The material described by ZrTiMn4 is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the trigonal P-3m1 space group. Zr(1) is bonded in a 16-coordinate geometry to three equivalent Zr(1), one Ti(1), three equivalent Mn(2), and nine equivalent Mn(1) atoms. Ti(1) is bonded in a 16-coordinate geometry to one Zr(1), three equivalent Ti(1), three equivalent Mn(3), and nine equivalent Mn(1) atoms. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to three equivalent Zr(1), three equivalent Ti(1), one Mn(2), one Mn(3), and four equivalent Mn(1) atoms to form MnZr3Ti3Mn6 cuboctahedra that share corners with two equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with two equivalent Mn(2)Zr6Mn6 cuboctahedra, corners with fourteen equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra, edges with six equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra, faces with three equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with three equivalent Mn(2)Zr6Mn6 cuboctahedra, and faces with twelve equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra. In the second Mn site, Mn(2) is bonded to six equivalent Zr(1) and six equivalent Mn(1) atoms to form MnZr6Mn6 cuboctahedra that share corners with twelve equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra, edges with six equivalent Mn(2)Zr6Mn6 cuboctahedra, faces with two equivalent Mn(3)Ti6Mn6 cuboctahedra, and faces with eighteen equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra. In the third Mn site, Mn(3) is bonded to six equivalent Ti(1) and six equivalent Mn(1) atoms to form MnTi6Mn6 cuboctahedra that share corners with twelve equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra, edges with six equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with two equivalent Mn(2)Zr6Mn6 cuboctahedra, and faces with eighteen equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_ZrTiMn4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.842
_cell_length_b   4.842
_cell_length_c   8.043
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   163.318
_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
  Zr  Zr0  1  0.667  0.333  0.569  1.0
  Zr  Zr1  1  0.333  0.667  0.431  1.0
  Ti  Ti2  1  0.333  0.667  0.059  1.0
  Ti  Ti3  1  0.667  0.333  0.941  1.0
  Mn  Mn4  1  0.829  0.171  0.241  1.0
  Mn  Mn5  1  0.829  0.658  0.241  1.0
  Mn  Mn6  1  0.342  0.171  0.241  1.0
  Mn  Mn7  1  0.171  0.829  0.759  1.0
  Mn  Mn8  1  0.171  0.342  0.759  1.0
  Mn  Mn9  1  0.658  0.829  0.759  1.0
  Mn  Mn10  1  0.000  0.000  0.500  1.0
  Mn  Mn11  1  0.000  0.000  0.000  1.0
[/CIF]
.
The material described by ZrTiMn4 is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the trigonal P-3m1 space group. Zr(1) is bonded in a 16-coordinate geometry to three equivalent Zr(1), one Ti(1), three equivalent Mn(2), and nine equivalent Mn(1) atoms. Ti(1) is bonded in a 16-coordinate geometry to one Zr(1), three equivalent Ti(1), three equivalent Mn(3), and nine equivalent Mn(1) atoms. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to three equivalent Zr(1), three equivalent Ti(1), one Mn(2), one Mn(3), and four equivalent Mn(1) atoms to form MnZr3Ti3Mn6 cuboctahedra that share corners with two equivalent Mn(3)Ti6Mn6 cuboctahedra, corners with two equivalent Mn(2)Zr6Mn6 cuboctahedra, corners with fourteen equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra, edges with six equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra, faces with three equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with three equivalent Mn(2)Zr6Mn6 cuboctahedra, and faces with twelve equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra. In the second Mn site, Mn(2) is bonded to six equivalent Zr(1) and six equivalent Mn(1) atoms to form MnZr6Mn6 cuboctahedra that share corners with twelve equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra, edges with six equivalent Mn(2)Zr6Mn6 cuboctahedra, faces with two equivalent Mn(3)Ti6Mn6 cuboctahedra, and faces with eighteen equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra. In the third Mn site, Mn(3) is bonded to six equivalent Ti(1) and six equivalent Mn(1) atoms to form MnTi6Mn6 cuboctahedra that share corners with twelve equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra, edges with six equivalent Mn(3)Ti6Mn6 cuboctahedra, faces with two equivalent Mn(2)Zr6Mn6 cuboctahedra, and faces with eighteen equivalent Mn(1)Zr3Ti3Mn6 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_ZrTiMn4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.842
_cell_length_b   4.842
_cell_length_c   8.043
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   163.318
_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
  Zr  Zr0  1  0.667  0.333  0.569  1.0
  Zr  Zr1  1  0.333  0.667  0.431  1.0
  Ti  Ti2  1  0.333  0.667  0.059  1.0
  Ti  Ti3  1  0.667  0.333  0.941  1.0
  Mn  Mn4  1  0.829  0.171  0.241  1.0
  Mn  Mn5  1  0.829  0.658  0.241  1.0
  Mn  Mn6  1  0.342  0.171  0.241  1.0
  Mn  Mn7  1  0.171  0.829  0.759  1.0
  Mn  Mn8  1  0.171  0.342  0.759  1.0
  Mn  Mn9  1  0.658  0.829  0.759  1.0
  Mn  Mn10  1  0.000  0.000  0.500  1.0
  Mn  Mn11  1  0.000  0.000  0.000  1.0
[/CIF]
.