The crystal structure described by MgLu4(Te5O13)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 4-coordinate geometry to one O(13), one O(15), one O(20), and one O(26) atom. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a distorted octahedral geometry to one O(12), one O(13), one O(15), one O(17), one O(23), one O(24), and one O(6) atom. In the second Lu site, Lu(2) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(11), one O(18), one O(2), one O(4), one O(5), and one O(8) atom. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to one O(14), one O(18), one O(2), one O(3), one O(5), and one O(7) atom. In the fourth Lu site, Lu(4) is bonded in a 7-coordinate geometry to one O(1), one O(15), one O(17), one O(19), one O(20), one O(23), and one O(24) atom. There are ten inequivalent Te sites. In the first Te site, Te(1) is bonded in a 3-coordinate geometry to one O(17), one O(23), and one O(9) atom. In the second Te site, Te(2) is bonded in a distorted L-shaped geometry to one O(21) and one O(24) atom. In the third Te site, Te(3) is bonded in a distorted rectangular see-saw-like geometry to one O(10), one O(22), one O(23), and one O(5) atom. In the fourth Te site, Te(4) is bonded in a 4-coordinate geometry to one O(1), one O(12), one O(26), and one O(8) atom. In the fifth Te site, Te(5) is bonded in a rectangular see-saw-like geometry to one O(16), one O(18), one O(2), and one O(25) atom. In the sixth Te site, Te(6) is bonded in a 3-coordinate geometry to one O(14), one O(25), and one O(4) atom. In the seventh Te site, Te(7) is bonded in a 4-coordinate geometry to one O(22), one O(3), one O(4), and one O(8) atom. In the eighth Te site, Te(8) is bonded in a distorted trigonal non-coplanar geometry to one O(11), one O(16), and one O(7) atom. In the ninth Te site, Te(9) is bonded in a 4-coordinate geometry to one O(13), one O(19), one O(20), and one O(9) atom. In the tenth Te site, Te(10) is bonded in a 4-coordinate geometry to one O(14), one O(19), one O(21), and one O(6) atom. There are twenty-six inequivalent O sites. In the first O site, O(1) is bonded in a distorted bent 120 degrees geometry to one Lu(2), one Lu(4), and one Te(4) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Lu(2), one Lu(3), and one Te(5) atom. In the third O site, O(3) is bonded in a linear geometry to one Lu(3) and one Te(7) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Lu(2), one Te(6), and one Te(7) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Lu(2), one Lu(3), and one Te(3) atom. In the sixth O site, O(6) is bonded in a distorted bent 120 degrees geometry to one Lu(1) and one Te(10) atom. In the seventh O site, O(7) is bonded in a bent 120 degrees geometry to one Lu(3) and one Te(8) atom. In the eighth O site, O(8) is bonded in a distorted bent 120 degrees geometry to one Lu(2), one Te(4), and one Te(7) atom. In the ninth O site, O(9) is bonded in a bent 150 degrees geometry to one Te(1) and one Te(9) atom. In the tenth O site, O(10) is bonded in a 2-coordinate geometry to one Lu(2) and one Te(3) atom. In the eleventh O site, O(11) is bonded in a distorted bent 120 degrees geometry to one Lu(2) and one Te(8) atom. In the twelfth O site, O(12) is bonded in a bent 120 degrees geometry to one Lu(1) and one Te(4) atom. In the thirteenth O site, O(13) is bonded in a T-shaped geometry to one Mg(1), one Lu(1), and one Te(9) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal non-coplanar geometry to one Lu(3), one Te(10), and one Te(6) atom. In the fifteenth O site, O(15) is bonded in a trigonal planar geometry to one Mg(1), one Lu(1), and one Lu(4) atom. In the sixteenth O site, O(16) is bonded in a bent 120 degrees geometry to one Te(5) and one Te(8) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(4), and one Te(1) atom. In the eighteenth O site, O(18) is bonded in a distorted trigonal non-coplanar geometry to one Lu(2), one Lu(3), and one Te(5) atom. In the nineteenth O site, O(19) is bonded in a distorted trigonal planar geometry to one Lu(4), one Te(10), and one Te(9) atom. In the twentieth O site, O(20) is bonded in a 3-coordinate geometry to one Mg(1), one Lu(4), and one Te(9) atom. In the twenty-first O site, O(21) is bonded in a bent 150 degrees geometry to one Te(10) and one Te(2) atom. In the twenty-second O site, O(22) is bonded in a distorted bent 150 degrees geometry to one Te(3) and one Te(7) atom. In the twenty-third O site, O(23) is bonded in a 4-coordinate geometry to one Lu(1), one Lu(4), one Te(1), and one Te(3) atom. In the twenty-fourth O site, O(24) is bonded in a trigonal planar geometry to one Lu(1), one Lu(4), and one Te(2) atom. In the twenty-fifth O site, O(25) is bonded in a bent 120 degrees geometry to one Te(5) and one Te(6) atom. In the twenty-sixth O site, O(26) is bonded in a bent 150 degrees geometry to one Mg(1) and one Te(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu4Mg(Te5O13)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.884
_cell_length_b   8.650
_cell_length_c   11.208
_cell_angle_alpha   89.736
_cell_angle_beta   88.408
_cell_angle_gamma   75.968
_symmetry_Int_Tables_number   1
_cell_volume   647.184
_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
  Lu  Lu0  1  0.989  0.274  0.764  1.0
  Lu  Lu1  1  0.553  0.528  0.186  1.0
  Lu  Lu2  1  0.999  0.735  0.247  1.0
  Lu  Lu3  1  0.436  0.431  0.812  1.0
  Mg  Mg4  1  0.390  0.016  0.783  1.0
  Te  Te5  1  0.861  0.651  0.897  1.0
  Te  Te6  1  0.655  0.075  0.612  1.0
  Te  Te7  1  0.118  0.355  0.106  1.0
  Te  Te8  1  0.703  0.116  0.012  1.0
  Te  Te9  1  0.447  0.902  0.303  1.0
  Te  Te10  1  0.725  0.604  0.508  1.0
  Te  Te11  1  0.841  0.197  0.345  1.0
  Te  Te12  1  0.281  0.867  0.004  1.0
  Te  Te13  1  0.159  0.801  0.655  1.0
  Te  Te14  1  0.252  0.403  0.491  1.0
  O  O15  1  0.526  0.322  0.989  1.0
  O  O16  1  0.676  0.766  0.231  1.0
  O  O17  1  0.927  0.980  0.304  1.0
  O  O18  1  0.650  0.492  0.380  1.0
  O  O19  1  0.235  0.500  0.188  1.0
  O  O20  1  0.034  0.345  0.569  1.0
  O  O21  1  0.043  0.816  0.063  1.0
  O  O22  1  0.660  0.265  0.221  1.0
  O  O23  1  0.931  0.741  0.735  1.0
  O  O24  1  0.866  0.509  0.107  1.0
  O  O25  1  0.465  0.669  0.022  1.0
  O  O26  1  0.936  0.170  0.943  1.0
  O  O27  1  0.113  0.017  0.710  1.0
  O  O28  1  0.963  0.643  0.434  1.0
  O  O29  1  0.296  0.246  0.784  1.0
  O  O30  1  0.347  0.988  0.135  1.0
  O  O31  1  0.753  0.500  0.816  1.0
  O  O32  1  0.312  0.738  0.289  1.0
  O  O33  1  0.330  0.515  0.620  1.0
  O  O34  1  0.359  0.747  0.771  1.0
  O  O35  1  0.472  0.201  0.491  1.0
  O  O36  1  0.068  0.266  0.268  1.0
  O  O37  1  0.118  0.507  0.903  1.0
  O  O38  1  0.688  0.256  0.703  1.0
  O  O39  1  0.548  0.812  0.478  1.0
  O  O40  1  0.624  0.991  0.889  1.0
[/CIF]
.
The crystal structure described by MgLu4(Te5O13)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 4-coordinate geometry to one O(13), one O(15), one O(20), and one O(26) atom. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a distorted octahedral geometry to one O(12), one O(13), one O(15), one O(17), one O(23), one O(24), and one O(6) atom. In the second Lu site, Lu(2) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(11), one O(18), one O(2), one O(4), one O(5), and one O(8) atom. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to one O(14), one O(18), one O(2), one O(3), one O(5), and one O(7) atom. In the fourth Lu site, Lu(4) is bonded in a 7-coordinate geometry to one O(1), one O(15), one O(17), one O(19), one O(20), one O(23), and one O(24) atom. There are ten inequivalent Te sites. In the first Te site, Te(1) is bonded in a 3-coordinate geometry to one O(17), one O(23), and one O(9) atom. In the second Te site, Te(2) is bonded in a distorted L-shaped geometry to one O(21) and one O(24) atom. In the third Te site, Te(3) is bonded in a distorted rectangular see-saw-like geometry to one O(10), one O(22), one O(23), and one O(5) atom. In the fourth Te site, Te(4) is bonded in a 4-coordinate geometry to one O(1), one O(12), one O(26), and one O(8) atom. In the fifth Te site, Te(5) is bonded in a rectangular see-saw-like geometry to one O(16), one O(18), one O(2), and one O(25) atom. In the sixth Te site, Te(6) is bonded in a 3-coordinate geometry to one O(14), one O(25), and one O(4) atom. In the seventh Te site, Te(7) is bonded in a 4-coordinate geometry to one O(22), one O(3), one O(4), and one O(8) atom. In the eighth Te site, Te(8) is bonded in a distorted trigonal non-coplanar geometry to one O(11), one O(16), and one O(7) atom. In the ninth Te site, Te(9) is bonded in a 4-coordinate geometry to one O(13), one O(19), one O(20), and one O(9) atom. In the tenth Te site, Te(10) is bonded in a 4-coordinate geometry to one O(14), one O(19), one O(21), and one O(6) atom. There are twenty-six inequivalent O sites. In the first O site, O(1) is bonded in a distorted bent 120 degrees geometry to one Lu(2), one Lu(4), and one Te(4) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Lu(2), one Lu(3), and one Te(5) atom. In the third O site, O(3) is bonded in a linear geometry to one Lu(3) and one Te(7) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Lu(2), one Te(6), and one Te(7) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Lu(2), one Lu(3), and one Te(3) atom. In the sixth O site, O(6) is bonded in a distorted bent 120 degrees geometry to one Lu(1) and one Te(10) atom. In the seventh O site, O(7) is bonded in a bent 120 degrees geometry to one Lu(3) and one Te(8) atom. In the eighth O site, O(8) is bonded in a distorted bent 120 degrees geometry to one Lu(2), one Te(4), and one Te(7) atom. In the ninth O site, O(9) is bonded in a bent 150 degrees geometry to one Te(1) and one Te(9) atom. In the tenth O site, O(10) is bonded in a 2-coordinate geometry to one Lu(2) and one Te(3) atom. In the eleventh O site, O(11) is bonded in a distorted bent 120 degrees geometry to one Lu(2) and one Te(8) atom. In the twelfth O site, O(12) is bonded in a bent 120 degrees geometry to one Lu(1) and one Te(4) atom. In the thirteenth O site, O(13) is bonded in a T-shaped geometry to one Mg(1), one Lu(1), and one Te(9) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal non-coplanar geometry to one Lu(3), one Te(10), and one Te(6) atom. In the fifteenth O site, O(15) is bonded in a trigonal planar geometry to one Mg(1), one Lu(1), and one Lu(4) atom. In the sixteenth O site, O(16) is bonded in a bent 120 degrees geometry to one Te(5) and one Te(8) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(4), and one Te(1) atom. In the eighteenth O site, O(18) is bonded in a distorted trigonal non-coplanar geometry to one Lu(2), one Lu(3), and one Te(5) atom. In the nineteenth O site, O(19) is bonded in a distorted trigonal planar geometry to one Lu(4), one Te(10), and one Te(9) atom. In the twentieth O site, O(20) is bonded in a 3-coordinate geometry to one Mg(1), one Lu(4), and one Te(9) atom. In the twenty-first O site, O(21) is bonded in a bent 150 degrees geometry to one Te(10) and one Te(2) atom. In the twenty-second O site, O(22) is bonded in a distorted bent 150 degrees geometry to one Te(3) and one Te(7) atom. In the twenty-third O site, O(23) is bonded in a 4-coordinate geometry to one Lu(1), one Lu(4), one Te(1), and one Te(3) atom. In the twenty-fourth O site, O(24) is bonded in a trigonal planar geometry to one Lu(1), one Lu(4), and one Te(2) atom. In the twenty-fifth O site, O(25) is bonded in a bent 120 degrees geometry to one Te(5) and one Te(6) atom. In the twenty-sixth O site, O(26) is bonded in a bent 150 degrees geometry to one Mg(1) and one Te(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Lu4Mg(Te5O13)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.884
_cell_length_b   8.650
_cell_length_c   11.208
_cell_angle_alpha   89.736
_cell_angle_beta   88.408
_cell_angle_gamma   75.968
_symmetry_Int_Tables_number   1
_cell_volume   647.184
_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
  Lu  Lu0  1  0.989  0.274  0.764  1.0
  Lu  Lu1  1  0.553  0.528  0.186  1.0
  Lu  Lu2  1  0.999  0.735  0.247  1.0
  Lu  Lu3  1  0.436  0.431  0.812  1.0
  Mg  Mg4  1  0.390  0.016  0.783  1.0
  Te  Te5  1  0.861  0.651  0.897  1.0
  Te  Te6  1  0.655  0.075  0.612  1.0
  Te  Te7  1  0.118  0.355  0.106  1.0
  Te  Te8  1  0.703  0.116  0.012  1.0
  Te  Te9  1  0.447  0.902  0.303  1.0
  Te  Te10  1  0.725  0.604  0.508  1.0
  Te  Te11  1  0.841  0.197  0.345  1.0
  Te  Te12  1  0.281  0.867  0.004  1.0
  Te  Te13  1  0.159  0.801  0.655  1.0
  Te  Te14  1  0.252  0.403  0.491  1.0
  O  O15  1  0.526  0.322  0.989  1.0
  O  O16  1  0.676  0.766  0.231  1.0
  O  O17  1  0.927  0.980  0.304  1.0
  O  O18  1  0.650  0.492  0.380  1.0
  O  O19  1  0.235  0.500  0.188  1.0
  O  O20  1  0.034  0.345  0.569  1.0
  O  O21  1  0.043  0.816  0.063  1.0
  O  O22  1  0.660  0.265  0.221  1.0
  O  O23  1  0.931  0.741  0.735  1.0
  O  O24  1  0.866  0.509  0.107  1.0
  O  O25  1  0.465  0.669  0.022  1.0
  O  O26  1  0.936  0.170  0.943  1.0
  O  O27  1  0.113  0.017  0.710  1.0
  O  O28  1  0.963  0.643  0.434  1.0
  O  O29  1  0.296  0.246  0.784  1.0
  O  O30  1  0.347  0.988  0.135  1.0
  O  O31  1  0.753  0.500  0.816  1.0
  O  O32  1  0.312  0.738  0.289  1.0
  O  O33  1  0.330  0.515  0.620  1.0
  O  O34  1  0.359  0.747  0.771  1.0
  O  O35  1  0.472  0.201  0.491  1.0
  O  O36  1  0.068  0.266  0.268  1.0
  O  O37  1  0.118  0.507  0.903  1.0
  O  O38  1  0.688  0.256  0.703  1.0
  O  O39  1  0.548  0.812  0.478  1.0
  O  O40  1  0.624  0.991  0.889  1.0
[/CIF]
.