The compound described by Ti5Mn7 is Frank-Kasper $\mu$ Phase-like structured and crystallizes in the trigonal P-3m1 space group. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 16-coordinate geometry to one Ti(2), three equivalent Ti(1), three equivalent Ti(3), and nine equivalent Mn(1) atoms. In the second Ti site, Ti(2) is bonded in a 16-coordinate geometry to one Ti(1), three equivalent Ti(2), three equivalent Mn(2), and nine equivalent Mn(1) atoms. In the third Ti site, Ti(3) is bonded to six equivalent Ti(1) and six equivalent Mn(1) atoms to form distorted TiTi6Mn6 cuboctahedra that share corners with twelve equivalent Mn(1)Ti7Mn5 cuboctahedra, edges with six equivalent Ti(3)Ti6Mn6 cuboctahedra, faces with two equivalent Mn(2)Ti6Mn6 cuboctahedra, and faces with eighteen equivalent Mn(1)Ti7Mn5 cuboctahedra. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one Ti(3), three equivalent Ti(1), three equivalent Ti(2), one Mn(2), and four equivalent Mn(1) atoms to form MnTi7Mn5 cuboctahedra that share corners with two equivalent Ti(3)Ti6Mn6 cuboctahedra, corners with two equivalent Mn(2)Ti6Mn6 cuboctahedra, corners with fourteen equivalent Mn(1)Ti7Mn5 cuboctahedra, edges with six equivalent Mn(1)Ti7Mn5 cuboctahedra, faces with three equivalent Ti(3)Ti6Mn6 cuboctahedra, faces with three equivalent Mn(2)Ti6Mn6 cuboctahedra, and faces with twelve equivalent Mn(1)Ti7Mn5 cuboctahedra. In the second Mn site, Mn(2) is bonded to six equivalent Ti(2) and six equivalent Mn(1) atoms to form distorted MnTi6Mn6 cuboctahedra that share corners with twelve equivalent Mn(1)Ti7Mn5 cuboctahedra, edges with six equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with two equivalent Ti(3)Ti6Mn6 cuboctahedra, and faces with eighteen equivalent Mn(1)Ti7Mn5 cuboctahedra. is represented by the CIF file [CIF]
data_Ti5Mn7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.123
_cell_length_b   5.123
_cell_length_c   7.744
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.999
_symmetry_Int_Tables_number   1
_cell_volume   175.988
_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
  Ti  Ti0  1  0.667  0.333  0.066  1.0
  Ti  Ti1  1  0.333  0.667  0.934  1.0
  Ti  Ti2  1  0.333  0.667  0.561  1.0
  Ti  Ti3  1  0.667  0.333  0.439  1.0
  Ti  Ti4  1  1.000  0.000  0.000  1.0
  Mn  Mn5  1  0.656  0.828  0.259  1.0
  Mn  Mn6  1  0.172  0.828  0.259  1.0
  Mn  Mn7  1  0.172  0.344  0.259  1.0
  Mn  Mn8  1  0.344  0.172  0.741  1.0
  Mn  Mn9  1  0.828  0.172  0.741  1.0
  Mn  Mn10  1  0.828  0.656  0.741  1.0
  Mn  Mn11  1  0.000  1.000  0.500  1.0
[/CIF]
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The compound described by Ti5Mn7 is Frank-Kasper $\mu$ Phase-like structured and crystallizes in the trigonal P-3m1 space group. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded in a 16-coordinate geometry to one Ti(2), three equivalent Ti(1), three equivalent Ti(3), and nine equivalent Mn(1) atoms. In the second Ti site, Ti(2) is bonded in a 16-coordinate geometry to one Ti(1), three equivalent Ti(2), three equivalent Mn(2), and nine equivalent Mn(1) atoms. In the third Ti site, Ti(3) is bonded to six equivalent Ti(1) and six equivalent Mn(1) atoms to form distorted TiTi6Mn6 cuboctahedra that share corners with twelve equivalent Mn(1)Ti7Mn5 cuboctahedra, edges with six equivalent Ti(3)Ti6Mn6 cuboctahedra, faces with two equivalent Mn(2)Ti6Mn6 cuboctahedra, and faces with eighteen equivalent Mn(1)Ti7Mn5 cuboctahedra. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one Ti(3), three equivalent Ti(1), three equivalent Ti(2), one Mn(2), and four equivalent Mn(1) atoms to form MnTi7Mn5 cuboctahedra that share corners with two equivalent Ti(3)Ti6Mn6 cuboctahedra, corners with two equivalent Mn(2)Ti6Mn6 cuboctahedra, corners with fourteen equivalent Mn(1)Ti7Mn5 cuboctahedra, edges with six equivalent Mn(1)Ti7Mn5 cuboctahedra, faces with three equivalent Ti(3)Ti6Mn6 cuboctahedra, faces with three equivalent Mn(2)Ti6Mn6 cuboctahedra, and faces with twelve equivalent Mn(1)Ti7Mn5 cuboctahedra. In the second Mn site, Mn(2) is bonded to six equivalent Ti(2) and six equivalent Mn(1) atoms to form distorted MnTi6Mn6 cuboctahedra that share corners with twelve equivalent Mn(1)Ti7Mn5 cuboctahedra, edges with six equivalent Mn(2)Ti6Mn6 cuboctahedra, faces with two equivalent Ti(3)Ti6Mn6 cuboctahedra, and faces with eighteen equivalent Mn(1)Ti7Mn5 cuboctahedra. is represented by the CIF file [CIF]
data_Ti5Mn7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.123
_cell_length_b   5.123
_cell_length_c   7.744
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.999
_symmetry_Int_Tables_number   1
_cell_volume   175.988
_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
  Ti  Ti0  1  0.667  0.333  0.066  1.0
  Ti  Ti1  1  0.333  0.667  0.934  1.0
  Ti  Ti2  1  0.333  0.667  0.561  1.0
  Ti  Ti3  1  0.667  0.333  0.439  1.0
  Ti  Ti4  1  1.000  0.000  0.000  1.0
  Mn  Mn5  1  0.656  0.828  0.259  1.0
  Mn  Mn6  1  0.172  0.828  0.259  1.0
  Mn  Mn7  1  0.172  0.344  0.259  1.0
  Mn  Mn8  1  0.344  0.172  0.741  1.0
  Mn  Mn9  1  0.828  0.172  0.741  1.0
  Mn  Mn10  1  0.828  0.656  0.741  1.0
  Mn  Mn11  1  0.000  1.000  0.500  1.0
[/CIF]
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