Bi2MgO4 is Spinel-like structured and crystallizes in the trigonal R3m space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-57°. In the second Mg site, Mg(2) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Bi(1)O4 tetrahedra, and edges with six equivalent Bi(2)O6 octahedra. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(2) and three equivalent O(1) atoms to form BiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-66°. In the second Bi site, Bi(2) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form BiO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Bi(1)O4 tetrahedra, edges with two equivalent Mg(2)O6 octahedra, and edges with four equivalent Bi(2)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Mg(2), one Bi(1), and two equivalent Bi(2) atoms. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Bi(1) and three equivalent Bi(2) atoms. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Bi(2) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(2), and two equivalent Bi(2) atoms.
Bi2MgO4 is Spinel-like structured and crystallizes in the trigonal R3m space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-57°. The Mg(1)-O(3) bond length is 2.05 Å. All Mg(1)-O(4) bond lengths are 2.14 Å. In the second Mg site, Mg(2) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Bi(1)O4 tetrahedra, and edges with six equivalent Bi(2)O6 octahedra. All Mg(2)-O(1) bond lengths are 2.14 Å. All Mg(2)-O(4) bond lengths are 2.35 Å. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(2) and three equivalent O(1) atoms to form BiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-66°. The Bi(1)-O(2) bond length is 2.17 Å. All Bi(1)-O(1) bond lengths are 2.30 Å. In the second Bi site, Bi(2) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form BiO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Bi(1)O4 tetrahedra, edges with two equivalent Mg(2)O6 octahedra, and edges with four equivalent Bi(2)O6 octahedra. The Bi(2)-O(2) bond length is 2.42 Å. The Bi(2)-O(3) bond length is 2.40 Å. Both Bi(2)-O(1) bond lengths are 2.40 Å. Both Bi(2)-O(4) bond lengths are 2.39 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Mg(2), one Bi(1), and two equivalent Bi(2) atoms. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Bi(1) and three equivalent Bi(2) atoms. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Bi(2) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(2), and two equivalent Bi(2) atoms.