The material described by LuNi2Ga is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the trigonal P-3m1 space group. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 12-coordinate geometry to three equivalent Ni(4) and nine equivalent Ga(1) atoms. In the second Lu site, Lu(2) is bonded in a 12-coordinate geometry to three equivalent Ni(3) and nine equivalent Ni(5) atoms. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to three equivalent Ni(1), three equivalent Ni(2), six equivalent Ni(5), and six equivalent Ga(1) atoms. There are five inequivalent Ni sites. In the first Ni site, Ni(1) is bonded in a 9-coordinate geometry to three equivalent Lu(3), three equivalent Ni(5), and three equivalent Ga(1) atoms. In the second Ni site, Ni(2) is bonded in a 9-coordinate geometry to three equivalent Lu(3), three equivalent Ni(5), and three equivalent Ga(1) atoms. In the third Ni site, Ni(3) is bonded to six equivalent Lu(2) and six equivalent Ni(5) atoms to form NiLu6Ni6 cuboctahedra that share corners with twelve equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with six equivalent Ni(3)Lu6Ni6 cuboctahedra, and faces with eighteen equivalent Ni(5)Lu5Ni7 cuboctahedra. In the fourth Ni site, Ni(4) is bonded to six equivalent Lu(1) and six equivalent Ga(1) atoms to form NiLu6Ga6 cuboctahedra that share corners with twelve equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, edges with six equivalent Ni(4)Lu6Ga6 cuboctahedra, and faces with eighteen equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra. In the fifth Ni site, Ni(5) is bonded to two equivalent Lu(3), three equivalent Lu(2), one Ni(1), one Ni(2), one Ni(3), and four equivalent Ni(5) atoms to form NiLu5Ni7 cuboctahedra that share corners with two equivalent Ni(3)Lu6Ni6 cuboctahedra, corners with six equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, corners with nine equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra,  a faceface with one Ga(1)Lu5Ga4Ni3 cuboctahedra, faces with three equivalent Ni(3)Lu6Ni6 cuboctahedra, and faces with ten equivalent Ni(5)Lu5Ni7 cuboctahedra. Ga(1) is bonded to two equivalent Lu(3), three equivalent Lu(1), one Ni(1), one Ni(2), one Ni(4), and four equivalent Ga(1) atoms to form distorted GaLu5Ga4Ni3 cuboctahedra that share corners with two equivalent Ni(4)Lu6Ga6 cuboctahedra, corners with six equivalent Ni(5)Lu5Ni7 cuboctahedra, corners with nine equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, edges with four equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra,  a faceface with one Ni(5)Lu5Ni7 cuboctahedra, faces with three equivalent Ni(4)Lu6Ga6 cuboctahedra, and faces with ten equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra. is represented by the CIF card [CIF]
data_LuGaNi2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.092
_cell_length_b   5.092
_cell_length_c   16.097
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   361.447
_cell_formula_units_Z   6
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  0.333  0.667  0.966  1.0
  Lu  Lu1  1  0.667  0.333  0.034  1.0
  Lu  Lu2  1  0.667  0.333  0.461  1.0
  Lu  Lu3  1  0.333  0.667  0.539  1.0
  Lu  Lu4  1  0.333  0.667  0.743  1.0
  Lu  Lu5  1  0.667  0.333  0.257  1.0
  Ga  Ga6  1  0.833  0.167  0.870  1.0
  Ga  Ga7  1  0.833  0.665  0.870  1.0
  Ga  Ga8  1  0.335  0.167  0.870  1.0
  Ga  Ga9  1  0.167  0.833  0.130  1.0
  Ga  Ga10  1  0.167  0.335  0.130  1.0
  Ga  Ga11  1  0.665  0.833  0.130  1.0
  Ni  Ni12  1  0.333  0.667  0.254  1.0
  Ni  Ni13  1  0.667  0.333  0.746  1.0
  Ni  Ni14  1  0.000  0.000  0.253  1.0
  Ni  Ni15  1  0.000  0.000  0.747  1.0
  Ni  Ni16  1  0.000  0.000  0.500  1.0
  Ni  Ni17  1  0.000  0.000  0.000  1.0
  Ni  Ni18  1  0.168  0.832  0.376  1.0
  Ni  Ni19  1  0.168  0.335  0.376  1.0
  Ni  Ni20  1  0.665  0.832  0.376  1.0
  Ni  Ni21  1  0.832  0.168  0.624  1.0
  Ni  Ni22  1  0.832  0.665  0.624  1.0
  Ni  Ni23  1  0.335  0.168  0.624  1.0
[/CIF]
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The material described by LuNi2Ga is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the trigonal P-3m1 space group. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 12-coordinate geometry to three equivalent Ni(4) and nine equivalent Ga(1) atoms. In the second Lu site, Lu(2) is bonded in a 12-coordinate geometry to three equivalent Ni(3) and nine equivalent Ni(5) atoms. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to three equivalent Ni(1), three equivalent Ni(2), six equivalent Ni(5), and six equivalent Ga(1) atoms. There are five inequivalent Ni sites. In the first Ni site, Ni(1) is bonded in a 9-coordinate geometry to three equivalent Lu(3), three equivalent Ni(5), and three equivalent Ga(1) atoms. In the second Ni site, Ni(2) is bonded in a 9-coordinate geometry to three equivalent Lu(3), three equivalent Ni(5), and three equivalent Ga(1) atoms. In the third Ni site, Ni(3) is bonded to six equivalent Lu(2) and six equivalent Ni(5) atoms to form NiLu6Ni6 cuboctahedra that share corners with twelve equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with six equivalent Ni(3)Lu6Ni6 cuboctahedra, and faces with eighteen equivalent Ni(5)Lu5Ni7 cuboctahedra. In the fourth Ni site, Ni(4) is bonded to six equivalent Lu(1) and six equivalent Ga(1) atoms to form NiLu6Ga6 cuboctahedra that share corners with twelve equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, edges with six equivalent Ni(4)Lu6Ga6 cuboctahedra, and faces with eighteen equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra. In the fifth Ni site, Ni(5) is bonded to two equivalent Lu(3), three equivalent Lu(2), one Ni(1), one Ni(2), one Ni(3), and four equivalent Ni(5) atoms to form NiLu5Ni7 cuboctahedra that share corners with two equivalent Ni(3)Lu6Ni6 cuboctahedra, corners with six equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, corners with nine equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra,  a faceface with one Ga(1)Lu5Ga4Ni3 cuboctahedra, faces with three equivalent Ni(3)Lu6Ni6 cuboctahedra, and faces with ten equivalent Ni(5)Lu5Ni7 cuboctahedra. Ga(1) is bonded to two equivalent Lu(3), three equivalent Lu(1), one Ni(1), one Ni(2), one Ni(4), and four equivalent Ga(1) atoms to form distorted GaLu5Ga4Ni3 cuboctahedra that share corners with two equivalent Ni(4)Lu6Ga6 cuboctahedra, corners with six equivalent Ni(5)Lu5Ni7 cuboctahedra, corners with nine equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, edges with four equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra,  a faceface with one Ni(5)Lu5Ni7 cuboctahedra, faces with three equivalent Ni(4)Lu6Ga6 cuboctahedra, and faces with ten equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra. is represented by the CIF card [CIF]
data_LuGaNi2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.092
_cell_length_b   5.092
_cell_length_c   16.097
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   361.447
_cell_formula_units_Z   6
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  0.333  0.667  0.966  1.0
  Lu  Lu1  1  0.667  0.333  0.034  1.0
  Lu  Lu2  1  0.667  0.333  0.461  1.0
  Lu  Lu3  1  0.333  0.667  0.539  1.0
  Lu  Lu4  1  0.333  0.667  0.743  1.0
  Lu  Lu5  1  0.667  0.333  0.257  1.0
  Ga  Ga6  1  0.833  0.167  0.870  1.0
  Ga  Ga7  1  0.833  0.665  0.870  1.0
  Ga  Ga8  1  0.335  0.167  0.870  1.0
  Ga  Ga9  1  0.167  0.833  0.130  1.0
  Ga  Ga10  1  0.167  0.335  0.130  1.0
  Ga  Ga11  1  0.665  0.833  0.130  1.0
  Ni  Ni12  1  0.333  0.667  0.254  1.0
  Ni  Ni13  1  0.667  0.333  0.746  1.0
  Ni  Ni14  1  0.000  0.000  0.253  1.0
  Ni  Ni15  1  0.000  0.000  0.747  1.0
  Ni  Ni16  1  0.000  0.000  0.500  1.0
  Ni  Ni17  1  0.000  0.000  0.000  1.0
  Ni  Ni18  1  0.168  0.832  0.376  1.0
  Ni  Ni19  1  0.168  0.335  0.376  1.0
  Ni  Ni20  1  0.665  0.832  0.376  1.0
  Ni  Ni21  1  0.832  0.168  0.624  1.0
  Ni  Ni22  1  0.832  0.665  0.624  1.0
  Ni  Ni23  1  0.335  0.168  0.624  1.0
[/CIF]
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