The material described by AlNbCr is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. There are six inequivalent Nb sites. In the first Nb site, Nb(1) is bonded in a 16-coordinate geometry to one Nb(1); three Nb(2,2); one Cr(3); two equivalent Cr(1); two equivalent Cr(2); three equivalent Al(1); and four equivalent Al(2) atoms. In the second Nb site, Nb(2) is bonded in a 16-coordinate geometry to one Nb(2), three equivalent Nb(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Al(2), and three equivalent Al(1) atoms. In the third Nb site, Nb(2) is bonded in a 16-coordinate geometry to one Nb(2); three Nb(1,1); one Cr(1); two equivalent Cr(3); four equivalent Cr(2); two equivalent Al(2); and three equivalent Al(1) atoms. In the fourth Nb site, Nb(1) is bonded in a 16-coordinate geometry to one Nb(1), three equivalent Nb(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Al(1), and four equivalent Al(2) atoms. In the fifth Nb site, Nb(2) is bonded in a 16-coordinate geometry to one Nb(2), three equivalent Nb(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Al(2), and three equivalent Al(1) atoms. In the sixth Nb site, Nb(1) is bonded in a 16-coordinate geometry to one Nb(1), three equivalent Nb(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Al(1), and four equivalent Al(2) atoms. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two Nb(2,2); four Nb(1,1); two equivalent Al(1); and four equivalent Al(2) atoms to form distorted CrNb6Al6 cuboctahedra that share corners with two equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Cr(1)Nb6Al6 cuboctahedra, corners with four equivalent Al(1)Nb6Al2Cr4 cuboctahedra, corners with eight equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, edges with two equivalent Cr(1)Nb6Al6 cuboctahedra, edges with four equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, faces with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, faces with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra, and faces with eight equivalent Al(2)Nb6Al4Cr2 cuboctahedra. In the second Cr site, Cr(2) is bonded to two Nb(1,1); four Nb(2,2,2); two equivalent Cr(2); two equivalent Cr(3); and two equivalent Al(1) atoms to form CrNb6Al2Cr4 cuboctahedra that share corners with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Cr(1)Nb6Al6 cuboctahedra, corners with four equivalent Al(1)Nb6Al2Cr4 cuboctahedra, corners with six equivalent Al(2)Nb6Al4Cr2 cuboctahedra, edges with two equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, edges with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, faces with two equivalent Cr(1)Nb6Al6 cuboctahedra, faces with two equivalent Al(2)Nb6Al4Cr2 cuboctahedra, faces with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, faces with four equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, and faces with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra. In the third Cr site, Cr(3) is bonded to two Nb(1,1); four Nb(2,2); four equivalent Cr(2); and two equivalent Al(1) atoms to form CrNb6Al2Cr4 cuboctahedra that share corners with two equivalent Cr(1)Nb6Al6 cuboctahedra, corners with four equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Al(1)Nb6Al2Cr4 cuboctahedra, corners with eight equivalent Al(2)Nb6Al4Cr2 cuboctahedra, edges with two equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, edges with four equivalent Cr(1)Nb6Al6 cuboctahedra, faces with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, faces with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra, and faces with eight equivalent Cr(2)Nb6Al2Cr4 cuboctahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to three equivalent Nb(1); three Nb(2,2); one Cr(1); one Cr(3); two equivalent Cr(2); and two equivalent Al(2) atoms to form distorted AlNb6Al2Cr4 cuboctahedra that share corners with two equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, corners with two equivalent Cr(1)Nb6Al6 cuboctahedra, corners with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, edges with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra, faces with two equivalent Al(1)Nb6Al2Cr4 cuboctahedra, faces with three equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, faces with three equivalent Cr(1)Nb6Al6 cuboctahedra, faces with six equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, and faces with six equivalent Al(2)Nb6Al4Cr2 cuboctahedra. In the second Al site, Al(2) is bonded to two Nb(2,2); four Nb(1,1,1); two equivalent Cr(1); two equivalent Al(1); and two equivalent Al(2) atoms to form distorted AlNb6Al4Cr2 cuboctahedra that share corners with four equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Al(1)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, corners with six equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, edges with two equivalent Al(2)Nb6Al4Cr2 cuboctahedra, edges with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, faces with two equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, faces with two equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, faces with four equivalent Cr(1)Nb6Al6 cuboctahedra, faces with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, and faces with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_NbAlCr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.972
_cell_length_b   4.972
_cell_length_c   8.355
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   60.329
_symmetry_Int_Tables_number   1
_cell_volume   179.450
_cell_formula_units_Z   4
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
  Nb  Nb0  1  0.336  0.336  0.559  1.0
  Nb  Nb1  1  0.668  0.668  0.431  1.0
  Nb  Nb2  1  0.668  0.668  0.069  1.0
  Nb  Nb3  1  0.336  0.336  0.941  1.0
  Al  Al4  1  0.995  0.995  0.495  1.0
  Al  Al5  1  0.995  0.995  0.005  1.0
  Al  Al6  1  0.833  0.343  0.750  1.0
  Al  Al7  1  0.343  0.833  0.750  1.0
  Cr  Cr8  1  0.834  0.834  0.750  1.0
  Cr  Cr9  1  0.171  0.649  0.250  1.0
  Cr  Cr10  1  0.649  0.171  0.250  1.0
  Cr  Cr11  1  0.172  0.172  0.250  1.0
[/CIF]
.
The material described by AlNbCr is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. There are six inequivalent Nb sites. In the first Nb site, Nb(1) is bonded in a 16-coordinate geometry to one Nb(1); three Nb(2,2); one Cr(3); two equivalent Cr(1); two equivalent Cr(2); three equivalent Al(1); and four equivalent Al(2) atoms. In the second Nb site, Nb(2) is bonded in a 16-coordinate geometry to one Nb(2), three equivalent Nb(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Al(2), and three equivalent Al(1) atoms. In the third Nb site, Nb(2) is bonded in a 16-coordinate geometry to one Nb(2); three Nb(1,1); one Cr(1); two equivalent Cr(3); four equivalent Cr(2); two equivalent Al(2); and three equivalent Al(1) atoms. In the fourth Nb site, Nb(1) is bonded in a 16-coordinate geometry to one Nb(1), three equivalent Nb(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Al(1), and four equivalent Al(2) atoms. In the fifth Nb site, Nb(2) is bonded in a 16-coordinate geometry to one Nb(2), three equivalent Nb(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Al(2), and three equivalent Al(1) atoms. In the sixth Nb site, Nb(1) is bonded in a 16-coordinate geometry to one Nb(1), three equivalent Nb(2), one Cr(3), two equivalent Cr(1), two equivalent Cr(2), three equivalent Al(1), and four equivalent Al(2) atoms. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two Nb(2,2); four Nb(1,1); two equivalent Al(1); and four equivalent Al(2) atoms to form distorted CrNb6Al6 cuboctahedra that share corners with two equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Cr(1)Nb6Al6 cuboctahedra, corners with four equivalent Al(1)Nb6Al2Cr4 cuboctahedra, corners with eight equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, edges with two equivalent Cr(1)Nb6Al6 cuboctahedra, edges with four equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, faces with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, faces with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra, and faces with eight equivalent Al(2)Nb6Al4Cr2 cuboctahedra. In the second Cr site, Cr(2) is bonded to two Nb(1,1); four Nb(2,2,2); two equivalent Cr(2); two equivalent Cr(3); and two equivalent Al(1) atoms to form CrNb6Al2Cr4 cuboctahedra that share corners with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Cr(1)Nb6Al6 cuboctahedra, corners with four equivalent Al(1)Nb6Al2Cr4 cuboctahedra, corners with six equivalent Al(2)Nb6Al4Cr2 cuboctahedra, edges with two equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, edges with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, faces with two equivalent Cr(1)Nb6Al6 cuboctahedra, faces with two equivalent Al(2)Nb6Al4Cr2 cuboctahedra, faces with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, faces with four equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, and faces with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra. In the third Cr site, Cr(3) is bonded to two Nb(1,1); four Nb(2,2); four equivalent Cr(2); and two equivalent Al(1) atoms to form CrNb6Al2Cr4 cuboctahedra that share corners with two equivalent Cr(1)Nb6Al6 cuboctahedra, corners with four equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Al(1)Nb6Al2Cr4 cuboctahedra, corners with eight equivalent Al(2)Nb6Al4Cr2 cuboctahedra, edges with two equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, edges with four equivalent Cr(1)Nb6Al6 cuboctahedra, faces with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, faces with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra, and faces with eight equivalent Cr(2)Nb6Al2Cr4 cuboctahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to three equivalent Nb(1); three Nb(2,2); one Cr(1); one Cr(3); two equivalent Cr(2); and two equivalent Al(2) atoms to form distorted AlNb6Al2Cr4 cuboctahedra that share corners with two equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, corners with two equivalent Cr(1)Nb6Al6 cuboctahedra, corners with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, edges with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra, faces with two equivalent Al(1)Nb6Al2Cr4 cuboctahedra, faces with three equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, faces with three equivalent Cr(1)Nb6Al6 cuboctahedra, faces with six equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, and faces with six equivalent Al(2)Nb6Al4Cr2 cuboctahedra. In the second Al site, Al(2) is bonded to two Nb(2,2); four Nb(1,1,1); two equivalent Cr(1); two equivalent Al(1); and two equivalent Al(2) atoms to form distorted AlNb6Al4Cr2 cuboctahedra that share corners with four equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Al(1)Nb6Al2Cr4 cuboctahedra, corners with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, corners with six equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, edges with two equivalent Al(2)Nb6Al4Cr2 cuboctahedra, edges with four equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, faces with two equivalent Cr(2)Nb6Al2Cr4 cuboctahedra, faces with two equivalent Cr(3)Nb6Al2Cr4 cuboctahedra, faces with four equivalent Cr(1)Nb6Al6 cuboctahedra, faces with four equivalent Al(2)Nb6Al4Cr2 cuboctahedra, and faces with six equivalent Al(1)Nb6Al2Cr4 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_NbAlCr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.972
_cell_length_b   4.972
_cell_length_c   8.355
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   60.329
_symmetry_Int_Tables_number   1
_cell_volume   179.450
_cell_formula_units_Z   4
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
  Nb  Nb0  1  0.336  0.336  0.559  1.0
  Nb  Nb1  1  0.668  0.668  0.431  1.0
  Nb  Nb2  1  0.668  0.668  0.069  1.0
  Nb  Nb3  1  0.336  0.336  0.941  1.0
  Al  Al4  1  0.995  0.995  0.495  1.0
  Al  Al5  1  0.995  0.995  0.005  1.0
  Al  Al6  1  0.833  0.343  0.750  1.0
  Al  Al7  1  0.343  0.833  0.750  1.0
  Cr  Cr8  1  0.834  0.834  0.750  1.0
  Cr  Cr9  1  0.171  0.649  0.250  1.0
  Cr  Cr10  1  0.649  0.171  0.250  1.0
  Cr  Cr11  1  0.172  0.172  0.250  1.0
[/CIF]
.