The crystal structure described by Lu4Zn5Ge6 crystallizes in the orthorhombic Cmc2_1 space group. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 11-coordinate geometry to one Zn(2), two equivalent Zn(1), two equivalent Zn(5), two equivalent Ge(2), two equivalent Ge(4), and two equivalent Ge(5) atoms. In the second Lu site, Lu(2) is bonded to one Ge(3), one Ge(6), two equivalent Ge(1), and two equivalent Ge(4) atoms to form distorted LuGe6 octahedra that share  a cornercorner with one Lu(3)Ge6 octahedra,  a cornercorner with one Zn(4)Ge4 tetrahedra, edges with two equivalent Lu(2)Ge6 octahedra, edges with two equivalent Lu(3)Ge6 octahedra, and edges with two equivalent Zn(4)Ge4 tetrahedra. The corner-sharing octahedral tilt angles are 43°. In the third Lu site, Lu(3) is bonded to one Ge(1), one Ge(6), two equivalent Ge(2), and two equivalent Ge(3) atoms to form distorted LuGe6 octahedra that share  a cornercorner with one Lu(2)Ge6 octahedra,  a cornercorner with one Zn(4)Ge4 tetrahedra, edges with two equivalent Lu(2)Ge6 octahedra, edges with two equivalent Lu(3)Ge6 octahedra, and edges with two equivalent Zn(4)Ge4 tetrahedra. The corner-sharing octahedral tilt angles are 43°. In the fourth Lu site, Lu(4) is bonded in a 10-coordinate geometry to one Zn(2), two equivalent Zn(3), one Ge(6), two equivalent Ge(2), two equivalent Ge(4), and two equivalent Ge(5) atoms. There are five inequivalent Zn sites. In the first Zn site, Zn(1) is bonded in a 4-coordinate geometry to two equivalent Lu(1), one Ge(4), one Ge(5), and two equivalent Ge(6) atoms. In the second Zn site, Zn(2) is bonded in a 4-coordinate geometry to one Lu(1), one Lu(4), one Ge(1), one Ge(3), and two equivalent Ge(5) atoms. In the third Zn site, Zn(3) is bonded in a 4-coordinate geometry to two equivalent Lu(4), one Ge(4), one Ge(5), and two equivalent Ge(3) atoms. In the fourth Zn site, Zn(4) is bonded to one Ge(1), one Ge(3), and two equivalent Ge(6) atoms to form distorted ZnGe4 tetrahedra that share  a cornercorner with one Lu(2)Ge6 octahedra,  a cornercorner with one Lu(3)Ge6 octahedra, corners with two equivalent Zn(4)Ge4 tetrahedra, edges with two equivalent Lu(2)Ge6 octahedra, and edges with two equivalent Lu(3)Ge6 octahedra. The corner-sharing octahedral tilt angles range from 11-12°. In the fifth Zn site, Zn(5) is bonded in a 4-coordinate geometry to two equivalent Lu(1), one Ge(2), one Ge(5), and two equivalent Ge(1) atoms. There are six inequivalent Ge sites. In the first Ge site, Ge(1) is bonded to one Lu(3), two equivalent Lu(2), one Zn(2), one Zn(4), and two equivalent Zn(5) atoms to form distorted edge-sharing GeLu3Zn4 pentagonal bipyramids. In the second Ge site, Ge(2) is bonded in a 8-coordinate geometry to two equivalent Lu(1), two equivalent Lu(3), two equivalent Lu(4), one Zn(5), and one Ge(4) atom. In the third Ge site, Ge(3) is bonded to one Lu(2), two equivalent Lu(3), one Zn(2), one Zn(4), and two equivalent Zn(3) atoms to form distorted edge-sharing GeLu3Zn4 pentagonal bipyramids. In the fourth Ge site, Ge(4) is bonded in a 9-coordinate geometry to two equivalent Lu(1), two equivalent Lu(2), two equivalent Lu(4), one Zn(1), one Zn(3), and one Ge(2) atom. In the fifth Ge site, Ge(5) is bonded in a 9-coordinate geometry to two equivalent Lu(1), two equivalent Lu(4), one Zn(1), one Zn(3), one Zn(5), and two equivalent Zn(2) atoms. In the sixth Ge site, Ge(6) is bonded in a 7-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), two equivalent Zn(1), and two equivalent Zn(4) atoms. is represented by the CIF file [CIF]
data_Lu4Zn5Ge6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.419
_cell_length_b   9.419
_cell_length_c   15.138
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   154.151
_symmetry_Int_Tables_number   1
_cell_volume   585.550
_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
  Lu  Lu0  1  0.032  0.968  0.736  1.0
  Lu  Lu1  1  0.968  0.032  0.236  1.0
  Lu  Lu2  1  0.833  0.167  0.697  1.0
  Lu  Lu3  1  0.167  0.833  0.197  1.0
  Lu  Lu4  1  0.175  0.825  0.557  1.0
  Lu  Lu5  1  0.825  0.175  0.057  1.0
  Lu  Lu6  1  0.982  0.018  0.502  1.0
  Lu  Lu7  1  0.018  0.982  0.002  1.0
  Zn  Zn8  1  0.565  0.435  0.314  1.0
  Zn  Zn9  1  0.435  0.565  0.814  1.0
  Zn  Zn10  1  0.849  0.151  0.374  1.0
  Zn  Zn11  1  0.151  0.849  0.874  1.0
  Zn  Zn12  1  0.349  0.651  0.519  1.0
  Zn  Zn13  1  0.651  0.349  0.019  1.0
  Zn  Zn14  1  0.699  0.301  0.377  1.0
  Zn  Zn15  1  0.301  0.699  0.877  1.0
  Zn  Zn16  1  0.655  0.345  0.727  1.0
  Zn  Zn17  1  0.345  0.655  0.227  1.0
  Ge  Ge18  1  0.230  0.770  0.734  1.0
  Ge  Ge19  1  0.570  0.430  0.591  1.0
  Ge  Ge20  1  0.225  0.775  0.016  1.0
  Ge  Ge21  1  0.775  0.225  0.516  1.0
  Ge  Ge22  1  0.560  0.440  0.146  1.0
  Ge  Ge23  1  0.440  0.560  0.646  1.0
  Ge  Ge24  1  0.566  0.434  0.872  1.0
  Ge  Ge25  1  0.434  0.566  0.372  1.0
  Ge  Ge26  1  0.888  0.112  0.884  1.0
  Ge  Ge27  1  0.112  0.888  0.384  1.0
  Ge  Ge28  1  0.430  0.570  0.091  1.0
  Ge  Ge29  1  0.770  0.230  0.234  1.0
[/CIF]
.
The crystal structure described by Lu4Zn5Ge6 crystallizes in the orthorhombic Cmc2_1 space group. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 11-coordinate geometry to one Zn(2), two equivalent Zn(1), two equivalent Zn(5), two equivalent Ge(2), two equivalent Ge(4), and two equivalent Ge(5) atoms. In the second Lu site, Lu(2) is bonded to one Ge(3), one Ge(6), two equivalent Ge(1), and two equivalent Ge(4) atoms to form distorted LuGe6 octahedra that share  a cornercorner with one Lu(3)Ge6 octahedra,  a cornercorner with one Zn(4)Ge4 tetrahedra, edges with two equivalent Lu(2)Ge6 octahedra, edges with two equivalent Lu(3)Ge6 octahedra, and edges with two equivalent Zn(4)Ge4 tetrahedra. The corner-sharing octahedral tilt angles are 43°. In the third Lu site, Lu(3) is bonded to one Ge(1), one Ge(6), two equivalent Ge(2), and two equivalent Ge(3) atoms to form distorted LuGe6 octahedra that share  a cornercorner with one Lu(2)Ge6 octahedra,  a cornercorner with one Zn(4)Ge4 tetrahedra, edges with two equivalent Lu(2)Ge6 octahedra, edges with two equivalent Lu(3)Ge6 octahedra, and edges with two equivalent Zn(4)Ge4 tetrahedra. The corner-sharing octahedral tilt angles are 43°. In the fourth Lu site, Lu(4) is bonded in a 10-coordinate geometry to one Zn(2), two equivalent Zn(3), one Ge(6), two equivalent Ge(2), two equivalent Ge(4), and two equivalent Ge(5) atoms. There are five inequivalent Zn sites. In the first Zn site, Zn(1) is bonded in a 4-coordinate geometry to two equivalent Lu(1), one Ge(4), one Ge(5), and two equivalent Ge(6) atoms. In the second Zn site, Zn(2) is bonded in a 4-coordinate geometry to one Lu(1), one Lu(4), one Ge(1), one Ge(3), and two equivalent Ge(5) atoms. In the third Zn site, Zn(3) is bonded in a 4-coordinate geometry to two equivalent Lu(4), one Ge(4), one Ge(5), and two equivalent Ge(3) atoms. In the fourth Zn site, Zn(4) is bonded to one Ge(1), one Ge(3), and two equivalent Ge(6) atoms to form distorted ZnGe4 tetrahedra that share  a cornercorner with one Lu(2)Ge6 octahedra,  a cornercorner with one Lu(3)Ge6 octahedra, corners with two equivalent Zn(4)Ge4 tetrahedra, edges with two equivalent Lu(2)Ge6 octahedra, and edges with two equivalent Lu(3)Ge6 octahedra. The corner-sharing octahedral tilt angles range from 11-12°. In the fifth Zn site, Zn(5) is bonded in a 4-coordinate geometry to two equivalent Lu(1), one Ge(2), one Ge(5), and two equivalent Ge(1) atoms. There are six inequivalent Ge sites. In the first Ge site, Ge(1) is bonded to one Lu(3), two equivalent Lu(2), one Zn(2), one Zn(4), and two equivalent Zn(5) atoms to form distorted edge-sharing GeLu3Zn4 pentagonal bipyramids. In the second Ge site, Ge(2) is bonded in a 8-coordinate geometry to two equivalent Lu(1), two equivalent Lu(3), two equivalent Lu(4), one Zn(5), and one Ge(4) atom. In the third Ge site, Ge(3) is bonded to one Lu(2), two equivalent Lu(3), one Zn(2), one Zn(4), and two equivalent Zn(3) atoms to form distorted edge-sharing GeLu3Zn4 pentagonal bipyramids. In the fourth Ge site, Ge(4) is bonded in a 9-coordinate geometry to two equivalent Lu(1), two equivalent Lu(2), two equivalent Lu(4), one Zn(1), one Zn(3), and one Ge(2) atom. In the fifth Ge site, Ge(5) is bonded in a 9-coordinate geometry to two equivalent Lu(1), two equivalent Lu(4), one Zn(1), one Zn(3), one Zn(5), and two equivalent Zn(2) atoms. In the sixth Ge site, Ge(6) is bonded in a 7-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), two equivalent Zn(1), and two equivalent Zn(4) atoms. is represented by the CIF file [CIF]
data_Lu4Zn5Ge6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.419
_cell_length_b   9.419
_cell_length_c   15.138
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   154.151
_symmetry_Int_Tables_number   1
_cell_volume   585.550
_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
  Lu  Lu0  1  0.032  0.968  0.736  1.0
  Lu  Lu1  1  0.968  0.032  0.236  1.0
  Lu  Lu2  1  0.833  0.167  0.697  1.0
  Lu  Lu3  1  0.167  0.833  0.197  1.0
  Lu  Lu4  1  0.175  0.825  0.557  1.0
  Lu  Lu5  1  0.825  0.175  0.057  1.0
  Lu  Lu6  1  0.982  0.018  0.502  1.0
  Lu  Lu7  1  0.018  0.982  0.002  1.0
  Zn  Zn8  1  0.565  0.435  0.314  1.0
  Zn  Zn9  1  0.435  0.565  0.814  1.0
  Zn  Zn10  1  0.849  0.151  0.374  1.0
  Zn  Zn11  1  0.151  0.849  0.874  1.0
  Zn  Zn12  1  0.349  0.651  0.519  1.0
  Zn  Zn13  1  0.651  0.349  0.019  1.0
  Zn  Zn14  1  0.699  0.301  0.377  1.0
  Zn  Zn15  1  0.301  0.699  0.877  1.0
  Zn  Zn16  1  0.655  0.345  0.727  1.0
  Zn  Zn17  1  0.345  0.655  0.227  1.0
  Ge  Ge18  1  0.230  0.770  0.734  1.0
  Ge  Ge19  1  0.570  0.430  0.591  1.0
  Ge  Ge20  1  0.225  0.775  0.016  1.0
  Ge  Ge21  1  0.775  0.225  0.516  1.0
  Ge  Ge22  1  0.560  0.440  0.146  1.0
  Ge  Ge23  1  0.440  0.560  0.646  1.0
  Ge  Ge24  1  0.566  0.434  0.872  1.0
  Ge  Ge25  1  0.434  0.566  0.372  1.0
  Ge  Ge26  1  0.888  0.112  0.884  1.0
  Ge  Ge27  1  0.112  0.888  0.384  1.0
  Ge  Ge28  1  0.430  0.570  0.091  1.0
  Ge  Ge29  1  0.770  0.230  0.234  1.0
[/CIF]
.