The material described by Mg4ZrN4 crystallizes in the triclinic P-1 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one N(1), one N(2), one N(3), and one N(4) atom to form distorted MgN4 tetrahedra that share  a cornercorner with one Mg(3)N5 square pyramid, corners with three equivalent Mg(4)N5 square pyramids, corners with four equivalent Zr(1)N4 tetrahedra,  an edgeedge with one Mg(4)N5 square pyramid, and edges with two equivalent Mg(3)N5 square pyramids. In the second Mg site, Mg(2) is bonded in a 4-coordinate geometry to two equivalent N(2) and two equivalent N(3) atoms. In the third Mg site, Mg(3) is bonded to one N(3), two equivalent N(1), and two equivalent N(4) atoms to form MgN5 square pyramids that share corners with three equivalent Mg(4)N5 square pyramids,  a cornercorner with one Mg(1)N4 tetrahedra, corners with three equivalent Zr(1)N4 tetrahedra, edges with two equivalent Mg(3)N5 square pyramids, edges with three equivalent Mg(4)N5 square pyramids,  an edgeedge with one Zr(1)N4 tetrahedra, and edges with two equivalent Mg(1)N4 tetrahedra. In the fourth Mg site, Mg(4) is bonded to one N(3), two equivalent N(1), and two equivalent N(4) atoms to form distorted MgN5 square pyramids that share corners with three equivalent Mg(3)N5 square pyramids,  a cornercorner with one Zr(1)N4 tetrahedra, corners with three equivalent Mg(1)N4 tetrahedra, edges with two equivalent Mg(4)N5 square pyramids, edges with three equivalent Mg(3)N5 square pyramids,  an edgeedge with one Mg(1)N4 tetrahedra, and edges with two equivalent Zr(1)N4 tetrahedra. Zr(1) is bonded to one N(1), one N(2), one N(3), and one N(4) atom to form ZrN4 tetrahedra that share  a cornercorner with one Mg(4)N5 square pyramid, corners with three equivalent Mg(3)N5 square pyramids, corners with four equivalent Mg(1)N4 tetrahedra,  an edgeedge with one Mg(3)N5 square pyramid, and edges with two equivalent Mg(4)N5 square pyramids. There are four inequivalent N sites. In the first N site, N(1) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Zr(1) atom to form NMg5Zr octahedra that share corners with two equivalent N(3)Mg5Zr octahedra, corners with two equivalent N(4)Mg5Zr octahedra, corners with two equivalent N(2)Mg3Zr tetrahedra, edges with two equivalent N(1)Mg5Zr octahedra, edges with two equivalent N(3)Mg5Zr octahedra, and edges with four equivalent N(4)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 11-16°. In the second N site, N(2) is bonded to one Mg(1), two equivalent Mg(2), and one Zr(1) atom to form NMg3Zr tetrahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with two equivalent N(4)Mg5Zr octahedra, corners with six equivalent N(3)Mg5Zr octahedra, and  an edgeedge with one N(2)Mg3Zr tetrahedra. The corner-sharing octahedral tilt angles range from 55-65°. In the third N site, N(3) is bonded to one Mg(1), one Mg(3), one Mg(4), two equivalent Mg(2), and one Zr(1) atom to form NMg5Zr octahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with six equivalent N(2)Mg3Zr tetrahedra,  an edgeedge with one N(3)Mg5Zr octahedra, edges with two equivalent N(1)Mg5Zr octahedra, and edges with three equivalent N(4)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 11-15°. In the fourth N site, N(4) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Zr(1) atom to form distorted NMg5Zr octahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with two equivalent N(2)Mg3Zr tetrahedra, edges with two equivalent N(4)Mg5Zr octahedra, edges with three equivalent N(3)Mg5Zr octahedra, and edges with four equivalent N(1)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 12-16°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg4ZrN4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.646
_cell_length_b   5.691
_cell_length_c   8.468
_cell_angle_alpha   70.256
_cell_angle_beta   84.012
_cell_angle_gamma   67.402
_symmetry_Int_Tables_number   1
_cell_volume   236.330
_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
  Mg  Mg0  1  0.718  0.617  0.217  1.0
  Mg  Mg1  1  0.282  0.383  0.783  1.0
  Mg  Mg2  1  0.757  0.236  1.000  1.0
  Mg  Mg3  1  0.243  0.764  0.000  1.0
  Mg  Mg4  1  0.741  0.482  0.572  1.0
  Mg  Mg5  1  0.259  0.518  0.428  1.0
  Mg  Mg6  1  0.255  0.922  0.581  1.0
  Mg  Mg7  1  0.745  0.078  0.419  1.0
  Zr  Zr8  1  0.730  0.827  0.782  1.0
  Zr  Zr9  1  0.270  0.173  0.218  1.0
  N  N10  1  0.995  0.700  0.600  1.0
  N  N11  1  0.005  0.300  0.400  1.0
  N  N12  1  0.847  0.834  0.005  1.0
  N  N13  1  0.153  0.166  0.995  1.0
  N  N14  1  0.493  0.612  0.804  1.0
  N  N15  1  0.507  0.388  0.196  1.0
  N  N16  1  0.477  0.798  0.383  1.0
  N  N17  1  0.523  0.202  0.617  1.0
[/CIF]
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The material described by Mg4ZrN4 crystallizes in the triclinic P-1 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one N(1), one N(2), one N(3), and one N(4) atom to form distorted MgN4 tetrahedra that share  a cornercorner with one Mg(3)N5 square pyramid, corners with three equivalent Mg(4)N5 square pyramids, corners with four equivalent Zr(1)N4 tetrahedra,  an edgeedge with one Mg(4)N5 square pyramid, and edges with two equivalent Mg(3)N5 square pyramids. In the second Mg site, Mg(2) is bonded in a 4-coordinate geometry to two equivalent N(2) and two equivalent N(3) atoms. In the third Mg site, Mg(3) is bonded to one N(3), two equivalent N(1), and two equivalent N(4) atoms to form MgN5 square pyramids that share corners with three equivalent Mg(4)N5 square pyramids,  a cornercorner with one Mg(1)N4 tetrahedra, corners with three equivalent Zr(1)N4 tetrahedra, edges with two equivalent Mg(3)N5 square pyramids, edges with three equivalent Mg(4)N5 square pyramids,  an edgeedge with one Zr(1)N4 tetrahedra, and edges with two equivalent Mg(1)N4 tetrahedra. In the fourth Mg site, Mg(4) is bonded to one N(3), two equivalent N(1), and two equivalent N(4) atoms to form distorted MgN5 square pyramids that share corners with three equivalent Mg(3)N5 square pyramids,  a cornercorner with one Zr(1)N4 tetrahedra, corners with three equivalent Mg(1)N4 tetrahedra, edges with two equivalent Mg(4)N5 square pyramids, edges with three equivalent Mg(3)N5 square pyramids,  an edgeedge with one Mg(1)N4 tetrahedra, and edges with two equivalent Zr(1)N4 tetrahedra. Zr(1) is bonded to one N(1), one N(2), one N(3), and one N(4) atom to form ZrN4 tetrahedra that share  a cornercorner with one Mg(4)N5 square pyramid, corners with three equivalent Mg(3)N5 square pyramids, corners with four equivalent Mg(1)N4 tetrahedra,  an edgeedge with one Mg(3)N5 square pyramid, and edges with two equivalent Mg(4)N5 square pyramids. There are four inequivalent N sites. In the first N site, N(1) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Zr(1) atom to form NMg5Zr octahedra that share corners with two equivalent N(3)Mg5Zr octahedra, corners with two equivalent N(4)Mg5Zr octahedra, corners with two equivalent N(2)Mg3Zr tetrahedra, edges with two equivalent N(1)Mg5Zr octahedra, edges with two equivalent N(3)Mg5Zr octahedra, and edges with four equivalent N(4)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 11-16°. In the second N site, N(2) is bonded to one Mg(1), two equivalent Mg(2), and one Zr(1) atom to form NMg3Zr tetrahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with two equivalent N(4)Mg5Zr octahedra, corners with six equivalent N(3)Mg5Zr octahedra, and  an edgeedge with one N(2)Mg3Zr tetrahedra. The corner-sharing octahedral tilt angles range from 55-65°. In the third N site, N(3) is bonded to one Mg(1), one Mg(3), one Mg(4), two equivalent Mg(2), and one Zr(1) atom to form NMg5Zr octahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with six equivalent N(2)Mg3Zr tetrahedra,  an edgeedge with one N(3)Mg5Zr octahedra, edges with two equivalent N(1)Mg5Zr octahedra, and edges with three equivalent N(4)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 11-15°. In the fourth N site, N(4) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Zr(1) atom to form distorted NMg5Zr octahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with two equivalent N(2)Mg3Zr tetrahedra, edges with two equivalent N(4)Mg5Zr octahedra, edges with three equivalent N(3)Mg5Zr octahedra, and edges with four equivalent N(1)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 12-16°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg4ZrN4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.646
_cell_length_b   5.691
_cell_length_c   8.468
_cell_angle_alpha   70.256
_cell_angle_beta   84.012
_cell_angle_gamma   67.402
_symmetry_Int_Tables_number   1
_cell_volume   236.330
_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
  Mg  Mg0  1  0.718  0.617  0.217  1.0
  Mg  Mg1  1  0.282  0.383  0.783  1.0
  Mg  Mg2  1  0.757  0.236  1.000  1.0
  Mg  Mg3  1  0.243  0.764  0.000  1.0
  Mg  Mg4  1  0.741  0.482  0.572  1.0
  Mg  Mg5  1  0.259  0.518  0.428  1.0
  Mg  Mg6  1  0.255  0.922  0.581  1.0
  Mg  Mg7  1  0.745  0.078  0.419  1.0
  Zr  Zr8  1  0.730  0.827  0.782  1.0
  Zr  Zr9  1  0.270  0.173  0.218  1.0
  N  N10  1  0.995  0.700  0.600  1.0
  N  N11  1  0.005  0.300  0.400  1.0
  N  N12  1  0.847  0.834  0.005  1.0
  N  N13  1  0.153  0.166  0.995  1.0
  N  N14  1  0.493  0.612  0.804  1.0
  N  N15  1  0.507  0.388  0.196  1.0
  N  N16  1  0.477  0.798  0.383  1.0
  N  N17  1  0.523  0.202  0.617  1.0
[/CIF]
.