The structure described by K8Li3Mn4O16 crystallizes in the triclinic P1 space group. There are eight inequivalent K sites. In the first K site, K(1) is bonded in a 8-coordinate geometry to one O(1), one O(14), one O(2), one O(5), one O(6), one O(7), and two equivalent O(10) atoms. In the second K site, K(2) is bonded in a 8-coordinate geometry to one O(16), one O(3), one O(4), one O(6), one O(7), one O(9), and two equivalent O(12) atoms. 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), and two equivalent O(13) atoms. In the fourth K site, K(4) is bonded in a 8-coordinate geometry to one O(10), one O(13), one O(14), one O(16), one O(6), one O(8), and two equivalent O(2) atoms. In the fifth K site, K(5) is bonded in a 8-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(7), one O(9), and two equivalent O(15) atoms. In the sixth K site, K(6) is bonded in a 4-coordinate geometry to one O(11), one O(12), one O(15), and one O(4) atom. In the seventh K site, K(7) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(13), one O(14), and two equivalent O(5) atoms. In the eighth K site, K(8) is bonded to one O(11), one O(12), one O(15), one O(16), one O(3), and one O(7) atom to form distorted KO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mn(3)O4 tetrahedra,  a cornercorner with one Mn(4)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Mn(1)O4 tetrahedra, and corners with two equivalent Mn(2)O4 tetrahedra. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), one O(8), and one O(9) atom to form distorted LiO4 tetrahedra that share corners with two equivalent Mn(4)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra, and  an edgeedge with one Mn(1)O4 tetrahedra. In the second Li site, Li(2) is bonded to one O(14), one O(3), one O(5), and one O(6) atom to form LiO4 tetrahedra that share  a cornercorner with one K(8)O6 octahedra, corners with two equivalent Mn(3)O4 tetrahedra, and  an edgeedge with one Mn(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. In the third Li site, Li(3) is bonded to one O(15), one O(16), one O(8), and one O(9) atom to form distorted LiO4 tetrahedra that share corners with two equivalent K(8)O6 octahedra, corners with two equivalent Mn(1)O4 tetrahedra,  an edgeedge with one Li(1)O4 tetrahedra, and  an edgeedge with one Mn(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 25-65°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(16), one O(2), one O(7), and one O(9) atom to form MnO4 tetrahedra that share corners with two equivalent K(8)O6 octahedra, corners with two equivalent Li(3)O4 tetrahedra, and  an edgeedge with one Li(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-68°. In the second Mn site, Mn(2) is bonded to one O(11), one O(3), one O(4), and one O(5) atom to form MnO4 tetrahedra that share corners with two equivalent K(8)O6 octahedra and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 39-48°. In the third Mn site, Mn(3) is bonded to one O(12), one O(13), one O(14), and one O(6) atom to form MnO4 tetrahedra that share  a cornercorner with one K(8)O6 octahedra and corners with two equivalent Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 37°. In the fourth Mn site, Mn(4) is bonded to one O(1), one O(10), one O(15), and one O(8) atom to form MnO4 tetrahedra that share  a cornercorner with one K(8)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 65°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one K(1), one K(5), one Li(1), and one Mn(4) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one K(1), one K(3), two equivalent K(4), one Li(1), and one Mn(1) atom. In the third O site, O(3) is bonded in a 2-coordinate geometry to one K(2), one K(5), one K(8), one Li(2), and one Mn(2) atom. In the fourth O site, O(4) is bonded in a 1-coordinate geometry to one K(2), one K(3), one K(5), one K(6), and one Mn(2) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one K(1), one K(3), two equivalent K(7), one Li(2), and one Mn(2) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one K(1), one K(2), one K(3), one K(4), one Li(2), and one Mn(3) atom. In the seventh O site, O(7) is bonded in a distorted single-bond geometry to one K(1), one K(2), one K(5), one K(8), and one Mn(1) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one K(4), one Li(1), one Li(3), and one Mn(4) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one K(2), one K(5), one Li(1), one Li(3), and one Mn(1) atom. In the tenth O site, O(10) is bonded in a 1-coordinate geometry to one K(4), one K(7), two equivalent K(1), and one Mn(4) atom. In the eleventh O site, O(11) is bonded in a 1-coordinate geometry to one K(5), one K(6), one K(7), one K(8), and one Mn(2) atom. In the twelfth O site, O(12) is bonded in a 1-coordinate geometry to one K(6), one K(8), two equivalent K(2), and one Mn(3) atom. In the thirteenth O site, O(13) is bonded in a distorted single-bond geometry to one K(4), one K(7), two equivalent K(3), and one Mn(3) atom. In the fourteenth O site, O(14) is bonded in a distorted bent 120 degrees geometry to one K(1), one K(4), one K(7), one Li(2), and one Mn(3) atom. In the fifteenth O site, O(15) is bonded in a 6-coordinate geometry to one K(6), one K(8), two equivalent K(5), one Li(3), and one Mn(4) atom. In the sixteenth O site, O(16) is bonded in a 2-coordinate geometry to one K(2), one K(4), one K(8), one Li(3), and one Mn(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K8Li3Mn4O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.744
_cell_length_b   8.141
_cell_length_c   11.135
_cell_angle_alpha   91.841
_cell_angle_beta   86.223
_cell_angle_gamma   90.085
_symmetry_Int_Tables_number   1
_cell_volume   519.304
_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  0.245  0.976  0.172  1.0
  K  K1  1  0.241  0.259  0.655  1.0
  K  K2  1  0.249  0.458  0.330  1.0
  K  K3  1  0.738  0.243  0.151  1.0
  K  K4  1  0.257  0.753  0.855  1.0
  K  K5  1  0.746  0.527  0.681  1.0
  K  K6  1  0.771  0.773  0.366  1.0
  K  K7  1  0.752  0.014  0.783  1.0
  Li  Li8  1  0.305  0.525  0.064  1.0
  Li  Li9  1  0.193  0.027  0.443  1.0
  Li  Li10  1  0.690  0.465  0.937  1.0
  Mn  Mn11  1  0.200  0.268  0.941  1.0
  Mn  Mn12  1  0.291  0.770  0.558  1.0
  Mn  Mn13  1  0.717  0.229  0.444  1.0
  Mn  Mn14  1  0.793  0.725  0.059  1.0
  O  O15  1  0.076  0.693  0.095  1.0
  O  O16  1  0.208  0.293  0.096  1.0
  O  O17  1  0.134  0.933  0.614  1.0
  O  O18  1  0.182  0.587  0.599  1.0
  O  O19  1  0.290  0.789  0.405  1.0
  O  O20  1  0.443  0.177  0.401  1.0
  O  O21  1  0.304  0.083  0.889  1.0
  O  O22  1  0.621  0.560  0.109  1.0
  O  O23  1  0.374  0.429  0.886  1.0
  O  O24  1  0.698  0.908  0.120  1.0
  O  O25  1  0.560  0.791  0.604  1.0
  O  O26  1  0.722  0.223  0.597  1.0
  O  O27  1  0.772  0.425  0.401  1.0
  O  O28  1  0.920  0.099  0.371  1.0
  O  O29  1  0.778  0.706  0.904  1.0
  O  O30  1  0.922  0.297  0.896  1.0
[/CIF]
.
The structure described by K8Li3Mn4O16 crystallizes in the triclinic P1 space group. There are eight inequivalent K sites. In the first K site, K(1) is bonded in a 8-coordinate geometry to one O(1), one O(14), one O(2), one O(5), one O(6), one O(7), and two equivalent O(10) atoms. In the second K site, K(2) is bonded in a 8-coordinate geometry to one O(16), one O(3), one O(4), one O(6), one O(7), one O(9), and two equivalent O(12) atoms. 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), and two equivalent O(13) atoms. In the fourth K site, K(4) is bonded in a 8-coordinate geometry to one O(10), one O(13), one O(14), one O(16), one O(6), one O(8), and two equivalent O(2) atoms. In the fifth K site, K(5) is bonded in a 8-coordinate geometry to one O(1), one O(11), one O(3), one O(4), one O(7), one O(9), and two equivalent O(15) atoms. In the sixth K site, K(6) is bonded in a 4-coordinate geometry to one O(11), one O(12), one O(15), and one O(4) atom. In the seventh K site, K(7) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(13), one O(14), and two equivalent O(5) atoms. In the eighth K site, K(8) is bonded to one O(11), one O(12), one O(15), one O(16), one O(3), and one O(7) atom to form distorted KO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mn(3)O4 tetrahedra,  a cornercorner with one Mn(4)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Mn(1)O4 tetrahedra, and corners with two equivalent Mn(2)O4 tetrahedra. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), one O(8), and one O(9) atom to form distorted LiO4 tetrahedra that share corners with two equivalent Mn(4)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra, and  an edgeedge with one Mn(1)O4 tetrahedra. In the second Li site, Li(2) is bonded to one O(14), one O(3), one O(5), and one O(6) atom to form LiO4 tetrahedra that share  a cornercorner with one K(8)O6 octahedra, corners with two equivalent Mn(3)O4 tetrahedra, and  an edgeedge with one Mn(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. In the third Li site, Li(3) is bonded to one O(15), one O(16), one O(8), and one O(9) atom to form distorted LiO4 tetrahedra that share corners with two equivalent K(8)O6 octahedra, corners with two equivalent Mn(1)O4 tetrahedra,  an edgeedge with one Li(1)O4 tetrahedra, and  an edgeedge with one Mn(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 25-65°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(16), one O(2), one O(7), and one O(9) atom to form MnO4 tetrahedra that share corners with two equivalent K(8)O6 octahedra, corners with two equivalent Li(3)O4 tetrahedra, and  an edgeedge with one Li(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-68°. In the second Mn site, Mn(2) is bonded to one O(11), one O(3), one O(4), and one O(5) atom to form MnO4 tetrahedra that share corners with two equivalent K(8)O6 octahedra and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 39-48°. In the third Mn site, Mn(3) is bonded to one O(12), one O(13), one O(14), and one O(6) atom to form MnO4 tetrahedra that share  a cornercorner with one K(8)O6 octahedra and corners with two equivalent Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 37°. In the fourth Mn site, Mn(4) is bonded to one O(1), one O(10), one O(15), and one O(8) atom to form MnO4 tetrahedra that share  a cornercorner with one K(8)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 65°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 2-coordinate geometry to one K(1), one K(5), one Li(1), and one Mn(4) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one K(1), one K(3), two equivalent K(4), one Li(1), and one Mn(1) atom. In the third O site, O(3) is bonded in a 2-coordinate geometry to one K(2), one K(5), one K(8), one Li(2), and one Mn(2) atom. In the fourth O site, O(4) is bonded in a 1-coordinate geometry to one K(2), one K(3), one K(5), one K(6), and one Mn(2) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one K(1), one K(3), two equivalent K(7), one Li(2), and one Mn(2) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one K(1), one K(2), one K(3), one K(4), one Li(2), and one Mn(3) atom. In the seventh O site, O(7) is bonded in a distorted single-bond geometry to one K(1), one K(2), one K(5), one K(8), and one Mn(1) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one K(4), one Li(1), one Li(3), and one Mn(4) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one K(2), one K(5), one Li(1), one Li(3), and one Mn(1) atom. In the tenth O site, O(10) is bonded in a 1-coordinate geometry to one K(4), one K(7), two equivalent K(1), and one Mn(4) atom. In the eleventh O site, O(11) is bonded in a 1-coordinate geometry to one K(5), one K(6), one K(7), one K(8), and one Mn(2) atom. In the twelfth O site, O(12) is bonded in a 1-coordinate geometry to one K(6), one K(8), two equivalent K(2), and one Mn(3) atom. In the thirteenth O site, O(13) is bonded in a distorted single-bond geometry to one K(4), one K(7), two equivalent K(3), and one Mn(3) atom. In the fourteenth O site, O(14) is bonded in a distorted bent 120 degrees geometry to one K(1), one K(4), one K(7), one Li(2), and one Mn(3) atom. In the fifteenth O site, O(15) is bonded in a 6-coordinate geometry to one K(6), one K(8), two equivalent K(5), one Li(3), and one Mn(4) atom. In the sixteenth O site, O(16) is bonded in a 2-coordinate geometry to one K(2), one K(4), one K(8), one Li(3), and one Mn(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K8Li3Mn4O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.744
_cell_length_b   8.141
_cell_length_c   11.135
_cell_angle_alpha   91.841
_cell_angle_beta   86.223
_cell_angle_gamma   90.085
_symmetry_Int_Tables_number   1
_cell_volume   519.304
_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  0.245  0.976  0.172  1.0
  K  K1  1  0.241  0.259  0.655  1.0
  K  K2  1  0.249  0.458  0.330  1.0
  K  K3  1  0.738  0.243  0.151  1.0
  K  K4  1  0.257  0.753  0.855  1.0
  K  K5  1  0.746  0.527  0.681  1.0
  K  K6  1  0.771  0.773  0.366  1.0
  K  K7  1  0.752  0.014  0.783  1.0
  Li  Li8  1  0.305  0.525  0.064  1.0
  Li  Li9  1  0.193  0.027  0.443  1.0
  Li  Li10  1  0.690  0.465  0.937  1.0
  Mn  Mn11  1  0.200  0.268  0.941  1.0
  Mn  Mn12  1  0.291  0.770  0.558  1.0
  Mn  Mn13  1  0.717  0.229  0.444  1.0
  Mn  Mn14  1  0.793  0.725  0.059  1.0
  O  O15  1  0.076  0.693  0.095  1.0
  O  O16  1  0.208  0.293  0.096  1.0
  O  O17  1  0.134  0.933  0.614  1.0
  O  O18  1  0.182  0.587  0.599  1.0
  O  O19  1  0.290  0.789  0.405  1.0
  O  O20  1  0.443  0.177  0.401  1.0
  O  O21  1  0.304  0.083  0.889  1.0
  O  O22  1  0.621  0.560  0.109  1.0
  O  O23  1  0.374  0.429  0.886  1.0
  O  O24  1  0.698  0.908  0.120  1.0
  O  O25  1  0.560  0.791  0.604  1.0
  O  O26  1  0.722  0.223  0.597  1.0
  O  O27  1  0.772  0.425  0.401  1.0
  O  O28  1  0.920  0.099  0.371  1.0
  O  O29  1  0.778  0.706  0.904  1.0
  O  O30  1  0.922  0.297  0.896  1.0
[/CIF]
.