The material described by K4Mg(WO4)3 crystallizes in the triclinic P-1 space group. There are five inequivalent K sites. In the first K site, K(1) is bonded to one O(11), one O(2), one O(3), one O(4), and two equivalent O(12) atoms to form distorted KO6 octahedra that share  a cornercorner with one K(2)O6 octahedra,  a cornercorner with one W(3)O4 tetrahedra, corners with two equivalent W(2)O4 tetrahedra, corners with three equivalent W(1)O4 tetrahedra, and  an edgeedge with one K(1)O6 octahedra. The corner-sharing octahedral tilt angles are 73°. In the second K site, K(2) is bonded to two equivalent O(11), two equivalent O(8), and two equivalent O(9) atoms to form KO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with two equivalent W(1)O4 tetrahedra, corners with two equivalent W(2)O4 tetrahedra, and corners with two equivalent W(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 73°. In the third K site, K(3) is bonded in a 6-coordinate geometry to one O(2), one O(4), one O(5), one O(6), one O(8), and one O(9) atom. In the fourth K site, K(4) is bonded in a 7-coordinate geometry to one O(2), one O(4), one O(5), two equivalent O(3), and two equivalent O(7) atoms. In the fifth K site, K(5) is bonded in a 6-coordinate geometry to two equivalent O(1), two equivalent O(8), and two equivalent O(9) atoms. Mg(1) is bonded to one O(1), one O(10), one O(5), one O(6), and one O(7) atom to form MgO5 trigonal bipyramids that share  a cornercorner with one W(1)O4 tetrahedra, corners with two equivalent W(2)O4 tetrahedra, and corners with two equivalent W(3)O4 tetrahedra. There are three inequivalent W sites. In the first W site, W(1) is bonded to one O(12), one O(4), one O(7), and one O(8) atom to form WO4 tetrahedra that share  a cornercorner with one K(2)O6 octahedra, corners with three equivalent K(1)O6 octahedra, and  a cornercorner with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 30-60°. In the second W site, W(2) is bonded to one O(1), one O(11), one O(2), and one O(5) atom to form WO4 tetrahedra that share  a cornercorner with one K(2)O6 octahedra, corners with two equivalent K(1)O6 octahedra, and corners with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 44-63°. In the third W site, W(3) is bonded to one O(10), one O(3), one O(6), and one O(9) atom to form WO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra,  a cornercorner with one K(2)O6 octahedra, and corners with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 51-56°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one K(5), one Mg(1), and one W(2) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one K(1), one K(3), one K(4), and one W(2) atom. In the third O site, O(3) is bonded to one K(1), two equivalent K(4), and one W(3) atom to form distorted edge-sharing OK3W trigonal pyramids. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one K(1), one K(3), one K(4), and one W(1) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one K(3), one K(4), one Mg(1), and one W(2) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one K(3), one Mg(1), and one W(3) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to two equivalent K(4), one Mg(1), and one W(1) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one K(2), one K(3), one K(5), and one W(1) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one K(2), one K(3), one K(5), and one W(3) atom. In the tenth O site, O(10) is bonded in a bent 120 degrees geometry to one Mg(1) and one W(3) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one K(1), one K(2), and one W(2) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to two equivalent K(1) and one W(1) atom. is represented by the CIF card [CIF]
data_K4Mg(WO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.943
_cell_length_b   10.143
_cell_length_c   10.261
_cell_angle_alpha   93.130
_cell_angle_beta   106.587
_cell_angle_gamma   106.073
_symmetry_Int_Tables_number   1
_cell_volume   753.268
_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  0.648  0.567  0.887  1.0
  K  K1  1  0.352  0.433  0.113  1.0
  K  K2  1  0.000  0.000  0.000  1.0
  K  K3  1  0.779  0.239  0.776  1.0
  K  K4  1  0.221  0.761  0.224  1.0
  K  K5  1  0.744  0.522  0.474  1.0
  K  K6  1  0.256  0.478  0.526  1.0
  K  K7  1  0.500  0.000  0.000  1.0
  Mg  Mg8  1  0.162  0.878  0.552  1.0
  Mg  Mg9  1  0.838  0.122  0.448  1.0
  W  W10  1  0.122  0.644  0.813  1.0
  W  W11  1  0.878  0.356  0.187  1.0
  W  W12  1  0.236  0.187  0.743  1.0
  W  W13  1  0.764  0.813  0.257  1.0
  W  W14  1  0.618  0.851  0.611  1.0
  W  W15  1  0.382  0.149  0.389  1.0
  O  O16  1  0.243  0.008  0.729  1.0
  O  O17  1  0.757  0.992  0.271  1.0
  O  O18  1  0.446  0.307  0.732  1.0
  O  O19  1  0.554  0.693  0.268  1.0
  O  O20  1  0.610  0.674  0.631  1.0
  O  O21  1  0.390  0.326  0.369  1.0
  O  O22  1  0.905  0.511  0.790  1.0
  O  O23  1  0.095  0.489  0.210  1.0
  O  O24  1  0.033  0.220  0.626  1.0
  O  O25  1  0.967  0.780  0.374  1.0
  O  O26  1  0.387  0.850  0.509  1.0
  O  O27  1  0.613  0.150  0.491  1.0
  O  O28  1  0.113  0.702  0.645  1.0
  O  O29  1  0.887  0.298  0.355  1.0
  O  O30  1  0.158  0.785  0.946  1.0
  O  O31  1  0.842  0.215  0.054  1.0
  O  O32  1  0.680  0.949  0.779  1.0
  O  O33  1  0.320  0.051  0.221  1.0
  O  O34  1  0.203  0.074  0.468  1.0
  O  O35  1  0.797  0.926  0.532  1.0
  O  O36  1  0.223  0.218  0.913  1.0
  O  O37  1  0.777  0.782  0.087  1.0
  O  O38  1  0.305  0.566  0.865  1.0
  O  O39  1  0.695  0.434  0.135  1.0
[/CIF]
.
The material described by K4Mg(WO4)3 crystallizes in the triclinic P-1 space group. There are five inequivalent K sites. In the first K site, K(1) is bonded to one O(11), one O(2), one O(3), one O(4), and two equivalent O(12) atoms to form distorted KO6 octahedra that share  a cornercorner with one K(2)O6 octahedra,  a cornercorner with one W(3)O4 tetrahedra, corners with two equivalent W(2)O4 tetrahedra, corners with three equivalent W(1)O4 tetrahedra, and  an edgeedge with one K(1)O6 octahedra. The corner-sharing octahedral tilt angles are 73°. In the second K site, K(2) is bonded to two equivalent O(11), two equivalent O(8), and two equivalent O(9) atoms to form KO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with two equivalent W(1)O4 tetrahedra, corners with two equivalent W(2)O4 tetrahedra, and corners with two equivalent W(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 73°. In the third K site, K(3) is bonded in a 6-coordinate geometry to one O(2), one O(4), one O(5), one O(6), one O(8), and one O(9) atom. In the fourth K site, K(4) is bonded in a 7-coordinate geometry to one O(2), one O(4), one O(5), two equivalent O(3), and two equivalent O(7) atoms. In the fifth K site, K(5) is bonded in a 6-coordinate geometry to two equivalent O(1), two equivalent O(8), and two equivalent O(9) atoms. Mg(1) is bonded to one O(1), one O(10), one O(5), one O(6), and one O(7) atom to form MgO5 trigonal bipyramids that share  a cornercorner with one W(1)O4 tetrahedra, corners with two equivalent W(2)O4 tetrahedra, and corners with two equivalent W(3)O4 tetrahedra. There are three inequivalent W sites. In the first W site, W(1) is bonded to one O(12), one O(4), one O(7), and one O(8) atom to form WO4 tetrahedra that share  a cornercorner with one K(2)O6 octahedra, corners with three equivalent K(1)O6 octahedra, and  a cornercorner with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 30-60°. In the second W site, W(2) is bonded to one O(1), one O(11), one O(2), and one O(5) atom to form WO4 tetrahedra that share  a cornercorner with one K(2)O6 octahedra, corners with two equivalent K(1)O6 octahedra, and corners with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 44-63°. In the third W site, W(3) is bonded to one O(10), one O(3), one O(6), and one O(9) atom to form WO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra,  a cornercorner with one K(2)O6 octahedra, and corners with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 51-56°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one K(5), one Mg(1), and one W(2) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one K(1), one K(3), one K(4), and one W(2) atom. In the third O site, O(3) is bonded to one K(1), two equivalent K(4), and one W(3) atom to form distorted edge-sharing OK3W trigonal pyramids. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one K(1), one K(3), one K(4), and one W(1) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one K(3), one K(4), one Mg(1), and one W(2) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one K(3), one Mg(1), and one W(3) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to two equivalent K(4), one Mg(1), and one W(1) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one K(2), one K(3), one K(5), and one W(1) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one K(2), one K(3), one K(5), and one W(3) atom. In the tenth O site, O(10) is bonded in a bent 120 degrees geometry to one Mg(1) and one W(3) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one K(1), one K(2), and one W(2) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to two equivalent K(1) and one W(1) atom. is represented by the CIF card [CIF]
data_K4Mg(WO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.943
_cell_length_b   10.143
_cell_length_c   10.261
_cell_angle_alpha   93.130
_cell_angle_beta   106.587
_cell_angle_gamma   106.073
_symmetry_Int_Tables_number   1
_cell_volume   753.268
_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  0.648  0.567  0.887  1.0
  K  K1  1  0.352  0.433  0.113  1.0
  K  K2  1  0.000  0.000  0.000  1.0
  K  K3  1  0.779  0.239  0.776  1.0
  K  K4  1  0.221  0.761  0.224  1.0
  K  K5  1  0.744  0.522  0.474  1.0
  K  K6  1  0.256  0.478  0.526  1.0
  K  K7  1  0.500  0.000  0.000  1.0
  Mg  Mg8  1  0.162  0.878  0.552  1.0
  Mg  Mg9  1  0.838  0.122  0.448  1.0
  W  W10  1  0.122  0.644  0.813  1.0
  W  W11  1  0.878  0.356  0.187  1.0
  W  W12  1  0.236  0.187  0.743  1.0
  W  W13  1  0.764  0.813  0.257  1.0
  W  W14  1  0.618  0.851  0.611  1.0
  W  W15  1  0.382  0.149  0.389  1.0
  O  O16  1  0.243  0.008  0.729  1.0
  O  O17  1  0.757  0.992  0.271  1.0
  O  O18  1  0.446  0.307  0.732  1.0
  O  O19  1  0.554  0.693  0.268  1.0
  O  O20  1  0.610  0.674  0.631  1.0
  O  O21  1  0.390  0.326  0.369  1.0
  O  O22  1  0.905  0.511  0.790  1.0
  O  O23  1  0.095  0.489  0.210  1.0
  O  O24  1  0.033  0.220  0.626  1.0
  O  O25  1  0.967  0.780  0.374  1.0
  O  O26  1  0.387  0.850  0.509  1.0
  O  O27  1  0.613  0.150  0.491  1.0
  O  O28  1  0.113  0.702  0.645  1.0
  O  O29  1  0.887  0.298  0.355  1.0
  O  O30  1  0.158  0.785  0.946  1.0
  O  O31  1  0.842  0.215  0.054  1.0
  O  O32  1  0.680  0.949  0.779  1.0
  O  O33  1  0.320  0.051  0.221  1.0
  O  O34  1  0.203  0.074  0.468  1.0
  O  O35  1  0.797  0.926  0.532  1.0
  O  O36  1  0.223  0.218  0.913  1.0
  O  O37  1  0.777  0.782  0.087  1.0
  O  O38  1  0.305  0.566  0.865  1.0
  O  O39  1  0.695  0.434  0.135  1.0
[/CIF]
.