The material described by K2MgGd2(MoO4)4 crystallizes in the triclinic P1 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 3-coordinate geometry to one O(14), one O(16), one O(3), one O(4), and one O(7) atom. In the second K site, K(2) is bonded in a 11-coordinate geometry to one Mg(1), one O(1), one O(11), one O(13), one O(15), one O(2), one O(3), one O(4), one O(6), one O(8), and one O(9) atom. Mg(1) is bonded in a 4-coordinate geometry to one K(2), one O(1), one O(14), one O(2), and one O(6) atom. There are two inequivalent Gd sites. In the first Gd site, Gd(1) is bonded to one O(11), one O(13), one O(15), one O(6), one O(7), one O(8), and one O(9) atom to form distorted GdO7 pentagonal bipyramids that share  a cornercorner with one Mo(1)O6 octahedra, corners with two equivalent Mo(2)O6 octahedra, corners with two equivalent Mo(3)O6 octahedra, corners with two equivalent Mo(4)O6 octahedra,  an edgeedge with one Mo(1)O6 octahedra, and  an edgeedge with one Gd(2)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 19-58°. In the second Gd site, Gd(2) is bonded to one O(10), one O(12), one O(14), one O(16), one O(5), one O(7), and one O(8) atom to form distorted GdO7 pentagonal bipyramids that share  a cornercorner with one Mo(2)O6 octahedra, corners with two equivalent Mo(1)O6 octahedra, corners with two equivalent Mo(3)O6 octahedra, corners with two equivalent Mo(4)O6 octahedra,  an edgeedge with one Mo(2)O6 octahedra, and  an edgeedge with one Gd(1)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 26-58°. There are four inequivalent Mo sites. In the first Mo site, Mo(1) is bonded to one O(1), one O(10), one O(13), one O(4), one O(7), and one O(9) atom to form distorted MoO6 octahedra that share corners with two equivalent Mo(4)O6 octahedra,  a cornercorner with one Gd(1)O7 pentagonal bipyramid, corners with two equivalent Gd(2)O7 pentagonal bipyramids,  an edgeedge with one Mo(2)O6 octahedra, and  an edgeedge with one Gd(1)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 40-51°. In the second Mo site, Mo(2) is bonded to one O(10), one O(14), one O(2), one O(3), one O(8), and one O(9) atom to form distorted MoO6 octahedra that share corners with two equivalent Mo(3)O6 octahedra,  a cornercorner with one Gd(2)O7 pentagonal bipyramid, corners with two equivalent Gd(1)O7 pentagonal bipyramids,  an edgeedge with one Mo(1)O6 octahedra, and  an edgeedge with one Gd(2)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 40-49°. In the third Mo site, Mo(3) is bonded to one O(11), one O(12), one O(15), one O(2), one O(3), and one O(5) atom to form MoO6 octahedra that share corners with two equivalent Mo(2)O6 octahedra, corners with two equivalent Gd(1)O7 pentagonal bipyramids, corners with two equivalent Gd(2)O7 pentagonal bipyramids, and  an edgeedge with one Mo(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 40-49°. In the fourth Mo site, Mo(4) is bonded to one O(1), one O(11), one O(12), one O(16), one O(4), and one O(6) atom to form MoO6 octahedra that share corners with two equivalent Mo(1)O6 octahedra, corners with two equivalent Gd(1)O7 pentagonal bipyramids, corners with two equivalent Gd(2)O7 pentagonal bipyramids, and  an edgeedge with one Mo(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 40-51°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one K(2), one Mg(1), one Mo(1), and one Mo(4) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one K(2), one Mg(1), one Mo(2), and one Mo(3) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one K(1), one K(2), one Mo(2), and one Mo(3) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one K(1), one K(2), one Mo(1), and one Mo(4) atom. In the fifth O site, O(5) is bonded in a distorted bent 150 degrees geometry to one Gd(2) and one Mo(3) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one K(2), one Mg(1), one Gd(1), and one Mo(4) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one K(1), one Gd(1), one Gd(2), and one Mo(1) atom. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one K(2), one Gd(1), one Gd(2), and one Mo(2) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one K(2), one Gd(1), one Mo(1), and one Mo(2) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Gd(2), one Mo(1), and one Mo(2) atom. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one K(2), one Gd(1), one Mo(3), and one Mo(4) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to one Gd(2), one Mo(3), and one Mo(4) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one K(2), one Gd(1), and one Mo(1) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one K(1), one Mg(1), one Gd(2), and one Mo(2) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one K(2), one Gd(1), and one Mo(3) atom. In the sixteenth O site, O(16) is bonded in a distorted T-shaped geometry to one K(1), one Gd(2), and one Mo(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K2Gd2Mg(MoO4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.009
_cell_length_b   7.513
_cell_length_c   8.053
_cell_angle_alpha   112.956
_cell_angle_beta   124.250
_cell_angle_gamma   93.052
_symmetry_Int_Tables_number   1
_cell_volume   344.354
_cell_formula_units_Z   1
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  0.448  0.267  0.323  1.0
  K  K1  1  0.579  0.767  0.721  1.0
  Gd  Gd2  1  0.036  0.751  0.245  1.0
  Gd  Gd3  1  0.975  0.250  0.771  1.0
  Mg  Mg4  1  0.361  0.011  0.884  1.0
  Mo  Mo5  1  0.984  0.297  0.297  1.0
  Mo  Mo6  1  0.995  0.684  0.693  1.0
  Mo  Mo7  1  0.521  0.713  0.202  1.0
  Mo  Mo8  1  0.488  0.308  0.799  1.0
  O  O9  1  0.657  0.213  0.049  1.0
  O  O10  1  0.340  0.782  0.951  1.0
  O  O11  1  0.688  0.631  0.436  1.0
  O  O12  1  0.292  0.378  0.552  1.0
  O  O13  1  0.728  0.966  0.395  1.0
  O  O14  1  0.274  0.026  0.610  1.0
  O  O15  1  0.037  0.377  0.135  1.0
  O  O16  1  0.943  0.621  0.863  1.0
  O  O17  1  0.058  0.636  0.479  1.0
  O  O18  1  0.929  0.354  0.517  1.0
  O  O19  1  0.669  0.615  0.051  1.0
  O  O20  1  0.338  0.393  0.954  1.0
  O  O21  1  0.953  0.027  0.179  1.0
  O  O22  1  0.079  0.987  0.828  1.0
  O  O23  1  0.345  0.742  0.277  1.0
  O  O24  1  0.648  0.250  0.707  1.0
[/CIF]
.
The material described by K2MgGd2(MoO4)4 crystallizes in the triclinic P1 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 3-coordinate geometry to one O(14), one O(16), one O(3), one O(4), and one O(7) atom. In the second K site, K(2) is bonded in a 11-coordinate geometry to one Mg(1), one O(1), one O(11), one O(13), one O(15), one O(2), one O(3), one O(4), one O(6), one O(8), and one O(9) atom. Mg(1) is bonded in a 4-coordinate geometry to one K(2), one O(1), one O(14), one O(2), and one O(6) atom. There are two inequivalent Gd sites. In the first Gd site, Gd(1) is bonded to one O(11), one O(13), one O(15), one O(6), one O(7), one O(8), and one O(9) atom to form distorted GdO7 pentagonal bipyramids that share  a cornercorner with one Mo(1)O6 octahedra, corners with two equivalent Mo(2)O6 octahedra, corners with two equivalent Mo(3)O6 octahedra, corners with two equivalent Mo(4)O6 octahedra,  an edgeedge with one Mo(1)O6 octahedra, and  an edgeedge with one Gd(2)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 19-58°. In the second Gd site, Gd(2) is bonded to one O(10), one O(12), one O(14), one O(16), one O(5), one O(7), and one O(8) atom to form distorted GdO7 pentagonal bipyramids that share  a cornercorner with one Mo(2)O6 octahedra, corners with two equivalent Mo(1)O6 octahedra, corners with two equivalent Mo(3)O6 octahedra, corners with two equivalent Mo(4)O6 octahedra,  an edgeedge with one Mo(2)O6 octahedra, and  an edgeedge with one Gd(1)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 26-58°. There are four inequivalent Mo sites. In the first Mo site, Mo(1) is bonded to one O(1), one O(10), one O(13), one O(4), one O(7), and one O(9) atom to form distorted MoO6 octahedra that share corners with two equivalent Mo(4)O6 octahedra,  a cornercorner with one Gd(1)O7 pentagonal bipyramid, corners with two equivalent Gd(2)O7 pentagonal bipyramids,  an edgeedge with one Mo(2)O6 octahedra, and  an edgeedge with one Gd(1)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 40-51°. In the second Mo site, Mo(2) is bonded to one O(10), one O(14), one O(2), one O(3), one O(8), and one O(9) atom to form distorted MoO6 octahedra that share corners with two equivalent Mo(3)O6 octahedra,  a cornercorner with one Gd(2)O7 pentagonal bipyramid, corners with two equivalent Gd(1)O7 pentagonal bipyramids,  an edgeedge with one Mo(1)O6 octahedra, and  an edgeedge with one Gd(2)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 40-49°. In the third Mo site, Mo(3) is bonded to one O(11), one O(12), one O(15), one O(2), one O(3), and one O(5) atom to form MoO6 octahedra that share corners with two equivalent Mo(2)O6 octahedra, corners with two equivalent Gd(1)O7 pentagonal bipyramids, corners with two equivalent Gd(2)O7 pentagonal bipyramids, and  an edgeedge with one Mo(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 40-49°. In the fourth Mo site, Mo(4) is bonded to one O(1), one O(11), one O(12), one O(16), one O(4), and one O(6) atom to form MoO6 octahedra that share corners with two equivalent Mo(1)O6 octahedra, corners with two equivalent Gd(1)O7 pentagonal bipyramids, corners with two equivalent Gd(2)O7 pentagonal bipyramids, and  an edgeedge with one Mo(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 40-51°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one K(2), one Mg(1), one Mo(1), and one Mo(4) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one K(2), one Mg(1), one Mo(2), and one Mo(3) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one K(1), one K(2), one Mo(2), and one Mo(3) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one K(1), one K(2), one Mo(1), and one Mo(4) atom. In the fifth O site, O(5) is bonded in a distorted bent 150 degrees geometry to one Gd(2) and one Mo(3) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one K(2), one Mg(1), one Gd(1), and one Mo(4) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one K(1), one Gd(1), one Gd(2), and one Mo(1) atom. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one K(2), one Gd(1), one Gd(2), and one Mo(2) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one K(2), one Gd(1), one Mo(1), and one Mo(2) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Gd(2), one Mo(1), and one Mo(2) atom. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one K(2), one Gd(1), one Mo(3), and one Mo(4) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to one Gd(2), one Mo(3), and one Mo(4) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one K(2), one Gd(1), and one Mo(1) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one K(1), one Mg(1), one Gd(2), and one Mo(2) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one K(2), one Gd(1), and one Mo(3) atom. In the sixteenth O site, O(16) is bonded in a distorted T-shaped geometry to one K(1), one Gd(2), and one Mo(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K2Gd2Mg(MoO4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.009
_cell_length_b   7.513
_cell_length_c   8.053
_cell_angle_alpha   112.956
_cell_angle_beta   124.250
_cell_angle_gamma   93.052
_symmetry_Int_Tables_number   1
_cell_volume   344.354
_cell_formula_units_Z   1
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  0.448  0.267  0.323  1.0
  K  K1  1  0.579  0.767  0.721  1.0
  Gd  Gd2  1  0.036  0.751  0.245  1.0
  Gd  Gd3  1  0.975  0.250  0.771  1.0
  Mg  Mg4  1  0.361  0.011  0.884  1.0
  Mo  Mo5  1  0.984  0.297  0.297  1.0
  Mo  Mo6  1  0.995  0.684  0.693  1.0
  Mo  Mo7  1  0.521  0.713  0.202  1.0
  Mo  Mo8  1  0.488  0.308  0.799  1.0
  O  O9  1  0.657  0.213  0.049  1.0
  O  O10  1  0.340  0.782  0.951  1.0
  O  O11  1  0.688  0.631  0.436  1.0
  O  O12  1  0.292  0.378  0.552  1.0
  O  O13  1  0.728  0.966  0.395  1.0
  O  O14  1  0.274  0.026  0.610  1.0
  O  O15  1  0.037  0.377  0.135  1.0
  O  O16  1  0.943  0.621  0.863  1.0
  O  O17  1  0.058  0.636  0.479  1.0
  O  O18  1  0.929  0.354  0.517  1.0
  O  O19  1  0.669  0.615  0.051  1.0
  O  O20  1  0.338  0.393  0.954  1.0
  O  O21  1  0.953  0.027  0.179  1.0
  O  O22  1  0.079  0.987  0.828  1.0
  O  O23  1  0.345  0.742  0.277  1.0
  O  O24  1  0.648  0.250  0.707  1.0
[/CIF]
.