one O(5), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form KO6 octahedra that share corners with two equivalent Si(1)O4 tetrahedra and corners with four equivalent Si(2)O4 tetrahedra. Ba(1) is bonded in a 8-coordinate geometry to one O(5), one O(6), two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms. There are two inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(5), one O(6), and two equivalent O(3) atoms to form SiO4 tetrahedra that share corners with two equivalent K(4)O6 octahedra and corners with two equivalent Si(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-60°. In the second Si site, Si(2) 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 K(4)O6 octahedra,  a cornercorner with one Si(1)O4 tetrahedra, and  a cornercorner with one Si(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 30-39°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 1-coordinate geometry to one K(1), one K(2), one K(3), one K(4), one Ba(1), and one Si(2) atom. In the second O site, O(2) is bonded in a distorted bent 150 degrees geometry to one K(1), two equivalent K(2), and two equivalent Si(2) atoms. In the third O site, O(3) is bonded in a distorted linear geometry to one K(1), one K(2), one K(3), one Ba(1), one Si(1), and one Si(2) atom. In the fourth O site, O(4) is bonded in a distorted single-bond geometry to one K(1), one K(2), one K(4), one Ba(1), and one Si(2) atom. In the fifth O site, O(5) is bonded in a distorted single-bond geometry to one K(2), one K(4), two equivalent K(1), one Ba(1), and one Si(1) atom. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one K(4), two equivalent K(3), one Ba(1), and one Si(1) atom. is represented by the CIF card [CIF]
data_K4Ba(SiO3)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.332
_cell_length_b   7.332
_cell_length_c   11.290
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   111.770
_symmetry_Int_Tables_number   1
_cell_volume   563.727
_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  0.490  0.510  0.000  1.0
  K  K1  1  0.327  0.774  0.750  1.0
  K  K2  1  0.960  0.040  0.000  1.0
  K  K3  1  0.226  0.673  0.250  1.0
  K  K4  1  0.960  0.040  0.500  1.0
  K  K5  1  0.490  0.510  0.500  1.0
  K  K6  1  0.752  0.765  0.250  1.0
  K  K7  1  0.235  0.248  0.750  1.0
  Ba  Ba8  1  0.740  0.266  0.750  1.0
  Ba  Ba9  1  0.734  0.260  0.250  1.0
  Si  Si10  1  0.808  0.737  0.750  1.0
  Si  Si11  1  0.019  0.587  0.527  1.0
  Si  Si12  1  0.263  0.192  0.250  1.0
  Si  Si13  1  0.413  0.981  0.473  1.0
  Si  Si14  1  0.413  0.981  0.027  1.0
  Si  Si15  1  0.019  0.587  0.973  1.0
  O  O16  1  0.051  0.400  0.914  1.0
  O  O17  1  0.245  0.755  0.000  1.0
  O  O18  1  0.310  0.076  0.368  1.0
  O  O19  1  0.600  0.949  0.414  1.0
  O  O20  1  0.924  0.690  0.868  1.0
  O  O21  1  0.444  0.113  0.591  1.0
  O  O22  1  0.421  0.417  0.250  1.0
  O  O23  1  0.887  0.556  0.409  1.0
  O  O24  1  0.887  0.556  0.091  1.0
  O  O25  1  0.600  0.949  0.086  1.0
  O  O26  1  0.033  0.155  0.250  1.0
  O  O27  1  0.245  0.755  0.500  1.0
  O  O28  1  0.583  0.579  0.750  1.0
  O  O29  1  0.310  0.076  0.132  1.0
  O  O30  1  0.444  0.113  0.909  1.0
  O  O31  1  0.924  0.690  0.632  1.0
  O  O32  1  0.051  0.400  0.586  1.0
  O  O33  1  0.845  0.967  0.750  1.0
[/CIF]
.